Pair your accounts.

Export articles to Mendeley

Get article recommendations from ACS based on references in your Mendeley library.

Pair your accounts.

Export articles to Mendeley

Get article recommendations from ACS based on references in your Mendeley library.

You’ve supercharged your research process with ACS and Mendeley!

STEP 1:
Click to create an ACS ID

Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

MENDELEY PAIRING EXPIRED
Your Mendeley pairing has expired. Please reconnect
ACS Publications. Most Trusted. Most Cited. Most Read
My Activity
CONTENT TYPES

Persistence of Structural Distortion and Bulk Band Rashba Splitting in SnTe above Its Ferroelectric Critical Temperature

Cite this: Nano Lett. 2024, 24, 1, 82–88
Publication Date (Web):December 18, 2023
https://doi.org/10.1021/acs.nanolett.3c03280

Copyright © 2023 The Authors. Published by American Chemical Society. This publication is licensed under

CC-BY 4.0.
  • Open Access

Article Views

1270

Altmetric

-

Citations

-
LEARN ABOUT THESE METRICS
PDF (3 MB)
Supporting Info (1)»

Abstract

The ferroelectric semiconductor α-SnTe has been regarded as a topological crystalline insulator, and the dispersion of its surface states has been intensively measured with angle-resolved photoemission spectroscopy (ARPES) over the past decade. However, much less attention has been given to the impact of the ferroelectric transition on its electronic structure, and in particular on its bulk states. Here, we investigate the low-energy electronic structure of α-SnTe with ARPES and follow the evolution of the bulk-state Rashba splitting as a function of temperature, across its ferroelectric critical temperature of about Tc ≈ 110 K. Unexpectedly, we observe a persistent band splitting up to room temperature, which is consistent with an order–disorder contribution of local dipoles to the phase transition that requires the presence of fluctuating dipoles above Tc. We conclude that no topological surface state can occur under these conditions at the (111) surface of SnTe, at odds with recent literature.

This publication is licensed under

CC-BY 4.0.
  • cc licence
  • by licence

Semiconductors-based spintronics materials are one of the most promising playgrounds for modern applications and technologies. (1,2) Among these materials, class IV–VI semiconductors are particularly interesting because they can combine semiconductor properties with ferroelectricity. This is due to a spontaneous distortion of the crystalline lattice structure that leads to a macroscopic electric polarization of the material. (3−6) In addition, the concomitant inversion symmetry breaking induces a momentum-dependent energy splitting in the electronic band structure, i.e., the so-called Rashba effect, which means that these bands are not anymore spin degenerate. (7,8)

In this framework, the electronic band structure of α-GeTe, a ferroelectric Rashba semiconductor with a critical temperature Tc = 670 K, (9) has been investigated in details. Different surface states, surface resonances, and bulk states have been identified using angle-resolved photoemission spectroscopy (ARPES), (10,11) and those studies have led to the observation of one of the largest Rashba parameters. (12) Its potential for application is then particularly large, e.g., with the ability to enhance spin Hall conductivity, (13) to control the spin-to-charge conversion, to store information in a nonvolatile way, (14−18) or to manipulate the crystal distortion and thus the ferroelectricity using intense femtosecond pulses. (19) The isostructural compound SnTe has similar properties to those of GeTe and it shows ferroelectricity typically below 100 K. (20)

For both GeTe and SnTe, the nature of the ferroelectric transition is still subject to debate, even though it has attracted a great deal of attention in the literature. Early studies using neutron diffraction or Raman scattering to reveal the atomic structure and related phonons (9,20,21) suggested that the transition temperature could strongly depend on the number of Sn (Ge) vacancies and that the transition is of second order. (9,22,23) Subsequently, this was confirmed by theoretical (24−27) and experimental studies that demonstrated a phonon softening at Tc, indicating a displacive phase transition. (28) However, extended X-ray absorption fine structure, X-ray scattering measurements, and analysis of the pair distribution function evidenced the persistence of a local rhombohedral lattice distortion above Tc, indicating the presence of local ferroelectric dipoles. (29−32) This conclusion was criticized in another work based on the analysis of pair distribution function, (33,34) emphasizing that a vivid debate on the ferroelectric phase transition in GeTe and SnTe still remains.

SnTe has been regarded as an outstanding representative of a class of topological crystalline insulators. However, the ferroelectric transition also has considerable effect on its topological properties. Symmetry arguments have been used to claim that in the paraelectric phase this semiconductor has gapless protected surface states. (35) This was first predicted theoretically, (36,37) and the existence of linear-dispersive bands attributed to topologically protected surface states was later on confirmed by ARPES for the (100) and (111) surface-plane orientations. (38−43) However, as shown by Plekhanov et al., (44) the topological surface state does not subsist in a ferroelectric state on the (111) surface.

In the present work, we study the low-energy electronic structure of SnTe(111) across its ferroelectric phase transition with ARPES. Taking advantage of our high energy and momentum resolution and also of the unprecedented crystalline quality of our thin films, we reveal multiple states in the first eV below the Fermi level that have not been resolved in the literature so far. Based on one-step model photoemission calculations and photon-energy dependent ARPES measurements, we classify them as surface or bulk states. Most importantly, we systematically characterize the change in the Rashba splitting of bulk states as a function of temperature. We observe clear inconsistencies of the ferroelectric phase transition with a simple mean-field-like transition that can be explained with an order–disorder type contribution to the transition. Finally, we comment on its consequences for the topological properties of the (111) surface of SnTe.

SnTe undergoes a transition from a paraelectric state, with a cubic rocksalt structure with equidistant stackings of Sn and Te layers along the [111] direction (space group Fm3̅m, see Figure 1a), to a ferroelectric state with a rhombohedral structure (space group R3m, see Figure 1b) at low temperature around 100 K. (20) In the ferroelectric state, the bulk inversion symmetry is broken by a displacement of the Sn and Te lattice planes against each other, which leads to a nonzero electric dipole between the ionic charges σ+ and σ of the Sn and Te atoms. This induces a Rashba-like splitting in the electronic structure, as can be seen by comparing the bulk DFT band structure in Figure 1d calculated for the paraelectric (blue bands) and ferroelectric (red bands) states. Our objective is to experimentally resolve this splitting and to follow its evolution as a function of temperature in order to characterize the ARPES signatures of the paraelectric-to-ferroelectric phase transition.

Figure 1

Figure 1. (a) Rocksalt structure of SnTe in the paraelectric state along the [111] crystalline direction. Blue (yellow) dots represent Sn (Te). (b) Rhombohedral structure of SnTe in the ferroelectric state (not to scale). Structures were generated with VESTA. (45) (c) Bulk Brillouin zone of SnTe and its surface projected plane along the [111] direction. The black lines in the surface projected plane represent the directions of data presented in this work. (d) Bulk DFT band structure between the high symmetry points Z and A. A k value of 50% of the ΓZ distance has been selected to approximate the reciprocal space plane sampled at a photon energy of 11.2 eV. Bands are plotted for the paraelectric (PE) cubic rocksalt (blue) and ferroelectric (FE) rhombohedral (red) structures.

We have performed ARPES measurements of SnTe(111) along the KΓK¯ high-symmetry direction, which corresponds to the projection of the AZA direction on the (111) surface. Photoemission intensity maps obtained at 30 K with two different photon energies are shown in Figure 2a for = 11.2 eV and Figure 2b for = 21.2 eV, respectively. Thanks to the high energy resolution of our experiment and the high quality of our thin films, we distinguish several bands in the low-energy region, where previously only a linear dispersive band was resolved and attributed to a Dirac cone. (39−41) Near the Fermi level, we identify one surface state (labeled S1) that appears for both photon energies at higher parallel momenta. At lower momenta, we observe another surface state (S2) which partially overlaps with a bulk state (B1) that disperses with photon energy. A more detailed series of photon-energy dependent ARPES measurements using synchrotron radiation is shown in the Supporting Information and corroborates these observations. Similar to the isostructural compound α-GeTe, (10) we attribute the state S2 to a surface resonance state.

Figure 2

Figure 2. ARPES measurements along the KΓK¯ high-symmetry line at 30 K with a photon energy of (a) 11.2 eV and (b) 21.2 eV. The dashed line in panel (b) represents a change of saturation by a factor of 2. (c) One-step photoemission calculation for a semi-infinite slab geometry in a ferroelectric structure, with a photon energy of 11.2 eV and a Te termination. (d) Same calculation with a transparent barrier.

To support our interpretation of the origin of the bands, we have performed DFT calculations using a semi-infinite slab geometry for the ferroelectric structure. The surface with a Te-termination and short bonds between the first Te and Sn planes gives the best agreement with the experimental data (Supporting Information).

Figure 2c and d show the calculations for a 11.2 eV photon energy with an active and a transparent surface barrier, respectively. The position of the Fermi level in the calculation has been corrected to match with the experiment, and the k sampled at 21.2 eV (11.2 eV) has been estimated to be approximately 80% (50%, respectively) of the total ΓZ distance. The transparent surface barrier suppresses the surface states and allows us to discriminate the origin of the bands (see Supporting Information for more details about this procedure). The resulting comparison between theory and experiment confirms our attribution of the bands S1,2 and B1 to surface and bulk states, respectively.

Having clarified the nature of the low-energy band structure, we focus now on the bulk state B1 that shows a large energy splitting at low temperature in the ferroelectric phase. We concentrate ourselves now on the data as measured at 11.2 eV photon energy (see Figure 2b), which allows us to disentangle the bulk states from the surface states and to clearly resolve the bulk Rashba splitting. By presenting ARPES measurements as a function of temperature, we address the effect of the ferroelectric to paraelectric transition on the amplitude of the bulk Rashba splitting, which is directly correlated to the ferroelectric distortion.

Figure 3a and b show ARPES spectra taken at 30 K and at 200 K, respectively, with = 11.2 eV. At 30 K, a clear splitting is observed in all bands, namely the surface ones S1,2 and the bulk one B1. At 200 K, the bands become significantly broader due to thermal effects, but a splitting of the surface-related bands S1,2 is still obvious, in contrast to the bulk band B1, for which the splitting is no longer clearly resolved. We therefore plot in Figure 3e energy distribution curves (EDCs) integrated over k ∈ [−0.20, −0.19] Å–1 (blue region in panel Figure 3a) for a large temperature range up to room temperature. These EDCs allow us to clearly distinguish the two peaks related to the split bulk band at low temperature (in the ferroelectric phase) and to follow the splitting up to about 160 K. At higher temperature, the two peaks seem to merge together so that it is difficult to directly assess whether the band splitting persists at high temperatures or whether it collapses.

Figure 3

Figure 3. ARPES measurements along the KΓK¯ high-symmetry line (k∥,y = 0 Å–1) with a photon energy of 11.2 eV at (a) 30 K and (b) 200 K. ARPES measurements along the line KΓK¯ shifted in direction to M̅ (k∥,y = −0.13 Å–1) with a photon energy of 6.3 eV at (c) 30 K and (d) 190 K. (e) EDCs as a function of temperature for a photon energy of 11.2 eV, with k ∈ [−0.20, – 0.19] Å–1 (blue region in panel (a)). Light-gray lines are guides to the eye for the reader. (f) EDCs as a function of temperature for a photon energy of 6.3 eV, with k ∈ [0.04, 0.05] Å–1. (g) Constant energy map at binding energy EB = 0.4 eV, photon energy = 11.2 eV and at T = 30 K.

To answer this question, we have acquired ARPES data using a photon energy of 6.3 eV to take advantage of the higher momentum resolution at lower photon energy. For this purpose and to maximize the effect of the splitting, we oriented the analyzer slit in a plane parallel to KΓK¯, but shifted toward M̅ at k∥,y = −0.13 Å–1 (which allows to see the same bulk band B1 at a different position in the reciprocal space, see Figure 3g).

The corresponding photoemission intensity maps are shown in Figure 3c and d for temperatures of 30 and 190 K, respectively. We observe two hole-like bands with a clear splitting at low temperature (Figure 3c). One-step model photoemission calculations confirm that these are the same bulk band B1 (see the calculations with and without a transparent surface barrier in the Supporting Information). Moreover, the band splitting is still visible at 190 K (Figure 3d). We have extracted EDCs in this configuration for k ∈ [0.04, 0.05] Å–1 to follow the reduction of the splitting as a function of temperature (see Figure 3f), which allows us to track the splitting up to 250 K at least.

For a quantitative characterization of the temperature evolution of the bulk states across the ferroelectric transition, we have fitted the EDCs of Figure 3e and f with two Voigt functions (see Supporting Information for more details on the procedure). The variation of the splitting as a function of temperature is plotted in Figure 4. We caution that although we obtained good fits with two Voigt functions for temperatures above 250 K, equally good fits could be obtained with a single broader Voigt function in this temperature range. However, this would lead to an abrupt and nonphysical behavior of the width of the Voigt function around 200 K; therefore, we focus on the scenario with two peaks up to room temperature (a single peak scenario starting above the transition temperature where two peaks are still clearly visible in the EDCs, e.g., at 190 K, gives an absurdly large width. Moreover, this width decreases with increasing temperature, indicating that we are trying to fit with one peak two contributions that are moving closer together.). First of all, we see that the evolution of the band splitting in temperature is the same for the two sets of EDCs, confirming the same mechanism observed with both photon energies. Second, the reduction of the splitting is particularly pronounced below 100 K, but a finite value remains at higher temperatures, up to room temperature, at odds with the expectation for a paraelectric cubic state at high temperature. The evolution of the band splitting was reversible and reproducible across different heating and cooling cycles.

Figure 4

Figure 4. Evolution of the Rashba bulk band splitting as a function of temperature extracted from ARPES data obtained using a photon energy of 11.2 eV (6.3 eV) in blue (red). A mean-field-like second-order phase transition with a Tc = 110 K is added on top (orange curve). However, the nonzero splitting above Tc (dashed green line) indicates the persistence of a structural distortion up to room temperature, in disagreement with a mean-field transition. The error bars are due to temperature measurement precision and the fitting procedure.

Although the origin of the transition (displacive vs order–disorder) remains a matter of debate in the literature, its second-order character is agreed upon. (9,20,21,24−26,28,29,46) We therefore superimpose on the experimental data in Figure 4 a mean-field-like (orange) curve with a critical temperature of Tc = 110 K and adding a constant offset of ΔE/Emax = 0.7. We stress that within a mean-field-like scenario, one would expect a zero offset at room temperature. The obtained curve agrees well with the low temperature data, but it reveals a rounding of the phase transition above Tc. This could be due to strong thermal fluctuations, in agreement with the general increased broadening of the bands observed at and above about 200 K in ARPES (Figure 3b). However, this fails to explain the persistence of a splitting well above Tc, which is a clear indication of inversion symmetry breaking inside the crystal, even at high temperature.

This surprising observation is consistent with a contribution from an order–disorder type of phase transition. Whereas for a displacive transition, the onset of the anion/cation displacement appears only at TTc and continuously grows as the temperature decreases, the order–disorder phase transition is based on the ordering below Tc of unit cells that are already distorted above Tc, but with random orientation of the anion/cation displacement. As a result, although above Tc the net macroscopic polarization is zero, there are still clusters with a nonzero local polarization extending over a few-unit cells and with alternation of the sign of the polarization from cluster to cluster. These clusters would therefore still have locally a structural distortion and thus give rise to the spin-split bulk bands above Tc as we experimentally observe. This agrees with extended X-ray absorption fine structure and X-ray scattering analysis of the pair distribution function that have revealed the persistence of local lattice distortions, i.e., the presence of local ferroelectric dipoles above Tc. (29−32) We caution though that we cannot rule out another structural mechanism occurring specifically near the surface of SnTe that could cause the persistence of the band splitting at high temperature, (47) given that ferroelectricity has been observed up to room temperature in the two-dimensional limit of SnTe. (48)

From our data at a photon energy of 11.2 eV (see Figure 2a), we can estimate a minimal value for the Rashba parameter αR. With the standard relation αR = 2ER/k0, we extract ER = 0.34 eV and k0 = 0.19 Å–1 at 30 K. The Rashba parameter is then αR = 3.58 eV Å. We note that this experimental value is relatively close to the theoretical estimation from DFT in ref (44)R = 4.4 eV Å), therefore providing an experimental confirmation of the giant Rashba effect in SnTe.

Given our discovery of the persistence of a structural distortion in SnTe at higher temperatures, an open question is what is its impact on the topological surface states? Symmetry arguments have been used to derive a nonzero mirror Chern number on the (001), (111), and (110) surfaces of the rocksalt paraelectric structure and therefore the presence of Dirac cones in the ARPES spectra. (35) Such considerations were supported by earlier theoretical (36,40) and experimental studies on the (001) surface. (38) As for the (111) orientation, Plekhanov et al. showed that in a rhombohedral distorted structure there are no gapless topological surface states near the Fermi level. In that respect, static ARPES studies have claimed to have measured a topological surface state at Γ̅. (39−41) However, the highly p-type character of SnTe precludes the direct observation of the Dirac cone by ARPES. Our results provide a new perspective to these findings by resolving more bands, namely, two surfaces states instead of one, and with an unprecedented resolution. By looking at our ARPES measurements, we identify the S1 and S2 surface states as the candidate for the linear dispersion in the occupied states that has been interpreted as a topological surface state in previous studies. In light of the study of Plekhanov and co-workers, (44) our observation of the persistence of local rhombohedral lattice distortions above Tc therefore excludes the possible existence of topological surface states at high temperature on the (111) surface, at odds with recent time-resolved ARPES studies. (49) Our new results therefore require a reassessment of these observations.

We have characterized the band structure of SnTe(111) using high-energy resolution ARPES measurements with unprecedented quality. Combined with state-of-the-art photoemission calculations with and without a surface barrier, our ARPES study at selected photon energies enabled us to differentiate surface and bulk states. The presence of bulk-split bands has been directly connected to the inversion symmetry breaking. We also studied the evolution of this splitting as a function of temperature to characterize the ferroelectric transition. This study demonstrated inconsistencies with a displacive mean-field like transition, revealing a rounding of the phase transition and a splitting persisting above Tc, at least up to 250 K. This observation is consistent with an order–disorder type phase transition, in agreement with findings from other studies using local probes. (29,30,47) Above the critical temperature, fluctuations of the polarization vector from one cluster to another imply that a structural distortion remains and explain the persistence of the band splitting at high temperature. We propose that the possible persistence of ferroelectricity at high temperature in the near-surface region could be tested with spin-resolved and microfocus ARPES measurements by looking for the existence of a finite spin polarization, as well as by evidencing circular dichroism in ARPES. (50,51) Finally, the persistence of rhombohedral distortions above the critical temperature requires a reassessment of the topological nature of the SnTe(111) surface since it has been shown in the literature (44) and confirmed by our DFT calculation that the break of symmetry destroys the topological surface state along the (111) direction.

Supporting Information

ARTICLE SECTIONS
Jump To

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.3c03280.

  • Details on the samples growth and characterization; methods used to perform the ARPES measurements and the calculations; photon-energy dependent ARPES measurements; one-step photoemission calculations for the 6.3 eV ARPES data; DFT calculations for different surface terminations; fitting of the Rashba splitting (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

ARTICLE SECTIONS
Jump To

  • Corresponding Authors
  • Authors
    • Aki Pulkkinen - Department of Physics and Fribourg Center for Nanomaterials, Université de Fribourg, Fribourg 1700, SwitzerlandNew Technologies-Research Center, University of West Bohemia, Plzeň 301 00, Czech RepublicOrcidhttps://orcid.org/0000-0002-4339-6928
    • Geoffroy Kremer - Department of Physics and Fribourg Center for Nanomaterials, Université de Fribourg, Fribourg 1700, SwitzerlandInstitut Jean Lamour, UMR 7198, CNRS-Université de Lorraine, Campus ARTEM, 2 allée André Guinier, BP 50840, Nancy 54011, FranceOrcidhttps://orcid.org/0000-0003-1753-3471
    • Tetiana Zakusylo - Institut für Halbleiter-und Festkörperphysik, Johannes Kepler Universität, Linz 4040, AustriaOrcidhttps://orcid.org/0000-0001-5933-7108
    • Gauthier Krizman - Institut für Halbleiter-und Festkörperphysik, Johannes Kepler Universität, Linz 4040, AustriaOrcidhttps://orcid.org/0000-0003-2375-5302
    • Mahdi Hajlaoui - Institut für Halbleiter-und Festkörperphysik, Johannes Kepler Universität, Linz 4040, Austria
    • J. Hugo Dil - Institute of Physics, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, SwitzerlandPhoton Science Division, Paul Scherrer Institut, Villigen 5232, SwitzerlandOrcidhttps://orcid.org/0000-0002-6016-6120
    • Juraj Krempaský - Photon Science Division, Paul Scherrer Institut, Villigen 5232, SwitzerlandOrcidhttps://orcid.org/0000-0001-9043-511X
    • Ján Minár - New Technologies-Research Center, University of West Bohemia, Plzeň 301 00, Czech Republic
    • Gunther Springholz - Institut für Halbleiter-und Festkörperphysik, Johannes Kepler Universität, Linz 4040, AustriaOrcidhttps://orcid.org/0000-0003-3133-4815
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

ARTICLE SECTIONS
Jump To

Aki Pulkkinen and Geoffroy Kremer contributed equally to this work. G.S. would like to thank the Austrian Science Fund (FWF), who supported this study with Project Nos. P30960–N27 and I 4493-N. We are grateful to Natalia Olszowska and Jacek Kołodziej for their support of the ARPES measurements at SOLARIS, funded by the Polish Ministry of Education and Science under Contract No. 1/SOL/2021/2. J.M. and A.P. would like to thank the QM4ST project with Reg. No. CZ.02.01.01/00/22_008/0004572, cofunded by the ERDF as part of the MŠMT. We are very grateful to M. Rumo and B. Salzmann for fruitful discussions. Skillful technical assistance was provided by F. Bourqui, B. Hediger, and M. Audrey.

References

ARTICLE SECTIONS
Jump To

This article references 51 other publications.

  1. 1
    Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molnár, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Spintronics: A Spin-Based Electronics Vision for the Future. Science 2001, 294, 14881495,  DOI: 10.1126/science.1065389
  2. 2
    Xu, Y.; Awschalom, D.; Nitta, J. Handbook of Spintronics; Springer, 2015; pp 11596.
  3. 3
    Rabe, K. M.; Dawber, M.; Lichtensteiger, C.; Ahn, C. H.; Triscone, J.-M. Physics of Ferroelectrics: A Modern Perspective. Topics in Applied Physics; Springer, 2007; pp 130.
  4. 4
    Noël, P.; Trier, F.; Vicente Arche, L. M.; Bréhin, J.; Vaz, D. C.; Garcia, V.; Fusil, S.; Barthélémy, A.; Vila, L.; Bibes, M.; Attané, J.-P. Non-volatile electric control of spin–charge conversion in a SrTiO3 Rashba system. Nature 2020, 580, 483486,  DOI: 10.1038/s41586-020-2197-9
  5. 5
    A century of ferroelectricity. Nat. Mater. 2020, 19, 129. DOI: 10.1038/s41563-020-0611-1
  6. 6
    Bhalla, A. S.; Saxena, A. Ferroelectricity: 100 years on. Phys. World 2021, 33, 38,  DOI: 10.1088/2058-7058/33/11/31
  7. 7
    Bychkov, Y. A.; Rashba, É. I. Properties of a 2D electron gas with lifted spectral degeneracy. JETP lett 1984, 39, 78
  8. 8
    Rotenberg, E.; Chung, J. W.; Kevan, S. D. Spin-Orbit Coupling Induced Surface Band Splitting in Li/W(110) and Li/Mo(110). Phys. Rev. Lett. 1999, 82, 40664069,  DOI: 10.1103/PhysRevLett.82.4066
  9. 9
    Pawley, G. S.; Cochran, W.; Cowley, R. A.; Dolling, G. Diatomic Ferroelectrics. Phys. Rev. Lett. 1966, 17, 753755,  DOI: 10.1103/PhysRevLett.17.753
  10. 10
    Krempaský, J. Disentangling bulk and surface Rashba effects in ferroelectric α-GeTe. Phys. Rev. B 2016, 94, 205111,  DOI: 10.1103/PhysRevB.94.205111
  11. 11
    Elmers, H. J. Spin mapping of surface and bulk Rashba states in ferroelectric α-GeTe(111) films. Phys. Rev. B 2016, 94, 201403,  DOI: 10.1103/PhysRevB.94.201403
  12. 12
    Di Sante, D.; Barone, P.; Bertacco, R.; Picozzi, S. Electric Control of the Giant Rashba Effect in Bulk GeTe. Adv. Mater. 2013, 25, 509513,  DOI: 10.1002/adma.201203199
  13. 13
    Wang, H.; Gopal, P.; Picozzi, S.; Curtarolo, S.; Buongiorno Nardelli, M.; Sławińska, J. Spin Hall effect in prototype Rashba ferroelectrics GeTe and SnTe. npj Computational Materials 2020, 6, 17,  DOI: 10.1038/s41524-020-0274-0
  14. 14
    Rinaldi, C.; Rojas-Sánchez, J. C.; Wang, R. N.; Fu, Y.; Oyarzun, S.; Vila, L.; Bertoli, S.; Asa, M.; Baldrati, L.; Cantoni, M.; George, J.-M.; Calarco, R.; Fert, A.; Bertacco, R. Evidence for spin to charge conversion in GeTe(111). APL Materials 2016, 4, 032501,  DOI: 10.1063/1.4941276
  15. 15
    Picozzi, S. Ferroelectric Rashba semiconductors as a novel class of multifunctional materials. Frontiers in Physics 2014, 2, 15,  DOI: 10.3389/fphy.2014.00010
  16. 16
    Liebmann, M. Giant Rashba-Type Spin Splitting in Ferroelectric GeTe(111). Adv. Mater. 2016, 28, 560565,  DOI: 10.1002/adma.201503459
  17. 17
    Krempaský, J. Entanglement and manipulation of the magnetic and spin–orbit order in multiferroic Rashba semiconductors. Nat. Commun. 2016, 7, 13071,  DOI: 10.1038/ncomms13071
  18. 18
    Krempaský, J.; Muff, S.; Minár, J.; Pilet, N.; Fanciulli, M.; Weber, A.; Guedes, E.; Caputo, M.; Müller, E.; Volobuev, V.; Gmitra, M.; Vaz, C.; Scagnoli, V.; Springholz, G.; Dil, J. Operando Imaging of All-Electric Spin Texture Manipulation in Ferroelectric and Multiferroic Rashba Semiconductors. Physical Review X 2018, 8, 021067,  DOI: 10.1103/PhysRevX.8.021067
  19. 19
    Kremer, G.; Maklar, J.; Nicolaï, L.; Nicholson, C. W.; Yue, C.; Silva, C.; Werner, P.; Dil, J. H.; Krempaský, J.; Springholz, G.; Ernstorfer, R.; Minár, J.; Rettig, L.; Monney, C. Field-induced ultrafast modulation of Rashba coupling at room temperature in ferroelectric α-GeTe(111). Nat. Commun. 2022, 13, 6396,  DOI: 10.1038/s41467-022-33978-3
  20. 20
    Iizumi, M.; Hamaguchi, Y.; Komatsubara, K. F.; Kato, Y. Phase Transition in SnTe with Low Carrier Concentration. J. Phys. Soc. Jpn. 1975, 38, 443449,  DOI: 10.1143/JPSJ.38.443
  21. 21
    Brillson, L. J.; Burstein, E.; Muldawer, L. Raman observation of the ferroelectric phase transition in SnTe. Phys. Rev. B 1974, 9, 15471551,  DOI: 10.1103/PhysRevB.9.1547
  22. 22
    Kobayashi, K. L. I.; Kato, Y.; Katayama, Y.; Komatsubara, K. F. Carrier-Concentration-Dependent Phase Transition in SnTe. Phys. Rev. Lett. 1976, 37, 772774,  DOI: 10.1103/PhysRevLett.37.772
  23. 23
    Mazelsky, R.; Lubell, M. S.; Kramer, W. E. Phase Studies of the Group IV-A Tellurides. J. Chem. Phys. 1962, 37, 4547,  DOI: 10.1063/1.1732972
  24. 24
    Littlewood, P. B. The crystal structure of IV-VI compounds. II. A microscopic model for cubic/rhombohedral materials. Journal of Physics C: Solid State Physics 1980, 13, 4875,  DOI: 10.1088/0022-3719/13/26/010
  25. 25
    Rabe, K. M.; Joannopoulos, J. D. Ab initio relativistic pseudopotential study of the zero-temperature structural properties of SnTe and PbTe. Phys. Rev. B 1985, 32, 23022314,  DOI: 10.1103/PhysRevB.32.2302
  26. 26
    Salje, E. K. H. Tin telluride: A weakly co-elastic metal. Phys. Rev. B 2010, 82, 184112,  DOI: 10.1103/PhysRevB.82.184112
  27. 27
    Li, Z.; Li, S.; Castellan, J.-P.; Heid, R.; Xiao, Y.; Zhao, L.-D.; Chen, Y.; Weber, F. Anomalous transverse optical phonons in SnTe and PbTe. Phys. Rev. B 2022, 105, 014308,  DOI: 10.1103/PhysRevB.105.014308
  28. 28
    O’Neill, C. D.; Sokolov, D. A.; Hermann, A.; Bossak, A.; Stock, C.; Huxley, A. D. Inelastic x-ray investigation of the ferroelectric transition in SnTe. Phys. Rev. B 2017, 95, 144101,  DOI: 10.1103/PhysRevB.95.144101
  29. 29
    Fornasini, P.; Grisenti, R.; Dapiaggi, M.; Agostini, G. Local structural distortions in SnTe investigated by EXAFS. J. Phys.: Condens. Matter 2021, 33, 295404,  DOI: 10.1088/1361-648X/ac0082
  30. 30
    Mitrofanov, K. V.; Kolobov, A. V.; Fons, P.; Krbal, M.; Shintani, T.; Tominaga, J.; Uruga, T. Local structure of the SnTe topological crystalline insulator: Rhombohedral distortions emerging from the rocksalt phase. Phys. Rev. B 2014, 90, 134101,  DOI: 10.1103/PhysRevB.90.134101
  31. 31
    Fons, P.; Kolobov, A. V.; Krbal, M.; Tominaga, J.; Andrikopoulos, K. S.; Yannopoulos, S. N.; Voyiatzis, G. A.; Uruga, T. Phase transition in crystalline GeTe: Pitfalls of averaging effects. Phys. Rev. B 2010, 82, 155209,  DOI: 10.1103/PhysRevB.82.155209
  32. 32
    Matsunaga, T.; Fons, P.; Kolobov, A. V.; Tominaga, J.; Yamada, N. The order-disorder transition in GeTe: Views from different length-scales. Appl. Phys. Lett. 2011, 99, 231907,  DOI: 10.1063/1.3665067
  33. 33
    Chatterji, T.; Kumar, C. M. N.; Wdowik, U. D. Anomalous temperature-induced volume contraction in GeTe. Phys. Rev. B 2015, 91, 054110,  DOI: 10.1103/PhysRevB.91.054110
  34. 34
    Kimber, S. A. J.; Zhang, J.; Liang, C. H.; Guzmán-Verri, G. G.; Littlewood, P. B.; Cheng, Y.; Abernathy, D. L.; Hudspeth, J. M.; Luo, Z.-Z.; Kanatzidis, M. G.; Chatterji, T.; Ramirez-Cuesta, A. J.; Billinge, S. J. L. Dynamic crystallography reveals spontaneous anisotropy in cubic GeTe. Nat. Mater. 2023, 22, 311315,  DOI: 10.1038/s41563-023-01483-7
  35. 35
    Fu, L. Topological Crystalline Insulators. Phys. Rev. Lett. 2011, 106, 106802,  DOI: 10.1103/PhysRevLett.106.106802
  36. 36
    Hsieh, T. H.; Lin, H.; Liu, J.; Duan, W.; Bansil, A.; Fu, L. Topological crystalline insulators in the SnTe material class. Nat. Commun. 2012, 3, 982,  DOI: 10.1038/ncomms1969
  37. 37
    Shi, Y.; Wu, M.; Zhang, F.; Feng, J. 111) surface states of SnTe. Phys. Rev. B 2014, 90, 235114,  DOI: 10.1103/PhysRevB.90.235114
  38. 38
    Tanaka, Y.; Ren, Z.; Sato, T.; Nakayama, K.; Souma, S.; Takahashi, T.; Segawa, K.; Ando, Y. Experimental realization of a topological crystalline insulator in SnTe. Nature Phys. 2012, 8, 800803,  DOI: 10.1038/nphys2442
  39. 39
    Tanaka, Y.; Shoman, T.; Nakayama, K.; Souma, S.; Sato, T.; Takahashi, T.; Novak, M.; Segawa, K.; Ando, Y. Two types of Dirac-cone surface states on the (111) surface of the topological crystalline insulator SnTe. Phys. Rev. B 2013, 88, 235126,  DOI: 10.1103/PhysRevB.88.235126
  40. 40
    Yan, C.; Liu, J.; Zang, Y.; Wang, J.; Wang, Z.; Wang, P.; Zhang, Z.-D.; Wang, L.; Ma, X.; Ji, S.; He, K.; Fu, L.; Duan, W.; Xue, Q.-K.; Chen, X. Experimental Observation of Dirac-like Surface States and Topological Phase Transition in Pb1–xSnxTe (111) Films. Phys. Rev. Lett. 2014, 112, 186801,  DOI: 10.1103/PhysRevLett.112.186801
  41. 41
    Zhang, Y.; Liu, Z.; Zhou, B.; Kim, Y.; Yang, L.; Ryu, H.; Hwang, C.; Chen, Y.; Hussain, Z.; Shen, Z.-X.; Mo, S.-K. ARPES study of the epitaxially grown topological crystalline insulator SnTe(111). J. Electron Spectrosc. Relat. Phenom. 2017, 219, 3540,  DOI: 10.1016/j.elspec.2016.10.003
  42. 42
    Polley, C. M.; Jovic, V.; Su, T.-Y.; Saghir, M.; Newby, D.; Kowalski, B. J.; Jakiela, R.; Barcz, A.; Guziewicz, M.; Balasubramanian, T.; Balakrishnan, G.; Laverock, J.; Smith, K. E. Observation of surface states on heavily indium-doped SnTe(111), a superconducting topological crystalline insulator. Phys. Rev. B 2016, 93, 075132,  DOI: 10.1103/PhysRevB.93.075132
  43. 43
    Maiti, A.; Pandeya, R. P.; Singh, B.; Iyer, K. K.; Thamizhavel, A.; Maiti, K. Anomalies in the temperature evolution of Dirac states in the topological crystalline insulator SnTe. Phys. Rev. B 2021, 104, 195403,  DOI: 10.1103/PhysRevB.104.195403
  44. 44
    Plekhanov, E.; Barone, P.; Di Sante, D.; Picozzi, S. Engineering relativistic effects in ferroelectric SnTe. Phys. Rev. B 2014, 90, 161108,  DOI: 10.1103/PhysRevB.90.161108
  45. 45
    Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 12721276,  DOI: 10.1107/S0021889811038970
  46. 46
    Knox, K. R.; Bozin, E. S.; Malliakas, C. D.; Kanatzidis, M. G.; Billinge, S. J. L. Local off-centering symmetry breaking in the high-temperature regime of SnTe. Phys. Rev. B 2014, 89, 014102,  DOI: 10.1103/PhysRevB.89.014102
  47. 47
    Aggarwal, L.; Banik, A.; Anand, S.; Waghmare, U. V.; Biswas, K.; Sheet, G. Local ferroelectricity in thermoelectric SnTe above room temperature driven by competing phonon instabilities and soft resonant bonding. Journal of Materiomics 2016, 2, 196202,  DOI: 10.1016/j.jmat.2016.04.001
  48. 48
    Chang, K.; Liu, J.; Lin, H.; Wang, N.; Zhao, K.; Zhang, A.; Jin, F.; Zhong, Y.; Hu, X.; Duan, W.; Zhang, Q.; Fu, L.; Xue, Q.-K.; Chen, X.; Ji, S.-H. Discovery of robust in-plane ferroelectricity in atomic-thick SnTe. Science 2016, 353, 274278,  DOI: 10.1126/science.aad8609
  49. 49
    Ito, H.; Otaki, Y.; Tomohiro, Y.; Ishida, Y.; Akiyama, R.; Kimura, A.; Shin, S.; Kuroda, S. Observation of unoccupied states of SnTe(111) using pump-probe ARPES measurement. Phys. Rev. Research 2020, 2, 043120,  DOI: 10.1103/PhysRevResearch.2.043120
  50. 50
    Cho, S.; Park, J.-H.; Hong, J.; Jung, J.; Kim, B. S.; Han, G.; Kyung, W.; Kim, Y.; Mo, S.-K.; Denlinger, J. D.; Shim, J. H.; Han, J. H.; Kim, C.; Park, S. R. Experimental Observation of Hidden Berry Curvature in Inversion-Symmetric Bulk 2H-WSe2. Phys. Rev. Lett. 2018, 121, 186401,  DOI: 10.1103/PhysRevLett.121.186401
  51. 51
    Kim, J.; Kim, K.-W.; Shin, D.; Lee, S.-H.; Sinova, J.; Park, N.; Jin, H. Prediction of ferroelectricity-driven Berry curvature enabling charge- and spin-controllable photocurrent in tin telluride monolayers. Nat. Commun. 2019, 10, 3965,  DOI: 10.1038/s41467-019-11964-6

Cited By

ARTICLE SECTIONS
Jump To

This article has not yet been cited by other publications.

  • Abstract

    Figure 1

    Figure 1. (a) Rocksalt structure of SnTe in the paraelectric state along the [111] crystalline direction. Blue (yellow) dots represent Sn (Te). (b) Rhombohedral structure of SnTe in the ferroelectric state (not to scale). Structures were generated with VESTA. (45) (c) Bulk Brillouin zone of SnTe and its surface projected plane along the [111] direction. The black lines in the surface projected plane represent the directions of data presented in this work. (d) Bulk DFT band structure between the high symmetry points Z and A. A k value of 50% of the ΓZ distance has been selected to approximate the reciprocal space plane sampled at a photon energy of 11.2 eV. Bands are plotted for the paraelectric (PE) cubic rocksalt (blue) and ferroelectric (FE) rhombohedral (red) structures.

    Figure 2

    Figure 2. ARPES measurements along the KΓK¯ high-symmetry line at 30 K with a photon energy of (a) 11.2 eV and (b) 21.2 eV. The dashed line in panel (b) represents a change of saturation by a factor of 2. (c) One-step photoemission calculation for a semi-infinite slab geometry in a ferroelectric structure, with a photon energy of 11.2 eV and a Te termination. (d) Same calculation with a transparent barrier.

    Figure 3

    Figure 3. ARPES measurements along the KΓK¯ high-symmetry line (k∥,y = 0 Å–1) with a photon energy of 11.2 eV at (a) 30 K and (b) 200 K. ARPES measurements along the line KΓK¯ shifted in direction to M̅ (k∥,y = −0.13 Å–1) with a photon energy of 6.3 eV at (c) 30 K and (d) 190 K. (e) EDCs as a function of temperature for a photon energy of 11.2 eV, with k ∈ [−0.20, – 0.19] Å–1 (blue region in panel (a)). Light-gray lines are guides to the eye for the reader. (f) EDCs as a function of temperature for a photon energy of 6.3 eV, with k ∈ [0.04, 0.05] Å–1. (g) Constant energy map at binding energy EB = 0.4 eV, photon energy = 11.2 eV and at T = 30 K.

    Figure 4

    Figure 4. Evolution of the Rashba bulk band splitting as a function of temperature extracted from ARPES data obtained using a photon energy of 11.2 eV (6.3 eV) in blue (red). A mean-field-like second-order phase transition with a Tc = 110 K is added on top (orange curve). However, the nonzero splitting above Tc (dashed green line) indicates the persistence of a structural distortion up to room temperature, in disagreement with a mean-field transition. The error bars are due to temperature measurement precision and the fitting procedure.

  • References

    ARTICLE SECTIONS
    Jump To

    This article references 51 other publications.

    1. 1
      Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molnár, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Spintronics: A Spin-Based Electronics Vision for the Future. Science 2001, 294, 14881495,  DOI: 10.1126/science.1065389
    2. 2
      Xu, Y.; Awschalom, D.; Nitta, J. Handbook of Spintronics; Springer, 2015; pp 11596.
    3. 3
      Rabe, K. M.; Dawber, M.; Lichtensteiger, C.; Ahn, C. H.; Triscone, J.-M. Physics of Ferroelectrics: A Modern Perspective. Topics in Applied Physics; Springer, 2007; pp 130.
    4. 4
      Noël, P.; Trier, F.; Vicente Arche, L. M.; Bréhin, J.; Vaz, D. C.; Garcia, V.; Fusil, S.; Barthélémy, A.; Vila, L.; Bibes, M.; Attané, J.-P. Non-volatile electric control of spin–charge conversion in a SrTiO3 Rashba system. Nature 2020, 580, 483486,  DOI: 10.1038/s41586-020-2197-9
    5. 5
      A century of ferroelectricity. Nat. Mater. 2020, 19, 129. DOI: 10.1038/s41563-020-0611-1
    6. 6
      Bhalla, A. S.; Saxena, A. Ferroelectricity: 100 years on. Phys. World 2021, 33, 38,  DOI: 10.1088/2058-7058/33/11/31
    7. 7
      Bychkov, Y. A.; Rashba, É. I. Properties of a 2D electron gas with lifted spectral degeneracy. JETP lett 1984, 39, 78
    8. 8
      Rotenberg, E.; Chung, J. W.; Kevan, S. D. Spin-Orbit Coupling Induced Surface Band Splitting in Li/W(110) and Li/Mo(110). Phys. Rev. Lett. 1999, 82, 40664069,  DOI: 10.1103/PhysRevLett.82.4066
    9. 9
      Pawley, G. S.; Cochran, W.; Cowley, R. A.; Dolling, G. Diatomic Ferroelectrics. Phys. Rev. Lett. 1966, 17, 753755,  DOI: 10.1103/PhysRevLett.17.753
    10. 10
      Krempaský, J. Disentangling bulk and surface Rashba effects in ferroelectric α-GeTe. Phys. Rev. B 2016, 94, 205111,  DOI: 10.1103/PhysRevB.94.205111
    11. 11
      Elmers, H. J. Spin mapping of surface and bulk Rashba states in ferroelectric α-GeTe(111) films. Phys. Rev. B 2016, 94, 201403,  DOI: 10.1103/PhysRevB.94.201403
    12. 12
      Di Sante, D.; Barone, P.; Bertacco, R.; Picozzi, S. Electric Control of the Giant Rashba Effect in Bulk GeTe. Adv. Mater. 2013, 25, 509513,  DOI: 10.1002/adma.201203199
    13. 13
      Wang, H.; Gopal, P.; Picozzi, S.; Curtarolo, S.; Buongiorno Nardelli, M.; Sławińska, J. Spin Hall effect in prototype Rashba ferroelectrics GeTe and SnTe. npj Computational Materials 2020, 6, 17,  DOI: 10.1038/s41524-020-0274-0
    14. 14
      Rinaldi, C.; Rojas-Sánchez, J. C.; Wang, R. N.; Fu, Y.; Oyarzun, S.; Vila, L.; Bertoli, S.; Asa, M.; Baldrati, L.; Cantoni, M.; George, J.-M.; Calarco, R.; Fert, A.; Bertacco, R. Evidence for spin to charge conversion in GeTe(111). APL Materials 2016, 4, 032501,  DOI: 10.1063/1.4941276
    15. 15
      Picozzi, S. Ferroelectric Rashba semiconductors as a novel class of multifunctional materials. Frontiers in Physics 2014, 2, 15,  DOI: 10.3389/fphy.2014.00010
    16. 16
      Liebmann, M. Giant Rashba-Type Spin Splitting in Ferroelectric GeTe(111). Adv. Mater. 2016, 28, 560565,  DOI: 10.1002/adma.201503459
    17. 17
      Krempaský, J. Entanglement and manipulation of the magnetic and spin–orbit order in multiferroic Rashba semiconductors. Nat. Commun. 2016, 7, 13071,  DOI: 10.1038/ncomms13071
    18. 18
      Krempaský, J.; Muff, S.; Minár, J.; Pilet, N.; Fanciulli, M.; Weber, A.; Guedes, E.; Caputo, M.; Müller, E.; Volobuev, V.; Gmitra, M.; Vaz, C.; Scagnoli, V.; Springholz, G.; Dil, J. Operando Imaging of All-Electric Spin Texture Manipulation in Ferroelectric and Multiferroic Rashba Semiconductors. Physical Review X 2018, 8, 021067,  DOI: 10.1103/PhysRevX.8.021067
    19. 19
      Kremer, G.; Maklar, J.; Nicolaï, L.; Nicholson, C. W.; Yue, C.; Silva, C.; Werner, P.; Dil, J. H.; Krempaský, J.; Springholz, G.; Ernstorfer, R.; Minár, J.; Rettig, L.; Monney, C. Field-induced ultrafast modulation of Rashba coupling at room temperature in ferroelectric α-GeTe(111). Nat. Commun. 2022, 13, 6396,  DOI: 10.1038/s41467-022-33978-3
    20. 20
      Iizumi, M.; Hamaguchi, Y.; Komatsubara, K. F.; Kato, Y. Phase Transition in SnTe with Low Carrier Concentration. J. Phys. Soc. Jpn. 1975, 38, 443449,  DOI: 10.1143/JPSJ.38.443
    21. 21
      Brillson, L. J.; Burstein, E.; Muldawer, L. Raman observation of the ferroelectric phase transition in SnTe. Phys. Rev. B 1974, 9, 15471551,  DOI: 10.1103/PhysRevB.9.1547
    22. 22
      Kobayashi, K. L. I.; Kato, Y.; Katayama, Y.; Komatsubara, K. F. Carrier-Concentration-Dependent Phase Transition in SnTe. Phys. Rev. Lett. 1976, 37, 772774,  DOI: 10.1103/PhysRevLett.37.772
    23. 23
      Mazelsky, R.; Lubell, M. S.; Kramer, W. E. Phase Studies of the Group IV-A Tellurides. J. Chem. Phys. 1962, 37, 4547,  DOI: 10.1063/1.1732972
    24. 24
      Littlewood, P. B. The crystal structure of IV-VI compounds. II. A microscopic model for cubic/rhombohedral materials. Journal of Physics C: Solid State Physics 1980, 13, 4875,  DOI: 10.1088/0022-3719/13/26/010
    25. 25
      Rabe, K. M.; Joannopoulos, J. D. Ab initio relativistic pseudopotential study of the zero-temperature structural properties of SnTe and PbTe. Phys. Rev. B 1985, 32, 23022314,  DOI: 10.1103/PhysRevB.32.2302
    26. 26
      Salje, E. K. H. Tin telluride: A weakly co-elastic metal. Phys. Rev. B 2010, 82, 184112,  DOI: 10.1103/PhysRevB.82.184112
    27. 27
      Li, Z.; Li, S.; Castellan, J.-P.; Heid, R.; Xiao, Y.; Zhao, L.-D.; Chen, Y.; Weber, F. Anomalous transverse optical phonons in SnTe and PbTe. Phys. Rev. B 2022, 105, 014308,  DOI: 10.1103/PhysRevB.105.014308
    28. 28
      O’Neill, C. D.; Sokolov, D. A.; Hermann, A.; Bossak, A.; Stock, C.; Huxley, A. D. Inelastic x-ray investigation of the ferroelectric transition in SnTe. Phys. Rev. B 2017, 95, 144101,  DOI: 10.1103/PhysRevB.95.144101
    29. 29
      Fornasini, P.; Grisenti, R.; Dapiaggi, M.; Agostini, G. Local structural distortions in SnTe investigated by EXAFS. J. Phys.: Condens. Matter 2021, 33, 295404,  DOI: 10.1088/1361-648X/ac0082
    30. 30
      Mitrofanov, K. V.; Kolobov, A. V.; Fons, P.; Krbal, M.; Shintani, T.; Tominaga, J.; Uruga, T. Local structure of the SnTe topological crystalline insulator: Rhombohedral distortions emerging from the rocksalt phase. Phys. Rev. B 2014, 90, 134101,  DOI: 10.1103/PhysRevB.90.134101
    31. 31
      Fons, P.; Kolobov, A. V.; Krbal, M.; Tominaga, J.; Andrikopoulos, K. S.; Yannopoulos, S. N.; Voyiatzis, G. A.; Uruga, T. Phase transition in crystalline GeTe: Pitfalls of averaging effects. Phys. Rev. B 2010, 82, 155209,  DOI: 10.1103/PhysRevB.82.155209
    32. 32
      Matsunaga, T.; Fons, P.; Kolobov, A. V.; Tominaga, J.; Yamada, N. The order-disorder transition in GeTe: Views from different length-scales. Appl. Phys. Lett. 2011, 99, 231907,  DOI: 10.1063/1.3665067
    33. 33
      Chatterji, T.; Kumar, C. M. N.; Wdowik, U. D. Anomalous temperature-induced volume contraction in GeTe. Phys. Rev. B 2015, 91, 054110,  DOI: 10.1103/PhysRevB.91.054110
    34. 34
      Kimber, S. A. J.; Zhang, J.; Liang, C. H.; Guzmán-Verri, G. G.; Littlewood, P. B.; Cheng, Y.; Abernathy, D. L.; Hudspeth, J. M.; Luo, Z.-Z.; Kanatzidis, M. G.; Chatterji, T.; Ramirez-Cuesta, A. J.; Billinge, S. J. L. Dynamic crystallography reveals spontaneous anisotropy in cubic GeTe. Nat. Mater. 2023, 22, 311315,  DOI: 10.1038/s41563-023-01483-7
    35. 35
      Fu, L. Topological Crystalline Insulators. Phys. Rev. Lett. 2011, 106, 106802,  DOI: 10.1103/PhysRevLett.106.106802
    36. 36
      Hsieh, T. H.; Lin, H.; Liu, J.; Duan, W.; Bansil, A.; Fu, L. Topological crystalline insulators in the SnTe material class. Nat. Commun. 2012, 3, 982,  DOI: 10.1038/ncomms1969
    37. 37
      Shi, Y.; Wu, M.; Zhang, F.; Feng, J. 111) surface states of SnTe. Phys. Rev. B 2014, 90, 235114,  DOI: 10.1103/PhysRevB.90.235114
    38. 38
      Tanaka, Y.; Ren, Z.; Sato, T.; Nakayama, K.; Souma, S.; Takahashi, T.; Segawa, K.; Ando, Y. Experimental realization of a topological crystalline insulator in SnTe. Nature Phys. 2012, 8, 800803,  DOI: 10.1038/nphys2442
    39. 39
      Tanaka, Y.; Shoman, T.; Nakayama, K.; Souma, S.; Sato, T.; Takahashi, T.; Novak, M.; Segawa, K.; Ando, Y. Two types of Dirac-cone surface states on the (111) surface of the topological crystalline insulator SnTe. Phys. Rev. B 2013, 88, 235126,  DOI: 10.1103/PhysRevB.88.235126
    40. 40
      Yan, C.; Liu, J.; Zang, Y.; Wang, J.; Wang, Z.; Wang, P.; Zhang, Z.-D.; Wang, L.; Ma, X.; Ji, S.; He, K.; Fu, L.; Duan, W.; Xue, Q.-K.; Chen, X. Experimental Observation of Dirac-like Surface States and Topological Phase Transition in Pb1–xSnxTe (111) Films. Phys. Rev. Lett. 2014, 112, 186801,  DOI: 10.1103/PhysRevLett.112.186801
    41. 41
      Zhang, Y.; Liu, Z.; Zhou, B.; Kim, Y.; Yang, L.; Ryu, H.; Hwang, C.; Chen, Y.; Hussain, Z.; Shen, Z.-X.; Mo, S.-K. ARPES study of the epitaxially grown topological crystalline insulator SnTe(111). J. Electron Spectrosc. Relat. Phenom. 2017, 219, 3540,  DOI: 10.1016/j.elspec.2016.10.003
    42. 42
      Polley, C. M.; Jovic, V.; Su, T.-Y.; Saghir, M.; Newby, D.; Kowalski, B. J.; Jakiela, R.; Barcz, A.; Guziewicz, M.; Balasubramanian, T.; Balakrishnan, G.; Laverock, J.; Smith, K. E. Observation of surface states on heavily indium-doped SnTe(111), a superconducting topological crystalline insulator. Phys. Rev. B 2016, 93, 075132,  DOI: 10.1103/PhysRevB.93.075132
    43. 43
      Maiti, A.; Pandeya, R. P.; Singh, B.; Iyer, K. K.; Thamizhavel, A.; Maiti, K. Anomalies in the temperature evolution of Dirac states in the topological crystalline insulator SnTe. Phys. Rev. B 2021, 104, 195403,  DOI: 10.1103/PhysRevB.104.195403
    44. 44
      Plekhanov, E.; Barone, P.; Di Sante, D.; Picozzi, S. Engineering relativistic effects in ferroelectric SnTe. Phys. Rev. B 2014, 90, 161108,  DOI: 10.1103/PhysRevB.90.161108
    45. 45
      Momma, K.; Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 12721276,  DOI: 10.1107/S0021889811038970
    46. 46
      Knox, K. R.; Bozin, E. S.; Malliakas, C. D.; Kanatzidis, M. G.; Billinge, S. J. L. Local off-centering symmetry breaking in the high-temperature regime of SnTe. Phys. Rev. B 2014, 89, 014102,  DOI: 10.1103/PhysRevB.89.014102
    47. 47
      Aggarwal, L.; Banik, A.; Anand, S.; Waghmare, U. V.; Biswas, K.; Sheet, G. Local ferroelectricity in thermoelectric SnTe above room temperature driven by competing phonon instabilities and soft resonant bonding. Journal of Materiomics 2016, 2, 196202,  DOI: 10.1016/j.jmat.2016.04.001
    48. 48
      Chang, K.; Liu, J.; Lin, H.; Wang, N.; Zhao, K.; Zhang, A.; Jin, F.; Zhong, Y.; Hu, X.; Duan, W.; Zhang, Q.; Fu, L.; Xue, Q.-K.; Chen, X.; Ji, S.-H. Discovery of robust in-plane ferroelectricity in atomic-thick SnTe. Science 2016, 353, 274278,  DOI: 10.1126/science.aad8609
    49. 49
      Ito, H.; Otaki, Y.; Tomohiro, Y.; Ishida, Y.; Akiyama, R.; Kimura, A.; Shin, S.; Kuroda, S. Observation of unoccupied states of SnTe(111) using pump-probe ARPES measurement. Phys. Rev. Research 2020, 2, 043120,  DOI: 10.1103/PhysRevResearch.2.043120
    50. 50
      Cho, S.; Park, J.-H.; Hong, J.; Jung, J.; Kim, B. S.; Han, G.; Kyung, W.; Kim, Y.; Mo, S.-K.; Denlinger, J. D.; Shim, J. H.; Han, J. H.; Kim, C.; Park, S. R. Experimental Observation of Hidden Berry Curvature in Inversion-Symmetric Bulk 2H-WSe2. Phys. Rev. Lett. 2018, 121, 186401,  DOI: 10.1103/PhysRevLett.121.186401
    51. 51
      Kim, J.; Kim, K.-W.; Shin, D.; Lee, S.-H.; Sinova, J.; Park, N.; Jin, H. Prediction of ferroelectricity-driven Berry curvature enabling charge- and spin-controllable photocurrent in tin telluride monolayers. Nat. Commun. 2019, 10, 3965,  DOI: 10.1038/s41467-019-11964-6
  • Supporting Information

    Supporting Information

    ARTICLE SECTIONS
    Jump To

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.3c03280.

    • Details on the samples growth and characterization; methods used to perform the ARPES measurements and the calculations; photon-energy dependent ARPES measurements; one-step photoemission calculations for the 6.3 eV ARPES data; DFT calculations for different surface terminations; fitting of the Rashba splitting (PDF)


    Terms & Conditions

    Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.