Unraveling the Impact of Graphene Addition to Thermoelectric SrTiO3 and La-Doped SrTiO3 Materials: A Density Functional Theory Study

We present a detailed theoretical investigation of the interaction of graphene with the SrO-terminated (001) surface of pristine and La-doped SrTiO3. The adsorption of graphene is thermodynamically favorable with interfacial adsorption energies of −0.08 and −0.32 J/m2 to pristine SrTiO3 and La-doped SrTiO3 surfaces, respectively. We find that graphene introduces C 2p states at the Fermi level, rendering the composite semimetallic, and thus the electrical properties are predicted to be highly sensitive to the amount and quality of the graphene. An investigation of the lattice dynamics predicts that graphene adsorption may lead to a 60–90% reduction in the thermal conductivity due to a reduction in the phonon group velocities, accounting for the reduced thermal conductivity of the composite materials observed experimentally. This effect is enhanced by La doping. We also find evidence that both La dopant ions and adsorbed graphene introduce low-frequency modes that may scatter heat-carrying acoustic phonons, and that, if present, these effects likely arise from stronger phonon–phonon interactions.


Electronic Transport Calculations
We performed transport calculations on the pristine and La-doped SrTiO3 surface-slab models using the BoltzWann code 1,2 with an interpolated 50  50  1 k-point mesh. Due to the large number of bands and the semi-metallic nature of the surfaces with adsorbed graphene, we were not able to perform BoltzWann calculations on these models.
During the BoltzWann calculations, transport coefficients were calculated using maximally localized Wannier functions (MLWFs), which can be used for Wannier interpolation of the band energies onto a fine k-point sampling mesh. 3 Test calculations on bulk SrTiO3 showed that Wannier projections onto the oxygen p and titanium d orbitals using atom-centered Gaussian-type orbitals yielded the best MLWFs. In each case the final spreads for the WFs were < 1 Å with convergence to < 10 -5 Å 2 , and all the WFs were real. Figure S1 shows example Wannier functions obtained for the SrTiO3 surface slab model.
The disentanglement method was used to freeze the bands around the Fermi level. 4 In this region of the band structure the Bloch states and therefore the bands are preserved, whereas in the outer energy window the Bloch states can change depending on the choice of unitary transformation.
The disentanglement window was chosen to be between -6 eV below the Fermi level and ~1 eV above the lowest-energy conduction band. The bands contained in the outer window are not relevant for transport properties as they lie more than a few kBT from the Fermi level. 2         S-9

Rotation of Surfaces and Group Velocities
The surface-slab models employed in this work are rotated with respect to bulk SrTiO3 ( Figure S11).
The thermal conductivity and related tensor quantities computed for the rotated cell, denoted , can be related to the original cell, , 11 as outlined below.

Convergence of ⁄ with respect to the q-point sampling mesh
As described in the text, we computed for each of the four surface-slab models the function latt CRTA ⁄ defined in Eq. 16. As depicted in Figure S12, we found that the convergence of this function with respect to the q-point sampling mesh was somewhat erratic. To handle this, we calculated the function over a large number of meshes with systematically increasing numbers of subdivisions. We then calculated the mean value at each temperature, over all the mesh sizes tested, and removed outliers for which the calculation was more than a standard deviation from the mean. Finally, we then recalculated the standard deviation and took this as a measure of the spread, which is shown in Figure 6 in the text. S-12