Hong-Yi Xie

Enhanced Thermoelectric Power in Graphene: Violation of the Mott Relation by Inelastic Scattering

We report the enhancement of the thermoelectric power (TEP) in graphene with extremely low disorder. At high temperature we observe that the TEP is substantially larger than the prediction of the Mott relation, approaching to the hydrodynamic limit due to strong inelastic scattering among the charge carriers. However, closer to room temperature the inelastic carrier-optical-phonon scattering becomes more significant and limits the TEP below the hydrodynamic prediction. We support our observation by employing a Boltzmann theory incorporating disorder, electron interactions, and optical phonons.

Topological protection, disorder, and interactions: Survival at the surface of three-dimensional topological superconductors

We consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as “pseudomagnetic” fields (Abelian and non-Abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wave functions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel’stein nonlinear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII, we show that interactions are always irrelevant, while in class AIII, there is a finite window of stability, controlled by the disorder. Outside of this window, we identify new interaction-stabilized fixed points.

Transport coefficients of graphene: Interplay of impurity scattering, Coulomb interaction, and optical phonons

We study the electric and thermal transport of the Dirac carriers in monolayer graphene using the Boltzmann-equation approach. Motivated by recent thermopower measurements [F. Ghahari, H.-Y.~Xie, T. Taniguchi, K. Watanabe, M.~S.~Foster, and P.~Kim, Phys.\ Rev.\ Lett.\ {\bf 116}, 136802 (2016)], we consider the effects of quenched disorder, Coulomb interactions, and electron--optical-phonon scattering. Via an unbiased numerical solution to the Boltzmann equation we calculate the electrical conductivity, thermopower, and electronic component of the thermal conductivity, and discuss the validity of Motts formula and of the Wiedemann-Franz law. An analytical solution for the disorder-only case shows that screened Coulomb impurity scattering, although elastic, violates the Wiedemann-Franz law even at low temperature. For the combination of carrier-carrier Coulomb and short-ranged impurity scattering, we observe the crossover from the interaction-limited (hydrodynamic) regime to the disorder-limited (Fermi-liquid) regime. In the former, the thermopower and the thermal conductivity follow the results anticipated by the relativistic hydrodynamic theory. On the other hand, we find that optical phonons become nonnegligible at relatively low temperatures and that the induced electron thermopower violates Motts formula. Combining all of these scattering mechanisms, we obtain the thermopower that quantitatively coincides with the experimental data.

Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.