Anomalous thermoelectric Hall response of interacting 2D Dirac fermions

Abstract

We study the anomalous thermoelectric Hall response of two-dimensional massive Dirac fermions to first order in the electron-electron interaction. We compute both the Nernst response to a Luttinger-type gravitational potential and the particle magnetization, the latter being required to remove spurious non-transport contributions. We show that, for arbitrary interactions, the magnetization is described by a remarkably simple formula. Surprisingly, and contrary to expectations, subtracting the magnetization currents does not make the thermoelectric Hall coefficient vanish in the zero-temperature limit. We attribute this to violation of locality on the smallest length scales, which is inevitable in a quantized field theory, that happens to manifest itself in infrared physics.

Figures (2)

• Figure 1: Diagrams contributing to $K^{12}_{xy}$ defined in Eq. (\ref{['eq:kubo']}) to first order in the interaction. Panel (a) shows the non-interacting bubble diagram, consisting of two single-particle propagators (solid lines) attached to a heat-current vertex $(\hat{\bm{j}}^Q_0)_y$ (right) and a particle-current vertex $(\hat{\bm{j}}^N_0)_x$ (left). Panel (b) shows the exchange diagram, in which the density–density interaction line (dashed) connects the two propagators across the bubble. Panels (c) and (d) illustrate the self-energy corrections, where one of the propagators in the bubble is dressed by a single Fock insertion. Panels (e) and (f) display the heat current vertex corrections, arising from the interaction-dependent part of the heat-current operator. In all diagrams, solid lines represent the non-interacting Matsubara Green’s functions $G^{(0)}(\bm k,i\omega_n)$, dashed lines denote the instantaneous density–density interaction $V_{\bm q}$, and dots indicate the insertion of current vertices.
• Figure 2: Diagrams contributing to the right-hand side of Eq. \ref{['eq:streda']} to first order in the interactions. Panel (a) shows the zeroth order bubble. Panel (b) shows the exchange diagram. Panels (c) and (d) depict diagrams with self-energy insertions. The external frequency vanishes and the external momentum is kept finite.