Transverse thermoelectric response as a probe for existence of quasiparticles

The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey ${\sigma }_{xy}=-{\sigma }_{yx}$. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, ${\alpha }_{xy}=-{\alpha }_{yx}$, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces ${\alpha }_{xy}=-{\alpha }_{yx}$. This suggests that quasiparticle-free ground states (so-called non-Fermi liquids) may be detected by examining the relationship between ${\alpha }_{xy}$ and ${\alpha }_{yx}$ in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results. (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles. (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid, the latter lead to deviations that vanish as $T^3$. (iii) We calculate the thermoelectric response in a model of weakly coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of $\widehat{\alpha }$. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.

Figure 1

The integration region in $\mathbf{k}$ space.

Figure 2

The scaling functions that determine ${\alpha }_{yx}$, shown here for $K=2$. The inset depicts the sign change of $f_{\alpha }^{\left(1\right)}+f_{\alpha }^{\left(2\right)}$, and thus of ${\alpha }_{yx}$ for large $b{l}_T$.

Figure 3

The dimensionless Nernst signal $-(ed/l_T)S_{yx}$ for the case $K=2$. The inset depicts the scaling function of ${\sigma }_{yy}$.

Figure 4

The integration contour for calculating $C(q,i{\omega }_n)$.