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A recently developed formula for the Hall coefficient [A. Auerbach, Phys. Rev. Lett. 121, 66601 (2018)] is applied to nodal line and Weyl semimetals (including graphene), and to spin-orbit split semiconductor bands in two and three dimensions. The calculation reduces to a ratio of two equilibrium susceptibilities, where corrections are negligible at weak disorder. Deviations from Drudes inverse carrier density are associated with band degeneracies, Fermi surface topology, and interband scattering. Experiments which can measure these deviations are proposed.
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In this study, we report the first results of the high-pressure Hall coefficient (RH) measurements in the putative topological Kondo insulator SmB6 up to 37 GPa. Below 10 GPa, our data reveal that RH(T) exhibits a prominent peak upon cooling below 20 K. Remarkably, the temperature at which surface conduction dominates coincides with the temperature of the peak in RH(T). The temperature dependent resistance and Hall coefficient can be well fitted by a two-channel model with contributions from the metallic surface and the thermally activated bulk states. When the bulk of SmB6 becomes metallic and magnetic at ~ 10 GPa, both the RH(T) peak and the resistance plateau disappear simultaneously. Our results indicate that the RH(T) peak is a fingerprint to diagnose the presence of a metallic surface state in SmB6. The high-pressure magnetic state of SmB6 is robust to 180 GPa, and no evidence of superconductivity is observed in the metallic phase.
We present Hall-effect measurements of two-leg ladder compounds Sr_{14-x}Ca_xCu_24O_41 (0 <= x <= 11.5) with the aim to determine the number of carriers participating in dc transport. Distribution of holes between the ladder and chain subsystems is one of the crucial questions important for understanding the physics of these compounds. Our Hall effect and resistivity measurements show typical semiconducting behavior for x < 11.5. However, for x=11.5, the results are completely different, and the Hall coefficient and resistivity behavior is qualitatively similar to that of high temperature copper-oxide superconductors. We have determined the effective number of carriers at room temperature and compared it to the number of holes in the ladders obtained by other experimental techniques. We propose that going from x=0 to x=11.5 less than 1 hole per formula unit is added to the ladders and is responsible for a pronounced change in resistivity with Ca doping.
Since its experimental discovery, many phenomenological theories successfully reproduced the rapid rise from $p$ to $1+p$ found in the Hall number $n_H$ at the critical doping $p^*$ of the pseudogap in superconducting cuprates. Further comparison with experiments is now needed in order to narrow down candidates. In this paper, we consider three previously successful phenomenological theories in a unified formalism---an antiferromagnetic mean field (AF), a spiral incommensurate antiferromagnetic mean field (sAF), and the Yang-Rice-Zhang (YRZ) theory. We find a rapid rise in the specific heat and a rapid drop in the Seebeck coefficient for increasing doping across the transition in each of those models. The predicted rises and drops are locked, not to~$p^*$, but to the doping where anti-nodal electron pockets, characteristic of each model, appear at the Fermi surface shortly before~$p^*$. While such electron pockets are still to be found in experiments, we discuss how they could provide distinctive signatures for each model. We also show that the range of doping where those electron pockets would be found is strongly affected by the position of the van~Hove singularity.
The Hall coefficient $R_H$ of Sr$_2$RuO$_4$ exhibits a non-monotonic temperature dependence with two sign reversals. We show that this puzzling behavior is the signature of two crossovers which are key to the physics of this material. The increase of $R_H$ and the first sign change upon cooling are associated with a crossover into a regime of coherent quasiparticles with strong orbital differentiation of the inelastic scattering rates. The eventual decrease and the second sign change at lower temperature is driven by the crossover from inelastic to impurity-dominated scattering. This qualitative picture is supported by quantitative calculations of $R_H(T)$ using Boltzmann transport theory in combination with dynamical mean-field theory, taking into account the effect of spin-orbit coupling. Our insights shed new light on the temperature dependence of the Hall coefficient in materials with strong orbital differentiation, as observed in Hunds metals.
Using determinant Quantum Monte Carlo, we compare three methods of evaluating the dc Hall coefficient $R_H$ of the Hubbard model: the direct measurement of the off-diagonal current-current correlator $chi_{xy}$ in a system coupled to a finite magnetic field (FF), $chi_{xy}^{text{FF}}$; the three-current linear response to an infinitesimal field as measured in the zero-field (ZF) Hubbard Hamiltonian, $chi_{xy}^{text{ZF}}$; and the leading order of the recurrent expansion $R_H^{(0)}$ in terms of thermodynamic susceptibilities. The two quantities $chi_{xy}^{text{FF}}$ and $chi_{xy}^{text{ZF}}$ can be compared directly in imaginary time. Proxies for $R_H$ constructed from the three-current correlator $chi_{xy}^{text{ZF}}$ can be determined under different simplifying assumptions and compared with $R_H^{(0)}$. We find these different quantities to be consistent with one another, validating previous conclusions about the close correspondence between Fermi surface topology and the sign of $R_H$, even for strongly correlated systems. These various quantities also provide a useful set of numerical tools for testing theoretical predictions about the full behavior of the Hall conductivity for strong correlations.
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