We show that partially separated Andreev bound states (ps-ABSs), comprised of pairs of overlapping Majorana bound states (MBSs) emerging in quantum dot-semiconductor-superconductor heterostructures, produce robust zero bias conductance plateaus in end-of-wire charge tunneling experiments. These plateaus remain quantized at 2e 2 /h over large ranges of experimental control parameters. In light of recent experiments reporting the observation of robust 2e 2 /h-quantized conductance plateaus in local charge tunneling experiments, we perform extensive numerical calculations to explicitly show that such quantized conductance plateaus, which are obtained by varying control parameters such as the tunnel barrier height, the super gate potential, and the applied magnetic field, can arise as a result of the existence of ps-ABSs. Because ps-ABSs can form rather generically in the topologically trivial regime, even in the absence of disorder, our results suggest that the observation of a robust quantized conductance plateau does not represent sufficient evidence to demonstrate the existence of non-Abelian topologically-protected Majorana zero modes localized at the opposite ends of a wire. arXiv:1804.03164v1 [cond-mat.mes-hall]

In a series of recent papers, anomalous Hall and Nernst effects have been theoretically discussed in the nonlinear regime and have seen some early success in experiments. In this paper, by utilizing the role of Berry curvature dipole, we derive the fundamental mathematical relations between the anomalous electric and thermoelectric transport coefficients in the nonlinear regime. The formulas we derive replace the celebrated Wiedemann-Franz law and Mott relation of anomalous thermoelectric transport coefficients defined in the linear response regime. In addition to fundamental and testable new formulas, an important by-product of this work is the prediction of nonlinear anomalous thermal Hall effect which can be observed in experiments.

Unlike the linear anomalous Nernst effect, the non-linear anomalous Nernst effect (NLANE) can survive in an inversion symmetry broken system even in the presence of time-reversal symmetry. Using semiclassical Boltzmann transport theory, we study the non-linear anomalous Nernst effect that arises as the second-order response function to the applied temperature gradient. We find that the non-linear Nernst current, which flows perpendicular to the temperature gradient even in the absence of a magnetic field, arises due to the Berry curvature of the states near the Fermi surface, and thus is associated with purely a Fermi surface contribution. We apply these results to bilayer WTe2, which is an inversion broken but time reversal symmetric type-II Weyl semimetal supporting chiral Weyl fermions. By tuning the spin-orbit coupling, we show that the sign of the NLANE can change in this system. Together with the angular dependence, we calculate the temperature and chemical potential dependencies of NLANE in bilayer WTe2, and predict specific experimental signatures that can be checked in experiments. arXiv:1905.09814v3 [cond-mat.mes-hall]

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