Here, the cyclotron and Bloch oscillation frequencies are set as ω c = 0.3 and Ω = 0.5 in units of t 3, respectively. The Landau-Stark quantization manifests itself as a series of discrete peaks in the local density of states (DOS) shown in right panels indicating individual contributions from various LLs. (c) Energy spectrum under parallel electric and magnetic fields applied in the z direction, showing the formation of Wannier-Stark ladder (WSL) eigenstates in each LL, called Landau-Stark eigenstates, with the energy eigenvalue of ε n l = ε ¯ n + l Ω.
C denotes the Chern number of the 2D k z slices of the Brillouin zone before the application of magnetic fields. With each LL labeled by the LL index n, the n = 0, or chiral LL is plotted in red, while all other nonchiral LLs are in dark/light blue.
(b) Energy spectrum under a magnetic field applied in the z direction, showing the formation of Landau level (LL) eigenstates with the energy eigenvalue of ε n ( k z ). χ denotes the chirality of each Weyl node. (a) Energy spectrum of a minimal tight-binding model for Weyl semimetals without external fields. We argue that, going beyond the usual behavior of linear response, the non-Ohmic behavior observed in BiSb alloys can be regarded as a precursor to the occurrence of electric quantum oscillation, which is both topologically and energetically protected in Weyl semimetals.
Specifically, by using the Keldysh nonequilibrium Green function method, it is shown that there is a rich structure in the chiral anomaly transport, including the negative magnetoresistance, the non-Ohmic behavior, the Esaki-Tsu peak, and finally the resonant oscillation of the dc electric current as a function of electric field, called the electric quantum oscillation. Here, we develop a full nonequilibrium quantum transport theory of the chiral anomaly, based on the fact that the chiral charge pumping is essentially nothing but the Bloch oscillation.
Electronic transport in Weyl semimetals is quite extraordinary due to the topological property of the chiral anomaly generating the charge pumping between two distant Weyl nodes with opposite chiralities under parallel electric and magnetic fields.
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