Quantum oscillations in Weyl semimetals: A surface theory approach

Abstract

We develop an effective surface theory for the surface states of a Weyl semimetal. This theory includes the peculiar Fermi arc states on the surface as well as leakage of the states from the surface to the bulk. Subjecting the model to a magnetic field perpendicular to the surface results in quantum oscillations. The oscillations are different from the usual ones since they do not involve a closed Fermi surface cross section. It has been shown previously that the Quantum oscillations can be understood semiclassically as resulting from motion of electrons on the surface Fermi arcs as well as tunneling through chiral Landau levels associated with the bulk. In this work we develop an effective surface theory and use it to analyze the quantum oscillation in the semiclassical regime and beyond. Specifically, we show that when a pair of Weyl points are close to each other the surface quantum oscillations acquire a phase offset which originates from the bulk. While the surface states are responsible for a large part of the electron motion, tunneling through the bulk is necessary for completing the orbit. This tunneling makes use of the bulk, zero energy, chiral Landau level in each Weyl node. When the nodes are close in momentum space their chiral levels overlap and a gap at zero energy is formed. This gap causes the phase offset in the surface quantum oscillations.

Emergence of gapped bulk and metallic side walls in the zeroth Landau level in Dirac and Weyl semimetals

“…A second surprise is that the exponential rise in resistivity saturates at low temperature and the saturated resistivity decreases at even higher field strength (B ∼ 80 T) 7 . Gap opening has also been suggested in other Weyl materials such as TaP 8 and previous numerical studies also support similar ideas 9,10 .…”

Semiclassical theory of anomalous transport in type-II topological Weyl semimetals

“…In parallel magnetic and electric fields, Weyl semimetals exhibit negative longitudinal magnetoresistance as a result of the chiral anomaly [29][30][31][32][33][34][35] . The surface Fermi arcs also lead to a remarkable mixed realand momentum-space channel of charge transport [36][37][38][39] and have also been predicted to lead to a novel mechanism for entropy transport 40 . In bulk thermoelectric transport, Weyl semimetals have been predicted to have a number of distinct signatures [41][42][43] , most notably a Nernst thermopower at zero applied magnetic field in time-reversal breaking Weyl semimetals 42 .…”

Quantum transport simulation of non-local response in Weyl semimetals

“…There are many available ways to obtain surface (G 00 ) and bulk Green's function recursively [52][53][54][55][56] , especially, when N → ∞. As our requirement is to find the bond current not only on the top surface, but as well as on the bottom surface, we require not only G 00 , but also G 0N and G N 0 .…”