Edge and bulk electron states in a quasi-one-dimensional metal in a magnetic field: The semi-infinite Wannier-Stark ladder

TL;DR

This paper investigates the energy spectra of edge and bulk electron states in a quasi-one-dimensional metal under a magnetic field, revealing a Wannier-Stark ladder structure and the absence of orbital magnetization.

Contribution

It provides an analytical and numerical analysis of the Wannier-Stark ladder in a Q1D metal, linking it to edge and bulk electron states in a magnetic field.

Findings

Energy spectrum near Fermi energy has continuous and discrete parts.

Discrete spectrum forms a Wannier-Stark ladder.

Electric currents vanish at edges and in the bulk, implying no orbital magnetization.

Abstract

We study edge and bulk open-orbit electron states in a quasi-one-dimensional (Q1D) metal subject to a magnetic field. For both types of the states, the energy spectrum near the Fermi energy consists of two terms. One term has a continuous dependence on the momentum along the chains, whereas the other term is quantized discretely. The discrete energy spectrum is mathematically equivalent to the Wannier-Stark energy ladder of a semi-infinite 1D lattice in an effective electric field. We solve the latter problem analytically in the semiclassical approximation and by numerical diagonalization. We show explicitly that equilibrium electric currents vanish both at the edges and in the bulk, so no orbital magnetization is expected in a Q1D metal in a magnetic field.