Density of states anomalies in multichannel quantum wires

TL;DR

This paper extends the Tomonaga--Luttinger liquid theory to multichannel quantum wires, providing a rigorous formula for the local density of states that accounts for inter- and intra-band interactions and applies to both bulk and edge contacts.

Contribution

It introduces a generalized theoretical framework for multichannel quantum wires, enabling precise calculation of LDOS anomalies considering multiple subbands and their couplings.

Findings

Derived a universal formula for LDOS exponents in multichannel wires.

Showed the dependence of LDOS anomalies on inter- and intra-subbands couplings.

Applicable to both bulk and edge contact scenarios.

Abstract

We reformulate the Tomonaga--Luttinger liquid theory for quasi-one-dimensional Fermion systems with many subbands across the Fermi energy. Our theory enables us to obtain a rigorous expression of the local density of states (LDOS) for general multichannel quantum wires, describing how the power-law anomalies of LDOS depend on inter- and intra-subbands couplings as well as the Fermi velocity of each band. The resulting formula for the exponents is valid in the case of both bulk contact and edge contact, and thus plays a fundamental role in the physical properties of multicomponent Tomonaga--Luttinger liquid systems.