Geometry-Driven Shift in the Tomonaga-Luttinger Exponent of Deformed Cylinders

TL;DR

This paper investigates how geometric deformation of a hollow cylinder affects the Tomonaga-Luttinger liquid states, revealing that curvature variations significantly increase the TLL exponent due to curvature-induced potentials.

Contribution

It introduces a novel analysis of how periodic geometric perturbations influence TLL exponents in cylindrical systems, highlighting the role of curvature-induced potentials.

Findings

Curvature variation leads to a significant increase in the TLL exponent.

Surface curvature causes low-energy electrons to localize in high-curvature regions.

Geometric perturbations can tune electronic properties in cylindrical nanostructures.

Abstract

We demonstrate the effects of geometric perturbation on the Tomonaga-Luttinger liquid (TLL) states in a long, thin, hollow cylinder whose radius varies periodically. The variation in the surface curvature inherent to the system gives rise to a significant increase in the power-law exponent of the single-particle density of states. The increase in the TLL exponent is caused by a curvature-induced potential that attracts low-energy electrons to region that has large curvature.