Quantum size effects in a one-dimensional semimetal

TL;DR

This paper theoretically investigates quantum size effects in a one-dimensional semimetal nanowire, deriving formulas for transport properties and analyzing the transition to a semiconductor as size decreases.

Contribution

It provides analytic expressions for transport coefficients in 1D semimetals and discusses the size-induced semimetal-semiconductor transition.

Findings

Transport coefficients oscillate with size reduction

Semimetal transitions to semiconductor below a critical size

Analytic formulas for conductivity, Hall coefficient, magnetoresistance, thermoelectric power

Abstract

We study theoretically the quantum size effects in a one-dimensional semimetal by a Boltzmann transport equation. We derive analytic expressions for the electrical conductivity, Hall coefficient, magnetoresistance, and the thermoelectric power in a nanowire. The transport coefficients of semimetal oscillate as the size of the sample shrinks. Below a certain size the semimetal evolves into a semiconductor. The semimetal-semiconductor transition is discussed quantitatively. The results should make a theoretical ground for better understanding of transport phenomena in low-dimensional semimetals. They can also provide useful information while studying low-dimensional semiconductors in general.