Band-Gap-Dependent Electronic Compressibility of Carbon Nanotubes in the Wigner Crystal Regime

TL;DR

This study measures the electronic compressibility of individual carbon nanotubes in the Wigner crystal regime, revealing how band gap influences electron interactions and crystalline order through low-temperature quantum transport experiments.

Contribution

It provides the first detailed experimental analysis of compressibility in suspended ultraclean nanotubes, linking band gap and confining potential to electron interaction regimes.

Findings

Compressibility varies with carrier number in two distinct ways.

Theoretical model explains trends considering band gap and confinement.

Compressibility distinguishes between strong and weak electron interactions.

Abstract

Electronic compressibility, the second derivative of ground state energy with respect to total electron number, is a measurable quantity that reveals the interaction strength of a system and can be used to characterize the orderly crystalline lattice of electrons known as the Wigner crystal. Here, we measure the electronic compressibility of individual suspended ultraclean carbon nanotubes in the low-density Wigner crystal regime. Using low-temperature quantum transport measurements, we determine the compressibility as a function of carrier number in nanotubes with varying band gaps. We observe two qualitatively different trends in compressibility versus carrier number, both of which can be explained using a theoretical model of a Wigner crystal that accounts for both the band gap and the confining potential experienced by charge carriers. We extract the interaction strength as a function of carrier number for individual nanotubes and show that the compressibility can be used to distinguish between strongly and weakly interacting regimes.