Variable range hopping theory for the nodal gap in strongly underdoped cuprate Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$

TL;DR

This paper investigates the nodal gap in strongly underdoped cuprates, proposing that it arises from variable range hopping behavior described by the Efros-Schklovskii gap model, supported by calculations of doping and temperature dependence.

Contribution

It introduces a theoretical model linking the nodal gap in underdoped cuprates to the Efros-Schklovskii variable range hopping mechanism, supported by calculations matching experimental observations.

Findings

Support for Efros-Schklovskii gap as the origin of the nodal gap

Doping and temperature dependence consistent with the ES model

Alignment with ARPES and transport experimental data

Abstract

Recent angle resolved photoemission spectrascope (ARPES) experiments on strongly underdoped Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ cuprates have reported an unusual gap in the nodal direction. Transport experiments on these cuprates found variable range hopping behavior observed. These cuprates have both electron and hole doping which has led to proposals that this cuprate is analogous to a partially compensated semiconductors. The nodal gap then corresponds to the Efros-Schklovskii(ES) gap in such semiconductors. We calculate the doping dependence and temperature dependence of a ES gap model and find support for an Efros-Schklovskii model.