Anisotropic Quantum Transport in Layered High--$T_c$ Cuprates

TL;DR

This paper models layered high-$T_c$ cuprates using a random lattice with dilute interlayer bonds, revealing persistent extended states and highly anisotropic electronic transport that explains observed resistivity behaviors.

Contribution

It introduces a novel random lattice model with dilute interlayer bonds to analyze anisotropic quantum transport in high-$T_c$ cuprates.

Findings

States remain extended in all directions for any finite interlayer bond density p.

Transport is highly anisotropic with large conductance fluctuations in the layering direction.

The model explains the coexistence of metallic in-plane and semiconducting out-of-plane resistivity.

Abstract

A random lattice model with dilute interlayer bonds of density $p$ is proposed to describe the underdoped high--$T_c$ cuprates. We show analytically via an appropriate perturbation expansion and verify independently by numerical scaling of the conductance that for any finite $p$ the states remain extended in all directions, despite the presence of interlayer disorder. However, the obtained electronic transport is highly anisotropic with violent conductance fluctuations occuring in the layering direction, which can be responsible for the experimentally observed metallic "in-plane" and semiconducting "out-of-plane" resistivity of the cuprates.