Role of Umklapp Processes in Conductivity of Doped Two-Leg Ladders

TL;DR

This paper investigates how umklapp processes influence the electrical conductivity of doped two-leg ladder materials, explaining experimental observations through a bosonic model that incorporates disorder effects.

Contribution

It introduces a bosonic model highlighting the role of umklapp processes in explaining conductivity features in doped two-leg ladders, including disorder effects.

Findings

Umklapp processes explain the linear power law in resistivity.

Disorder inclusion reproduces experimental conductivity curves.

Differences between single chain and two-leg ladder effects are discussed.

Abstract

Recent conductivity measurements performed on the hole-doped two-leg ladder material $\mathrm{Sr_{14-x}Ca_xCu_{24}O_{41}}$ reveal an approximately linear power law regime in the c-axis DC resistivity as a function of temperature for $x=11$. In this work, we employ a bosonic model to argue that umklapp processes are responsible for this feature and for the high spectral weight in the optical conductivity which occurs beyond the finite frequency Drude-like peak. Including quenched disorder in our model allows us to reproduce experimental conductivity and resistivity curves over a wide range of energies. We also point out the differences between the effect of umklapp processes in a single chain and in the two-leg ladder.