Energy relaxation in disordered charge and spin density waves

TL;DR

This paper explores how disorder affects energy relaxation and specific heat in charge and spin density waves, revealing distinct classical and quantum contributions and explaining experimental power-law behaviors.

Contribution

It provides a detailed analysis of classical and quantum effects on energy relaxation and specific heat in disordered CDWs and SDWs, highlighting the role of different disorder types.

Findings

No slow relaxation in commensurate systems in classical limit

Broad spectrum of relaxation times in incommensurate systems

Quantum effects induce energy relaxation in commensurate systems

Abstract

We investigate collective effects in the strong pinning model of disordered charge and spin density waves (CDWs and SDWs) in connection with heat relaxation experiments. We discuss the classical and quantum limits that contribute to two distinct contribution to the specific heat (a $C_v \sim T^{-2}$ contribution and a $C_v \sim T^{\alpha}$ contribution respectively), with two different types of disorder (strong pinning versus substitutional impurities). From the calculation of the two level system energy splitting distribution in the classical limit we find no slow relaxation in the commensurate case and a broad spectrum of relaxation times in the incommensurate case. In the commensurate case quantum effects restore a non vanishing energy relaxation, and generate stronger disorder effects in incommensurate systems. For substitutional disorder we obtain Friedel oscillations of bound states close to the Fermi energy. With negligible interchain couplings this explains the power-law specific heat $C_v \sim T^{\alpha}$ observed in experiments on CDWs and SDWs combined to the power-law susceptibility $\chi(T)\sim T^{-1+\alpha}$ observed in the CDW o-TaS$_3$.