# Theory of hydrodynamic transport in fluctuating electronic charge density wave states

## TL;DR

This paper develops a hydrodynamic theory for fluctuating charge density wave states, accounting for disorder and dislocations, revealing effects on charge transport and phase relaxation.

## Contribution

It introduces a comprehensive hydrodynamic framework that includes pinning and phase relaxation effects in charge density waves, linking viscosity to dislocation dynamics.

## Key findings

- Disorder and dislocations significantly influence charge transport.
- Derived a formula connecting phase relaxation rate and viscosity.
- Estimated viscosity of BSCCO's superconducting state from vortex lattice melting.

## Abstract

We describe the collective hydrodynamic motion of an incommensurate charge density wave state in a clean electronic system. Our description simultaneously incorporates the effects of both pinning due to weak disorder and also phase relaxation due to proliferating dislocations. We show that the interplay between these two phenomena has important consequences for charge and momentum transport. For instance, it can lead to metal-insulator transitions. We furthermore identify signatures of fluctuating density waves in frequency and spatially resolved conductivities. Phase disordering is well known to lead to a large viscosity. We derive a precise formula for the phase relaxation rate in terms of the viscosity in the dislocation cores. We thereby determine the viscosity of the superconducting state of BSCCO from the observed melting dynamics of Abrikosov lattices and show that the result is consistent with dissipation into Bogoliubov quasiparticles.