Theory of hydrodynamic transport in fluctuating electronic charge density wave states

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.arXiv:1702.05104v4 [cond-mat.str-el]

Bad Metals from Fluctuating Density Waves

“…We take this to be the x direction. Other cases are qualitatively similar [40]. The equilibrium physics of different patterns of symmetry breaking is described by the theory of elasticity, see e.g.…”

“…We shall only outline the ingredients going into the computation of σ(ω) here. More details can be found in [40]. For simplicity, we will focus here on the case of a smectic (uni-directional) charge density wave and consider current moving in the modulated direction.…”

“…The Galilean hydrodynamics of charge density wave states with mobile dislocations and defects was developed some time ago in [39]. In [40] we have worked out in detail the mathematical theory of charge density wave hydrodynamics that incorporates both momentum and phase-relaxing dynamics, and characterized the corresponding charge transport. In the supplementary material we outline the key steps in this derivation.…”

“…The role of fluctuating density waves for bad metals will therefore be further elucidated by a more detailed exploration of current dynamics. In particular, the presence of fluctuating density waves leads to concrete signatures in spatially resolved current dynamics [40], in the behavior of currents in a magnetic field [78], and in the nonlinear current response [15]. …”

Diffusion in inhomogeneous media

“…However, motivated by recent experimental progress [3][4][5], there has been considerable theoretical work using hydrodynamics to study thermoelectric transport [2,[6][7][8][9][10][11][12][13][14][15][16][17][18] and it is therefore of interest to see how our general results on diffusion manifest themselves in this particular context. More specifically, we will study this within the context of relativistic hydrodynamics, describing the hydrodynamic limit of a relativistic quantum field theory.…”