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 have a large resistivity without being strongly disordered. In many bad metals the Drude peak moves away from zero frequency as the resistivity becomes large at increasing temperatures. We catalogue the position and width of the 'displaced Drude peak' in the observed optical conductivity of several families of bad metals, showing that ω peak ∼ ∆ω ∼ k B T /ħ h. This is the same quantum critical timescale that underpins the T -linear dc resistivity of many of these materials. We provide a unified theoretical description of the optical and dc transport properties of bad metals in terms of the hydrodynamics of short range quantum critical fluctuations of incommensurate density wave order. Within hydrodynamics, pinned translational order is essential to obtain the nonzero frequency peak. Check for updates doi:10.21468/SciPostPhys.3.3.025 Bad metals are defined by the fact that if their electrical resistivity is interpreted within a conventional Drude formalism, the corresponding mean free path of the quasiparticles is so short that the Boltzmann equation underlying Drude theory is not consistent [1][2][3]. As such, bad metals pose a long-standing challenge to theory. In this work we show that the hydrodynamics of phase-fluctuating charge density waves can lead to bad metallic behavior. Hydrodynamics is a tightly constrained formalism for the low energy and long wavelength dynamics of media [4,5]. Non-quasiparticle media, in particular, exhibit fast local thermalization leading to extended hydrodynamics regimes. Phase fluctuations in the density wave can be robustly incorporated into this description and will be essential in order for the states to be metallic, rather than insulating. We will use the hydrodynamic framework to explain observed dc and optical transport behavior that is common to several families of bad metal materials.Recent work has emphasized that the absence of quasiparticles is not sufficient to obtain a bad metal [6]. If the total momentum of the charge carriers is long-lived, then the resistivity will be small even if all single-particle excitations decay rapidly. The importance of the fate of momentum for transport has long been appreciated [7,8], but has acquired renewed relevance 1 SciPost Phys. 3, 025 (2017) in the context of modern unconventional metals, e.g. [9,10]. Two previously considered scenarios for removing the long-lived momentum (sound) mode from the collective description of charge transport are as follows. Firstly, that the low energy, non-quasiparticle, description of bad metals is strongly non-translationally invariant and hence momentum is absent from the hydrodynamic description [6]. Secondly, that an emergent particle-hole symmetry at low energies decouples charge transport from momentum [11]. These mechanisms do not seem to be at work in bad metals. The resistivity of bad metals is not typically strongly dependent on the strength of disorder and some bad metals appear to be relatively clean. Emergent particle-hole symmetry does not decouple momentum ...
We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E n(n) . We then consider "tensor gauge fields" coupled to the exceptional generalised gravity. Many of the properties of forms on manifolds are carried over to these fields.Ñ Ð Ñ ÖØ Òº ÖÛ ÐÐ ÐÑ Ö×º× ¸ Ó Ð×ØÙ Òغ ÐÑ Ö×º× ¸ Ö ÒÒ ÐÑ Ö׺×
Electron solid phases of matter are revealed by characteristic vibrational resonances.Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons.The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems.Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers. arXiv:1904.04872v1 [cond-mat.mes-hall]
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