Bad Metals from Fluctuating Density Waves

Abstract

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 ...

Mott transition and collective charge pinning in electron doped Sr2IrO4

“…1, together with T -linear DC resistivity at high enough temperature. The peak structure in the optical spectra derives in this case from finite energy oscillations of a charge density wave phason pinned by broken translation invariance of the system [42,43]. Experimentally for the y = 0.1 and y = 0.18 samples the pinned collective state appears shunted by a finite DC resistivity, preventing the resistivity from diverging for T → 0, which is also in good agreement with the model of Refs.…”

“…In the context of the model of Delacretaz et al the strongest temperature dependent blueshift is expected in a quantum critical state of matter [42,43], in which case ω 0 ∝ k B T /h. Our experimental temperature dependence has the same sign, but for T → 0 the SCM position saturates at 35 meV instead of converging to zero.…”

“…Experimentally for the y = 0.1 and y = 0.18 samples the pinned collective state appears shunted by a finite DC resistivity, preventing the resistivity from diverging for T → 0, which is also in good agreement with the model of Refs. [42,43]. It is possible that on a microscopic level this metallic conducting component is characterized by fermions with a Fermi surface of which a finite fraction remains ungapped.…”

Intertwined orders in holography: pair and charge density waves

“…While the phase structure is not impacted in any qualitative way by introducing ψ 1 and ψ 2 , we expect to find interesting changes in the transport behavior in the system. Indeed, we note that -in the absence of a superconducting condensate-when the translational symmetry breaking is spontaneous, the electrical conductivity should be divergent even along the direction of symmetry breaking [42]. This can be explained by the presence of Goldstone modes in the system, which can be excited at no cost.…”

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.…”