Universal Relaxation in a Holographic Metallic Density Wave Phase

Abstract

In this work, we uncover a universal relaxation mechanism of pinned density waves, combining Gauge/Gravity duality and effective field theory techniques. Upon breaking translations spontaneously, new gapless collective modes emerge, the Nambu-Goldstone bosons of broken translations.When translations are also weakly broken (eg by disorder or lattice effects), these phonons are pinned with a mass m and damped at a rate Ω, which we explicitly compute. This contribution to Ω is distinct from that of topological defects. We show that Ω Gm 2 Ξ, where G is the shear modulus and Ξ is related to a diffusivity of the purely spontaneous state. This result follows from the smallness of the bulk and shear moduli, as would be the case in a phase with fluctuating translational order. At low temperatures, the collective modes relax quickly into the heat current, so that late time transport is dominated by the thermal diffusivity. In this regime, the resistivity in our model is linear in temperature and the ac conductivity displays a significant rearranging of the degrees of freedom, as spectral weight is shifted from an off-axis, pinning peak to a Drude-like peak.These results could shed light on transport properties in cuprate high T c superconductors, where quantum critical behavior and translational order occur over large parts of the phase diagram and transport shows qualitatively similar features.

Gapless and gapped holographic phonons

“…At high temperature, we find that it is quite insensitive to the value of the source . This is in agreement with our earlier result [1] that the phonon mass and damping rate are controlled by λ at leading order (see also [47,49]). At low temperatures, the system quickly becomes more incoherent and relaxation is stronger, which leads to a failure of the relation above as increases, see figure 9.…”

“…4 In [45], we verified that transverse hydrodynamic modes with the dispersion relation (1.1) are present in the spectrum. In [1], we showed that these modes become gapped if a small source is turned on, with a dispersion relation (1.4). We found that Ω Gm 2 Ξ, where Ξ ≡ ξ /(K + G) is defined from the bulk and shear moduli K, G and the longitudinal phonon diffusivity ξ .…”

“…At zero wavector and for small sources λ, µ, the spectrum contains two light, gapped modes with a dispersion relation given by (1.4). In contrast to [1], Γ is non-negligible with = 0, which allows us to further test the validity of the hydrodynamic theory of relaxed Wigner crystals. We also check that the hydrodynamic prediction (4.2) for the ac conductivity agrees with our numerics.…”

“…In [22,23], only defects were considered as a microscopic origin for the damping rate Ω. However, as demonstrated in [1] and further investigated in [24,25], damping by explicit breaking of translations enters in the low energy effective theory in precisely the same way.…”

“…The effective, hydrodynamic theory of pinned charge density waves of [22,23] provides in most cases the correct framework to interpret these results. 3 In [1,37,39,40,45], we studied a bi-dimensional holographic 'Q-lattice' [11], where the UV CFT is deformed by complex, neutral scalar operators whose phases are linear in the boundary spatial coordinates and break translations. If the bulk field dual to the moduli of the complex operators is not sourced, λ = 0, the breaking is spontaneous.…”