Under The Dome: Doped holographic superconductors with broken translational symmetry

We comment on a simple way to accommodate translational symmetry breaking into the recently proposed holographic model which features a superconducting dome-shaped region on the temperature-doping phase diagram.Comment: 14 pages, 6 figure

Phases of holographic superconductors with broken translational symmetry

We consider holographic superconductors in a broad class of massive gravity backgrounds. These theories provide a holographic description of a superconductor with broken translational symmetry. Such models exhibit a rich phase structure: depending on the values of the temperature and the disorder strength the boundary system can be in superconducting, normal metallic or normal pseudoinsulating phases. Furthermore the system supports interesting collective excitation of the charge carriers, which appears in the normal phase, persists in the superconducting phase, but eventually gets destroyed by the superconducting condensate. We also show the possibility of building a phase diagram of a system with the superconducting phase occupying a dome-shaped region on the temperature-disorder plane.Comment: Minor revisions, interpretation clarified, version published in JHE

Hydrodynamics of disordered marginally-stable matter

We study the vibrational spectra and the specific heat of disordered systems using an effective hydrodynamic framework. We consider the contribution of diffusive modes, i.e. the 'diffusons', to the density of states and the specific heat. We prove analytically that these new modes provide a constant term to the vibrational density of states $g(\omega)$. This contribution is dominant at low frequencies, with respect to the Debye propagating modes. We compare our results with numerical simulations data and random matrix theory. Finally, we compute the specific heat and we show the existence of a linear in $T$ scaling $C(T) \sim c\,T$ at low temperatures due to the diffusive modes. We analytically derive the coefficient $c$ in terms of the diffusion constant $D$ of the quasi-localized modes and we obtain perfect agreement with numerical data. The linear in $T$ behavior in the specific heat is stronger the more localized the modes, and crosses over to a $T^{3}$ (Debye) regime at a temperature $T^{*}\sim \sqrt{v^{3}/D}$, where $v$ is the speed of sound. Our results suggest that the anomalous properties of glasses and disordered systems can be understood effectively within a hydrodynamic approach which accounts for diffusive quasi-localized modes generated via disorder-induced scattering.Comment: v2: 5 pages, 5 figures, minor revision, matching the published version in PRResearch as Rapid Communicatio