Towards a holographic realization of Homes’ law

Abstract

Gauge/gravity duality has proved to be a very successful tool for describing strongly coupled systems in particle physics and heavy ion physics. The application of the gauge/gravity duality to quantum matter is a promising candidate to explain questions concerning non-zero temperature dynamics and transport coefficients. To a large extent, the success of applications of gauge/gravity duality to the quark-gluon plasma is founded on the derivation of a universal result, the famous ratio of shear viscosity and entropy density. As a base for applications to condensed matter physics, it is highly desirable to have a similar universal relation in this context as well. A candidate for such a universal law is given by Homes' law : High T c superconductors, as well as some conventional superconductors, exhibit a universal scaling relation between the superfluid density at zero temperature and the conductivity at the critical temperature times the critical temperature itself. In this work we describe progress in employing the models of holographic superconductors to realize Homes' law and to find a universal relation governing strongly correlated quantum matter. We calculate diffusive processes, including the backreaction of the gravitational matter fields on the geometry. We consider both holographic s-wave and p-wave superconductors. We show that a particular form of Homes' law holds in the absence of backreaction. Moreover, we suggest further steps to be taken for holographically realizing Homes' law more generally in the presence of backreaction.

Soft wall model for a holographic superconductor

“…[19] for the deconfinement temperature). (v) Among theoretical challenges for the holographic superconductors one can mention the problem of a dual gravitational interpretation for the empirical Homes' scaling law in the high-T c superconductors [20] (see [21,22] for a discussion from the holographic perspective). Our preliminary analysis showed that this law imposes rather strong constraint on the mutual dependence of the model parameters and seems to prescribe for them a certain temperature dependence.…”

“…If we take the point of view that in the holographic approach, which is inherently large-N one, only quadratic in fields part is relevant, then we should either assume r 0 = 0 in (22), i.e. somehow motivate pure AdS metric in (21), or exclude the interaction term. In the latter case, the equation of motion for ϕ = ϕ(r ),…”

Demystifying the holographic mystique: A critical review

“…The holographic theory of Refs. [73,74] claimed its success with finding the prefactor C ≈ 6.2 to be close to the experimental values in the cuprates which happen to be C ≈ 8.1 and 4.4 for the ab-and c-axes transport, respectively. Somewhat ironically, though, this would seem like a case where, in the absence of a compelling underlying reason, a perfect quantitative agreement could do more harm than good to the cause.…”

“…Besides, it was also argued to be intermittent with the alternate 'universal' , ~ω -1 , behaviour. Another notable example is the holographic calculation [73,74] of the numerical prefactor C in the empirical Homes relation between the superfluid density, critical temperature, and normal state conductivity [75]:…”

Deconstructing superconductivity

“…There is a mapping between observables in the superconducting system and fields in the corresponding extra-dimensional model. Progress has been made in understanding properties of holographic models of superconductors and other condensed matter systems, including s, p, and d-wave superconductivity [8][9][10], the Nernst effect in the quantum critical regime [11], strange metallic behavior [12], enhancement of the superconducting gap compared to BCS theory [13], and Homes's empirical law for T c as a function of low-temperature superfluid density and normal-phase resistivity [14,15]. In some models of holographic superconductors there is no hard zero-temperature gap [16].…”