Abstract
We present a class of holographic models that behave effectively as prototypes of Mott insulators, materials where electron-electron interactions dominate transport phenomena. The main ingredient in the gravity dual is that the gauge-field dynamics contains self-interactions by way of a particular type of non-linear electrodynamics. The electrical response in these models exhibits typical features of Mott-like states: i) the low-temperature DC conductivity is unboundedly low; ii) metal-insulator transitions appear by varying various parameters; iii) for large enough self-interaction strength, the conductivity can even decrease with increasing doping (density of carriers), which appears as a sharp manifestation of `traffic-jam'-like behaviour; iv) the insulating state becomes very unstable towards superconductivity at large enough doping. We exhibit some of the properties of the resulting insulator-superconductor transition, which is sensitive to the amount of disorder in a specific way. These models imply a clear and generic correlation between Mott behaviour and significant effects in the nonlinear electrical response. We compute the nonlinear current-voltage curve in our model and find that indeed at large voltage the conductivity is largely reduced.
Highlights
1) Spotting Mott insulators in holographic nonlinear electrodynamics:
- We study general Nonlinear Electrodynamics (NED) models of the type (1.1) with arbitrary kinetic function K(z) embedded in the holographic setup
We find the NED charged, asymptotically AdS, planar Black Branes solutions to these models, the analogues of the ‘Reissner-Nordstrom’ solutions for NED theories
Summary
Two basic messages from these recent developments are: i) the bottom-up version of the gauge-gravity duality provides an effective description at low energies This should be taken strictly in the sense of Effective Field Theories (EFTs) that are formulated directly in terms of low-energy degrees of freedom (the Tμν, Jμ and OI operators and the excitations contained therein), which has the advantage that it represents an efficient re-summation of all the non-trivial interactions. A big difference with respect to standard EFTs is that instead of having an energy-gap in the mass spectrum of excitations, one has a gap in the spectrum of scaling dimensions of the various operators This is the key ingredient that allows for a well-defined notion of effective conformal theory which, in turn, allows to study and model strongly coupled systems with critical or scaling behavior. The only way to introduce such self-interactions while preserving gauge-invariance is that the the field strength
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