The superconducting dome for holographic doped Mott insulator with hyperscaling violation

TL;DR

This paper models the superconducting dome in doped Mott insulators using holography, highlighting the roles of two charges, three-point interactions, and hyperscaling violation in shaping the phase diagram and critical properties.

Contribution

It introduces a holographic model with two charges and a three-point interaction to explain the superconducting dome, incorporating hyperscaling violation effects on the phase diagram.

Findings

Dome size and optimal temperature increase with dynamical critical exponent z.

Larger hyperscaling violation parameter θ enlarges the condensate.

The condensate's magnitude depends on both θ and z values.

Abstract

We reconsider the holographic model featuring a superconducting dome on the temperature-doping phase diagram with a modified view on the role of the two charges. The first type charge with density $\rho_{A}$ make the Mott insulator, and the second one with $\rho_{B}$ is the extra charge by doping, so that the complex scalar describing the cooper pair condensation couples only with the second charge. We point out that the key role in creating the dome is played by the three point interaction $-c \chi^{2} F_{\mu\nu}G^{\mu\nu}$. The $Tc$ increases with their coupling. We also consider the effect of the quantum critical point hidden under the dome using the geometry of hyperscaling violation. Our results show that the dome size and optimal temperature increase with $z$ whatever is $\theta$, while we get bigger $\theta$ for larger (smaller) dome depending on $z>2$ ($z<2$). We also point out that the condensate increases for bigger value of $\theta$ but for smaller value of $z$.