New black holes with hyperscaling violation and transports of quantum critical points with magnetic impurity

TL;DR

This paper develops a holographic model with hyperscaling violation to study magneto-transport near quantum critical points in doped topological insulators, revealing phase transitions and localization phenomena.

Contribution

It introduces a new black hole solution with hyperscaling violation and applies holography to analyze transport properties of quantum critical systems with magnetic impurities.

Findings

Identification of two distinct quantum critical points in doped topological insulators.

Observation of phase transitions and crossovers in transport behavior.

Demonstration of weak localization to anti-localization transition.

Abstract

We consider the magneto-transports of quantum matters doped with magnetic impurities near the quantum critical points(QCP). For this, we first find new black hole solution with hyper-scaling violation which is dual to such system. By considering the fluctuation near this exact solution, we calculated all transport coefficients using the holographic method. We applied our result to the surface state of the topological insulator with magnetic doping and found two QCP's, one bosonic and the other fermionic. It turns out that doped Bi$_2$Se$_3$ and Bi$_2$Te$_3$ correspond to different QCP's. We also investigated transports of QCP's as functions of physical parameters and found that there are phase transitions as well as crossovers from weak localization to weak anti-localization.