A renormalisation group equation for transport co-efficients in (2+1)-dimensions derived from the AdS/CMT correspondence

TL;DR

This paper derives a non-linear renormalisation group equation for conductivity in 2D using AdS/CMT correspondence, analyzing transport properties like Hall and Ohmic conductivities under magnetic fields and temperature variations.

Contribution

It introduces a novel non-linear RG equation for 2D conductivity within the AdS/CMT framework and applies it to study magnetic and temperature effects on transport properties.

Findings

Cyclotron resonance Q-factor decreases with temperature increase.

Hall and Ohmic conductivities increase with charge density and decrease with temperature.

Analysis includes discussion of piezoelectric effects in the holographic model.

Abstract

Within the framework of the AdS/CMT correspondence asymptotically anti-de Sitter black holes in four space-time dimensions can be used to analyse transport properties in two space dimensions. A non-linear renormalisation group equation for the conductivity in two dimensions is derived in this model and, as an example of its application, both the Ohmic and Hall DC and AC conductivities are studied in the presence of a magnetic field, using a bulk dyonic solution of the Einstein-Maxwell equations in asymptotically AdS$_4$ space-time. The ${\cal Q}$-factor of the cyclotron resonance is shown to decrease as the temperature is increased and increase as the charge density is increased in a fixed magnetic field. Likewise the dissipative Ohmic conductivity at resonance increases as the temperature is decreased and as the charge density is increased. The analysis also involves a discussion of the piezoelectric effect in the context of the AdS/CMT framework.