Abstract
A holographic model of a quantum critical theory at a finite but low temperature and a finite density is studied. The model exhibits non-relativistic z = 2 Schrödinger symmetry and is realized by the anti-de-Sitter–Schwarzschild black hole in light-cone coordinates. Our approach addresses the electrical conductivities in the presence or absence of an applied magnetic field and contains a control parameter that can be associated with quantum tuning via charge carrier doping or an external field in correlated electron systems. The Ohmic resistivity, the inverse Hall angle, the Hall coefficient and magnetoresistance are shown to be in good agreement with experimental results of strange metals at very low temperature. The holographic model also predicts new scaling relations in the presence of a magnetic field.
Highlights
The holographic model we present provides a novel paradigm for the normal state of strange metals, in particular high-temperature superconducting cuprates in the overdoped region, where the charge carriers added to the parent insulator exceed the value necessary for optimal superconductivity
We successfully describe the T + T 2 behavior of the resistivity in [18] and the T + T 2 behavior of the inverse Hall angle observed in [19] at very low temperatures T < 30 K, where a single scattering rate is present. This newly emerged very-low-temperature scaling behavior of magnetotransport properties is in agreement with the distinct origin of the criticality at very low temperatures reported in [20], while the higher temperature, T > 100 K, scaling has different behavior between the linear temperature resistivity and the quadratic temperature inverse Hall angle, signaling two scattering rates [21]
In addition to the resistivity and inverse Hall angle, very good agreement is found with the experimental results of the Hall coefficient, magnetoresistance and Kohler rule on various high-temperature superconducting (high-Tc) cuprates [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]
Summary
The model we present is composed of two sectors. The first is gravitational and contains the metric as a single field. The metric (4) has the same symmetry called the Schrodinger group for both β = 0 and β = 0 [4, 5, 13] These are the translations along the coordinates x+ (energy conservation), x− (the total particle number M for the dual field theory, which is special for Schrodinger holography) and y, z (momentum conservation). The transport properties of the Schrodinger background are considered with a relativistic electric field (different compared to what we consider here in (9)) in [16], which turns out to be the same when they are independent of the embedding scalar discussed below [15] It is an interesting, yet unsolved, issue whether or not these two viable holographic realizations, ALCF and Schrodinger background, provide identical physical properties. 10 This is not true for the Schrodinger case [16] due to the non-trivial Kalb–Ramond field present in the solution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
