Holographic quantum criticality and strange metal transport

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 antide-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. 7 This unexpected (see, however, [49]) fact can be intuitively understood in analogy with simpler adjoint theories in 0 or 1 dimensions. There it turns out that the eigenvalues of the adjoint matrix in the relevant saddle point become continuous in the large N c limit, and appear as an extra dimension. In general, how many new dimensions may emerge in a given QFT in the large N c limit is not a straightforward question to answer, although exceptions exist. 8 There are several works that contain a version or elements of the idea of the EHT [50], although they vary in the focus or philosophy. 9 We refer to as the 'bulk' the spacetime in which strings propagate. This is always a spacetime with a single boundary. The boundary is isomorphic to the space on which the dual QFT (the gauge theory) lives.

Holographic competition of phases and superconductivity

“…Progress has been made in the application of the holographic description towards phenomena at finite densities, relevant for condensed matter systems, in the last few years, such as strange metals [11][12][13], (non-) Fermi liquid [14][15][16], superconductivity (superfluidity) [17,18] and Néel phase transition [19], see [20][21][22][23] for reviews and [24] for an excellent book on this emergent topic.…”

“…We do not include the strange metal phase in the present study, but we shall do it in the future. There are several holographic strange metal candidates, [11][12][13], that can be included.…”

“…Thus a diagnostic for an instability is whether the mass matrix M 2 has an eigenvalue that violates the AdS 2 BF bound. More precisely, for fixed theory parameters as well as x we look for a range of k where the smallest eigenvalue, say M 2 min [k], among four eigenvalues of 4 × 4 matrix M 2 violates the BF bound, which means 13) in our units with L = 1. Such BF-violating modes are associated with striped phases with periodic modulation in the x direction.…”

Charged dilatonic black holes and their transport properties

“…The Hall angle behavior was recently discussed using Lifshitz type metric with broken rotational symmetry [28]. Finally these all three benchmark behaviors including a crossover were reproduced in a single holographic system in [29].…”

Theoretical Investigations of the Knight Shifts and the Hyperfine Structure Constants for the Tetragonal Cu2+ Sites in the Bismuth- and Thallium-Based High-Tc Superconductors

“…The bismuth-and thallium-based high-T c superconductors have attracted extensive interest of researchers due to unique metal [1] and heat transportation [2,3], ferromagnetism [4], temperature-dependent resistivity [5], quantum resistive behaviours [6], and the quantum oscillation effect [7,8]. Meanwhile, the Knight shifts of 63 Cu 2+ of nuclear magnetic resonance (NMR) experiments in heavily strontium-or barium-doped bismuth-and thallium-based high-T c superconductors can yield important information about the local environments and electronic distribution in the copperoxygen planes.…”