Abstract
We examine transport in a holographic model in which the dynamics of the charged degrees of freedom is described by the nonlinear Dirac-Born-Infeld (DBI) action. Axionic scalar fields are included to break translational invariance and generate momentum dissipation in the system. Scaling exponents are introduced by using geometries which are nonrelativistic and hyperscaling-violating in the infrared. In the probe DBI limit the theory reproduces the anomalous temperature dependence of the resistivity and Hall angle of the cuprate strange metals, $\rho \sim T$ and $\cot\Theta_H \sim T^2$. These scaling laws would not be present without the nonlinear dynamics encoded by the DBI interactions. We further show that because of its richness the DBI theory supports a wide spectrum of temperature scalings. This model provides explicit examples in which transport is controlled by different relaxation times. On the other hand, when only one quantity sets the temperature scale of the system, the Hall angle and conductivity typically exhibit the same temperature behavior. We illustrate this point using new fully backreacted analytical dyonic black brane solutions.
Highlights
For nearly a decade holographic techniques developed within string theory have been applied to the realm of condensed matter physics
The main focus of this promising research area has been on probing phase transitions and transport in models that may be in the same universality class as strongly correlated electron systems. The latter exhibit unconventional behaviors which are believed to be tied to the complexity of their phase diagram, the presence of strong interactions and the lack of a quasiparticle description
Its anomalous features include a linear temperature dependence for the resistivity ρ ∼ T [2,3,4], often believed to be associated with an underlying quantum critical point. Another puzzling aspect of the cuprates is the observed scaling of the Hall angle [5,6] cotΘH ∼ T2, starkly different from that of ρ
Summary
For nearly a decade holographic techniques developed within string theory have been applied to the realm of condensed matter physics. Finding exact analytical solutions to the theory in the presence of backreaction is harder, and to do so one must rely on simplifications and restrictions on the parameters of the model This can lead to a situation where only one coupling sets the temperature scale in the system, and controls the behavior of all the conductivities. For these particular background solutions, the conductivity and Hall angle behave in much the same way as a function of T; such cases could not be used to describe the cuprates. Our analysis provides evidence that to capture the complexity of the phase diagram of non-Fermi liquids it may be crucial to include the nontrivial dynamics between the (charged) degrees of freedom, in addition to the interplay between the various physical scales in the system
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