Abstract

An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as "homogeneous holographic lattices." Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to correctly describe momentum relaxation and hence (finite) DC conductivities. However, it is not clear whether they are able to capture other lattice effects which are of interest in condensed matter. In this paper we investigate this question focusing our attention on the phenomenon of commensurability, which arises when the lattice scale is tuned to be equal to (an integer multiple of) another momentum scale in the system. We do so by studying the formation of spatially modulated phases in various models of homogeneous holographic lattices. Our results indicate that the onset of the instability is controlled by the near horizon geometry, which for insulating solutions does carry information about the lattice. However, we observe no sharp connection between the characteristic momentum of the broken phase and the lattice pitch, which calls into question the applicability of these models to the physics of commensurability.

Highlights

  • It is not clear whether they are able to capture other lattice effects which are of interest in condensed matter

  • The aim of this paper is to examine whether similar commensurability effects can be captured by the holographic homogeneous lattice models

  • In this work we have studied the spontaneous formation of a helical current state on homogeneous holographic lattices

Read more

Summary

Spatially modulated instabilities in Reissner-Nordstrom

Let us begin with the discussion of the formation of spatially modulated phases in the simplest example of a translational invariant background [22]. The presence of a nontrivial mode with zero frequency and non-zero momentum in the spectrum would signal the onset of the instability Such unstable modes can be captured considering the ansatz for the fluctuation of the spatial components of the gauge field δA = δA2(r) ω2(p), where ω2(p) belongs to the set of helical 1-forms with pitch p ω1(p) = dx, ω2(p) = cos(px)dy − sin(px)dz, ω3(p) = sin(px)dy + cos(px)dz. The argument is as follows: at very small temperatures, the near horizon geometry is approximately AdS2 × R3, so that the fluctuation equations reduce to field equations in AdS2 with effective masses that depend on the spatial (boundary) momentum p of the given modes. This will allow us to determine the onset of the instability which gives rise to the spontaneous formation of a helical state in the homogeneous lattices under consideration

Linear axion model
Q-lattice
Helical background
Conclusions
A Equations of motion
B Numerical finite difference method
C DC conductivity in the helical background
Full Text
Paper version not known

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