Striped instability of a holographic Fermi-like liquid

TL;DR

This work studies strongly coupled fermions in 2+1 dimensions using a top-down holographic D3-D7' model, identifying a Fermi-like liquid with $T$-dependent transport and non-Fermi heat capacity. By analyzing quasi-normal modes of the BH embedding and mapping the problem to an effective Maxwell-axion theory in a background electric field, the authors uncover a density-to-temperature-squared driven stripe instability, with a critical ratio $d/T^2$ and a characteristic finite momentum $k_{\text{phys}}$. The instability emerges above a critical density ($d_c \simeq 5.5$ in their units) and leads to a ground state with spatial modulations in charge, spin, and transverse currents, consistent with a charge- and spin-density wave. The results highlight the role of axion-like couplings in driving inhomogeneous phases in holographic fermionic systems and suggest that striped ground states are a generic feature of such models with finite density.

Abstract

We consider a holographic description of a system of strongly-coupled fermions in 2+1 dimensions based on a D7-brane probe in the background of D3-branes. The black hole embedding represents a Fermi-like liquid. We study the excitations of the Fermi liquid system. Above a critical density which depends on the temperature, the system becomes unstable towards an inhomogeneous modulated phase which is similar to a charge density and spin wave state. The essence of this instability can be effectively described by a Maxwell-axion theory with a background electric field. We also consider the fate of zero sound at non-zero temperature.

Figures (5)

• Figure 1: Left: Quasi-normal modes for $\delta\hat{e}_x$ at $\hat{d}=0$, $\hat{m}=0$ and $\psi_{\infty}=\pi/4$. Blue (solid) lines are the imaginary parts and red (dashed) lines are the real parts. Right: Diffusion constant as a function of $\sqrt{\hat{d}}$. Notice the linear behavior for small temperatures, $\hat{d}\gg 1$.
• Figure 2: Left: Quasi-normal mode for the coupled ($\delta\hat{e}_x,\delta\hat{z})$ system at $\hat{m}=0$, $\hat{d}=10^4$ and $\psi_{\infty}=\pi/4$. Right: Imaginary part of the quasi-normal mode of the $\delta\hat{e}_x,\delta\hat{z}$ system, with $\hat{m}=0$, $\hat{d}=5$ and $\psi_{\infty}=\pi/4$.
• Figure 3: Lowest quasi-normal mode for $\delta\hat{a}_y$ (left) and $\delta\psi$ (right), with $\hat{d}=0, \hat{m}=0$ and $\psi_{\infty}=\pi/4$.
• Figure 4: Properties of the unstable mode with $\hat{m}=0$ and $\psi_{\infty}=\pi/4$. Left: Lowest purely imaginary mode for the coupled $(\delta\hat{a}_y,\delta\hat{\psi})$ system. The lowest curve is for $\hat{d}=5$, and the upper curve is for $\hat{d}=6$. Right: Range of instability; $\hat{k}_{min}$ (blue) and $\hat{k}_{max}$ (red) are plotted against $\hat{d}$.
• Figure 5: Domains of instability for non-zero mass $\hat{m}$ and $\psi_\infty = \pi/4$ for $\hat{d}=6$ (smaller domain) and $\hat{d}=10$ (larger domain).