Spontaneously Generated Inhomogeneous Phases via Holography

Understand

We discuss a holographic model consisting of a $U(1)$ gauge field and a scalar field coupled to a charged AdS black hole under a spatially homogeneous chemical potential.

• By turning on a higher-derivative interaction term between the $U(1)$ gauge field and the scalar field, a spatially dependent profile of the scalar field is generated spontaneously.
• We calculate the critical temperature at which the transition to the inhomogeneous phase occurs for various values of the parameters of the system.
• We solve the equations of motion below the critical temperature, and show that the dual gauge theory on the boundary spontaneously develops a spatially inhomogeneous charge density.