Spontaneously Generated Inhomogeneous Phases via Holography

We discuss a holographic model consisting of a U(1) gauge field and a scalar field coupled to a charged AdS (anti-de Sitter) 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. In addition to that we discuss the zeroes and poles of the determinant of the retarded Green function (det G_R) at zero frequency in a holographic system of charged massless fermions interacting via a dipole coupling. For large negative values of the dipole coupling constant p, det G_R possesses only poles pointing to a Fermi liquid phase. We show that a duality exists relating systems of opposite p. This maps poles of det G_R at large negative p to zeroes of det G_R at large positive p, indicating that the latter corresponds to a Mott insulator phase. This duality suggests that the properties of a Mott insulator can be studied by mapping the system to a Fermi liquid and then for small values of p, det G_R contains both poles and zeroes (pseudo-gap phase). Finally, we study holographic fermions in the spontaneously generated holographic lattice background defined above. We solve the equations of motion below T_c (critical temperature) and analyze the change in Fermi surface due to introduction of the holographic lattice. The band structure of this fermionic system was also analyzed numerically and it was found that a band gap was formed due to lattice effects.