Quantum transition to supersolid phase

We study a possible coexistence of superconducting state and charge density waves which, in a broad sense, might be called a supersolid phase. We investigate the infinite dimensional (d = ∞) attractive Hubbard model by applying a sublattice dependent Gutzwiller wave function g_A ^DAg_B ^DB|BCS〉 as a variational wave function describing the ground state. One may naively expect that the BCS superconducting state evolves continuously to the Bose-Einstein condensed state of bipolarons as the attractive interaction increases, as far as the system is dilute. However, we show that our variational wave function has lower energy than the simple BCS wave function for all electron densities and the interaction strengths. Our variational parameters increase (g_A,B→∞) as we increase the interaction strength (U→∞). The energy gap turns out to be a mixture of s and extended-s waves. In the vicinity of half-filling, we find a quantum transition from a simple superconducting phase to a supersolid phase with increase of the electron density and/or the interaction strength.