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We construct a Ginsburg Landau (GL) theory to study the phases of liquid, solid, superfluid, especially a possible supersolid and phase transitions among these phases in a unified framework. In this GL, we put the two competing orders between the solid component and the superfluid component on the same footing. We only introduce two parameters: $ v $ which is the repulsive interaction between the normal component and the local superfluid mode and $ g $ which is a periodically changing chemical potential for the local superfluid mode. The microscopic origins of $ v $ and $ g $ are given. By using this GL action, we study the superfluid to supersolid transition, normal solid to the supersolid transition and analyze the conditions for the existence of the supersolid.

Elementary Excitations, Spectral Weights and Experimental Signatures of a Supersolid and a Fulde-Ferrell-Larkin-Ovchinnikov State