Bose-Einstein supersolid phase for a type of momentum-dependent interaction

A class of nonlocal interactions between bosons is found to favor a crystalline Bose-Einstein condensation ground state. By using both low-energy effective field theory and a variational wave function method, we compare this state not only with the homogeneous superfluid, as has been done previously, but also with the normal (nonsuperfluid) crystalline phase and obtain the phase diagram. The key characters are (1) the interaction potential displays a negative minimum at finite momentum, which determines the wave vector of this supersolid phase, and (2) the wavelength corresponding to the momentum minimum needs to be greater than the mean interboson distance.