Superfluid Interfaces in Quantum Solids

One scenario for the nonclassical moment of inertia of solid ${}^4\mathrm{He}$ discovered by Kim and Chan [ Nature (London) 427, 225 (2004)] is the superfluidity of microcrystallite interfaces. On the basis of the most simple model of a quantum crystal—the checkerboard lattice solid—we show that the superfluidity of interfaces between solid domains can exist in a wide range of parameters. At strong enough interparticle interaction, a superfluid interface becomes an insulator via a quantum phase transition. Under the conditions of particle-hole symmetry, the transition is of the standard $U(1)$ universality class in 3D, while in 2D the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations.