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Yevtushenko, Oleg M.; Tsvelik, A. M. (2018): Chiral lattice supersolid on edges of quantum spin Hall samples. In: Physical Review B, Vol. 98, No. 8, 81118
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Abstract

We show that the edges of quantum spin Hall topological insulators represent a natural platform for the realization of an exotic magnetic phase which has all the properties of a lattice supersolid. On one hand, fermionic edge modes are helical due to the nontrivial topology of the bulk. On the other hand, a disorder at the edge or magnetic adatoms may produce a dense array of localized spins interacting with the helical electrons. The spin subsystem is magnetically frustrated since the indirect exchange favors the formation of helical spin order and the direct one favors (anti)ferromagnetic ordering of the spins. At a moderately strong direct exchange, the competition between these spin interactions results in the spontaneous breaking of parity and in the Ising-type order of the z components at zero temperature. If the total spin is conserved, the spin order does not pin a collective massless helical mode which supports the ideal transport. In this case, the phase transition converts the helical spin order to the order of a chiral lattice supersolid. This represents a promising possibility for experimental studies of the elusive supersolidity.