Spin-Induced Orbital Frustration in a Hexagonal Optical Lattice

Complex lattices provide a versatile ground for fascinating quantum many-body physics. Here, we propose an exotic mechanics for generating orbital frustration in hexagonal lattices. We study two-component (pseudospin-$1/2$) Bose gases in $p$-orbital bands of two-dimensional hexagonal lattices, and find that the system exhibits previously untouched orbital frustration as a result of the interplay of spin and orbital degrees of freedom, in contrast to normal Ising-type orbital ordering of spinless $p$-orbital band bosons in two-dimensional hexagonal lattices. Based on the classification by symmetry analysis, we find the interplay of orbital frustration and strong interaction leads to exotic Mott and superfluid phases with spin-orbital intertwined orders, in spite of the complete absence of spin-orbital interaction in the Hamiltonian. Our study implies many-body correlations in a multi-orbital setting could induce rich spin-orbital intertwined physics in complex lattice structures.