Contrary to the standard Landau paradigm, topological phases are not distinguished by different spontaneous symmetry-breaking patterns, but rather by different non-local topological invariants. Non-trivial topology manifests itself in the presence of conducting edge states in bulk insulating phases,
quantized conductances or fractional charges, which in the case of symmetry-protected topological (SPT) phases are robust against perturbations that do not break certain protecting symmetries. Recently, this class has been enlarged to include higher-order SPT (HOSPT) phases, protected by crystalline symmetries and hosting edge states of co-dimension larger than one, such as corner states in 2D. We investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how
photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state that opens a non-trivial topological gap in 2D. The symmetry breaking results in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols.
Luca Dell'Anna
