Topological Bogoliubov quasiparticles from Bose-Einstein condensate in a flat band system

TL;DR

This paper explores topological properties of Bogoliubov quasiparticles in a Bose-Einstein condensate on a Kagome lattice with flat bands, revealing non-trivial topology and edge states influenced by condensate symmetry and interactions.

Contribution

It demonstrates that flat band condensates can host topologically non-trivial quasiparticle excitations, especially in the $ ext{Gamma}$-point condensate with extended interactions, a novel insight in bosonic topological phases.

Findings

Gamma-point condensate exhibits non-zero Chern numbers and edge states.

Band flatness breaks TRS, leading to topological quasiparticle bands.

Topological phase transition to high Chern number condensate observed.

Abstract

For bosons with flat energy dispersion, condensation can occur in different symmetry sectors. Here, we consider bosons in a Kagome lattice with $\pi$-flux hopping, which in the presence of mean-field interactions exhibit degenerate condensates in the $\Gamma$- and the $K$-point. We analyze the excitation above both condensates and find strikingly different properties: For the $K$-point condensate, the Bogoliubov-de Gennes (BdG) Hamiltonian has broken particle-hole symmetry (PHS) and exhibits a topologically trivial quasiparticle band structure. However, band flatness plays a key role in breaking the time reversal symmetry (TRS) of the BdG Hamiltonian for a $\Gamma$-point condensate. Consequently, its quasiparticle band structure exhibits non-trivial topology, characterized by non-zero Chern numbers and the presence of edge states. Although quantum fluctuations energetically favor the $K$-point condensate, the interesting properties of the $\Gamma$-point condensate become relevant for anisotropic hopping. The topological properties of the $\Gamma$-point condensate get even richer in the presence of extended Bose-Hubbard interactions. We find a topological phase transition into a topological condensate characterized by high Chern number and also comment on the realization and detection of such excitations.