  We present a detailed microscopic investigation of fractional quantum Hall
states with gapped boundaries in a coupled bilayer lattice model featuring
holes whose counterpropagating chiral edge states are hybridized and gapped
out. We focus on a lattice limit for cold-atom experiments, in which each hole
just consists of a single removed site. Although the holes distort the original
band structure and lead to ingap remnants of the continuum edge modes, we find
that the lowest nearly flat band representing a higher-genus system may
naturally form by controlling the local hopping terms that gap out the
boundaries. Remarkably, local interactions in this new flat band lead to
various Abelian and non-Abelian fractional quantum Hall states with gapped
boundaries residing on emergent higher-genus surfaces, which we identify by
extracting the nontrivial topological ground-state degeneracies and the
fractional statistics of quasiparticles. These results demonstrate the
feasibility of realizing novel fractional quantum Hall states with gapped
boundaries even in the extreme lattice limit, thus enabling a possible new
route towards universal topological quantum computation.
