Topological corner modes in a brick lattice with nonsymmorphic symmetry

The quest for new realizations of higher-order topological system has garnered much recent attention. In this work, we propose a paradigmatic brick lattice model where corner modes require protection by nonsymmorphic symmetry in addition to two commuting mirror symmetries. Unlike the well-known square corner mode lattice, it has an odd number of occupied bands, which necessitates a different definition for the ${\mathbb{Z}}₂\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}₂$ topological invariant. By studying both the quadrupolar polarization and effective edge model, our study culminates in a phase diagram containing two distinct topological regimes. Our brick lattice corner modes can be realized in an $RLC$ circuit setup and detected via colossal ``topolectrical'' resonances.