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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 requires 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 $\mathbb Z_2\times \mathbb Z_2$ 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 a RLC circuit setup and detected via collossal "topolectrical" resonances.