684 research outputs found
Average Symmetry Protected Higher-order Topological Amorphous Insulators
While topological phases have been extensively studied in amorphous systems
in recent years, it remains unclear whether the random nature of amorphous
materials can give rise to higher-order topological phases that have no
crystalline counterparts. Here we theoretically demonstrate the existence of
higher-order topological insulators in two-dimensional amorphous systems that
can host more than six corner modes, such as eight or twelve corner modes.
Although individual sample configuration lacks crystalline symmetry, we find
that an ensemble of all configurations exhibits an average crystalline symmetry
that provides protection for the new topological phases. To characterize the
topological phases, we construct two topological invariants. Even though the
bulk energy gap in the topological phase vanishes in the thermodynamic limit,
we show that the bulk states near zero energy are localized, as supported by
the level-spacing statistics. Our findings open an avenue for exploring average
symmetry protected higher-order topological phases in amorphous systems without
crystalline counterparts.Comment: 8 pages, 6 figure
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