Abstract
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. We show that the edge remains protected from localization in the topological phase, and the local disorder caused by the amorphous structure results in critical scaling of the transport in the system. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.
Highlights
We introduced statistical topological insulator phases in two-dimensional amorphous systems that rely on average spatial symmetries for protection
We demonstrated that in the nontrivial phase the edge behaves as a 1D critical system of the same symmetry class by observing power-law scaling of the transport properties
We found topological invariants characterizing the bulk, and showed that the critical edge physics is not a result of fine-tuning, but is protected by the average reflection symmetry that is present on all straight edges of amorphous samples
Summary
Materials with a quasiparticle band gap in the bulk host protected edge states if they have a nontrivial topology. We devise topological insulator (TI) phases in amorphous systems that rely on the presence of two average spatial symmetries: reflection symmetry and continuous rotation symmetry. The presence of both reflection symmetry and average continuous rotation symmetry promotes the protection of a crystalline topological phase to every edge orientation.
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