Topological Anderson insulators by latent symmetry
Source abstract
Abstract
Topological Anderson insulators represent a class of disorder-induced, nontrivial topological states of matter. In this study, we propose a feasible strategy to unveil and design topological Anderson insulators protected by latent symmetries. These are not visible in the original system, but become obvious after performing an isospectral reduction. Using this technique, we design a family of disordered multi-atomic chains that exhibit latent chiral symmetry or mirror (inversion) symmetry. Using topological invariants, bulk polarization, and the divergence of localization length of the topological bound edge states in the reduced disordered system, we show how to identify the gapped and ungapped topological Anderson states in the original systems. Our work thus extends the concept of topological Anderson insulating phases protected by geometric symmetries and tenfold-way classification to the various types of latent symmetry cases. Overall, our work paves the way for exploiting topological Anderson insulators in terms of latent symmetries.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Topological Materials and Phenomena · Quantum and electron transport phenomena · Electronic and Structural Properties of Oxides
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Henan University of Science and Technology
Funding
National Natural Science Foundation of China · Natural Science Foundation of Henan Province
References (80)
Show source-provided references
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68. To see this, it is important to keep the notation clear. To this end, we write the Hamiltonian of Ga,j in block-form as Ha=HxxHxS¯aHxyHS¯axHS¯aS¯aHS¯ayHyxHyS¯aHyy,where x:=A, y:=B are just another label for the two sites over which we reduce when taking the isospectral reduction of Ga,j, and S¯a are all the other sites in Ga,j. Analogously for Gb,j, we have Hb=HuuHuS¯bHuvHS¯buHS¯bS¯bHS¯bvHvuHvS¯bHvv,with u:=A, v:=B, and S¯b all the other sites in Gb,j. When gluing Ga,j and Gb,j together at the central site B(=y and u, respectively), the resulting total Hamiltonian reads (assuming Hyy=Huu for simplicity) H=HxxHxS¯aHxy00HS¯axHS¯aS¯aHS¯ay00HyxHyS¯aHyyHuS¯bHuv00HS¯buHS¯bS¯bHS¯bv00HvuHvS¯bHvv.We then take the isospectral reduction over S={x,y,v}, keeping in mind that y,v are identical now. The relevant matrices are HSS=HxxHxy0HyxHyyHuv0HvuHvv, (42) HSS¯=HS¯aS¯a00HS¯bS¯b, (43) HSS¯=HxS¯a0HyS¯aHyS¯b0HvS¯b, (44)and HS¯S=HS¯axHS¯ay00HS¯byHS¯bv. (45)Computing the isospectral reduction of only Ga,j and Gb,j individually, mapping the indices x,y,u,v back to A and B, and comparing with the isospectral reduction of the glued Hamiltonian H then yields the result graphically depicted in Fig. 1.
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