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Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Catalog of noninteracting tight-binding models with two energy bands in one dimension
AU - McCann, Edward
PY - 2023/6/15
Y1 - 2023/6/15
N2 - We classify Hermitian tight-binding models describing noninteracting electrons on a one-dimensional periodic lattice with two energy bands. To do this, we write a generalized Rice-Mele model with two orbitals per unit cell, including all possible complex-valued long-range hoppings consistent with Hermicity. We then apply different forms of time-reversal, charge-conjugation, and chiral symmetry in order to constrain the parameters, resulting in an array of possible models in different symmetry classes. For each symmetry class, we define a single, canonical form of the Hamiltonian and identify models that are related to the canonical form by an off-diagonal unitary transformation in the atomic basis. The models have either symmorphic or nonsymmorphic nonspatial symmetries (time T, chiral, and charge-conjugation). The nonsymmorphic category separates into two types of state of matter: an insulator with a Z2 topological index in the absence of nonsymmorphic time-reversal symmetry or, in the presence of nonsymmorphic time-reversal symmetry, a metallic state. The latter is an instance of Kramer's degeneracy with one degeneracy point in the Brillouin zone as opposed to no degeneracy points in symmorphic systems with T2=1 and two in symmorphic systems with T2=−1.
AB - We classify Hermitian tight-binding models describing noninteracting electrons on a one-dimensional periodic lattice with two energy bands. To do this, we write a generalized Rice-Mele model with two orbitals per unit cell, including all possible complex-valued long-range hoppings consistent with Hermicity. We then apply different forms of time-reversal, charge-conjugation, and chiral symmetry in order to constrain the parameters, resulting in an array of possible models in different symmetry classes. For each symmetry class, we define a single, canonical form of the Hamiltonian and identify models that are related to the canonical form by an off-diagonal unitary transformation in the atomic basis. The models have either symmorphic or nonsymmorphic nonspatial symmetries (time T, chiral, and charge-conjugation). The nonsymmorphic category separates into two types of state of matter: an insulator with a Z2 topological index in the absence of nonsymmorphic time-reversal symmetry or, in the presence of nonsymmorphic time-reversal symmetry, a metallic state. The latter is an instance of Kramer's degeneracy with one degeneracy point in the Brillouin zone as opposed to no degeneracy points in symmorphic systems with T2=1 and two in symmorphic systems with T2=−1.
U2 - 10.1103/PhysRevB.107.245401
DO - 10.1103/PhysRevB.107.245401
M3 - Journal article
VL - 107
JO - Physical Review B: Condensed Matter and Materials Physics
JF - Physical Review B: Condensed Matter and Materials Physics
SN - 2469-9950
IS - 24
M1 - 245401
ER -