Impact of impurities on the topological boundaries and edge state localization in a staggered chain of atoms: SSH model and its topoelectrical circuit realization
DOI:
https://doi.org/10.31349/RevMexFis.70.040501Keywords:
SSH model, Impurity superlattices, topological boundaries, edge statesAbstract
We study the Su-Schrieffer-Hegger model, perhaps the simplest realization of a topological insulator, in the presence of an embedded impurity superlattice. We consider the impact of the said impurity by changing the hopping amplitudes between them and their nearest neighbors in the topological boundaries and the edge state localization in the chain of atoms. Within a tight-binding approach and through a topolectrical circuit simulation, we consider three different impurity-hopping amplitudes. We found a relaxation of the condition between hopping parameters for the topologically trivial and non-trivial phase boundary and a more profound edge state localization given by the impurity position within the supercell.
References
K. V. Klitzin, The quantized hall effect. Reviews of Modern Physics, 58 (1986) 519, https://doi.org/10.1103/RevModPhys.58.519
K. V. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the finestructure constant based on quantized hall resistance. Physical review letters, 45 (1980) 494, https://doi.org/10.1103/PhysRevLett.45.494
H. L Stormer, D. C. Tsui, and A. C. Gossard, The fractional quantum hall effect. Reviews of Modern Physics, 71 (1999) S298, https://doi.org/10.1103/RevModPhys.71.S298
C. L. Kane and E. J. Mele, Z 2 topological order and the quantum spin hall effect. Physical review letters, 95 (2005) 146802, https://doi.org/10.1103/PhysRevLett.95.146802
N. Batra and G. Sheet, Physics with coffee and doughnuts. Resonance, 25 (2020) 765, https://doi.org/10.1007/s12045-020-0995-x
J. K. Asboth, L. Oroszl any, and A. Palyi, A Short Course on Topological Insulators, volume 919. (2016). https://doi.org/10.1007/978-3-319-25607-8
P. Kotetes, Topological Insulators. 2053-2571. Morgan Claypool Publishers, (2019)
A. Kitaev, Periodic table for topological insulators and superconductors. AIP Conference Proceedings, 1134 (2009) 22, https://doi.org/10.1063/1.3149495
W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene. Phys. Rev. Lett., 42 (1979) 1698, https://doi.org/10.1073/pnas.77.10.5626
W. P. Su, J. R. Schrieffer, and A. J. Heeger, Soliton excitations in polyacetylene. Phys. Rev. B, 22 (1980) 2099. https://doi.org/10.1103/PhysRevB.22.2099
M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators. Rev. Mod. Phys., 82 (2010) 3045, https://doi.org/10.1103/RevModPhys.82.3045
X.-L. Qi and S.-C. Zhan, Topological insulators and superconductors. Rev. Mod. Phys., 83 (2011) 1057, https://doi.org/10.1103/RevModPhys.83.1057
R. Shankar, Topological insulators - a review, (2018). https://doi.org/10.48550/arXiv.1804.06471
L. Wang, M. Troyer, and X. Dai, Topological charge pumping in a one-dimensional optical lattice. Physical review letters, 111 (2013) 026802, https://doi.org/10.1103/PhysRevLett.111.026802
A. J. Heeger, S. Kivelson, J. R. Schrieffer, and W-P Su, Solitons in conducting polymers. Reviews of Modern Physics, 60 (1988) 781, https://doi.org/10.1103/RevModPhys.60.781
L. Yu, Solitons and polarons in conducting polymers. (World Scientific, 1988)
S. Ryu, A. P. Schnyder, A. Furusaki, and A. W. W. Ludwi, Topological insulators and superconductors: tenfold way and dimensional hierarchy. New Journal of Physics, 12 (2010) 065010. https://doi.org/10.1088/1367-2630/12/6/065010
Y.-G. Peng et al., Experimental demonstration of anomalous floquet topological insulator for sound. Nature communications, 7 (2016) 13368. https://doi.org/10.1038/ncomms13368
A. Gomez-Leon and G. Platero, Floquet-bloch theory and topology in periodically driven lattices. Physical review letters, 110 (2013) 200403. https://doi.org/10.1103/PhysRevLett.110.200403
V. Dal Lago, M. Atala, and L. Foa Torres, Floquet topological transitions in a driven one-dimensional topological insulator. Physical Review A, 92 (2015) 023624, https://doi.org/10.1103/PhysRevA.92.023624
F. Alex An, E. J. Meier, and B. Gadway, Engineering a fluxdependent mobility edge in disordered zigzag chains. Physical Review X, 8 (2018) 031045, https://doi.org/10.1103/PhysRevX.8.031045
B. Perez-Gonzalez, M. Bello, A. Gomez- Leon, and G. Platero, Interplay between long-range hopping and disorder in topological systems. Physical Review B, 99 (2019) 035146, https://doi.org/10.1103/PhysRevB.99.035146
C.-F. Li, X.-P. Li, and L.-C. Wang, Topological phases of modulated su-schrieffer-heeger chains with long-range interactions. Europhysics Letters, 124 (2018) 37003, https://doi.org/10.1209/0295-5075/124/37003
C. Li, S. Lin, G. Zhang, and Z. Song, Topological nodal points in two coupled su-schrieffer-heeger chains. Physical Review B, 96 (2017) 125418, https://doi.org/10.1103/PhysRevB.96.125418
J. Junemann, A. Piga, S.-J. Ran, M. Lewenstein, M. Rizzi, and A. Bermudez, Exploring interacting topological insulators with ultracold atoms: The synthetic creutz-hubbard model. Physical Review X, 7 (2017) 031057, https://doi.org/10.1103/PhysRevX.7.031057
N. Sun and L.-K. Lim, Quantum charge pumps with topological phases in a creutz ladder. Physical Review B, 96 (2017) 035139, https://doi.org/10.1103/PhysRevB.96.035139
C.-A. Li, S.-J. Choi, S.-B. Zhang, and B. Trauzettel, Dirac states in an inclined two-dimensional su-schriefferheeger model. Physical Review Research, 4 (2022) 023193, https://doi.org/10.1103/PhysRevResearch.4.023193
D. Xie, W. Gou, T. Xiao, B. Gadway, and B. Yan, Topological characterizations of an extended su-schrieffer-heeger model. npj Quantum Information, 5 (2019) 55, https://doi.org/10.1038/s41534-019-0159-6
L. Li, Z. Xu, and S. Chen, Topological phases of generalized su-schrieffer-heeger models. Physical Review B, 89 (2014) 085111, https://doi.org/10.1103/PhysRevB.89.085111
A. Agrawal and J. N. Bandyopadhyay, Cataloging topological phases of n stacked su-schrieffer-heeger chains by a systematic breaking of symmetries. Physical Review B, 108 (2023) 104101 https://doi.org/10.1103/PhysRevB.108.104101
J.-R. Li, L.-L. Zhang, W.-B. Cui, and W.- J. Gong, Topological properties in non-hermitian tetratomic su-schrieffer-heeger lattices. Physical Review Research, 4 (2022) 023009, https://doi.org/10.1103/PhysRevResearch.4.023009
A. Sivan and M. Orenstein, Topology of multiple crosslinked su-schrieffer-heeger chains. Physical Review A, 106 (2022) 022216, https://doi.org/10.1103/PhysRevA.106.022216
J. Zak, Berry’s phase for energy bands in solids. Physical review letters, 62 (1989) 2747, https://doi.org/10.1103/PhysRevLett.62.2747
Y. Betancur-Ocampo, B. Manjarrez-Montañez, A. M. Martınez-Argüello, and R. A. Mendez- Sanchez, Twofold topological phase transitions induced by thirdnearest-neighbor interactions in 1d chains, 2023. 13 https://doi.org/10.48550/arXiv.2306.05595
B. Wang, T. Chen, and X. Zhang, Experimental observation of topologically protected bound states with vanishing chern numbers in a two-dimensional quantum walk. Physical Review Letters, 121 (2018) 100501, https://doi.org/10.1103/PhysRevLett.121.100501
C. Chen et al., Observation of topologically protected edge states in a photonic two-dimensional quantum walk. Physical review letters, 121 (2018) 100502, https://doi.org/10.1103/PhysRevLett.121.100502
M. Xiao et al., Geometric phase and band inversion in periodic acoustic systems. Nature Physics, 11 (2015) 240, https://doi.org/10.1038/nphys3228
B. K. Stuhl, H.-I. Lu, L. M. Aycock, D. Genkina, and I. B. Spielman, Visualizing edge states with an atomic bose gas in the quantum hall regime. Science, 349 (2015) 1514, https://doi.org/10.1126/science.aaa8515
E. J. Meier, F. A. An, and B. Gadway, Observation of the topological soliton state in the su-schrieffer-heeger model. Nature communications, 7 (2016) 13986, https://doi.org/10.1038/ncomms13986
E. J. Meier et al., Observation of the topological anderson insulator in disordered atomic wires. Science, 362 (2018) 929, https://doi.org/10.1126/science.aat3406
H. Cai et al., Experimental observation of momentum-space chiral edge currents in room-temperature atoms. Physical Review Letters, 122 (2019) 023601, https://doi.org/10.1103/PhysRevLett.122.023601
N. Goldman, J. C. Budich, and P. Zoller, Topological quantum matter with ultracold gases in optical lattices. Nature Physics, 12 (2016) 639, https://doi.org/10.1038/nphys3803
G. Jotzu et al., Experimental realization of the topological haldane model with ultracold fermions. Nature, 515 (2014) 237, https://doi.org/10.1038/nature13915
M. Ezawa, Electric-circuit simulation of the schrodinger equation and non-hermitian quantum walks. Phys. Rev. B, 100 (2019) 165419, https://doi.org/10.1103/PhysRevB.100.165419
R. Y. Qi Xun, Topological circuits - a stepping stone in the topological revolution. Molecular Frontiers Journal, 04 (2020) 9, https://doi.org/10.1142/S2529732520970020
A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics. Rev. Mod. Phys., 93 (2021) 025005, https://doi.org/10.1103/RevModPhys.93.025005
C. Hua Lee et al., Topolectrical circuits. Communications Physics, 1 (2018) 39, https://doi.org/10.1038/s42005-018-0035-2
E. Zhao, Topological circuits of inductors and capacitors. Annals of Physics, 399 (2018) 289, https://doi.org/10.1016/j.aop.(2018).10.006
J. Dong, V. Juricic, and B. Roy, Topolectric circuits: Theory and construction. Phys. Rev. Res., 3 (2021) 023056, https://doi.org/10.1103/PhysRevResearch.3.023056
R. Yang Qi Xun, Topological circuits-a stepping stone in the topological revolution. Molecular Frontiers Journal, 4 (2020) 9-14, https://doi.org/10.1142/S2529732520970020
J. Ningyuan, C. Owens, A. Sommer, D. Schuster, and J. Simon, Time-and site-resolved dynamics in a topological circuit. Physical Review X, 5 (2015) 021031, https://doi.org/10.1103/PhysRevX.5.021031
W. Zhu, S. Hou, Y. Long, H. Chen, and J. Ren, Simulating quantum spin hall effect in the topological lieb lattice of a linear circuit network. Physical Review B, 97 (2018) 075310, https://doi.org/10.1103/PhysRevB.97.075310
phythTB. Python tight binding, (2016). https://www.physics.rutgers.edu/pythtb/
PySpice. Pyspice, (2021). https://pypi.org/project/PySpice/
U. Fano, Effects of configuration interaction on intensities and phase shifts. Physical review, 124 (1961) 1866, https://doi.org/10.1103/PhysRev.124.1866
Bo Lv et al., Analysis and modeling of fano resonances using equivalent circuit elements. Scientific reports, 6 (2016) 31884, https://doi.org/10.1038/srep31884
M. Ilchenko and A. Zhivkov, Bridge equivalent circuits for microwave filters and fano resonance. In Mykhailo Ilchenko, Leonid Uryvsky, and Larysa Globa, editors, Advances in Information and Communication Technologies, pages 278-298, Cham, (2019). Springer International Publishing, https://doi.org/10.1007/978-3-030-16770-714
M. I Molina, Fano resonances in an electrical lattice. Physics Letters A, 428 (2022) 127948, https://doi.org/10.1016/j.physleta.2022.127948
J. Cserti, G. Szechenyi, and G. David, Uniform tiling with electrical resistors. Journal of Physics A: Mathematical and Theoretical, 44 (2011) 215201, https://doi.org/10.1088/1751-8113/44/21/215201
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