Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

Lobos, Alejandro M.; Dobry, Ariel O.; Galitski, Victor

doi:10.1103/PhysRevX.5.021017

Title: Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

Journal Article · Fri May 22 00:00:00 EDT 2015 · Physical Review. X

DOI:https://doi.org/10.1103/PhysRevX.5.021017· OSTI ID:1182821

Lobos, Alejandro M.; Dobry, Ariel O.; Galitski, Victor

Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model).We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U = 0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. In conclusion, our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.

View Journal Article

Cite

Export

Save

Research Organization:: Univ. of Maryland, College Park, MD (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0001911

OSTI ID:: 1182821

Alternate ID(s):: OSTI ID: 1452836

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Vol. 5 Journal Issue: 2; ISSN 2160-3308

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 14 works

Citation information provided by
Web of Science

References (70)

Topological Kondo Insulators Dzero, Maxim; Sun, Kai; Galitski, Victor Physical Review Letters, Vol. 104, Issue 10 https://doi.org/10.1103/PhysRevLett.104.106408	journal	March 2010
Rigorous results on valence-bond ground states in antiferromagnets Affleck, Ian; Kennedy, Tom; Lieb, Elliott H. Physical Review Letters, Vol. 59, Issue 7 https://doi.org/10.1103/PhysRevLett.59.799	journal	August 1987
Field Theories of Condensed Matter Physics Fradkin, Eduardo Cambridge University Press https://doi.org/10.1017/CBO9781139015509	book	January 2013
Topological insulators and superconductors Qi, Xiao-Liang; Zhang, Shou-Cheng Reviews of Modern Physics, Vol. 83, Issue 4 https://doi.org/10.1103/RevModPhys.83.1057	journal	October 2011
Spin Gap in a Doped Kondo Chain Sikkema, Arnold E.; Affleck, Ian; White, Steven R. Physical Review Letters, Vol. 79, Issue 5 https://doi.org/10.1103/PhysRevLett.79.929	journal	August 1997
Time reversal polarization and a $Z_{2}$ adiabatic spin pump Fu, Liang; Kane, C. L. Physical Review B, Vol. 74, Issue 19 https://doi.org/10.1103/PhysRevB.74.195312	journal	November 2006
Quantum phase diagram of the half filled Hubbard model with bond-charge interaction Dobry, A. O.; Aligia, A. A. Nuclear Physics B, Vol. 843, Issue 3 https://doi.org/10.1016/j.nuclphysb.2010.10.017	journal	February 2011
Quantum Spin Hall Insulator State in HgTe Quantum Wells Konig, M.; Wiedmann, S.; Brune, C. Science, Vol. 318, Issue 5851, p. 766-770 https://doi.org/10.1126/science.1148047	journal	November 2007
New approach to the mixed-valence problem Coleman, Piers Physical Review B, Vol. 29, Issue 6 https://doi.org/10.1103/PhysRevB.29.3035	journal	March 1984
Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6 Neupane, M.; Alidoust, N.; Xu, S-Y. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3991	journal	December 2013
Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains Shelton, D. G.; Nersesyan, A. A.; Tsvelik, A. M. Physical Review B, Vol. 53, Issue 13 https://doi.org/10.1103/PhysRevB.53.8521	journal	April 1996
Mean-field theory of intermediate valence/heavy fermion systems Newns, D. M.; Read, N. Advances in Physics, Vol. 36, Issue 6 https://doi.org/10.1080/00018738700101082	journal	January 1987
Dimerized phase of ionic Hubbard models Aligia, A. A.; Batista, C. D. Physical Review B, Vol. 71, Issue 12 https://doi.org/10.1103/PhysRevB.71.125110	journal	March 2005
A topological Dirac insulator in a quantum spin Hall phase Hsieh, D.; Qian, D.; Wray, L. Nature, Vol. 452, Issue 7190, p. 970-974 https://doi.org/10.1038/nature06843	journal	April 2008
Finite wave vector pairing in doped two-leg ladders Robinson, N. J.; Essler, F. H. L.; Jeckelmann, E. Physical Review B, Vol. 85, Issue 19 https://doi.org/10.1103/PhysRevB.85.195103	journal	May 2012
On the solution of the Coqblin-Schreiffer Hamiltonian by the large-N expansion technique Read, N.; Newns, D. M. Journal of Physics C: Solid State Physics, Vol. 16, Issue 17 https://doi.org/10.1088/0022-3719/16/17/014	journal	June 1983
Zero-modes and thermodynamics of disordered ladders Gogolin, Alexander O.; Nersesyan, Alexander A.; Tsvelik, Alexei M. Nuclear Physics B, Vol. 540, Issue 3 https://doi.org/10.1016/S0550-3213(98)00776-7	journal	February 1999
Scaling and Renormalization in Statistical Physics Cardy, John Cambridge University Press https://doi.org/10.1017/CBO9781316036440	book	January 2015
Low-temperature surface conduction in the Kondo insulator SmB $_{6}$ Wolgast, Steven; Kurdak, Çağlıyan; Sun, Kai Physical Review B, Vol. 88, Issue 18 https://doi.org/10.1103/PhysRevB.88.180405	journal	November 2013
$Z_{2}$ classification of quantum spin Hall systems: An approach using time-reversal invariance Roy, Rahul Physical Review B, Vol. 79, Issue 19, Article No. 195321 https://doi.org/10.1103/PhysRevB.79.195321	journal	May 2009
Periodic table for topological insulators and superconductors Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings https://doi.org/10.1063/1.3149495	conference	January 2009
Evidence for Helical Edge Modes in Inverted $InAs / GaSb$ Quantum Wells Knez, Ivan; Du, Rui-Rui; Sullivan, Gerard Physical Review Letters, Vol. 107, Issue 13 https://doi.org/10.1103/PhysRevLett.107.136603	journal	September 2011
Bosonization for beginners - refermionization for experts von Delft, Jan; Schoeller, Herbert Annalen der Physik, Vol. 7, Issue 4 https://doi.org/10.1002/(SICI)1521-3889(199811)7:4<225::AID-ANDP225>3.0.CO;2-L	journal	November 1998
Electron Localization in the Insulating State Resta, Raffaele; Sorella, Sandro Physical Review Letters, Vol. 82, Issue 2 https://doi.org/10.1103/PhysRevLett.82.370	journal	January 1999
Mixed valence as an almost broken symmetry Coleman, Piers Physical Review B, Vol. 35, Issue 10 https://doi.org/10.1103/PhysRevB.35.5072	journal	April 1987
Hybridization, Inter-Ion Correlation, and Surface States in the Kondo Insulator ${SmB}_{6}$ Zhang, Xiaohang; Butch, N. P.; Syers, P. Physical Review X, Vol. 3, Issue 1 https://doi.org/10.1103/PhysRevX.3.011011	journal	February 2013
Edge states in Schwinger-boson mean-field theory of low-dimensional quantum antiferromagnets Ng, T. K. Physical Review B, Vol. 47, Issue 17 https://doi.org/10.1103/PhysRevB.47.11575	journal	May 1993
Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice Janani, C.; Merino, J.; McCulloch, Ian P. Physical Review B, Vol. 90, Issue 3 https://doi.org/10.1103/PhysRevB.90.035120	journal	July 2014
Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain Dobry, Ariel; Jaefari, Akbar; Fradkin, Eduardo Physical Review B, Vol. 87, Issue 24 https://doi.org/10.1103/PhysRevB.87.245102	journal	June 2013
Topological insulators and superconductors: tenfold way and dimensional hierarchy Ryu, Shinsei; Schnyder, Andreas P.; Furusaki, Akira New Journal of Physics, Vol. 12, Issue 6 https://doi.org/10.1088/1367-2630/12/6/065010	journal	June 2010
End states in a one-dimensional topological Kondo insulator in large- $N$ limit Alexandrov, Victor; Coleman, Piers Physical Review B, Vol. 90, Issue 11 https://doi.org/10.1103/PhysRevB.90.115147	journal	September 2014
Spin-liquid ground state of the half-filled Kondo lattice in one dimension Tsunetsugu, Hirokazu; Hatsugai, Yasuhiro; Ueda, Kazuo Physical Review B, Vol. 46, Issue 5 https://doi.org/10.1103/PhysRevB.46.3175	journal	August 1992
Hopes surface for exotic insulator Samuel Reich, Eugenie Nature, Vol. 492, Issue 7428 https://doi.org/10.1038/492165a	journal	December 2012
Exact Results for a 1D Kondo Lattice from Bosonization Zachar, Oron; Kivelson, S. A.; Emery, V. J. Physical Review Letters, Vol. 77, Issue 7 https://doi.org/10.1103/PhysRevLett.77.1342	journal	August 1996
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State Haldane, F. D. M. Physical Review Letters, Vol. 50, Issue 15 https://doi.org/10.1103/PhysRevLett.50.1153	journal	April 1983
Images of Edge Current in $InAs / GaSb$ Quantum Wells Spanton, Eric M.; Nowack, Katja C.; Du, Lingjie Physical Review Letters, Vol. 113, Issue 2 https://doi.org/10.1103/PhysRevLett.113.026804	journal	July 2014
Haldane Phase in the Hubbard Model at 2/3-Filling for the Organic Molecular Compound ${Mo}_{3} S_{7} {(dmit)}_{3}$ Janani, C.; Merino, J.; McCulloch, I. P. Physical Review Letters, Vol. 113, Issue 26 https://doi.org/10.1103/PhysRevLett.113.267204	journal	December 2014
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevB.80.155131	journal	October 2009
New method for the Anderson model Barnes, S. E. Journal of Physics F: Metal Physics, Vol. 6, Issue 7 https://doi.org/10.1088/0305-4608/6/7/018	journal	July 1976
Hidden $Z_{2}$ × $Z_{2}$ symmetry breaking in Haldane-gap antiferromagnets Kennedy, Tom; Tasaki, Hal Physical Review B, Vol. 45, Issue 1 https://doi.org/10.1103/PhysRevB.45.304	journal	January 1992
$Z_{2}$ Topological Order and the Quantum Spin Hall Effect Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 14, Article No. 146802 https://doi.org/10.1103/PhysRevLett.95.146802	journal	September 2005
Surface Hall Effect and Nonlocal Transport in SmB6: Evidence for Surface Conduction Kim, D. J.; Thomas, S.; Grant, T. Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep03150	journal	November 2013
Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices Soltan-Panahi, Parvis; Lühmann, Dirk-Sören; Struck, Julian Nature Physics, Vol. 8, Issue 1 https://doi.org/10.1038/nphys2128	journal	October 2011
Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands Li, Xiaopeng; Zhao, Erhai; Vincent Liu, W. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2523	journal	February 2013
Rise and fall of hidden string order of lattice bosons Berg, Erez; Dalla Torre, Emanuele G.; Giamarchi, Thierry Physical Review B, Vol. 77, Issue 24 https://doi.org/10.1103/PhysRevB.77.245119	journal	June 2008
Quantum Spin Hall Effect in Graphene Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.226801	journal	November 2005
Colloquium: Topological insulators Hasan, M. Z.; Kane, C. L. Reviews of Modern Physics, Vol. 82, Issue 4, p. 3045-3067 https://doi.org/10.1103/RevModPhys.82.3045	journal	November 2010
Schwinger-boson mean-field theory for S=1 open spin chains Ng, T. Physical Review B, Vol. 45, Issue 14 https://doi.org/10.1103/PhysRevB.45.8181	journal	April 1992
Observation of a large-gap topological-insulator class with a single Dirac cone on the surface Xia, Y.; Qian, D.; Hsieh, D. Nature Physics, Vol. 5, Issue 6, p. 398-402 https://doi.org/10.1038/nphys1274	journal	May 2009
Imaging currents in HgTe quantum wells in the quantum spin Hall regime Nowack, Katja C.; Spanton, Eric M.; Baenninger, Matthias Nature Materials, Vol. 12, Issue 9 https://doi.org/10.1038/nmat3682	journal	June 2013
Pair-Density-Wave Correlations in the Kondo-Heisenberg Model Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A. Physical Review Letters, Vol. 105, Issue 14 https://doi.org/10.1103/PhysRevLett.105.146403	journal	September 2010
Topological Insulators in Three Dimensions Fu, Liang; Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 98, Issue 10, Article No. 106803 https://doi.org/10.1103/PhysRevLett.98.106803	journal	March 2007
On the Surface States Associated with a Periodic Potential Shockley, William Physical Review, Vol. 56, Issue 4 https://doi.org/10.1103/PhysRev.56.317	journal	August 1939
Spin Order in One-Dimensional Kondo and Hund Lattices Garcia, D. J.; Hallberg, K.; Alascio, B. Physical Review Letters, Vol. 93, Issue 17 https://doi.org/10.1103/PhysRevLett.93.177204	journal	October 2004
Edge states in antiferromagnetic quantum spin chains Ng, Tai-Kai Physical Review B, Vol. 50, Issue 1 https://doi.org/10.1103/PhysRevB.50.555	journal	July 1994
Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice Wirth, Georg; Ölschläger, Matthias; Hemmerich, Andreas Nature Physics, Vol. 7, Issue 2 https://doi.org/10.1038/nphys1857	journal	December 2010
Magnetization and dimerization profiles of the cut two-leg spin ladder Lecheminant, P.; Orignac, E. Physical Review B, Vol. 65, Issue 17 https://doi.org/10.1103/PhysRevB.65.174406	journal	April 2002
Entanglement spectrum of a topological phase in one dimension Pollmann, Frank; Turner, Ari M.; Berg, Erez Physical Review B, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevB.81.064439	journal	February 2010
Staggered liquid phases of the one-dimensional Kondo-Heisenberg lattice model Zachar, Oron Physical Review B, Vol. 63, Issue 20 https://doi.org/10.1103/PhysRevB.63.205104	journal	April 2001
Topological invariants of time-reversal-invariant band structures Moore, J. E.; Balents, L. Physical Review B, Vol. 75, Issue 12, Article No. 121306(R) https://doi.org/10.1103/PhysRevB.75.121306	journal	March 2007
One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain Zachar, Oron; Tsvelik, Alexei M. Physical Review B, Vol. 64, Issue 3 https://doi.org/10.1103/PhysRevB.64.033103	journal	June 2001
Shockley model description of surface states in topological insulators Pershoguba, Sergey S.; Yakovenko, Victor M. Physical Review B, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevB.86.075304	journal	August 2012
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model Haldane, F. D. M. Physics Letters A, Vol. 93, Issue 9 https://doi.org/10.1016/0375-9601(83)90631-X	journal	February 1983
Macroscopic polarization as a geometric quantum phase: Many-body formulation Ortiz, Gerardo; Martin, Richard M. Physical Review B, Vol. 49, Issue 20 https://doi.org/10.1103/PhysRevB.49.14202	journal	May 1994
Interaction Driven Subgap Spin Exciton in the Kondo Insulator ${SmB}_{6}$ Fuhrman, W. T.; Leiner, J.; Nikolić, P. Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/PhysRevLett.114.036401	journal	January 2015
Topological Pair-Density-Wave Superconducting States Cho, Gil Young; Soto-Garrido, Rodrigo; Fradkin, Eduardo Physical Review Letters, Vol. 113, Issue 25 https://doi.org/10.1103/PhysRevLett.113.256405	journal	December 2014
Quantum phase diagram of the generalized ionic Hubbard model for ${AB}_{n}$ chains Torio, M. E.; Aligia, A. A.; Japaridze, G. I. Physical Review B, Vol. 73, Issue 11 https://doi.org/10.1103/PhysRevB.73.115109	journal	March 2006
Berry phase effects on electronic properties Xiao, Di; Chang, Ming-Che; Niu, Qian Reviews of Modern Physics, Vol. 82, Issue 3 https://doi.org/10.1103/RevModPhys.82.1959	journal	July 2010
Valence bond ground states in isotropic quantum antiferromagnets Affleck, Ian; Kennedy, Tom; Lieb, Elliott H. Communications in Mathematical Physics, Vol. 115, Issue 3 https://doi.org/10.1007/BF01218021	journal	September 1988
Symmetry protection of topological phases in one-dimensional quantum spin systems Pollmann, Frank; Berg, Erez; Turner, Ari M. Physical Review B, Vol. 85, Issue 7 https://doi.org/10.1103/PhysRevB.85.075125	journal	February 2012

Similar Records

A microscopic Kondo lattice model for the heavy fermion antiferromagnet CeIn₃

Journal Article · Tue Dec 12 00:00:00 EST 2023 · Nature Communications · OSTI ID:1182821

Simeth, Wolfgang; Wang, Zhentao; Ghioldi, E. A.; +14 more

Critical role of magnetic moments in heavy-fermion materials: Revisiting mysteries of SmB₆

Journal Article · Mon May 23 00:00:00 EDT 2022 · Physical Review. B · OSTI ID:1182821

Zhang, Ruiqi; Singh, Bahadur; Lane, Christopher; +6 more

RKKY to Kondo crossover in helical edge of a topological insulator

Journal Article · Mon Jul 10 00:00:00 EDT 2023 · Physical Review Research · OSTI ID:1182821

Ferrer, Pol Alonso-Cuevillas; Yevtushenko, Oleg M.; Weichselbaum, Andreas

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS

Title: Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator

Citation Formats

References (70)

Similar Records

Related Subjects