skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

Abstract

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 dimensionmore » 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.« less

Authors:
; ;
Publication Date:
Research Org.:
Univ. of Maryland, College Park, MD (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1182821
Alternate Identifier(s):
OSTI ID: 1452836
Grant/Contract Number:  
SC0001911
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 5 Journal Issue: 2; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Lobos, Alejandro M., Dobry, Ariel O., and Galitski, Victor. Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator. United States: N. p., 2015. Web. doi:10.1103/PhysRevX.5.021017.
Lobos, Alejandro M., Dobry, Ariel O., & Galitski, Victor. Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator. United States. doi:10.1103/PhysRevX.5.021017.
Lobos, Alejandro M., Dobry, Ariel O., and Galitski, Victor. Fri . "Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator". United States. doi:10.1103/PhysRevX.5.021017.
@article{osti_1182821,
title = {Magnetic End States in a Strongly Interacting One-Dimensional Topological Kondo Insulator},
author = {Lobos, Alejandro M. and Dobry, Ariel O. and Galitski, Victor},
abstractNote = {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.},
doi = {10.1103/PhysRevX.5.021017},
journal = {Physical Review. X},
number = 2,
volume = 5,
place = {United States},
year = {2015},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevX.5.021017

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Topological Kondo Insulators
journal, March 2010


Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987


Topological insulators and superconductors
journal, October 2011


Spin Gap in a Doped Kondo Chain
journal, August 1997


Time reversal polarization and a Z 2 adiabatic spin pump
journal, November 2006


Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
journal, February 2011


Quantum Spin Hall Insulator State in HgTe Quantum Wells
journal, November 2007


New approach to the mixed-valence problem
journal, March 1984


Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6
journal, December 2013

  • Neupane, M.; Alidoust, N.; Xu, S-Y.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms3991

Antiferromagnetic spin ladders: Crossover between spin S =1/2 and S =1 chains
journal, April 1996


Mean-field theory of intermediate valence/heavy fermion systems
journal, January 1987


Dimerized phase of ionic Hubbard models
journal, March 2005


A topological Dirac insulator in a quantum spin Hall phase
journal, April 2008

  • Hsieh, D.; Qian, D.; Wray, L.
  • Nature, Vol. 452, Issue 7190, p. 970-974
  • DOI: 10.1038/nature06843

Finite wave vector pairing in doped two-leg ladders
journal, May 2012


On the solution of the Coqblin-Schreiffer Hamiltonian by the large-N expansion technique
journal, June 1983


Zero-modes and thermodynamics of disordered ladders
journal, February 1999


Low-temperature surface conduction in the Kondo insulator SmB 6
journal, November 2013


Z2classification of quantum spin Hall systems: An approach using time-reversal invariance
journal, May 2009


Periodic table for topological insulators and superconductors
conference, January 2009

  • Kitaev, Alexei; Lebedev, Vladimir; Feigel’man, Mikhail
  • ADVANCES IN THEORETICAL PHYSICS: Landau Memorial Conference, AIP Conference Proceedings
  • DOI: 10.1063/1.3149495

Evidence for Helical Edge Modes in Inverted InAs / GaSb Quantum Wells
journal, September 2011


Bosonization for beginners - refermionization for experts
journal, November 1998


Electron Localization in the Insulating State
journal, January 1999


Mixed valence as an almost broken symmetry
journal, April 1987


Hybridization, Inter-Ion Correlation, and Surface States in the Kondo Insulator SmB 6
journal, February 2013


Low-energy effective theories of the two-thirds filled Hubbard model on the triangular necklace lattice
journal, July 2014


Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain
journal, June 2013


Topological insulators and superconductors: tenfold way and dimensional hierarchy
journal, June 2010


End states in a one-dimensional topological Kondo insulator in large- N limit
journal, September 2014


Spin-liquid ground state of the half-filled Kondo lattice in one dimension
journal, August 1992

  • Tsunetsugu, Hirokazu; Hatsugai, Yasuhiro; Ueda, Kazuo
  • Physical Review B, Vol. 46, Issue 5
  • DOI: 10.1103/PhysRevB.46.3175

Hopes surface for exotic insulator
journal, December 2012


Exact Results for a 1D Kondo Lattice from Bosonization
journal, August 1996


Images of Edge Current in InAs / GaSb Quantum Wells
journal, July 2014


Haldane Phase in the Hubbard Model at 2/3-Filling for the Organic Molecular Compound Mo 3 S 7 ( dmit ) 3
journal, December 2014


Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order
journal, October 2009


New method for the Anderson model
journal, July 1976


Hidden Z 2 × Z 2 symmetry breaking in Haldane-gap antiferromagnets
journal, January 1992


Z2 Topological Order and the Quantum Spin Hall Effect
journal, September 2005


Surface Hall Effect and Nonlocal Transport in SmB6: Evidence for Surface Conduction
journal, November 2013

  • Kim, D. J.; Thomas, S.; Grant, T.
  • Scientific Reports, Vol. 3, Issue 1
  • DOI: 10.1038/srep03150

Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices
journal, October 2011

  • Soltan-Panahi, Parvis; Lühmann, Dirk-Sören; Struck, Julian
  • Nature Physics, Vol. 8, Issue 1
  • DOI: 10.1038/nphys2128

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands
journal, February 2013

  • Li, Xiaopeng; Zhao, Erhai; Vincent Liu, W.
  • Nature Communications, Vol. 4, Issue 1
  • DOI: 10.1038/ncomms2523

Rise and fall of hidden string order of lattice bosons
journal, June 2008


Quantum Spin Hall Effect in Graphene
journal, November 2005


Colloquium: Topological insulators
journal, November 2010


Schwinger-boson mean-field theory for S=1 open spin chains
journal, April 1992


Observation of a large-gap topological-insulator class with a single Dirac cone on the surface
journal, May 2009

  • Xia, Y.; Qian, D.; Hsieh, D.
  • Nature Physics, Vol. 5, Issue 6, p. 398-402
  • DOI: 10.1038/nphys1274

Imaging currents in HgTe quantum wells in the quantum spin Hall regime
journal, June 2013

  • Nowack, Katja C.; Spanton, Eric M.; Baenninger, Matthias
  • Nature Materials, Vol. 12, Issue 9
  • DOI: 10.1038/nmat3682

Pair-Density-Wave Correlations in the Kondo-Heisenberg Model
journal, September 2010


Topological Insulators in Three Dimensions
journal, March 2007


On the Surface States Associated with a Periodic Potential
journal, August 1939


Spin Order in One-Dimensional Kondo and Hund Lattices
journal, October 2004


Edge states in antiferromagnetic quantum spin chains
journal, July 1994


Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice
journal, December 2010

  • Wirth, Georg; Ölschläger, Matthias; Hemmerich, Andreas
  • Nature Physics, Vol. 7, Issue 2
  • DOI: 10.1038/nphys1857

Magnetization and dimerization profiles of the cut two-leg spin ladder
journal, April 2002


Entanglement spectrum of a topological phase in one dimension
journal, February 2010


Staggered liquid phases of the one-dimensional Kondo-Heisenberg lattice model
journal, April 2001


Topological invariants of time-reversal-invariant band structures
journal, March 2007


One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
journal, June 2001


Shockley model description of surface states in topological insulators
journal, August 2012


Macroscopic polarization as a geometric quantum phase: Many-body formulation
journal, May 1994


Interaction Driven Subgap Spin Exciton in the Kondo Insulator SmB 6
journal, January 2015


Topological Pair-Density-Wave Superconducting States
journal, December 2014


Quantum phase diagram of the generalized ionic Hubbard model for AB n chains
journal, March 2006


Berry phase effects on electronic properties
journal, July 2010


Valence bond ground states in isotropic quantum antiferromagnets
journal, September 1988

  • Affleck, Ian; Kennedy, Tom; Lieb, Elliott H.
  • Communications in Mathematical Physics, Vol. 115, Issue 3
  • DOI: 10.1007/BF01218021

Symmetry protection of topological phases in one-dimensional quantum spin systems
journal, February 2012


    Works referencing / citing this record:

    Symmetry-protected topological phase transition in one-dimensional Kondo lattice and its realization with ultracold atoms
    journal, October 2017


    Kramers doublet ground state in topological Kondo insulators
    journal, February 2019