Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples

Tsvelik, Alexei M.; Yevtushenko, Oleg M.

doi:10.1103/PhysRevB.98.081118

Title: Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples

Abstract

We show that edges of Quantum Spin Hall topological insulators represent a natural platform for realization of exotic magnetic phase which has all properties of lattice supersolid. On one hand, fermionic edge modes are helical due to the nontrivial topology of the bulk. On the other hand, a disorder at the edge or magnetic adatoms may produce a dense array of localized spins interacting with the helical electrons. The spin subsystem is magnetically frustrated since the indirect exchange favors formation of helical spin order and the direct one favors (anti)ferromagnetic ordering of the spins. At a moderately strong direct exchange, the competition between these spin interactions results in the spontaneous breaking of parity and in the Ising type order of the z-components at zero temperature. If the total spin is conserved the spin order does not pin a collective massless helical mode which supports the ideal transport. In this case, the phase transition converts the helical spin order to the order of a chiral lattice supersolid. Furthermore, this represents a radically new possibility for experimental studies of the elusive supersolidity.

Authors:

^[1]; Yevtushenko, Oleg M. ^[2]

Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
Ludwig Maximilians Univ., Munich (Germany). Arnold Sommerfeld Center and Center for Nano-Science

Publication Date:: Fri Aug 31 00:00:00 EDT 2018

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

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

OSTI Identifier:: 1466588

Alternate Identifier(s):: OSTI ID: 1467935

Report Number(s):: BNL-207993-2018-JAAM
Journal ID: ISSN 2469-9950

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 98; Journal Issue: 8; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats


                    Tsvelik, Alexei M., and Yevtushenko, Oleg M. Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevB.98.081118.

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                    Tsvelik, Alexei M., & Yevtushenko, Oleg M. Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples.  United States.  https://doi.org/10.1103/PhysRevB.98.081118

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                    Tsvelik, Alexei M., and Yevtushenko, Oleg M. Fri .  
"Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples".  United States.  https://doi.org/10.1103/PhysRevB.98.081118.  https://www.osti.gov/servlets/purl/1466588.

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@article{osti_1466588,

  title        = {Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples},

  author       = {Tsvelik, Alexei M. and Yevtushenko, Oleg M.},

  abstractNote = {We show that edges of Quantum Spin Hall topological insulators represent a natural platform for realization of exotic magnetic phase which has all properties of lattice supersolid. On one hand, fermionic edge modes are helical due to the nontrivial topology of the bulk. On the other hand, a disorder at the edge or magnetic adatoms may produce a dense array of localized spins interacting with the helical electrons. The spin subsystem is magnetically frustrated since the indirect exchange favors formation of helical spin order and the direct one favors (anti)ferromagnetic ordering of the spins. At a moderately strong direct exchange, the competition between these spin interactions results in the spontaneous breaking of parity and in the Ising type order of the z-components at zero temperature. If the total spin is conserved the spin order does not pin a collective massless helical mode which supports the ideal transport. In this case, the phase transition converts the helical spin order to the order of a chiral lattice supersolid. Furthermore, this represents a radically new possibility for experimental studies of the elusive supersolidity.},

  doi          = {10.1103/PhysRevB.98.081118},

  journal      = {Physical Review B},

  number       = 8,

  volume       = 98,

  place        = {United States},

  year         = {Fri Aug 31 00:00:00 EDT 2018},

  month        = {Fri Aug 31 00:00:00 EDT 2018}

}

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Title: Chiral Lattice Supersolid on Edges of Quantum Spin Hall Samples

Abstract

Citation Formats

Stability of the quantum spin Hall effect: Effects of interactions, disorder, and Z 2 topology journal, January 2006

Conductivity of a generic helical liquid journal, August 2014

Dicke quantum phase transition with a superfluid gas in an optical cavity journal, April 2010

Topological insulators and superconductors journal, October 2011

Magnetization plateaus of the Shastry-Sutherland model for SrCu 2 ( BO 3 ) 2 : Spin-density wave, supersolid, and bound states journal, December 2000

Quantum lattice gas and the existence of a supersolid journal, March 1973

Chiral spin states and superconductivity journal, June 1989

Observation of Edge Transport in the Disordered Regime of Topologically Insulating InAs / GaSb Quantum Wells journal, January 2014

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

Observation of Superflow in Solid Helium journal, September 2004

Colloquium: Topological insulators journal, November 2010

Dirac-fermion-mediated ferromagnetism in a topological insulator journal, August 2012

Supersolid formation in a quantum gas breaking a continuous translational symmetry journal, March 2017

Ultra-robust high-field magnetization plateau and supersolidity in bond-frustrated MnCr 2 S 4 journal, March 2017

Can a Solid Be "Superfluid"? journal, November 1970

Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors journal, October 1962

Nuclear-spin-induced localization of edge states in two-dimensional topological insulators journal, August 2017

Bose-Einstein Condensation and Liquid Helium journal, November 1956

Probable observation of a supersolid helium phase journal, January 2004

Conductance of a Helical Edge Liquid Coupled to a Magnetic Impurity journal, June 2011

Quantum Field Theory in Condensed Matter Physics book, January 2010

Speculations on Bose-Einstein Condensation and Quantum Crystals journal, July 1970

Helical Liquid and the Edge of Quantum Spin Hall Systems journal, March 2006

Transport in helical Luttinger liquid with Kondo impurities journal, December 2015

Novel local symmetries and chiral-symmetry-broken phases in S=(1/2 triangular-lattice Heisenberg model journal, November 1989

Resistance of helical edges formed in a semiconductor heterostructure journal, September 2014

Superfluids and supersolids on frustrated two-dimensional lattices journal, February 1997

Off-Diagonal Long-Range Order in Solids journal, January 1970

Supersolid phase and magnetization plateaus observed in the anisotropic spin- 3 2 Heisenberg model on bipartite lattices journal, November 2011

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators journal, March 2018

Colloquium : Supersolids: What and where are they? journal, May 2012

Mesoscopic Fluctuations of Conductance of a Helical Edge Contaminated by Magnetic Impurities journal, May 2013

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

Fate of Vacancy-Induced Supersolidity in He 4 journal, August 2006

Helical Luttinger Liquid in Topological Insulator Nanowires journal, September 2010

Localization at the Edge of a 2D Topological Insulator by Kondo Impurities with Random Anisotropies journal, August 2013

Magnetic moments in a helical edge can make weak correlations seem strong journal, June 2016

Mapping of the two-channel Kondo problem to a resonant-level model journal, November 1992

Helical Spin Order from Topological Dirac and Weyl Semimetals journal, August 2015

Kondo lattice on the edge of a two-dimensional topological insulator journal, June 2012

Functional integral bosonization for an impurity in a Luttinger liquid journal, April 2004

Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State journal, June 2009

A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates journal, March 2017

Stability of the quantum spin Hall effect: Effects of interactions, disorder, and $Z_{2}$ topology
journal, January 2006

Conductivity of a generic helical liquid
journal, August 2014

Dicke quantum phase transition with a superfluid gas in an optical cavity
journal, April 2010

Topological insulators and superconductors
journal, October 2011

Magnetization plateaus of the Shastry-Sutherland model for ${SrCu}_{2} ({BO}_{3})_{2} :$ Spin-density wave, supersolid, and bound states
journal, December 2000

Quantum lattice gas and the existence of a supersolid
journal, March 1973

Chiral spin states and superconductivity
journal, June 1989

Observation of Edge Transport in the Disordered Regime of Topologically Insulating $InAs / GaSb$ Quantum Wells
journal, January 2014

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

Observation of Superflow in Solid Helium
journal, September 2004

Colloquium: Topological insulators
journal, November 2010

Dirac-fermion-mediated ferromagnetism in a topological insulator
journal, August 2012

Supersolid formation in a quantum gas breaking a continuous translational symmetry
journal, March 2017

Ultra-robust high-field magnetization plateau and supersolidity in bond-frustrated MnCr ₂ S ₄
journal, March 2017

Can a Solid Be "Superfluid"?
journal, November 1970

Concept of Off-Diagonal Long-Range Order and the Quantum Phases of Liquid He and of Superconductors
journal, October 1962

Nuclear-spin-induced localization of edge states in two-dimensional topological insulators
journal, August 2017

Bose-Einstein Condensation and Liquid Helium
journal, November 1956

Probable observation of a supersolid helium phase
journal, January 2004

Conductance of a Helical Edge Liquid Coupled to a Magnetic Impurity
journal, June 2011

Quantum Field Theory in Condensed Matter Physics
book, January 2010

Speculations on Bose-Einstein Condensation and Quantum Crystals
journal, July 1970

Helical Liquid and the Edge of Quantum Spin Hall Systems
journal, March 2006

Transport in helical Luttinger liquid with Kondo impurities
journal, December 2015

Novel local symmetries and chiral-symmetry-broken phases in S=(1/2 triangular-lattice Heisenberg model
journal, November 1989

Resistance of helical edges formed in a semiconductor heterostructure
journal, September 2014

Superfluids and supersolids on frustrated two-dimensional lattices
journal, February 1997

Off-Diagonal Long-Range Order in Solids
journal, January 1970

Supersolid phase and magnetization plateaus observed in the anisotropic spin- $\frac{3}{2}$ Heisenberg model on bipartite lattices
journal, November 2011

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators
journal, March 2018

Colloquium : Supersolids: What and where are they?
journal, May 2012

Mesoscopic Fluctuations of Conductance of a Helical Edge Contaminated by Magnetic Impurities
journal, May 2013

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

Fate of Vacancy-Induced Supersolidity in ${}^{4}{He}$
journal, August 2006

Helical Luttinger Liquid in Topological Insulator Nanowires
journal, September 2010

Localization at the Edge of a 2D Topological Insulator by Kondo Impurities with Random Anisotropies
journal, August 2013

Magnetic moments in a helical edge can make weak correlations seem strong
journal, June 2016

Mapping of the two-channel Kondo problem to a resonant-level model
journal, November 1992

Helical Spin Order from Topological Dirac and Weyl Semimetals
journal, August 2015

Kondo lattice on the edge of a two-dimensional topological insulator
journal, June 2012

Functional integral bosonization for an impurity in a Luttinger liquid
journal, April 2004

Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State
journal, June 2009

A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates
journal, March 2017