Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels

doi:10.1126/science.aat6467

Title: Pascal conductance series in ballistic one-dimensional LaAlO ₃ /SrTiO ₃ channels

Abstract

One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO ₃ /SrTiO ₃ ) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) ⋅ e ² /h , where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.

Authors:

^[1];

^[1]; Lee, Hyungwoo ^[2];

^[2]; He, Yuchi ^[3];

^[1]; Huang, Mengchen ^[1];

^[2]; Pekker, David ^[1]; Mong, Roger S. K. ^[1];

^[1];

^[1]

Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA., Pittsburgh Quantum Institute, Pittsburgh, PA 15260, USA.
Department of Materials Science and Engineering, University of Wisconsin, Madison, WI 53706, USA.
Pittsburgh Quantum Institute, Pittsburgh, PA 15260, USA., Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

Publication Date:: 2020-02-13

Sponsoring Org.:: USDOE

OSTI Identifier:: 1599696

Grant/Contract Number:: DEFG02-06ER46327; SC0014417

Resource Type:: Published Article

Journal Name:: Science

Additional Journal Information:: Journal Name: Science Journal Volume: 367 Journal Issue: 6479; Journal ID: ISSN 0036-8075

Publisher:: American Association for the Advancement of Science (AAAS)

Country of Publication:: United States

Language:: English

Citation Formats


                    Briggeman, Megan, Tomczyk, Michelle, Tian, Binbin, Lee, Hyungwoo, Lee, Jung-Woo, He, Yuchi, Tylan-Tyler, Anthony, Huang, Mengchen, Eom, Chang-Beom, Pekker, David, Mong, Roger S. K., Irvin, Patrick, and Levy, Jeremy. Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels.  United States: N. p., 2020. 
        Web.  doi:10.1126/science.aat6467.

Copy to clipboard


                    Briggeman, Megan, Tomczyk, Michelle, Tian, Binbin, Lee, Hyungwoo, Lee, Jung-Woo, He, Yuchi, Tylan-Tyler, Anthony, Huang, Mengchen, Eom, Chang-Beom, Pekker, David, Mong, Roger S. K., Irvin, Patrick, & Levy, Jeremy. Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels.  United States.  doi:10.1126/science.aat6467.

Copy to clipboard


                    Briggeman, Megan, Tomczyk, Michelle, Tian, Binbin, Lee, Hyungwoo, Lee, Jung-Woo, He, Yuchi, Tylan-Tyler, Anthony, Huang, Mengchen, Eom, Chang-Beom, Pekker, David, Mong, Roger S. K., Irvin, Patrick, and Levy, Jeremy. Thu .  
        "Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels".  United States.  doi:10.1126/science.aat6467.

Copy to clipboard


                    
@article{osti_1599696,

  title        = {Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels},

  author       = {Briggeman, Megan and Tomczyk, Michelle and Tian, Binbin and Lee, Hyungwoo and Lee, Jung-Woo and He, Yuchi and Tylan-Tyler, Anthony and Huang, Mengchen and Eom, Chang-Beom and Pekker, David and Mong, Roger S. K. and Irvin, Patrick and Levy, Jeremy},

  abstractNote = {One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO 3 /SrTiO 3 ) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) ⋅ e 2 /h , where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.},

  doi          = {10.1126/science.aat6467},

  journal      = {Science},

  number       = 6479,

  volume       = 367,

  place        = {United States},

  year         = {2020},

  month        = {2}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
DOI: 10.1126/science.aat6467

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Few-electron quantum dots
journal, May 2001

Kouwenhoven, L. P.; Austing, D. G.; Tarucha, S.
Reports on Progress in Physics, Vol. 64, Issue 6
DOI: 10.1088/0034-4885/64/6/201

Quantized conductance of point contacts in a two-dimensional electron gas
journal, February 1988

van Wees, B. J.; van Houten, H.; Beenakker, C. W. J.
Physical Review Letters, Vol. 60, Issue 9
DOI: 10.1103/PhysRevLett.60.848

Nonuniversal Conductance Quantization in Quantum Wires
journal, November 1996

Yacoby, A.; Stormer, H. L.; Wingreen, Ned S.
Physical Review Letters, Vol. 77, Issue 22
DOI: 10.1103/PhysRevLett.77.4612

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models
journal, December 1988

Affleck, Ian
Nuclear Physics B, Vol. 305, Issue 4
DOI: 10.1016/0550-3213(88)90117-4

Landauer conductance of Luttinger liquids with leads
journal, August 1995

Maslov, Dmitrii L.; Stone, Michael
Physical Review B, Vol. 52, Issue 8
DOI: 10.1103/PhysRevB.52.R5539

Oxide Nanoelectronics on Demand
journal, February 2009

Cen, C.; Thiel, S.; Mannhart, J.
Science, Vol. 323, Issue 5917
DOI: 10.1126/science.1168294

The density-matrix renormalization group
journal, April 2005

Schollwöck, U.
Reviews of Modern Physics, Vol. 77, Issue 1
DOI: 10.1103/RevModPhys.77.259

Electron attraction mediated by Coulomb repulsion
journal, July 2016

Hamo, A.; Benyamini, A.; Shapir, I.
Nature, Vol. 535, Issue 7612
DOI: 10.1038/nature18639

Spin-imbalance in a one-dimensional Fermi gas
journal, September 2010

Liao, Yean-an; Rittner, Ann Sophie C.; Paprotta, Tobias
Nature, Vol. 467, Issue 7315
DOI: 10.1038/nature09393

Finding the Elusive Sliding Phase in the Superfluid-Normal Phase Transition Smeared by $c$ -Axis Disorder
journal, August 2010

Pekker, David; Refael, Gil; Demler, Eugene
Physical Review Letters, Vol. 105, Issue 8
DOI: 10.1103/PhysRevLett.105.085302

From density-matrix renormalization group to matrix product states
journal, October 2007

McCulloch, Ian P.
Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, Issue 10
DOI: 10.1088/1742-5468/2007/10/P10014

Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points
journal, June 2009

Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M.
Physical Review Letters, Vol. 102, Issue 25
DOI: 10.1103/PhysRevLett.102.255701

Anomalously Elastic Intermediate Phase in Randomly Layered Superfluids, Superconductors, and Planar Magnets
journal, August 2010

Mohan, Priyanka; Goldbart, Paul M.; Narayanan, Rajesh
Physical Review Letters, Vol. 105, Issue 8
DOI: 10.1103/PhysRevLett.105.085301

“Water-cycle” mechanism for writing and erasing nanostructures at the LaAlO3/SrTiO3 interface
journal, October 2010

Bi, Feng; Bogorin, Daniela F.; Cen, Cheng
Applied Physics Letters, Vol. 97, Issue 17
DOI: 10.1063/1.3506509

Quantized Ballistic Transport of Electrons and Electron Pairs in LaAlO ₃ /SrTiO ₃ Nanowires
journal, June 2018

Annadi, Anil; Cheng, Guanglei; Lee, Hyungwoo
Nano Letters, Vol. 18, Issue 7
DOI: 10.1021/acs.nanolett.8b01614

Evidence for Efimov quantum states in an ultracold gas of caesium atoms
journal, March 2006

Kraemer, T.; Mark, M.; Waldburger, P.
Nature, Vol. 440, Issue 7082
DOI: 10.1038/nature04626

Nanoscale control of an interfacial metal–insulator transition at room temperature
journal, March 2008

Cen, C.; Thiel, S.; Hammerl, G.
Nature Materials, Vol. 7, Issue 4
DOI: 10.1038/nmat2136

Fermi gases in one dimension: From Bethe ansatz to experiments
journal, November 2013

Guan, Xi-Wen; Batchelor, Murray T.; Lee, Chaohong
Reviews of Modern Physics, Vol. 85, Issue 4
DOI: 10.1103/RevModPhys.85.1633

Density matrix formulation for quantum renormalization groups
journal, November 1992

White, Steven R.
Physical Review Letters, Vol. 69, Issue 19
DOI: 10.1103/PhysRevLett.69.2863

Carbon Nanotube Quantum Resistors
journal, June 1998

Frank, S.
Science, Vol. 280, Issue 5370
DOI: 10.1126/science.280.5370.1744

Giant conductivity switching of LaAlO3/SrTiO3 heterointerfaces governed by surface protonation
journal, February 2016

Brown, Keith A.; He, Shu; Eichelsdoerfer, Daniel J.
Nature Communications, Vol. 7, Issue 1
DOI: 10.1038/ncomms10681

Model for the Electronic Structure of Amorphous Semiconductors
journal, April 1975

Anderson, P. W.
Physical Review Letters, Vol. 34, Issue 15
DOI: 10.1103/PhysRevLett.34.953

Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction
journal, July 1957

Landauer, R.
IBM Journal of Research and Development, Vol. 1, Issue 3
DOI: 10.1147/rd.13.0223

Phase diagram of the anisotropic spin-2 XXZ model: Infinite-system density matrix renormalization group study
journal, June 2013

Kjäll, Jonas A.; Zaletel, Michael P.; Mong, Roger S. K.
Physical Review B, Vol. 87, Issue 23
DOI: 10.1103/PhysRevB.87.235106

Electron pairing without superconductivity
journal, May 2015

Cheng, Guanglei; Tomczyk, Michelle; Lu, Shicheng
Nature, Vol. 521, Issue 7551
DOI: 10.1038/nature14398

Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems
journal, July 1950

Tomonaga, S. -i.
Progress of Theoretical Physics, Vol. 5, Issue 4
DOI: 10.1143/ptp/5.4.544

An Exactly Soluble Model of a Many‐Fermion System
journal, September 1963

Luttinger, J. M.
Journal of Mathematical Physics, Vol. 4, Issue 9
DOI: 10.1063/1.1704046

Quantized Conductance in an InSb Nanowire
journal, December 2012

van Weperen, Ilse; Plissard, Sébastien R.; Bakkers, Erik P. A. M.
Nano Letters, Vol. 13, Issue 2
DOI: 10.1021/nl3035256

Direct observation of a fractional charge
journal, September 1997

de-Picciotto, R.; Reznikov, M.; Heiblum, M.
Nature, Vol. 389, Issue 6647
DOI: 10.1038/38241

Color Superfluidity and “Baryon” Formation in Ultracold Fermions
journal, April 2007

Rapp, Ákos; Zaránd, Gergely; Honerkamp, Carsten
Physical Review Letters, Vol. 98, Issue 16
DOI: 10.1103/PhysRevLett.98.160405

Tunable Electron-Electron Interactions in ${LaAlO}_{3} / {SrTiO}_{3}$ Nanostructures
journal, December 2016

Cheng, Guanglei; Tomczyk, Michelle; Tacla, Alexandre B.
Physical Review X, Vol. 6, Issue 4
DOI: 10.1103/PhysRevX.6.041042

Exact Solution of a Many‐Fermion System and Its Associated Boson Field
journal, February 1965

Mattis, Daniel C.; Lieb, Elliott H.
Journal of Mathematical Physics, Vol. 6, Issue 2
DOI: 10.1063/1.1704281

Sliding Phases in $XY$ Models, Crystals, and Cationic Lipid-DNA Complexes
journal, October 1999

O'Hern, C. S.; Lubensky, T. C.; Toner, J.
Physical Review Letters, Vol. 83, Issue 14
DOI: 10.1103/PhysRevLett.83.2745

Pairing in Luttinger Liquids and Quantum Hall States
journal, July 2017

Kane, Charles L.; Stern, Ady; Halperin, Bertrand I.
Physical Review X, Vol. 7, Issue 3
DOI: 10.1103/PhysRevX.7.031009

One-dimensional transport and the quantisation of the ballistic resistance
journal, March 1988

Wharam, D. A.; Thornton, T. J.; Newbury, R.
Journal of Physics C: Solid State Physics, Vol. 21, Issue 8
DOI: 10.1088/0022-3719/21/8/002

Similar Records in DOE PAGES and OSTI.GOV collections:

Electro- and Magnetotransport near a LaAlO{sub 3}/SrTiO{sub 3} Interphase Boundary

Journal Article Boikov, Yu. A., E-mail: yu.boikov@mail.ioffe.ru ; Danilov, V. A. ; Serenkov, I. T. ; ... - Physics of the Solid State

Comparison of the channel spectra of medium energy ion scattering, visualized for LaAlO{sub 3}/(001)SrTiO{sub 3} heterostructures with a thickness of the lanthanum aluminate layer of one to six unit cells, indicates that the lanthanum aluminate layer grows coherently on a TiO{sub 2}-terminated surface of a strontium titanate substrate. The resistance of the interphase boundary in the heterostructure with a thickness of the LaAlO{sub 3} layer of six unit cells decreased with temperature. At T < 100 K, the positive magnetoresistance and Hall mobility of electrons increased sharply with decreasing temperature.
DOI: 10.1134/S1063783418060082
Electrostatically tuned dimensional crossover in LaAlO ₃/SrTiO ₃ heterostructures

Journal Article Tomczyk, Michelle ; Zhou, Rongpu ; Lee, Hyungwoo ; ... - APL Materials

We report a gate-tunable dimensional crossover in sub-micrometer-scale channels created at the LaAlO ₃/SrTiO ₃ interface. Conducting channels of widths 10 nm and 200 nm are created using conducting atomic force microscope lithography. Under sufficient negative back-gate tuning, the orbital magnetoconductance of the 200 nm channel is strongly quenched, and residual signatures of low-field weak-antilocalization become strikingly similar to that of the 10 nm channel. The dimensional crossover for the 200 nm channel takes place near the conductance quantum G = 2e ²/h. The ability to tune the dimensionality of narrow LaAlO ₃/SrTiO ₃ channels has implications for interpreting transportmore »« less
Cited by 1
DOI: 10.1063/1.4999804

Full Text Available
Sol-gel synthesis of LaAlO{sub 3}; epitaxial growth of LaAlO{sub 3} thin films on SrTiO{sub 3} (100)

Journal Article Shoup, S S ; Paranthaman, M ; Beach, D B ; ... - Journal of Materials Research

A LaAlO{sub 3} precursor solution was prepared via an all alkoxide sol-gel route. The solution of lanthanum methoxyethoxide and aluminum methoxyethoxide in 2-methoxyethanol was prepared via ligand exchange starting from lanthanum isopropoxide and aluminum sec-butoxide and was used to make both LaAlO{sub 3} powders and films. Complete hydrolysis of the solution formed a gel that yielded well-crystallized LaAlO{sub 3} powders when fired in air at 800{degree}C. A partially hydrolyzed solution was spun-cast on SrTiO{sub 3} (100) single crystal substrates. Epitaxial films of LaAlO{sub 3} were subsequently formed during pyrolysis in O{sub 2} at 800{degree}C in a rapid thermal annealing furnacemore »« less
DOI: 10.1557/JMR.1997.0142
Improvement in performance of electrically tunable devices based on nonlinear dielectric SrTiO{sub 3} using a homoepitaxial LaAlO{sub 3} interlayer

Journal Article Jia, Q X ; Findikoglu, A T ; Reagor, D ; ... - Applied Physics Letters

Improved structural and dielectric properties of nonlinear dielectric SrTiO{sub 3} thin films on LaAlO{sub 3} substrates were accomplished by incorporating a {ital homoepitaxial} LaAlO{sub 3} interlayer between the substrate and the dielectric film. Using this interlayer, the quality factor of SrTiO{sub 3} films with high-temperature superconducting YBa{sub 2}Cu{sub 3}O{sub 7{minus}x} electrodes on LaAlO{sub 3} substrates was improved by more than 50{percent} at 4.2 GHz and 4 K. This improvement, combined with no change in nonlinearity, led to greater than a 50{percent} enhancement of the finesse factor (defined as the product of the quality factor and the fractional shift resonant frequency)more »« less
DOI: 10.1063/1.122031
Tailoring a two-dimensional electron gas at the LaAlO{sub 3}/SrTiO{sub 3} (001) interface by epitaxial strain.

Journal Article Bark, C W ; Felker, D A ; Wang, Y ; ... - Proc. Natl. Acad. Sci. U.S.A.

Recently a metallic state was discovered at the interface between insulating oxides, most notably LaAlO{sub 3} and SrTiO{sub 3}. Properties of this two-dimensional electron gas (2DEG) have attracted significant interest due to its potential applications in nanoelectronics. Control over this carrier density and mobility of the 2DEG is essential for applications of these unique systems, and may be achieved by epitaxial strain. However, despite the rich nature of strain effects on oxide materials properties, such as ferroelectricity, magnetism, and superconductivity, the relationship between the strain and electrical properties of the 2DEG at the LaAlO{sub 3}/SrTiO{sub 3} heterointerface remains largely unexplored.more »« less
DOI: 10.1073/pnas.1014849108

Similar Records

Title: Pascal conductance series in ballistic one-dimensional LaAlO 3 /SrTiO 3 channels

Abstract

Citation Formats

Few-electron quantum dots journal, May 2001

Quantized conductance of point contacts in a two-dimensional electron gas journal, February 1988

Nonuniversal Conductance Quantization in Quantum Wires journal, November 1996

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models journal, December 1988

Landauer conductance of Luttinger liquids with leads journal, August 1995

Oxide Nanoelectronics on Demand journal, February 2009

The density-matrix renormalization group journal, April 2005

Electron attraction mediated by Coulomb repulsion journal, July 2016

Spin-imbalance in a one-dimensional Fermi gas journal, September 2010

Finding the Elusive Sliding Phase in the Superfluid-Normal Phase Transition Smeared by c -Axis Disorder journal, August 2010

From density-matrix renormalization group to matrix product states journal, October 2007

Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points journal, June 2009

Anomalously Elastic Intermediate Phase in Randomly Layered Superfluids, Superconductors, and Planar Magnets journal, August 2010

“Water-cycle” mechanism for writing and erasing nanostructures at the LaAlO3/SrTiO3 interface journal, October 2010

Quantized Ballistic Transport of Electrons and Electron Pairs in LaAlO 3 /SrTiO 3 Nanowires journal, June 2018

Evidence for Efimov quantum states in an ultracold gas of caesium atoms journal, March 2006

Nanoscale control of an interfacial metal–insulator transition at room temperature journal, March 2008

Fermi gases in one dimension: From Bethe ansatz to experiments journal, November 2013

Density matrix formulation for quantum renormalization groups journal, November 1992

Carbon Nanotube Quantum Resistors journal, June 1998

Giant conductivity switching of LaAlO3/SrTiO3 heterointerfaces governed by surface protonation journal, February 2016

Model for the Electronic Structure of Amorphous Semiconductors journal, April 1975

Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction journal, July 1957

Phase diagram of the anisotropic spin-2 XXZ model: Infinite-system density matrix renormalization group study journal, June 2013

Electron pairing without superconductivity journal, May 2015

Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems journal, July 1950

An Exactly Soluble Model of a Many‐Fermion System journal, September 1963

Quantized Conductance in an InSb Nanowire journal, December 2012

Direct observation of a fractional charge journal, September 1997

Color Superfluidity and “Baryon” Formation in Ultracold Fermions journal, April 2007

Tunable Electron-Electron Interactions in LaAlO 3 / SrTiO 3 Nanostructures journal, December 2016

Exact Solution of a Many‐Fermion System and Its Associated Boson Field journal, February 1965

Sliding Phases in XY Models, Crystals, and Cationic Lipid-DNA Complexes journal, October 1999

Pairing in Luttinger Liquids and Quantum Hall States journal, July 2017

One-dimensional transport and the quantisation of the ballistic resistance journal, March 1988

Title: Pascal conductance series in ballistic one-dimensional LaAlO ₃ /SrTiO ₃ channels

Few-electron quantum dots
journal, May 2001

Quantized conductance of point contacts in a two-dimensional electron gas
journal, February 1988

Nonuniversal Conductance Quantization in Quantum Wires
journal, November 1996

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models
journal, December 1988

Landauer conductance of Luttinger liquids with leads
journal, August 1995

Oxide Nanoelectronics on Demand
journal, February 2009

The density-matrix renormalization group
journal, April 2005

Electron attraction mediated by Coulomb repulsion
journal, July 2016

Spin-imbalance in a one-dimensional Fermi gas
journal, September 2010

Finding the Elusive Sliding Phase in the Superfluid-Normal Phase Transition Smeared by $c$ -Axis Disorder
journal, August 2010

From density-matrix renormalization group to matrix product states
journal, October 2007

Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points
journal, June 2009

Anomalously Elastic Intermediate Phase in Randomly Layered Superfluids, Superconductors, and Planar Magnets
journal, August 2010

“Water-cycle” mechanism for writing and erasing nanostructures at the LaAlO3/SrTiO3 interface
journal, October 2010

Quantized Ballistic Transport of Electrons and Electron Pairs in LaAlO ₃ /SrTiO ₃ Nanowires
journal, June 2018

Evidence for Efimov quantum states in an ultracold gas of caesium atoms
journal, March 2006

Nanoscale control of an interfacial metal–insulator transition at room temperature
journal, March 2008

Fermi gases in one dimension: From Bethe ansatz to experiments
journal, November 2013

Density matrix formulation for quantum renormalization groups
journal, November 1992

Carbon Nanotube Quantum Resistors
journal, June 1998

Giant conductivity switching of LaAlO3/SrTiO3 heterointerfaces governed by surface protonation
journal, February 2016

Model for the Electronic Structure of Amorphous Semiconductors
journal, April 1975

Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction
journal, July 1957

Phase diagram of the anisotropic spin-2 XXZ model: Infinite-system density matrix renormalization group study
journal, June 2013

Electron pairing without superconductivity
journal, May 2015

Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems
journal, July 1950

An Exactly Soluble Model of a Many‐Fermion System
journal, September 1963

Quantized Conductance in an InSb Nanowire
journal, December 2012

Direct observation of a fractional charge
journal, September 1997

Color Superfluidity and “Baryon” Formation in Ultracold Fermions
journal, April 2007

Tunable Electron-Electron Interactions in ${LaAlO}_{3} / {SrTiO}_{3}$ Nanostructures
journal, December 2016

Exact Solution of a Many‐Fermion System and Its Associated Boson Field
journal, February 1965

Sliding Phases in $XY$ Models, Crystals, and Cationic Lipid-DNA Complexes
journal, October 1999

Pairing in Luttinger Liquids and Quantum Hall States
journal, July 2017

One-dimensional transport and the quantisation of the ballistic resistance
journal, March 1988