Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x

doi:https://doi.org/10.1038/nature17411

Title: Detection of a Cooper-pair density wave in Bi ₂Sr ₂CaCu ₂O _8+x

Abstract

The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold ⁶Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a ‘pair density wave’ state. In this paper we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi ₂Sr ₂CaCu ₂O _8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi ₂Sr ₂CaCu ₂O _8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors Q _P ≈ (0.25, 0)2π/a ₀ and (0, 0.25)2π/a ₀ in Bi ₂Sr ₂CaCu ₂O _8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. Finally, thismore »« less

Authors:

Hamidian, M. H. ^[1]; Edkins, S. D. ^[2]; Joo, Sang Hyun ^[3]; Kostin, A. ^[4]; Eisaki, H. ^[5]; Uchida, S. ^[6]; Lawler, M. J. ^[7]; Kim, E. -A. ^[4]; Mackenzie, A. P. ^[8]; Fujita, K. ^[9]; Lee, Jinho ^[3]; Davis, J. C. Seamus ^[10]

Harvard Univ., Cambridge, MA (United States). Dept. of Physics
Cornell Univ., Ithaca, NY (United States). Dept. of Physics. Lab. of Atomic and Solid State Physics; Univ. of St. Andrews, Scotland (United Kingdom). School of Physics and Astronomy
Seoul National Univ. (Korea, Republic of). Dept. of Physics and Astronomy. Inst. of Applied Physics; Inst. of Basic Science, Seoul (Korea, Republic of). Center for Correlated Electron Systems
Cornell Univ., Ithaca, NY (United States). Dept. of Physics. Lab. of Atomic and Solid State Physics
Inst. of Advanced Industrial Science and Technology, Tsukuba (Japan)
Inst. of Advanced Industrial Science and Technology, Tsukuba (Japan); Univ. of Tokyo (Japan). Dept. of Physics
Cornell Univ., Ithaca, NY (United States). Dept. of Physics. Lab. of Atomic and Solid State Physics; Binghamton Univ., NY (United States). Dept. of Physics
Univ. of St. Andrews, Scotland (United Kingdom). School of Physics and Astronomy; Max Planck Inst. for Chemical Physics of Solids, Dresden (Germany)
Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.
Cornell Univ., Ithaca, NY (United States). Dept. of Physics. Lab. of Atomic and Solid State Physics. Kavli Inst. at Cornell for Nanoscale Science; Univ. of St. Andrews, Scotland (United Kingdom). School of Physics and Astronomy; Brookhaven National Lab. (BNL), Upton, NY (United States). Condensed Matter Physics and Materials Science Dept.

Publication Date:: 2016-04-13

Research Org.:: Brookhaven National Lab. (BNL), Upton, NY (United States); Cornell Univ., Ithaca, NY (United States); Seoul National Univ. (Korea, Republic of); Univ. of St. Andrews, Scotland (United Kingdom); Inst. of Advanced Industrial Science and Technology, Tsukuba (Japan)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Moore Foundation (United States); Engineering and Physical Sciences Research Council (EPSRC); Ministry of Science and Education (Japan); Institute for Basic Science (Korea, Republic of)

Contributing Org.:: Harvard Univ., Cambridge, MA (United States); Inst. of Basic Science, Seoul (Korea, Republic of); Univ. of Tokyo (Japan); Binghamton Univ., NY (United States); Max Planck Inst. for Chemical Physics of Solids, Dresden (Germany)

OSTI Identifier:: 1341670

Report Number(s):: BNL-113397-2016-JA
Journal ID: ISSN 0028-0836; R&D Project: PM007; KC0201010

Grant/Contract Number:: AC02-98CH10886; SC0010313; GBMF4544; EP/G03673X/1; IBS-R009-D1

Resource Type:: Journal Article: Accepted Manuscript

Journal Name:: Nature (London)

Additional Journal Information:: Journal Volume: 532; Journal Issue: 7599; Journal ID: ISSN 0028-0836

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; superconducting properties and materials; electronic properties and materials

Citation Formats


                    Hamidian, M. H., Edkins, S. D., Joo, Sang Hyun, Kostin, A., Eisaki, H., Uchida, S., Lawler, M. J., Kim, E. -A., Mackenzie, A. P., Fujita, K., Lee, Jinho, and Davis, J. C.  Seamus. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x.  United States: N. p., 2016. 
        Web.  doi:10.1038/nature17411.

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                    Hamidian, M. H., Edkins, S. D., Joo, Sang Hyun, Kostin, A., Eisaki, H., Uchida, S., Lawler, M. J., Kim, E. -A., Mackenzie, A. P., Fujita, K., Lee, Jinho, & Davis, J. C.  Seamus. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x.  United States.  https://doi.org/10.1038/nature17411

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                    Hamidian, M. H., Edkins, S. D., Joo, Sang Hyun, Kostin, A., Eisaki, H., Uchida, S., Lawler, M. J., Kim, E. -A., Mackenzie, A. P., Fujita, K., Lee, Jinho, and Davis, J. C.  Seamus. Wed .  
        "Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x".  United States.  https://doi.org/10.1038/nature17411.  https://www.osti.gov/servlets/purl/1341670.

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@article{osti_1341670,

  title        = {Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x},

  author       = {Hamidian, M. H. and Edkins, S. D. and Joo, Sang Hyun and Kostin, A. and Eisaki, H. and Uchida, S. and Lawler, M. J. and Kim, E. -A. and Mackenzie, A. P. and Fujita, K. and Lee, Jinho and Davis, J. C.  Seamus},

  abstractNote = {The quantum condensate of Cooper pairs forming a superconductor was originally conceived as being translationally invariant. In theory, however, pairs can exist with finite momentum Q, thus generating a state with a spatially modulated Cooper-pair density. Such a state has been created in ultracold 6Li gas but never observed directly in any superconductor. It is now widely hypothesized that the pseudogap phase of the copper oxide superconductors contains such a ‘pair density wave’ state. In this paper we report the use of nanometre-resolution scanned Josephson tunnelling microscopy to image Cooper pair tunnelling from a d-wave superconducting microscope tip to the condensate of the superconductor Bi2Sr2CaCu2O8+x. We demonstrate condensate visualization capabilities directly by using the Cooper-pair density variations surrounding zinc impurity atoms and at the Bi2Sr2CaCu2O8+x crystal supermodulation. Then, by using Fourier analysis of scanned Josephson tunnelling images, we discover the direct signature of a Cooper-pair density modulation at wavevectors QP ≈ (0.25, 0)2π/a0 and (0, 0.25)2π/a0 in Bi2Sr2CaCu2O8+x. The amplitude of these modulations is about five per cent of the background condensate density and their form factor exhibits primarily s or s' symmetry. Finally, this phenomenology is consistent with Ginzburg–Landau theory when a charge density wave with d-symmetry form factor and wavevector QC = QP coexists with a d-symmetry superconductor; it is also predicted by several contemporary microscopic theories for the pseudogap phase.},

  doi          = {10.1038/nature17411},

  url          = {https://www.osti.gov/biblio/1341670},
  journal      = {Nature (London)},

  issn         = {0028-0836},

  number       = 7599,

  volume       = 532,

  place        = {United States},

  year         = {2016},

  month        = {4}

}

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Remarkable Stability of Charge Density Wave Order in ${La}_{1.875} {Ba}_{0.125} {CuO}_{4}$
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Chen, X. M.; Thampy, V.; Mazzoli, C.
Physical Review Letters, Vol. 117, Issue 16
https://doi.org/10.1103/physrevlett.117.167001

Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves
journal, November 2017

Cai, Rong-Gen; Li, Li; Wang, Yong-Qiang
Physical Review Letters, Vol. 119, Issue 18
https://doi.org/10.1103/physrevlett.119.181601

Magnetic-Field Tuning of Light-Induced Superconductivity in Striped ${La}_{2 - x} {Ba}_{x} {CuO}_{4}$
journal, December 2018

Nicoletti, D.; Fu, D.; Mehio, O.
Physical Review Letters, Vol. 121, Issue 26
https://doi.org/10.1103/physrevlett.121.267003

Evidence for a Spatially Modulated Superfluid Phase of ${}^{3}{He}$ under Confinement
journal, February 2019

Levitin, Lev V.; Yager, Ben; Sumner, Laura
Physical Review Letters, Vol. 122, Issue 8
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Pressure-Induced Collapse of the Charge Density Wave and Higgs Mode Visibility in $2 H − {TaS}_{2}$
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Grasset, Romain; Gallais, Yann; Sacuto, Alain
Physical Review Letters, Vol. 122, Issue 12
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Josephson Scanning Tunneling Spectroscopy in $d_{x^{2} - y^{2}}$ -Wave Superconductors: A Probe for the Nature of the Pseudogap in the Cuprate Superconductors
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Graham, Martin; Morr, Dirk K.
Physical Review Letters, Vol. 123, Issue 1
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Quasiclassical circuit theory of contiguous disordered multiband superconductors
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Kirmani, Ammar A.; Dzero, Maxim; Levchenko, Alex
Physical Review Research, Vol. 1, Issue 3
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Intertwined Orders in Heavy-Fermion Superconductor ${CeCoIn}_{5}$
journal, December 2016

Kim, Duk Y.; Lin, Shi-Zeng; Weickert, Franziska
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Evidence of pair-density wave in spin-valley locked systems
journal, March 2019

Venderley, Jordan; Kim, Eun-Ah
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Ultrafast time-resolved x-ray scattering reveals diffusive charge order dynamics in La _{2– x} Ba _x CuO ₄
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Mitrano, Matteo; Lee, Sangjun; Husain, Ali A.
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Probing optically silent superfluid stripes in cuprates
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Magnetic field–induced pair density wave state in the cuprate vortex halo
journal, June 2019

Edkins, S. D.; Kostin, A.; Fujita, K.
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https://doi.org/10.1126/science.aat1773

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The defining characteristic of Cooper pairs with finite center-of-mass momentum is a spatially modulating superconducting energy gap Δ(r). Recently, this concept has been generalized to the pair density wave (PDW) state predicted to exist in cuprates. Although the signature of a cuprate PDW has been detected in Cooperpair tunneling, the distinctive signature in single-electron tunneling of a periodic Δ(r) modulation has never been observed. Here, using a new approach, we discover strong Δ(r) modulations in Bi ₂Sr ₂CaCu ₂O _8+δ that have eight-unit-cell periodicity or wavevectors Q ≈ (2π/a0)(1/8, 0) and Q ≈ (2π/a0)(0, 1/8). Simultaneous imaging of the localdensity-more »« less
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Theories based upon strong real space (r-space) electron–electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4 _a0) periodicity should occur in the hole-doped cuprate Mott insulator (MI). But, increasing the hole density p is reported to cause the conventionally defined wavevector Q _A of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. We introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at |Q ₀|=2π/4 _a0 throughout the underdoped phase diagram of the canonicalmore »« less
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Title: Detection of a Cooper-pair density wave in Bi 2Sr 2CaCu 2O 8+x

Abstract

Citation Formats

Superconductivity in a Strong Spin-Exchange Field journal, August 1964

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

The electronic nature of high temperature cuprate superconductors journal, September 2003

Colloquium : Theory of intertwined orders in high temperature superconductors journal, May 2015

Stripe States with Spatially Oscillating d -Wave Superconductivity in the Two-Dimensional t − t ′ − J Model journal, February 2002

Unidirectional d -wave superconducting domains in the two-dimensional t − J model journal, October 2007

Nature of stripes in the generalized t – J model applied to the cuprate superconductors journal, May 2009

Mean-Field Pairing Theory for the Charge-Stripe Phase of High-Temperature Cuprate Superconductors journal, October 2011

Competing States in the t - J Model: Uniform d -Wave State versus Stripe State journal, July 2014

Dynamical Layer Decoupling in a Stripe-Ordered High- T c Superconductor journal, September 2007

Complementary pair-density-wave and d -wave-checkerboard orderings in high-temperature superconductors journal, September 2008

Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors journal, September 2009

Dislocations and vortices in pair-density-wave superconductors journal, June 2008

Quantum oscillations in a π -striped superconductor journal, September 2012

Pair Density Wave in the Pseudogap State of High Temperature Superconductors journal, October 2004

Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors journal, November 2014

Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors journal, July 2015

Interplay between pair- and charge-density-wave orders in underdoped cuprates journal, March 2015

Coexistence of Charge-Density-Wave and Pair-Density-Wave Orders in Underdoped Cuprates journal, May 2015

Fluctuation Dominated Josephson Tunneling with a Scanning Tunneling Microscope journal, August 2001

On the use of STM superconducting tips at very low temperatures journal, August 2004

Probing the superconducting condensate on a nanometer scale journal, March 2006

Muon Spin Relaxation Studies of Zn-Substitution Effects in High- T c Cuprate Superconductors journal, December 1996

Imaging the impact on cuprate superconductivity of varying the interatomic distances within individual crystal unit cells journal, February 2008

Resonant X-Ray Scattering Studies of Charge Order in Cuprates journal, March 2016

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates journal, July 2014

Symmetry of charge order in cuprates journal, May 2015

The microscopic structure of charge density waves in underdoped YBa2Cu3O6.54 revealed by X-ray diffraction journal, December 2015

Possible new effects in superconductive tunnelling journal, July 1962

Voltage Due to Thermal Noise in the dc Josephson Effect journal, June 1969

Effect of the electromagnetic environment on the Coulomb blockade in ultrasmall tunnel junctions journal, April 1990

Quantum Tunnelling in Small-Capacitance Josephson Junctions in a General Electromagnetic Environment journal, September 1991

Classical phase diffusion in small hysteretic Josephson junctions journal, October 1989

Charging effects and quantum properties of small superconducting tunnel junctions journal, April 1989

Josephson scanning tunneling microscopy journal, November 2001

Spectroscopic Imaging Scanning Tunneling Microscopy Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High- T c Superconductors journal, January 2012

Picometer registration of zinc impurity states in Bi 2 Sr 2 CaCu 2 O 8+ δ for phase determination in intra-unit-cell Fourier transform STM journal, May 2012

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state journal, October 2015

Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking journal, May 2014

Bond Order in Two-Dimensional Metals with Antiferromagnetic Exchange Interactions journal, July 2013

Evidence for a vestigial nematic state in the cuprate pseudogap phase journal, June 2019

Chiral superconductivity in heavy-fermion metal UTe2 journal, March 2020

Evidence for a vestigial nematic state in the cuprate pseudogap phase journal, June 2019

Dual gauge field theory of quantum liquid crystals in three dimensions journal, October 2017

Effective SU(2) theory for the pseudogap state journal, March 2017

Hidden Pair-Density-Wave Order in Cuprate Superconductors journal, January 2019

Diagonal nematicity in the pseudogap phase of HgBa2CuO4+δ journal, July 2019

Quantum engineered Kondo lattices journal, December 2019

Doping the holographic Mott insulator journal, July 2018

Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor journal, September 2018

A strongly inhomogeneous superfluid in an iron-based superconductor journal, July 2019

Electron pairing in the pseudogap state revealed by shot noise in copper oxide junctions journal, August 2019

High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ journal, October 2019

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors journal, February 2019

Magnetic phase diagram of underdoped YBa 2 Cu 3 O y inferred from torque magnetization and thermal conductivity journal, October 2016

Quantum oscillations in a biaxial pair density wave state journal, May 2018

Fulde–Ferrell state in superconducting core/shell nanowires: role of the orbital effect journal, November 2017

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy journal, October 2019

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering journal, October 2019

Incommensurate charge ordered states in the t – t ′– J model journal, January 2017

Stability of the coexistent superconducting-nematic phase under the presence of intersite interactions journal, June 2018

Odd-frequency pairing in a superconductor coupled to two parallel nanowires journal, July 2019

Theory of triangular lattice quasi-one-dimensional charge-transfer solids journal, September 2019

Intrinsic cluster-shaped density waves in cellular dynamical mean-field theory journal, December 2019

Selective hybridization between the main band and the superstructure band in the Bi 2 Sr 2 CaCu 2 O 8 + δ superconductor journal, January 2020

Topological density-wave states in a particle-hole symmetric Weyl metal journal, August 2016

Subgap structures and pseudogap in cuprate superconductors: Role of density waves journal, February 2017

Collective mode contributions to the Meissner effect: Fulde-Ferrell and pair-density wave superfluids journal, June 2017

Correlation-driven metal-insulator transition in proximity to an iron-based superconductor journal, November 2017

Multiparticle instability in a spin-imbalanced Fermi gas journal, January 2018

Pair density waves in superconducting vortex halos journal, May 2018

Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides journal, November 2018

Coexistence of superconductivity and antiferromagnetism in the Hubbard model for cuprates journal, May 2019

Remarkable Stability of Charge Density Wave Order in La 1.875 Ba 0.125 CuO 4 journal, October 2016

Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves journal, November 2017

Magnetic-Field Tuning of Light-Induced Superconductivity in Striped La 2 − x Ba x CuO 4 journal, December 2018

Evidence for a Spatially Modulated Superfluid Phase of He 3 under Confinement journal, February 2019

Title: Detection of a Cooper-pair density wave in Bi ₂Sr ₂CaCu ₂O _8+x

Superconductivity in a Strong Spin-Exchange Field
journal, August 1964

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

The electronic nature of high temperature cuprate superconductors
journal, September 2003

Colloquium : Theory of intertwined orders in high temperature superconductors
journal, May 2015

Stripe States with Spatially Oscillating $d$ -Wave Superconductivity in the Two-Dimensional $t - t^{'} - J$ Model
journal, February 2002

Unidirectional $d$ -wave superconducting domains in the two-dimensional $t − J$ model
journal, October 2007

Nature of stripes in the generalized t – J model applied to the cuprate superconductors
journal, May 2009

Mean-Field Pairing Theory for the Charge-Stripe Phase of High-Temperature Cuprate Superconductors
journal, October 2011

Competing States in the $t$ - $J$ Model: Uniform $d$ -Wave State versus Stripe State
journal, July 2014

Dynamical Layer Decoupling in a Stripe-Ordered High- $T_{c}$ Superconductor
journal, September 2007

Complementary pair-density-wave and $d$ -wave-checkerboard orderings in high-temperature superconductors
journal, September 2008

Charge-4e superconductivity from pair-density-wave order in certain high-temperature superconductors
journal, September 2009

Dislocations and vortices in pair-density-wave superconductors
journal, June 2008

Quantum oscillations in a $π$ -striped superconductor
journal, September 2012

Pair Density Wave in the Pseudogap State of High Temperature Superconductors
journal, October 2004

Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors
journal, November 2014

Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors
journal, July 2015

Interplay between pair- and charge-density-wave orders in underdoped cuprates
journal, March 2015

Coexistence of Charge-Density-Wave and Pair-Density-Wave Orders in Underdoped Cuprates
journal, May 2015

Fluctuation Dominated Josephson Tunneling with a Scanning Tunneling Microscope
journal, August 2001

On the use of STM superconducting tips at very low temperatures
journal, August 2004

Probing the superconducting condensate on a nanometer scale
journal, March 2006

Muon Spin Relaxation Studies of Zn-Substitution Effects in High- $T_{c}$ Cuprate Superconductors
journal, December 1996

Imaging the impact on cuprate superconductivity of varying the interatomic distances within individual crystal unit cells
journal, February 2008

Resonant X-Ray Scattering Studies of Charge Order in Cuprates
journal, March 2016

Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
journal, July 2014

Symmetry of charge order in cuprates
journal, May 2015

The microscopic structure of charge density waves in underdoped YBa2Cu3O6.54 revealed by X-ray diffraction
journal, December 2015

Possible new effects in superconductive tunnelling
journal, July 1962

Voltage Due to Thermal Noise in the dc Josephson Effect
journal, June 1969

Effect of the electromagnetic environment on the Coulomb blockade in ultrasmall tunnel junctions
journal, April 1990

Quantum Tunnelling in Small-Capacitance Josephson Junctions in a General Electromagnetic Environment
journal, September 1991

Classical phase diffusion in small hysteretic Josephson junctions
journal, October 1989

Charging effects and quantum properties of small superconducting tunnel junctions
journal, April 1989

Josephson scanning tunneling microscopy
journal, November 2001

Spectroscopic Imaging Scanning Tunneling Microscopy Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High- T _c Superconductors
journal, January 2012

Picometer registration of zinc impurity states in Bi ₂ Sr ₂ CaCu ₂ O _{8+ δ} for phase determination in intra-unit-cell Fourier transform STM
journal, May 2012

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state
journal, October 2015

Simultaneous Transitions in Cuprate Momentum-Space Topology and Electronic Symmetry Breaking
journal, May 2014

Bond Order in Two-Dimensional Metals with Antiferromagnetic Exchange Interactions
journal, July 2013

Evidence for a vestigial nematic state in the cuprate pseudogap phase
journal, June 2019

Chiral superconductivity in heavy-fermion metal UTe2
journal, March 2020

Evidence for a vestigial nematic state in the cuprate pseudogap phase
journal, June 2019

Dual gauge field theory of quantum liquid crystals in three dimensions
journal, October 2017

Effective SU(2) theory for the pseudogap state
journal, March 2017

Hidden Pair-Density-Wave Order in Cuprate Superconductors
journal, January 2019

Diagonal nematicity in the pseudogap phase of HgBa2CuO4+δ
journal, July 2019

Quantum engineered Kondo lattices
journal, December 2019

Doping the holographic Mott insulator
journal, July 2018

Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor
journal, September 2018

A strongly inhomogeneous superfluid in an iron-based superconductor
journal, July 2019

Electron pairing in the pseudogap state revealed by shot noise in copper oxide junctions
journal, August 2019

High-temperature superconductivity in monolayer Bi2Sr2CaCu2O8+δ
journal, October 2019

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors
journal, February 2019

Magnetic phase diagram of underdoped YBa ₂ Cu ₃ O _y inferred from torque magnetization and thermal conductivity
journal, October 2016

Quantum oscillations in a biaxial pair density wave state
journal, May 2018

Fulde–Ferrell state in superconducting core/shell nanowires: role of the orbital effect
journal, November 2017

Charge ordering in high-temperature superconductors visualized by scanning tunneling microscopy
journal, October 2019

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering
journal, October 2019

Incommensurate charge ordered states in the t – t ′– J model
journal, January 2017

Stability of the coexistent superconducting-nematic phase under the presence of intersite interactions
journal, June 2018

Odd-frequency pairing in a superconductor coupled to two parallel nanowires
journal, July 2019

Theory of triangular lattice quasi-one-dimensional charge-transfer solids
journal, September 2019

Intrinsic cluster-shaped density waves in cellular dynamical mean-field theory
journal, December 2019

Selective hybridization between the main band and the superstructure band in the ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ superconductor
journal, January 2020

Topological density-wave states in a particle-hole symmetric Weyl metal
journal, August 2016

Subgap structures and pseudogap in cuprate superconductors: Role of density waves
journal, February 2017

Collective mode contributions to the Meissner effect: Fulde-Ferrell and pair-density wave superfluids
journal, June 2017

Correlation-driven metal-insulator transition in proximity to an iron-based superconductor
journal, November 2017

Multiparticle instability in a spin-imbalanced Fermi gas
journal, January 2018

Pair density waves in superconducting vortex halos
journal, May 2018

Valence transition model of the pseudogap, charge order, and superconductivity in electron-doped and hole-doped copper oxides
journal, November 2018

Coexistence of superconductivity and antiferromagnetism in the Hubbard model for cuprates
journal, May 2019

Remarkable Stability of Charge Density Wave Order in ${La}_{1.875} {Ba}_{0.125} {CuO}_{4}$
journal, October 2016

Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves
journal, November 2017

Magnetic-Field Tuning of Light-Induced Superconductivity in Striped ${La}_{2 - x} {Ba}_{x} {CuO}_{4}$
journal, December 2018

Evidence for a Spatially Modulated Superfluid Phase of ${}^{3}{He}$ under Confinement
journal, February 2019

Pressure-Induced Collapse of the Charge Density Wave and Higgs Mode Visibility in $2 H − {TaS}_{2}$
journal, March 2019

Josephson Scanning Tunneling Spectroscopy in $d_{x^{2} - y^{2}}$ -Wave Superconductors: A Probe for the Nature of the Pseudogap in the Cuprate Superconductors
journal, July 2019