Pair-density waves, charge-density waves, and vortices in high-Tc cuprates

Dai, Zhehao; Zhang, Ya-Hui; Senthil, T.; Lee, Patrick A.

doi:10.1103/physrevb.97.174511

Title: Pair-density waves, charge-density waves, and vortices in high-T_c cuprates

Abstract

A recent scanning tunneling microscopy (STM) experiment reports the observation of a charge-density wave (CDW) with a period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately 4a period CDWs that are commonly observed in the cuprates. Inspired by this work, we study a model where a bidirectional pair-density wave (PDW) with period 8 is at play. This further divides into two classes: (1) where the PDW is a competing state of the d-wave superconductor and can exist only near the vortex core where the d-wave order is suppressed and (2) where the PDW is the primary order, the so-called “mother state” that persists with strong phase fluctuations to high temperature and high magnetic field and lies behind the pseudogap phenomenology. We study the charge-density wave structures near the vortex core in these models. We emphasize the importance of the phase winding of the d-wave order parameter. The PDW can be pinned by the vortex core due to this winding and become static. Furthermore, the period-8 CDW inherits the properties of this winding, which gives rise to a special feature of the Fourier transform peak, namely, it is split in certain directions.more »« less

Authors:

Dai, Zhehao ^[1]; Zhang, Ya-Hui ^[1]; Senthil, T. ^[1]; Lee, Patrick A. ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Publication Date:: Mon May 14 00:00:00 EDT 2018

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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

OSTI Identifier:: 1777869

Alternate Identifier(s):: OSTI ID: 1437086

Grant/Contract Number:: FG02-03ER46076; SC0008739; PHY-1607611

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B

Additional Journal Information:: Journal Volume: 97; Journal Issue: 17; 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; Superconductivity; Cuprates; High-temperature superconductors

Citation Formats


                    Dai, Zhehao, Zhang, Ya-Hui, Senthil, T., and Lee, Patrick A. Pair-density waves, charge-density waves, and vortices in high-Tc cuprates.  United States: N. p., 2018. 
Web.  doi:10.1103/physrevb.97.174511.

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                    Dai, Zhehao, Zhang, Ya-Hui, Senthil, T., & Lee, Patrick A. Pair-density waves, charge-density waves, and vortices in high-Tc cuprates.  United States.  https://doi.org/10.1103/physrevb.97.174511

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                    Dai, Zhehao, Zhang, Ya-Hui, Senthil, T., and Lee, Patrick A. Mon .  
"Pair-density waves, charge-density waves, and vortices in high-Tc cuprates".  United States.  https://doi.org/10.1103/physrevb.97.174511.  https://www.osti.gov/servlets/purl/1777869.

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@article{osti_1777869,

  title        = {Pair-density waves, charge-density waves, and vortices in high-Tc cuprates},

  author       = {Dai, Zhehao and Zhang, Ya-Hui and Senthil, T. and Lee, Patrick A.},

  abstractNote = {A recent scanning tunneling microscopy (STM) experiment reports the observation of a charge-density wave (CDW) with a period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately 4a period CDWs that are commonly observed in the cuprates. Inspired by this work, we study a model where a bidirectional pair-density wave (PDW) with period 8 is at play. This further divides into two classes: (1) where the PDW is a competing state of the d-wave superconductor and can exist only near the vortex core where the d-wave order is suppressed and (2) where the PDW is the primary order, the so-called “mother state” that persists with strong phase fluctuations to high temperature and high magnetic field and lies behind the pseudogap phenomenology. We study the charge-density wave structures near the vortex core in these models. We emphasize the importance of the phase winding of the d-wave order parameter. The PDW can be pinned by the vortex core due to this winding and become static. Furthermore, the period-8 CDW inherits the properties of this winding, which gives rise to a special feature of the Fourier transform peak, namely, it is split in certain directions. There is also a line of zeros in the inverse Fourier transform of filtered data. We propose that these are key experimental signatures that can distinguish between the PDW-driven scenario from the more mundane option that the period-8 CDW is primary. We discuss the pro's and con's of the options considered above. Lastly, we attempt to place the STM experiment in the broader context of pseudogap physics of underdoped cuprates and relate this observation to the unusual properties of x-ray scattering data on CDW carried out to very high magnetic field.},

  doi          = {10.1103/physrevb.97.174511},

  journal      = {Physical Review. B},

  number       = 17,

  volume       = 97,

  place        = {United States},

  year         = {Mon May 14 00:00:00 EDT 2018},

  month        = {Mon May 14 00:00:00 EDT 2018}

}

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Magnetic field–induced pair density wave state in the cuprate vortex halo

Journal Article Edkins, S. D. ; Kostin, A. ; Fujita, K. ; ... - Science

High magnetic fields suppress cuprate superconductivity to reveal an unusual density wave (DW) state coexisting with unexplained quantum oscillations. Although routinely labeled a charge density wave (CDW), this DW state could actually be an electron-pair density wave (PDW). To search for evidence of a field-induced PDW, we visualized modulations in the density of electronic states N(r) within the halo surrounding Bi₂Sr₂CaCu₂O₈ vortex cores. We detected numerous phenomena predicted for a field-induced PDW, including two sets of particle-hole symmetric N(r) modulations with wave vectors Q_P and 2Q_P, with the latter decaying twice as rapidly from the core as the former. Asmore »« less
Cited by 81
https://doi.org/10.1126/science.aat1773
Identification of a nematic pair density wave state in Bi₂Sr₂CaCu₂O_8+x

Journal Article Chen, Weijiong ; Ren, Wangping ; Kennedy, Niall ; ... - Proceedings of the National Academy of Sciences of the United States of America

Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. In this work, we use SJTM to visualize the interplay of PDW and DSC states in Bi₂Sr₂CaCu₂O_8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualizationmore »« less
https://doi.org/10.1073/pnas.2206481119

Full Text Available
Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Journal Article Du, Zengyi ; Li, Hui ; Gu, Genda ; ... - Physical Review. X

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging withmore »« less
https://doi.org/10.1103/PhysRevX.13.021025
Chern Fermi pocket, topological pair density wave, and charge-4e and charge-6e superconductivity in kagomé superconductors

Journal Article Zhou, Sen ; Wang, Ziqiang - Nature Communications

Abstract The recent discovery of novel charge density wave (CDW) and pair density wave (PDW) in kagomé lattice superconductors A V ₃ Sb ₅ ( A = K, Rb, Cs) hints at unexpected time-reversal symmetry breaking correlated and topological states whose physical origin and broader implications are not understood. Here, we make conceptual advances toward a mechanism behind the striking observations and new predictions for novel macroscopic phase coherent quantum states. We show that the metallic CDW state with circulating loop currents is a doped orbital Chern insulator near van Hove filling. The emergent Chern Fermi pockets (CFPs) carry concentrated Berrymore »« less
https://doi.org/10.1038/s41467-022-34832-2

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Title: Pair-density waves, charge-density waves, and vortices in high-Tc cuprates

Abstract

Citation Formats

Unconventional Low-Energy Excitations of Cuprate Superconductors journal, September 2009

Amperean Pairing Instability in the U(1) Spin Liquid State with Fermi Surface and Application to κ − ( BEDT − TTF ) 2 Cu 2 ( CN ) 3 journal, February 2007

Two-Dimensional Superconducting Fluctuations in Stripe-Ordered La 1.875 Ba 0.125 CuO 4 journal, August 2007

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

Quantum oscillations of the specific heat in d-wave superconductors with loop current order text, January 2013

Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates journal, November 2009

X-Ray Diffraction Observations of a Charge-Density-Wave Order in Superconducting Ortho-II YBa 2 Cu 3 O 6.54 Single Crystals in Zero Magnetic Field journal, March 2013

Resonant x-ray scattering study of charge-density wave correlations in YBa 2 Cu 3 O 6 + x journal, August 2014

Doping dependence of the spatially modulated dynamical spin correlations and the superconducting-transition temperature in La 2 − x Sr x CuO 4 journal, March 1998

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ journal, June 2013

Ideal charge-density-wave order in the high-field state of superconducting YBCO journal, December 2016

Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy journal, July 2017

Emergence of charge order from the vortex state of a high-temperature superconductor journal, July 2013

From a Single-Band Metal to a High-Temperature Superconductor via Two Thermal Phase Transitions journal, March 2011

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy journal, March 2015

Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields journal, November 2015

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

Synchrotron x-ray scattering study of charge-density-wave order in HgBa 2 CuO 4 + δ journal, October 2017

Towards resolution of the Fermi surface in underdoped high-Tc superconductors text, January 2011

Checkerboard order in vortex cores from pair-density-wave superconductivity journal, March 2015

Theory of the striped superconductor journal, February 2009

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

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy journal, September 2011

Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x journal, May 2016

c-Axis Optical Response in the Static Stripe Ordered Phase of the Cuprates text, January 2001

Competing states in the t-J model: uniform d-wave state versus stripe state text, January 2014

Spin susceptibility of charge-ordered YBa 2 Cu 3 O y across the upper critical field journal, November 2017

No evidence for orbital loop currents in charge-ordered YBa 2 Cu 3 O 6 + x from polarized neutron diffraction journal, December 2017

Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors text, January 2009

Quantum Oscillations in Hole-Doped Cuprates journal, March 2015

Ideal charge density wave order in the high-field state of superconducting YBCO text, January 2016

Evidence for stripe correlations of spins and holes in copper oxide superconductors journal, June 1995

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

Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x text, January 2016

Amperean pairing and the pseudogap phase of cuprate superconductors text, January 2014

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

Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O(6+x) text, January 2012

Novel magnetic order in the pseudogap state of high- copper oxides superconductors journal, June 2011

Theory of the pseudogap state of the cuprates journal, April 2006

c -Axis Optical Response in the Static Stripe Ordered Phase of the Cuprates journal, January 2001

Scanning tunneling spectroscopic evidence for magnetic-field–induced microscopic orders in the high-T c superconductor YBa 2 Cu 3 O 7- δ journal, August 2009

From quantum matter to high-temperature superconductivity in copper oxides journal, February 2015

Violation of the Onsager relation for quantum oscillations in superconductors journal, May 2009

Emergent loop current order from pair density wave superconductivity text, January 2014

Pair Density Waves in Superconducting Vortex Halos text, January 2018

Magnetic oscillations and quasiparticle band structure in the mixed state of type-II superconductors journal, March 1995

Checkerboard order in vortex cores from pair-density-wave superconductivity text, January 2014

Synchrotron X-Ray Scattering Study of Charge-Density-Wave Order in $HgBa_{2}CuO_{4+δ}$ text, January 2017

Long-Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x journal, July 2012

Observation of two distinct pairs fluctuation lifetimes and supercurrents in the pseudogap regime of cuprate junctions journal, November 2016

Quantum oscillations of the specific heat in d -wave superconductors with loop current order journal, July 2013

Amperean Pairing and the Pseudogap Phase of Cuprate Superconductors journal, July 2014

Spectral signatures of modulated d -wave superconducting phases journal, May 2008

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy text, January 2014

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

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

Loop current order and d -wave superconductivity: Some observable consequences journal, July 2012

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

Emergent loop current order from pair density wave superconductivity journal, February 2015

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

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

Quantum criticality in dissipative quantum two-dimensional X Y and Ashkin-Teller models: Application to the cuprates journal, May 2009

A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy journal, November 2016

Towards resolution of the Fermi surface in underdoped high- T c superconductors journal, September 2012

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

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

Quantum Oscillations in Hole-Doped Cuprates text, January 2015

Theory of the striped superconductor text, January 2008

Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates text, January 2015

Pair density waves in superconducting vortex halos journal, May 2018

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa 2 Cu 3 O y journal, October 2018

Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-$T_{\rm c}$ superconductors text, January 2020

Crossover from two-dimensional to three-dimensional superconducting states in bismuth-based cuprate superconductor journal, December 2019

Pair Density Waves in Superconducting Vortex Halos text, January 2018

Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-T c superconductors text, January 2020

Modeling the pseudogap metallic state in cuprates: Quantum disordered pair density wave journal, February 2020

Fragile superconductivity in the presence of weakly disordered charge density waves journal, April 2019

Title: Pair-density waves, charge-density waves, and vortices in high-T_c cuprates

Unconventional Low-Energy Excitations of Cuprate Superconductors
journal, September 2009

Amperean Pairing Instability in the U(1) Spin Liquid State with Fermi Surface and Application to $κ − (BEDT − TTF)_{2} {Cu}_{2} (CN)_{3}$
journal, February 2007

Two-Dimensional Superconducting Fluctuations in Stripe-Ordered ${La}_{1.875} {Ba}_{0.125} {CuO}_{4}$
journal, August 2007

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

Quantum oscillations of the specific heat in d-wave superconductors with loop current order
text, January 2013

Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates
journal, November 2009

X-Ray Diffraction Observations of a Charge-Density-Wave Order in Superconducting Ortho-II ${YBa}_{2} {Cu}_{3} O_{6.54}$ Single Crystals in Zero Magnetic Field
journal, March 2013

Resonant x-ray scattering study of charge-density wave correlations in ${YBa}_{2} {Cu}_{3} O_{6 + x}$
journal, August 2014

Doping dependence of the spatially modulated dynamical spin correlations and the superconducting-transition temperature in ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$
journal, March 1998

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ
journal, June 2013

Ideal charge-density-wave order in the high-field state of superconducting YBCO
journal, December 2016

Thermodynamic evidence for a nematic phase transition at the onset of the pseudogap in YBa2Cu3Oy
journal, July 2017

Emergence of charge order from the vortex state of a high-temperature superconductor
journal, July 2013

From a Single-Band Metal to a High-Temperature Superconductor via Two Thermal Phase Transitions
journal, March 2011

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
journal, March 2015

Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields
journal, November 2015

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

Synchrotron x-ray scattering study of charge-density-wave order in ${HgBa}_{2} {CuO}_{4 + δ}$
journal, October 2017

Towards resolution of the Fermi surface in underdoped high-Tc superconductors
text, January 2011

Checkerboard order in vortex cores from pair-density-wave superconductivity
journal, March 2015

Theory of the striped superconductor
journal, February 2009

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

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy
journal, September 2011

Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x
journal, May 2016

c-Axis Optical Response in the Static Stripe Ordered Phase of the Cuprates
text, January 2001

Competing states in the t-J model: uniform d-wave state versus stripe state
text, January 2014

Spin susceptibility of charge-ordered YBa ₂ Cu ₃ O _y across the upper critical field
journal, November 2017

No evidence for orbital loop currents in charge-ordered ${YBa}_{2} {Cu}_{3} O_{6 + x}$ from polarized neutron diffraction
journal, December 2017

Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
text, January 2009

Quantum Oscillations in Hole-Doped Cuprates
journal, March 2015

Ideal charge density wave order in the high-field state of superconducting YBCO
text, January 2016

Evidence for stripe correlations of spins and holes in copper oxide superconductors
journal, June 1995

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

Magnetic field controlled charge density wave coupling in underdoped YBa2Cu3O6+x
text, January 2016

Amperean pairing and the pseudogap phase of cuprate superconductors
text, January 2014

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

Long-range incommensurate charge fluctuations in (Y,Nd)Ba2Cu3O(6+x)
text, January 2012

Novel magnetic order in the pseudogap state of high- copper oxides superconductors
journal, June 2011

Theory of the pseudogap state of the cuprates
journal, April 2006

$c$ -Axis Optical Response in the Static Stripe Ordered Phase of the Cuprates
journal, January 2001

Scanning tunneling spectroscopic evidence for magnetic-field–induced microscopic orders in the high-T _c superconductor YBa ₂ Cu ₃ O _{7- δ}
journal, August 2009

From quantum matter to high-temperature superconductivity in copper oxides
journal, February 2015

Violation of the Onsager relation for quantum oscillations in superconductors
journal, May 2009

Emergent loop current order from pair density wave superconductivity
text, January 2014

Pair Density Waves in Superconducting Vortex Halos
text, January 2018

Magnetic oscillations and quasiparticle band structure in the mixed state of type-II superconductors
journal, March 1995

Checkerboard order in vortex cores from pair-density-wave superconductivity
text, January 2014

Synchrotron X-Ray Scattering Study of Charge-Density-Wave Order in $HgBa_{2}CuO_{4+δ}$
text, January 2017

Long-Range Incommensurate Charge Fluctuations in (Y,Nd)Ba2Cu3O6+x
journal, July 2012

Observation of two distinct pairs fluctuation lifetimes and supercurrents in the pseudogap regime of cuprate junctions
journal, November 2016

Quantum oscillations of the specific heat in $d$ -wave superconductors with loop current order
journal, July 2013

Amperean Pairing and the Pseudogap Phase of Cuprate Superconductors
journal, July 2014

Spectral signatures of modulated $d$ -wave superconducting phases
journal, May 2008

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy
text, January 2014

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

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

Loop current order and $d$ -wave superconductivity: Some observable consequences
journal, July 2012

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

Emergent loop current order from pair density wave superconductivity
journal, February 2015

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

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

Quantum criticality in dissipative quantum two-dimensional $X Y$ and Ashkin-Teller models: Application to the cuprates
journal, May 2009

A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy
journal, November 2016

Towards resolution of the Fermi surface in underdoped high- T _c superconductors
journal, September 2012

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

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

Quantum Oscillations in Hole-Doped Cuprates
text, January 2015

Theory of the striped superconductor
text, January 2008

Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
text, January 2015

Pair density waves in superconducting vortex halos
journal, May 2018

Unusual Interplay between Superconductivity and Field-Induced Charge Order in ${YBa}_{2} {Cu}_{3} O_{y}$
journal, October 2018

Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-$T_{\rm c}$ superconductors
text, January 2020

Crossover from two-dimensional to three-dimensional superconducting states in bismuth-based cuprate superconductor
journal, December 2019

Pair Density Waves in Superconducting Vortex Halos
text, January 2018

Hard antinodal gap revealed by quantum oscillations in the pseudogap regime of underdoped high-T c superconductors
text, January 2020

Modeling the pseudogap metallic state in cuprates: Quantum disordered pair density wave
journal, February 2020

Fragile superconductivity in the presence of weakly disordered charge density waves
journal, April 2019

Fragile superconductivity in the presence of weakly disordered charge density waves
text, January 2018

Magnetic field–induced pair density wave state in the cuprate vortex halo
journal, June 2019