Exploring intertwined orders in cuprate superconductors

Tranquada, John M.

doi:10.1016/j.physb.2014.11.056

Title: Exploring intertwined orders in cuprate superconductors

Abstract

In this study, the concept of intertwined orders has been introduced to describe the cooperative relationship between antiferromagnetic spin correlations and electron (or hole) pair correlations that develop in copper-oxide superconductors. This contrasts with systems in which, for example, charge-density-wave (CDW) order competes for Fermi surface area with superconductivity. La_2-xBa_xCuO₄ with x = 0.125 provides an example in which the ordering of spin stripes coincides with the onset of two-dimensional superconducting correlations. The apparent frustration of the interlayer Josephson coupling has motivated the concept of the pair-density-wave superconductor, a state that theoretical calculations show to be energetically competitive with the uniform d-wave superconductor. Even at x = 0.095, where there is robust superconductivity below 32 K in zero field, the coexistence of strong, low-energy, incommensurate spin excitations implies a spatially modulated and intertwined pair wave function. Recent observations of CDW order in YBa₂Cu₃O_6+x and other cuprate families have raised interesting questions regarding the general role of charge modulations and the relation to superconductivity. While there are differences in the doping dependence of the modulation wave vectors in YBa₂Cu₃O_6+x and La_2-xBa_xCuO₄, the maximum ordering strength is peaked at the hole concentration of 1/8 in both cases. There are also possible connectionsmore »« less

Authors:

Tranquada, John M. ^[1]

Brookhaven National Laboratory (BNL), Upton, NY (United States)

Publication Date:: Sat Nov 22 00:00:00 EST 2014

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

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

OSTI Identifier:: 1182475

Alternate Identifier(s):: OSTI ID: 1318768

Report Number(s):: BNL-107215-2014-JA; BNL-107215-2014-JAAM
Journal ID: ISSN 0921-4526; R&D Project: PO010; KC0201060

Grant/Contract Number:: AC02-98CH10886; NSF PHY11-25915

Resource Type:: Accepted Manuscript

Journal Name:: Physica. B, Condensed Matter

Additional Journal Information:: Journal Volume: 460; Journal Issue: C; Journal ID: ISSN 0921-4526

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

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                    Tranquada, John M. Exploring intertwined orders in cuprate superconductors.  United States: N. p., 2014. 
Web.  doi:10.1016/j.physb.2014.11.056.

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                    Tranquada, John M. Exploring intertwined orders in cuprate superconductors.  United States.  https://doi.org/10.1016/j.physb.2014.11.056

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                    Tranquada, John M. Sat .  
"Exploring intertwined orders in cuprate superconductors".  United States.  https://doi.org/10.1016/j.physb.2014.11.056.  https://www.osti.gov/servlets/purl/1182475.

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@article{osti_1182475,

  title        = {Exploring intertwined orders in cuprate superconductors},

  author       = {Tranquada, John M.},

  abstractNote = {In this study, the concept of intertwined orders has been introduced to describe the cooperative relationship between antiferromagnetic spin correlations and electron (or hole) pair correlations that develop in copper-oxide superconductors. This contrasts with systems in which, for example, charge-density-wave (CDW) order competes for Fermi surface area with superconductivity. La2-xBaxCuO4 with x = 0.125 provides an example in which the ordering of spin stripes coincides with the onset of two-dimensional superconducting correlations. The apparent frustration of the interlayer Josephson coupling has motivated the concept of the pair-density-wave superconductor, a state that theoretical calculations show to be energetically competitive with the uniform d-wave superconductor. Even at x = 0.095, where there is robust superconductivity below 32 K in zero field, the coexistence of strong, low-energy, incommensurate spin excitations implies a spatially modulated and intertwined pair wave function. Recent observations of CDW order in YBa2Cu3O6+x and other cuprate families have raised interesting questions regarding the general role of charge modulations and the relation to superconductivity. While there are differences in the doping dependence of the modulation wave vectors in YBa2Cu3O6+x and La2-xBaxCuO4, the maximum ordering strength is peaked at the hole concentration of 1/8 in both cases. There are also possible connections with the quantum oscillations that have been detected about the same hole concentration but at high magnetic fields. Resolving these relationships remains a research challenge.},

  doi          = {10.1016/j.physb.2014.11.056},

  journal      = {Physica. B, Condensed Matter},

  number       = C,

  volume       = 460,

  place        = {United States},

  year         = {Sat Nov 22 00:00:00 EST 2014},

  month        = {Sat Nov 22 00:00:00 EST 2014}

}

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Blanco-Canosa, S.; Frano, A.; Loew, T.
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Works referencing / citing this record:

Staging superstructures in high- $T_{c}$ Sr/O codoped ${La}_{2 - x} {Sr}_{x} {CuO}_{4 + y}$
journal, November 2017

Ray, P. J.; Andersen, N. H.; Jensen, T. B. S.
Physical Review B, Vol. 96, Issue 17
DOI: 10.1103/physrevb.96.174106

Phase diagrams of a 2D Ising spin-pseudospin model
text, January 2019

Panov, Yu. D.; Ulitko, V. A.; Budrin, K. S.
arXiv
DOI: 10.48550/arxiv.1902.00076

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Title: Exploring intertwined orders in cuprate superconductors

Abstract

Citation Formats

Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates journal, December 2013

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

Charged magnetic domain lines and the magnetism of high- T c oxides journal, October 1989

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

Competing charge, spin, and superconducting orders in underdoped YBa 2 Cu 3 O y journal, August 2014

Charged solitons in the Hartree-Fock approximation to the large- U Hubbard model journal, May 1989

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

Distinct Charge Orders in the Planes and Chains of Ortho-III-Ordered YBa 2 Cu 3 O 6 + δ Superconductors Identified by Resonant Elastic X-ray Scattering journal, October 2012

Fermi-surface reconstruction in a smectic phase of a high-temperature superconductor journal, July 2011

Interplay of Externally Doped and Thermally Activated Holes in La 2 − x Sr x CuO 4 and Their Impact on the Pseudogap Crossover journal, December 2006

Thermodynamic phase diagram of static charge order in underdoped YBa2Cu3Oy journal, December 2012

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

A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor journal, July 2008

A Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+delta journal, January 2002

Spin-gap proximity effect mechanism of high-temperature superconductivity journal, September 1997

Incommensurate antiferromagnetism in the two-dimensional Hubbard model journal, March 1990

Hard–X-ray diffraction study of charge stripe order in La 1.48 Nd 0.4 Sr 0.12 CuO 4 journal, March 1998

Evolution of superconducting correlations within magnetic-field-decoupled La 2 − x Ba x CuO 4 ( x = 0.095 ) journal, February 2013

Fluctuating stripes at the onset of the pseudogap in the high-Tc superconductor Bi2Sr2CaCu2O8+x journal, December 2010

Stripes in the two-dimensional t - J model with infinite projected entangled-pair states journal, July 2011

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

Mid-infrared conductivity from mid-gap states associated with charge stripes journal, May 2003

The effect of collective spin-1 excitations on electronic spectra in high- T c superconductors journal, January 2006

Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor journal, May 2007

Direct measurement of the upper critical field in cuprate superconductors journal, February 2014

Magnetic-Field-Enhanced Incommensurate Magnetic Order in the Underdoped High-Temperature Superconductor YBa 2 Cu 3 O 6.45 journal, June 2009

Coexistence of, and Competition between, Superconductivity and Charge-Stripe Order in La 1 . 6 − x Nd 0.4 Sr x CuO 4 journal, January 1997

Superconducting properties of La 2 − x Ba x CuO 4 journal, September 1988

Electronic liquid-crystal phases of a doped Mott insulator journal, June 1998

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

Energetics of Domain Walls in the 2D t − J Model journal, October 1998

An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates journal, March 2007

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

Study of an Ising model with competing long- and short-range interactions journal, March 1994

Frustrated electronic phase separation and high-temperature superconductors journal, May 1993

Two-dimensional superconductivity in stripe-ordered La 1.6 − x Nd 0.4 Sr x CuO 4 single crystals journal, June 2008

Spin susceptibility of underdoped cuprate superconductors: Insights from a stripe-ordered crystal journal, December 2008

From Mott state to superconductivity in 1T-TaS2 journal, November 2008

Incoherent charge dynamics of La 2 − x Sr x CuO 4 : Dynamical localization and resistivity saturation journal, October 2003

Local Magnetic Order vs Superconductivity in a Layered Cuprate journal, August 2000

Heat capacity through the magnetic-field-induced resistive transition in an underdoped high-temperature superconductor journal, February 2011

Nernst and Seebeck Coefficients of the Cuprate Superconductor YBa 2 Cu 3 O 6.67 : A Study of Fermi Surface Reconstruction journal, February 2010

Charge stripe order near the surface of 12-percent doped La2−xSrxCuO4 journal, January 2012

Charge ordering in the electron-doped superconductor Nd2-xCexCuO4 journal, January 2015

Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45 journal, January 2008

Ineluctable complexity journal, November 2012

Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67 journal, October 2012

Phase diagram of charge order in La 1 . 8 − x Eu 0 . 2 Sr x CuO 4 from resonant soft x-ray diffraction journal, March 2011

Spin-Stripe Density Varies Linearly With the Hole Content in Single-Layer Bi 2 + x Sr 2 − x CuO 6 + y Cuprate Superconductors journal, January 2013

Density Matrix Renormalization Group Study of the Striped Phase in the 2D t − J Model journal, February 1998

Spectroscopic evidence for a pseudogap in the normal state of underdoped high-Tc superconductors journal, July 1996

Electron pockets in the Fermi surface of hole-doped high-Tc superconductors journal, November 2007

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

Antiphase stripe order as the origin of electron pockets observed in 1/8-hole-doped cuprates journal, December 2007

Enhanced charge stripe order of superconducting La 2 − x Ba x CuO 4 in a magnetic field journal, January 2013

Optical spectroscopy of the charge-ordering transition in La 1.67 Sr 0.33 NiO 4 journal, November 1996

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

Neutron-Scattering Evidence for a Periodically Modulated Superconducting Phase in the Underdoped Cuprate La 1.905 Ba 0.095 CuO 4 journal, October 2014

Stripe order in superconducting La 2 − x Ba x CuO 4 ( 0 . 095 ⩽ x ⩽ 0 . 155 ) journal, March 2011

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

Possible highT c superconductivity in the Ba?La?Cu?O system journal, June 1986

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

Stripe order, depinning, and fluctuations in La 1.875 Ba 0.125 CuO 4 and La 1.875 Ba 0.075 Sr 0.050 CuO 4 journal, September 2004

Reconstructed Fermi Surface of Underdoped Bi 2 Sr 2 CaCu 2 O 8 + δ Cuprate Superconductors journal, July 2011

Breakdown of the universal Josephson relation in spin-ordered cuprate superconductors journal, September 2010

The pseudogap: friend or foe of high T c ? journal, December 2005

Direct observation of dynamic charge stripes in La2–xSrxNiO4 journal, March 2014

Periodic density-of-states modulations in superconducting Bi 2 Sr 2 CaCu 2 O 8 + δ journal, January 2003

Uniaxial linear resistivity of superconducting La 1.905 Ba 0.095 CuO 4 induced by an external magnetic field journal, April 2012

Charge Order Driven by Fermi-Arc Instability in Bi2Sr2-xLaxCuO6+ journal, December 2013

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

Charge density wave fluctuations in La 2 − x Sr x CuO 4 and their competition with superconductivity journal, June 2014

Electrodynamics of the nodal metal state in weakly doped high- T c cuprates journal, August 2005

Magnetism in La2CuO4 based compounds journal, April 1989

Evidence for unusual superconducting correlations coexisting with stripe order in La 1.875 Ba 0.125 CuO 4 journal, November 2008

Phase competition in trisected superconducting dome journal, October 2012

Ubiquitous Interplay Between Charge Ordering and High-Temperature Superconductivity in Cuprates
journal, December 2013

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

Charged magnetic domain lines and the magnetism of high- $T_{c}$ oxides
journal, October 1989

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

Competing charge, spin, and superconducting orders in underdoped ${YBa}_{2} {Cu}_{3} O_{y}$
journal, August 2014

Charged solitons in the Hartree-Fock approximation to the large- U Hubbard model
journal, May 1989

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

Distinct Charge Orders in the Planes and Chains of Ortho-III-Ordered ${YBa}_{2} {Cu}_{3} O_{6 + δ}$ Superconductors Identified by Resonant Elastic X-ray Scattering
journal, October 2012

Fermi-surface reconstruction in a smectic phase of a high-temperature superconductor
journal, July 2011

Interplay of Externally Doped and Thermally Activated Holes in ${La}_{2 - x} {Sr}_{x} {CuO}_{4}$ and Their Impact on the Pseudogap Crossover
journal, December 2006

Thermodynamic phase diagram of static charge order in underdoped YBa2Cu3Oy
journal, December 2012

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

A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor
journal, July 2008

A Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+delta
journal, January 2002

Spin-gap proximity effect mechanism of high-temperature superconductivity
journal, September 1997

Incommensurate antiferromagnetism in the two-dimensional Hubbard model
journal, March 1990

Hard–X-ray diffraction study of charge stripe order in La _1.48 Nd _0.4 Sr _0.12 CuO ₄
journal, March 1998

Evolution of superconducting correlations within magnetic-field-decoupled La $_{2 - x}$ Ba $_{x}$ CuO $_{4}$ ( $x = 0.095$ )
journal, February 2013

Fluctuating stripes at the onset of the pseudogap in the high-Tc superconductor Bi2Sr2CaCu2O8+x
journal, December 2010

Stripes in the two-dimensional $t$ - $J$ model with infinite projected entangled-pair states
journal, July 2011

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

Mid-infrared conductivity from mid-gap states associated with charge stripes
journal, May 2003

The effect of collective spin-1 excitations on electronic spectra in high- T _c superconductors
journal, January 2006

Quantum oscillations and the Fermi surface in an underdoped high-Tc superconductor
journal, May 2007

Direct measurement of the upper critical field in cuprate superconductors
journal, February 2014

Magnetic-Field-Enhanced Incommensurate Magnetic Order in the Underdoped High-Temperature Superconductor ${YBa}_{2} {Cu}_{3} O_{6.45}$
journal, June 2009

Coexistence of, and Competition between, Superconductivity and Charge-Stripe Order in ${La}_{1.6 - x} {Nd}_{0.4} {Sr}_{x} {CuO}_{4}$
journal, January 1997

Superconducting properties of ${La}_{2 - x}$ ${Ba}_{x}$ ${CuO}_{4}$
journal, September 1988

Electronic liquid-crystal phases of a doped Mott insulator
journal, June 1998

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

Energetics of Domain Walls in the 2D $t - J$ Model
journal, October 1998

An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates
journal, March 2007

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

Study of an Ising model with competing long- and short-range interactions
journal, March 1994

Frustrated electronic phase separation and high-temperature superconductors
journal, May 1993

Two-dimensional superconductivity in stripe-ordered ${La}_{1.6 - x} {Nd}_{0.4} {Sr}_{x} {CuO}_{4}$ single crystals
journal, June 2008

Spin susceptibility of underdoped cuprate superconductors: Insights from a stripe-ordered crystal
journal, December 2008

From Mott state to superconductivity in 1T-TaS2
journal, November 2008

Incoherent charge dynamics of ${La}_{2 - x} {Sr}_{x} {CuO}_{4} :$ Dynamical localization and resistivity saturation
journal, October 2003

Local Magnetic Order vs Superconductivity in a Layered Cuprate
journal, August 2000

Heat capacity through the magnetic-field-induced resistive transition in an underdoped high-temperature superconductor
journal, February 2011

Nernst and Seebeck Coefficients of the Cuprate Superconductor ${YBa}_{2} {Cu}_{3} O_{6.67}$ : A Study of Fermi Surface Reconstruction
journal, February 2010

Charge stripe order near the surface of 12-percent doped La2−xSrxCuO4
journal, January 2012

Charge ordering in the electron-doped superconductor Nd2-xCexCuO4
journal, January 2015

Electronic Liquid Crystal State in the High-Temperature Superconductor YBa2Cu3O6.45
journal, January 2008

Ineluctable complexity
journal, November 2012

Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6.67
journal, October 2012

Phase diagram of charge order in La $_{1.8 - x}$ Eu $_{0.2}$ Sr $_{x}$ CuO $_{4}$ from resonant soft x-ray diffraction
journal, March 2011

Spin-Stripe Density Varies Linearly With the Hole Content in Single-Layer ${Bi}_{2 + x} {Sr}_{2 - x} {CuO}_{6 + y}$ Cuprate Superconductors
journal, January 2013

Density Matrix Renormalization Group Study of the Striped Phase in the 2D $t - J$ Model
journal, February 1998

Spectroscopic evidence for a pseudogap in the normal state of underdoped high-Tc superconductors
journal, July 1996

Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
journal, November 2007

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

Antiphase stripe order as the origin of electron pockets observed in 1/8-hole-doped cuprates
journal, December 2007

Enhanced charge stripe order of superconducting La $_{2 - x}$ Ba $_{x}$ CuO $_{4}$ in a magnetic field
journal, January 2013

Optical spectroscopy of the charge-ordering transition in ${La}_{1.67}$ ${Sr}_{0.33}$ ${NiO}_{4}$
journal, November 1996

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

Neutron-Scattering Evidence for a Periodically Modulated Superconducting Phase in the Underdoped Cuprate ${La}_{1.905} {Ba}_{0.095} {CuO}_{4}$
journal, October 2014

Stripe order in superconducting La $_{2 - x}$ Ba $_{x}$ CuO $_{4}$ ( $0.095 ⩽ x ⩽ 0.155$ )
journal, March 2011

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

Possible highT c superconductivity in the Ba?La?Cu?O system
journal, June 1986

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

Stripe order, depinning, and fluctuations in ${La}_{1.875} {Ba}_{0.125} {CuO}_{4}$ and ${La}_{1.875} {Ba}_{0.075} {Sr}_{0.050} {CuO}_{4}$
journal, September 2004

Reconstructed Fermi Surface of Underdoped ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ Cuprate Superconductors
journal, July 2011

Breakdown of the universal Josephson relation in spin-ordered cuprate superconductors
journal, September 2010

The pseudogap: friend or foe of high T _c ?
journal, December 2005

Direct observation of dynamic charge stripes in La2–xSrxNiO4
journal, March 2014

Periodic density-of-states modulations in superconducting ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$
journal, January 2003

Uniaxial linear resistivity of superconducting La $_{1.905}$ Ba $_{0.095}$ CuO $_{4}$ induced by an external magnetic field
journal, April 2012

Charge Order Driven by Fermi-Arc Instability in Bi2Sr2-xLaxCuO6+
journal, December 2013

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

Charge density wave fluctuations in ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$ and their competition with superconductivity
journal, June 2014

Electrodynamics of the nodal metal state in weakly doped high- $T_{c}$ cuprates
journal, August 2005

Magnetism in La2CuO4 based compounds
journal, April 1989

Evidence for unusual superconducting correlations coexisting with stripe order in ${La}_{1.875} {Ba}_{0.125} {CuO}_{4}$
journal, November 2008

Phase competition in trisected superconducting dome
journal, October 2012

Vortex lattice melting and $H_{c 2}$ in underdoped YBa $_{2}$ Cu $_{3}$ O $_{y}$
journal, November 2012

Evidence for Short-Range-Ordered Charge Stripes Far above the Charge-Ordering Transition in ${La}_{1.67} {Sr}_{0.33} {NiO}_{4}$
journal, August 2013

Phase separation in the t - J model
journal, January 1990