Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering

Robinson, Neil J.; Johnson, Peter D.; Rice, T. Maurice; Tsvelik, Alexei M.

doi:10.1088/1361-6633/ab31ed

Title: Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering

Abstract

Over the past two decades, improvements in computational algorithms have shown a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. Firstly, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. In contrast, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reveals a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.

Authors:

^[1]; Johnson, Peter D. ^[2]; Rice, T. Maurice ^[3];

^[2]

Univ. of Amsterdam (Netherlands)
Brookhaven National Lab. (BNL), Upton, NY (United States)
Federal Inst. of Technology, Zurich (Switzerland)

Publication Date:: 2019-07-13

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

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

OSTI Identifier:: 1543397

Report Number(s):: BNL-211814-2019-JAAM
Journal ID: ISSN 0034-4885

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Reports on Progress in Physics

Additional Journal Information:: Journal Volume: 82; Journal Issue: 12; Journal ID: ISSN 0034-4885

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; high temperature superconductivity; cuprates; pseudogap; umklapp scattering

Citation Formats


                    Robinson, Neil J., Johnson, Peter D., Rice, T. Maurice, and Tsvelik, Alexei M. Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering.  United States: N. p., 2019. 
Web.  doi:10.1088/1361-6633/ab31ed.

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                    Robinson, Neil J., Johnson, Peter D., Rice, T. Maurice, & Tsvelik, Alexei M. Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering.  United States.  https://doi.org/10.1088/1361-6633/ab31ed

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                    Robinson, Neil J., Johnson, Peter D., Rice, T. Maurice, and Tsvelik, Alexei M. Sat .  
"Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering".  United States.  https://doi.org/10.1088/1361-6633/ab31ed.  https://www.osti.gov/servlets/purl/1543397.

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@article{osti_1543397,

  title        = {Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering},

  author       = {Robinson, Neil J. and Johnson, Peter D. and Rice, T. Maurice and Tsvelik, Alexei M.},

  abstractNote = {Over the past two decades, improvements in computational algorithms have shown a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. Firstly, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. In contrast, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reveals a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.},

  doi          = {10.1088/1361-6633/ab31ed},

  journal      = {Reports on Progress in Physics},

  number       = 12,

  volume       = 82,

  place        = {United States},

  year         = {2019},

  month        = {7}

}

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Figure 1: Competition between stripe states with period of λ lattice sites and the uniform d-wave superconducting state in the two-dimensional Hubbard model with U/t = 12. The energy difference per site between a plethora of stripe states and the uniform d-wave state is just ∆e/t ∼ 0.01. Results aremore »

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Works referencing / citing this record:

Peculiarities of pseudogap in Y0.95Pr0.05Ba2Cu3O7−δ single crystals under pressure up to 1.7 GPa
journal, December 2019

Solovjov, A. L.; Omelchenko, L. V.; Petrenko, E. V.
Scientific Reports, Vol. 9, Issue 1
DOI: 10.1038/s41598-019-55959-1

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

Dai, Zhehao; Senthil, T.; Lee, Patrick A.
Physical Review B, Vol. 101, Issue 6
DOI: 10.1103/physrevb.101.064502

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Intertwined charge, spin, and pairing orders in doped iron ladders

Journal Article Pandey, Bradraj ; Soni, Rahul ; Lin, Ling-Fang ; ... - Physical Review B

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe2S3. The model is constructed by using ab initio hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the (π,0) magnetic ordering at half filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard U coupling, other magnetic patterns, such as (0,π), are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interactionmore »« less
https://doi.org/10.1103/physrevb.103.214513

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Title: Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering

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A model of the insulator-metal transition Part I. Two-body correlations journal, March 1965

Violation of Kohler's Rule in the Normal-State Magnetoresistance of YBa 2 Cu 3 O 7 − δ and La 2 Sr x CuO 4 journal, August 1995

Many-body physics with ultracold gases journal, July 2008

SU(2) formulation of the t − J model: Application to underdoped cuprates journal, March 1998

Fermi Surface and Quasiparticle Excitations of Overdoped Tl 2 Ba 2 CuO 6 + δ journal, August 2005

Systematic evolution of temperature-dependent resistivity in La 2 − x Sr x CuO 4 journal, November 1992

Non-Bardeen-Cooper-Schrieffer behavior of optical properties across the phase diagram of cuprate superconductors journal, March 2009

High-temperature charge density wave correlations in La 1.875 Ba 0.125 CuO 4 without spin–charge locking journal, November 2017

c -axis optical conductivity from the Yang-Rice-Zhang model of the underdoped cuprates journal, May 2013

Microscopic Electron Models with Exact SO(5) Symmetry journal, April 1998

Doping and temperature dependence of c -axis optical phonons in YBa 2 Cu 3 O y single crystals journal, November 1995

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

Signatures of Fermi surface reconstruction in Raman spectra of underdoped cuprates journal, February 2010

Optical studies of high-temperature superconducting cuprates journal, July 2016

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

Band-Structure Effects in Itinerant Antiferromagnetism journal, November 1970

One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm journal, September 2012

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

Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model journal, October 2010

Some consequences of the Luttinger theorem: The Luttinger surfaces in non-Fermi liquids and Mott insulators journal, August 2003

The Theory of Electronic Semi-Conductors journal, October 1931

Efficient parametrization of the vertex function, Ω scheme, and the t , t ′ Hubbard model at van Hove filling journal, May 2009

Revisiting Cu 63 NMR evidence for charge order in superconducting La 1.885 Sr 0.115 CuO 4 journal, December 2017

Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis journal, March 2003

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

Stripe order in the underdoped region of the two-dimensional Hubbard model journal, November 2017

Basic aspects and main results of NMR-NQR spectroscopies in high-temperature superconductors journal, October 1998

Magnetic response in the underdoped cuprates journal, September 2012

Spin dynamics in the pseudogap state of a high-temperature superconductor journal, September 2007

Conduction in non-crystalline systems IX. the minimum metallic conductivity journal, October 1972

Transverse optical plasmons in layered superconductors journal, June 1996

Effects of the electron interaction on the energy levels of electrons in metals journal, January 1938

Scaling of the temperature dependent Hall effect in La 2 − x Sr x CuO 4 journal, April 1994

In-plane anisotropy of vortex-lattice melting in large YBa 2 Cu 3 O 7 single crystals journal, September 1998

Solitons with fermion number ½ journal, June 1976

Bulk superconductivity at 120 K in the Tl–Ca/Ba–Cu–O system journal, March 1988

Evidence of a Precursor Superconducting Phase at Temperatures as High as 180 K in R Ba 2 Cu 3 O 7 − δ ( R = Y , Gd , Eu ) Superconducting Crystals from Infrared Spectroscopy journal, January 2011

The pseudogap in high-temperature superconductors: an experimental survey journal, January 1999

Ladderlike optical conductivity in the spin-fermion model journal, March 2019

Splitting of electrons and violation of the Luttinger sum rule journal, March 2018

Coexistence of Fermi arcs and Fermi pockets in a high-Tc copper oxide superconductor journal, November 2009

Phase diagram of Bi2Sr2CaCu2O8+δ revisited journal, December 2018

Collisionally Induced Transport in Periodic Potentials journal, April 2004

Interplay of the scaling limit and the renormalization group: Implications for symmetry restoration journal, August 2002

Phenomenological theory of the pseudogap state journal, May 2006

Theory of hybrid state in a metal with a small Fermi surface and strong collective excitations journal, May 2005

Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette journal, March 1931

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond journal, March 2007

Normal-state transport properties of slightly overdoped Y Ba 2 Cu 3 O y crystals prepared by a crystal-pulling technique journal, December 1995

Exact SO(8) symmetry in the weakly-interacting two-leg ladder journal, July 1998

Quorum-sensing autoinducers resuscitate dormant Vibrio cholerae in environmental water samples journal, May 2013

Charge order and its connection with Fermi-liquid charge transport in a pristine high-Tc cuprate journal, December 2014

A Unified Theory Based on SO(5) Symmetry of Superconductivity and Antiferromagnetism journal, February 1997

Quantum oscillations in the high- T c cuprates journal, April 2011

Exact zero-temperature correlation functions for two-leg Hubbard ladders and carbon nanotubes journal, September 2001

Resistivity study of Bi 2 Sr 2 Ca 1 − x Y x Cu 2 O 8 single crystals journal, June 1992

NMR studies of high Tc superconductors journal, April 1996

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

Truncated conformal space approach for 2D Landau–Ginzburg theories journal, December 2014

Unconventional superconductivity in magic-angle graphene superlattices journal, March 2018

Strongly correlated superconductivity: A plaquette dynamical mean-field theory study journal, September 2007

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model journal, March 2017

NMR study of spin dynamics at planar oxygen and copper sites in YBa 2 Cu 4 O 8 journal, June 1994

Anisotropic Resistivities of Precisely Oxygen Controlled Single-Crystal Bi 2 Sr 2 CaCu 2 O 8 + δ : Systematic Study on ``Spin Gap'' Effect journal, September 1997

Enhanced superconductivity in Sr2CuO4−v journal, July 2009

Interaction-Controlled Transport of an Ultracold Fermi Gas journal, November 2007

Constraints on Models of Electrical Transport in Optimally Doped La2−x Sr x CuO4 from Measurements of Radiation-Induced Defect Resistance journal, September 2009

Giant phonon anomaly associated with superconducting fluctuations in the pseudogap phase of cuprates journal, January 2016

Complete solution of the one-dimensional Hubbard model journal, December 1991

Specific heat of underdoped cuprates: Resonating valence bond description versus Fermi arcs journal, August 2009

Rapid suppression of the charge density wave in YBa 2 Cu 3 O 6.6 under hydrostatic pressure journal, January 2018

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO4+δ journal, March 2016

Geometric interpretation of the weak-field Hall conductivity in two-dimensional metals with arbitrary Fermi surface journal, January 1991

A New High- T c Oxide Superconductor without a Rare Earth Element journal, February 1988

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

Superconductivity and Antiferromagnetism in the Two-Dimensional Hubbard Model: Scaling Theory journal, September 1987

A model of the insulator-metal transition Part I. Two-body correlations
journal, March 1965

Violation of Kohler's Rule in the Normal-State Magnetoresistance of ${YBa}_{2} {Cu}_{3} O_{7 - δ}$ and ${La}_{2} {Sr}_{x} {CuO}_{4}$
journal, August 1995

Many-body physics with ultracold gases
journal, July 2008

SU(2) formulation of the $t - J$ model: Application to underdoped cuprates
journal, March 1998

Fermi Surface and Quasiparticle Excitations of Overdoped ${Tl}_{2} {Ba}_{2} {CuO}_{6 + δ}$
journal, August 2005

Systematic evolution of temperature-dependent resistivity in ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$
journal, November 1992

Non-Bardeen-Cooper-Schrieffer behavior of optical properties across the phase diagram of cuprate superconductors
journal, March 2009

High-temperature charge density wave correlations in La _1.875 Ba _0.125 CuO ₄ without spin–charge locking
journal, November 2017

$c$ -axis optical conductivity from the Yang-Rice-Zhang model of the underdoped cuprates
journal, May 2013

Microscopic Electron Models with Exact SO(5) Symmetry
journal, April 1998

Doping and temperature dependence of c -axis optical phonons in ${YBa}_{2}$ ${Cu}_{3}$ $O_{y}$ single crystals
journal, November 1995

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

Signatures of Fermi surface reconstruction in Raman spectra of underdoped cuprates
journal, February 2010

Optical studies of high-temperature superconducting cuprates
journal, July 2016

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

Band-Structure Effects in Itinerant Antiferromagnetism
journal, November 1970

One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm
journal, September 2012

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

Momentum-space anisotropy and pseudogaps: A comparative cluster dynamical mean-field analysis of the doping-driven metal-insulator transition in the two-dimensional Hubbard model
journal, October 2010

Some consequences of the Luttinger theorem: The Luttinger surfaces in non-Fermi liquids and Mott insulators
journal, August 2003

The Theory of Electronic Semi-Conductors
journal, October 1931

Efficient parametrization of the vertex function, $Ω$ scheme, and the $t, t^{'}$ Hubbard model at van Hove filling
journal, May 2009

Revisiting ${}^{63}{Cu}$ NMR evidence for charge order in superconducting ${La}_{1.885} {Sr}_{0.115} {CuO}_{4}$
journal, December 2017

Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis
journal, March 2003

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

Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017

Basic aspects and main results of NMR-NQR spectroscopies in high-temperature superconductors
journal, October 1998

Magnetic response in the underdoped cuprates
journal, September 2012

Spin dynamics in the pseudogap state of a high-temperature superconductor
journal, September 2007

Conduction in non-crystalline systems IX. the minimum metallic conductivity
journal, October 1972

Transverse optical plasmons in layered superconductors
journal, June 1996

Effects of the electron interaction on the energy levels of electrons in metals
journal, January 1938

Scaling of the temperature dependent Hall effect in ${La}_{2 - x}$ ${Sr}_{x}$ ${CuO}_{4}$
journal, April 1994

In-plane anisotropy of vortex-lattice melting in large ${YBa}_{2} {Cu}_{3} O_{7}$ single crystals
journal, September 1998

Solitons with fermion number ½
journal, June 1976

Bulk superconductivity at 120 K in the Tl–Ca/Ba–Cu–O system
journal, March 1988

Evidence of a Precursor Superconducting Phase at Temperatures as High as 180 K in $R {Ba}_{2} {Cu}_{3} O_{7 - δ} (R = Y, Gd, Eu)$ Superconducting Crystals from Infrared Spectroscopy
journal, January 2011

The pseudogap in high-temperature superconductors: an experimental survey
journal, January 1999

Ladderlike optical conductivity in the spin-fermion model
journal, March 2019

Splitting of electrons and violation of the Luttinger sum rule
journal, March 2018

Coexistence of Fermi arcs and Fermi pockets in a high-Tc copper oxide superconductor
journal, November 2009

Phase diagram of Bi2Sr2CaCu2O8+δ revisited
journal, December 2018

Collisionally Induced Transport in Periodic Potentials
journal, April 2004

Interplay of the scaling limit and the renormalization group: Implications for symmetry restoration
journal, August 2002

Phenomenological theory of the pseudogap state
journal, May 2006

Theory of hybrid state in a metal with a small Fermi surface and strong collective excitations
journal, May 2005

Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
journal, March 1931

Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
journal, March 2007

Normal-state transport properties of slightly overdoped $Y {Ba}_{2} {Cu}_{3} O_{y}$ crystals prepared by a crystal-pulling technique
journal, December 1995

Exact SO(8) symmetry in the weakly-interacting two-leg ladder
journal, July 1998

Quorum-sensing autoinducers resuscitate dormant Vibrio cholerae in environmental water samples
journal, May 2013

Charge order and its connection with Fermi-liquid charge transport in a pristine high-Tc cuprate
journal, December 2014

A Unified Theory Based on SO(5) Symmetry of Superconductivity and Antiferromagnetism
journal, February 1997

Quantum oscillations in the high- T _c cuprates
journal, April 2011

Exact zero-temperature correlation functions for two-leg Hubbard ladders and carbon nanotubes
journal, September 2001

Resistivity study of ${Bi}_{2}$ ${Sr}_{2}$ ${Ca}_{1 - x}$ $Y_{x}$ ${Cu}_{2}$ $O_{8}$ single crystals
journal, June 1992

NMR studies of high Tc superconductors
journal, April 1996

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

Truncated conformal space approach for 2D Landau–Ginzburg theories
journal, December 2014

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018

Strongly correlated superconductivity: A plaquette dynamical mean-field theory study
journal, September 2007

Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
journal, March 2017

NMR study of spin dynamics at planar oxygen and copper sites in ${YBa}_{2}$ ${Cu}_{4}$ $O_{8}$
journal, June 1994

Anisotropic Resistivities of Precisely Oxygen Controlled Single-Crystal ${Bi}_{2} {Sr}_{2} {CaCu}_{2} O_{8 + δ}$ : Systematic Study on ``Spin Gap'' Effect
journal, September 1997

Enhanced superconductivity in Sr2CuO4−v
journal, July 2009

Interaction-Controlled Transport of an Ultracold Fermi Gas
journal, November 2007

Constraints on Models of Electrical Transport in Optimally Doped La2−x Sr x CuO4 from Measurements of Radiation-Induced Defect Resistance
journal, September 2009

Giant phonon anomaly associated with superconducting fluctuations in the pseudogap phase of cuprates
journal, January 2016

Complete solution of the one-dimensional Hubbard model
journal, December 1991

Specific heat of underdoped cuprates: Resonating valence bond description versus Fermi arcs
journal, August 2009

Rapid suppression of the charge density wave in ${YBa}_{2} {Cu}_{3} O_{6.6}$ under hydrostatic pressure
journal, January 2018

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO4+δ
journal, March 2016

Geometric interpretation of the weak-field Hall conductivity in two-dimensional metals with arbitrary Fermi surface
journal, January 1991

A New High- T _c Oxide Superconductor without a Rare Earth Element
journal, February 1988

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

Superconductivity and Antiferromagnetism in the Two-Dimensional Hubbard Model: Scaling Theory
journal, September 1987

Superconductivity at 93 K in a new mixed-phase Y-Ba-Cu-O compound system at ambient pressure
journal, March 1987

Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor
journal, August 2003

Resistivity and Hall effect of metallic oxygen-deficient $Y {Ba}_{2} {Cu}_{3} O_{x}$ films in the normal state
journal, April 1996

Dynamical Breakup of the Fermi Surface in a Doped Mott Insulator
journal, September 2005