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Title: Imaging the energy gap modulations of the cuprate pair-density-wave state

Abstract

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 Bi2Sr2CaCu2O8+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- of-states N(r, E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we discover them to be concentrated in areas where the PDW spatial phase changes by !, as predicted by the theory of half-vortices in a PDW state. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in the canonical cuprate Bi2Sr2CaCu2O8+δ.

Authors:
 [1];  [2];  [3]; ORCiD logo [4];  [3];  [5];  [1];  [1];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Brookhaven National Lab. (BNL), Upton, NY (United States); Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy
  3. Seoul National Univ. (Korea, Republic of)
  4. Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. of California, Berkeley, CA (United States)
  5. Univ. College Cork (Ireland); Univ. of Oxford (United Kingdom)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1615773
Report Number(s):
BNL-213873-2020-JAAM
Journal ID: ISSN 0028-0836
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Nature (London)
Additional Journal Information:
Journal Name: Nature (London); Journal Volume: 580; Journal Issue: 7801; Journal ID: ISSN 0028-0836
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Du, Zengyi, Li, Hui, Joo, Sang Hyun, Donoway, Elizabeth P., Lee, Jinho, Davis, J. C. Séamus, Gu, Genda, Johnson, Peter D., and Fujita, Kazuhiro. Imaging the energy gap modulations of the cuprate pair-density-wave state. United States: N. p., 2020. Web. doi:10.1038/s41586-020-2143-x.
Du, Zengyi, Li, Hui, Joo, Sang Hyun, Donoway, Elizabeth P., Lee, Jinho, Davis, J. C. Séamus, Gu, Genda, Johnson, Peter D., & Fujita, Kazuhiro. Imaging the energy gap modulations of the cuprate pair-density-wave state. United States. doi:https://doi.org/10.1038/s41586-020-2143-x
Du, Zengyi, Li, Hui, Joo, Sang Hyun, Donoway, Elizabeth P., Lee, Jinho, Davis, J. C. Séamus, Gu, Genda, Johnson, Peter D., and Fujita, Kazuhiro. Wed . "Imaging the energy gap modulations of the cuprate pair-density-wave state". United States. doi:https://doi.org/10.1038/s41586-020-2143-x. https://www.osti.gov/servlets/purl/1615773.
@article{osti_1615773,
title = {Imaging the energy gap modulations of the cuprate pair-density-wave state},
author = {Du, Zengyi and Li, Hui and Joo, Sang Hyun and Donoway, Elizabeth P. and Lee, Jinho and Davis, J. C. Séamus and Gu, Genda and Johnson, Peter D. and Fujita, Kazuhiro},
abstractNote = {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 Bi2Sr2CaCu2O8+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- of-states N(r, E) reveals electronic modulations with wavevectors Q and 2Q, as anticipated when the PDW coexists with superconductivity. Finally, by visualizing the topological defects in these N(r, E) density waves at 2Q, we discover them to be concentrated in areas where the PDW spatial phase changes by !, as predicted by the theory of half-vortices in a PDW state. Overall, this is a compelling demonstration, from multiple single-electron signatures, of a PDW state coexisting with superconductivity in the canonical cuprate Bi2Sr2CaCu2O8+δ.},
doi = {10.1038/s41586-020-2143-x},
journal = {Nature (London)},
number = 7801,
volume = 580,
place = {United States},
year = {2020},
month = {4}
}

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Works referenced in this record:

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


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

  • Fradkin, Eduardo; Kivelson, Steven A.; Tranquada, John M.
  • Reviews of Modern Physics, Vol. 87, Issue 2
  • DOI: 10.1103/RevModPhys.87.457

Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x
journal, April 2016

  • Hamidian, M. H.; Edkins, S. D.; Joo, Sang Hyun
  • Nature, Vol. 532, Issue 7599
  • DOI: 10.1038/nature17411

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

  • Agterberg, D. F.; Tsunetsugu, H.
  • Nature Physics, Vol. 4, Issue 8
  • DOI: 10.1038/nphys999

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

  • Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A.
  • Nature Physics, Vol. 5, Issue 11
  • DOI: 10.1038/nphys1389

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


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


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


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


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


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

  • Norman, M. R.; Davis, J. C. Séamus
  • Proceedings of the National Academy of Sciences, Vol. 115, Issue 21
  • DOI: 10.1073/pnas.1803009115

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 tJ 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


Genesis of charge orders in high temperature superconductors
journal, January 2016

  • Tu, Wei-Lin; Lee, Ting-Kuo
  • Scientific Reports, Vol. 6, Issue 1
  • DOI: 10.1038/srep18675

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


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


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


Probing optically silent superfluid stripes in cuprates
journal, February 2018


Topological Defects Coupling Smectic Modulations to Intra-Unit-Cell Nematicity in Cuprates
journal, July 2011


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

  • Fujita, K.; Hamidian, M. H.; Edkins, S. D.
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 30
  • DOI: 10.1073/pnas.1406297111

Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates
journal, May 2014

  • Nie, L.; Tarjus, G.; Kivelson, S. A.
  • Proceedings of the National Academy of Sciences, Vol. 111, Issue 22
  • DOI: 10.1073/pnas.1406019111

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


Pair-density waves, charge-density waves, and vortices in high- T c cuprates
journal, May 2018


Pair density waves in superconducting vortex halos
journal, May 2018


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