Visualizing the periodic modulation of Cooper pairing in a severely underdoped cuprate

Abstract

A major obstacle in understanding the mechanism of Cooper pairing in the cuprates is the existence of various intertwined orders associated with spin, charge, and Cooper pairs. Of particular importance is the ubiquitous charge order features that have been observed in a variety of cuprates, especially in the underdoped regime of the phase diagram. To explain the origin of the charge order and its implication to the superconducting phase, many theoretical models have been proposed, such as charge stripes, electronic nematicity, and Fermi surface instability. A highly appealing physical picture is the so-called pair density wave (PDW), a periodic modulation of Cooper paring in space, which may also induce a charge order. To elucidate the existence and nature of the PDW order, here we use scanning tunneling microscopy (STM) to investigate a severely underdoped Bi2Sr2CaCu2O8+δ, in which superconductivity just emerges on top of a pronounced checkerboard charge order. By analyzing the spatial distribution of the spectral features characteristic of superconductivity, we observe a periodic modulation of both the superconducting coherence peak and gap depth, demonstrating the existence of a density wave order of Cooper pairing. The PDW order has the same spatial periodicity as the charge order, and the amplitudes of the two orders exhibit clear positive correlation. These results shed important new lights on the origin of and interplay between the charge order and Cooper pairing modulation in the cuprates.

arXiv comment17 pages, 4 figures

References in corpus (28)

• How to detect fluctuating order in the high-temperature superconductors
• Theory of Intertwined Orders in High Temperature Superconductors
• A Four-Unit-Cell Periodic Pattern of Quasiparticle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+d
• Discovery of microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x
• Imaging the Effects of Individual Zinc Impurity Atoms on Superconductivity in Bi2Sr2CaCu2O8+delta
• A `checkerboard' electronic crystal state in lightly hole-doped Ca_{2-x}Na_{x}CuO_{2}Cl_{2}
• Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states
• Ubiquitous Interplay between Charge Ordering and High-Temperature Superconductivity in Cuprates
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+d
• Charge density wave origin of cuprate checkerboard visualized by scanning tunneling microscopy
• How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+d
• Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders
• Detection of a Cooper-Pair Density Wave in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$
• STM Studies of the Electronic Structure of Vortex Cores in Bi2Sr2CaCu2O8+d
• Signature of Superfluid Density in the Single-Particle Excitation Spectrum of Bi2Sr2CaCu2O8+delta
• Pair Density Wave in the Pseudogap State of High Temperature Superconductors
• Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor
• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Visualizing the evolution from the Mott insulator to a charge ordered insulator in lightly doped cuprates
• Visualizing the atomic scale electronic structure of the Ca2CuO2Cl2 Mott insulator
• Checkerboard charge density wave and pseudogap in high-$T_c$ cuprates
• Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors
• Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors
• Incommensurate charge ordered states in the $t-t^{\prime }-J$ model
• Genesis of charge orders in high temperature superconductors
• Complementary Pair Density Wave and d-wave Checkerboard Order in High Temperature Superconductors
• The phase diagram of the underdoped cuprates at high magnetic field

Cited by in corpus (45)

• Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal
• Imaging spinon density modulations in a 2D quantum spin liquid
• Charge-order-assisted topological surface states and flat bands in the kagome superconductor CsV${}_3$Sb${}_5$
• Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV${}_3$Sb${}_5$
• Discovery of a pair density wave state in a monolayer high-Tc iron-based superconductor
• Cuprate superconductors as viewed through a striped lens
• Magnetic-field sensitive charge density wave orders in the superconducting phase of UTe2
• A strongly inhomogeneous superfluid in an iron-based superconductor
• Spectroscopic Evidence of Superconductivity Pairing at 83 K in Single-Layer FeSe/SrTiO3 Films
• Large kagome family candidates with topological superconductivity and charge density waves
• Interplay between Pair Density Wave and a Nested Fermi Surface
• Pair density wave in doped three-band Hubbard model on two-leg square cylinders
• Gapless spin liquid and pair density wave of the Hubbard model on three-leg triangular cylinders
• Pair Density Waves from Local Band Geometry
• The emergence of global phase coherence from local pairing in underdoped cuprates
• Evidence of pair-density wave in doping Kitaev spin liquid on the honeycomb lattice
• Evolution of Charge and Pair Density Modulations in Overdoped Bi2Sr2CuO6+delta
• Possible superconductivity with Bogoliubov Fermi surface in lightly doped Kagome U(1) spin liquid
• Directly visualizing nematic superconductivity driven by the pair density wave in NbSe${}_2$
• Rectification and nonlinear Hall effect by fluctuating finite-momentum Cooper pairs
• Odd-frequency pair density wave correlations in underdoped cuprates
• Evidence of a distinct collective mode in Kagome superconductors
• Imaging antiferromagnetic domain fluctuations and the effect of atomic-scale disorder in a doped spin-orbit Mott insulator
• Self-consistent theory of $2\times 2$ pair density waves in kagome superconductors
• Observation of superconducting pair density modulation within lattice unit cell
• Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe2
• Theory of charge-6e condensed phase in Kagome lattice superconductors
• Charge- and pair-density-wave orders in the one-band Hubbard model with dynamical mean field theory
• Pair-density-wave superconductivity: a microscopic model on 2D honeycomb lattice
• Absence of a bulk charge density wave signature in x-ray measurements of UTe${}_2$
• Pair density wave characterized by a hidden string order parameter
• Density matrix renormalization group study of quantum-geometry-facilitated pair density wave order
• Imaging half-unit-cell Cooper-pair density waves in monolayer 1T${}^{\prime }$-MoTe${}_2$
• Paramagnetic contribution in superconductors with different-mass Cooper pairs
• Enhanced pair-density-wave vertices in a bilayer Hubbard model at half-filling
• Microscopic Mechanism of Pair-, Charge- and Spin-Density-Wave Instabilities in Interacting D-Dimensional Fermi Liquids
• Sublattice Dichotomy in Monolayer FeSe Superconductor
• Pair-density-wave phase of strongly interacting electrons on the triangular lattice: A variational Monte Carlo study
• Competing pair density wave orders in the square lattice $t$-$J$ model
• Emergent Pair Density Wave Order Across a Lifshitz Transition
• Probing Quantum Geometric Phases via Scanning Tunneling Microscopy
• Spin-triplet pair density wave superconductors
• Topological pair density waves in kagome superconductors
• Percolative Pathway to Stripe Order in KTaO3-Based Superconductivity
• Visualizing Pair-breaking Scattering Interference in Bulk FeSe