Imaging nanoscale Fermi surface variations in an inhomogeneous superconductor

Abstract

Particle-wave duality suggests we think of electrons as waves stretched across a sample, with wavevector k proportional to their momentum. Their arrangement in "k-space," and in particular the shape of the Fermi surface, where the highest energy electrons of the system reside, determine many material properties. Here we use a novel extension of Fourier transform scanning tunneling microscopy to probe the Fermi surface of the strongly inhomogeneous Bi-based cuprate superconductors. Surprisingly, we find that rather than being globally defined, the Fermi surface changes on nanometer length scales. Just as shifting tide lines expose variations of water height, changing Fermi surfaces indicate strong local doping variations. This discovery, unprecedented in any material, paves the way for an understanding of other inhomogeneous characteristics of the cuprates, like the pseudogap magnitude, and highlights a new approach to the study of nanoscale inhomogeneity in general.

References in corpus (26)

• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Complexity in Strongly Correlated Electronic Systems
• Imaging the granular structure of high-Tc superconductivity in underdoped Bi2Sr2CaCu2O8+x
• A `checkerboard' electronic crystal state in lightly hole-doped Ca_{2-x}Na_{x}CuO_{2}Cl_{2}
• Imaging Quasiparticle Interference in Bi2Sr2CaCu2O8+d
• Local Ordering in the Pseudogap State of the High-T${}_c$ Superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Visualizing pair formation on the atomic scale in the high-Tc superconductor Bi2Sr2CaCu2O8+d
• Distinct Fermi-Momentum Dependent Energy Gaps in Deeply Underdoped Bi2212
• Charge density wave origin of cuprate checkerboard visualized by scanning tunneling microscopy
• Two Energy Scales and two Quasiparticle Dynamics in the Superconducting State of Underdoped Cuprates
• Periodic Density of States Modulations in Superconducting $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{CaC}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$
• Quasiparticle Scattering Interference in High Temperature Superconductors
• Phenomenological Models for the Gap Anisotropy of Bi-2212 as Measured by ARPES
• Inherent Inhomogeneities in Tunneling Spectra of BSCCO Crystals in the Superconducting State
• Imaging the Two Gaps of the High-TC Superconductor Pb-Bi2Sr2CuO6+x
• Electronic Origin of the Inhomogeneous Pairing Interaction in the High-Tc Superconductor Bi2Sr2CaCu2O8+d
• Evidence for two energy scales in the superconducting state of optimally doped (Bi,Pb)2(Sr,La)2CuO6+d
• Quasi-particle interference and superconducting gap in a high-temperature superconductor Ca2-xNaxCuO2Cl2
• Evolution of the electronic excitation spectrum with strongly diminishing hole-density in superconducting Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}
• Imaging the impact on cuprate superconductivity of varying the inter-atomic distances within individual crystal unit-cells
• Dopant-modulated pair interaction in cuprate superconductors
• The Dichotomy between Nodal and Antinodal Quasiparticles in Underdoped (La${}_{2-x}$Sr${}_x$)CuO${}_4$ Superconductors
• From stripe to checkerboard order on the square lattice in the presence of quenched disorder
• Dispersion of the odd magnetic resonant mode in near-optimally doped Bi2Sr2CaCu2O8+d
• Correlating off-stoichiometric doping with nanoscale electronic disorder and quasiparticle interference pattern in high-$T_c$ superconductor Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Thermodynamic transitions in inhomogeneous cuprate superconductors

Cited by in corpus (58)

• Imaging the Fano Lattice to 'Hidden Order' Transition in URu2Si2
• Appearance of fluctuating stripes at the onset of the pseudogap in the high-Tc Superconductor Bi2Sr2CaCu2O8+x
• Disentangling Cooper-pair formation above Tc from the pseudogap state in the cuprates
• Particle-Hole Symmetry Breaking in the Pseudogap State of Bi2201
• ARPES studies of cuprate Fermiology: superconductivity, pseudogap, and quasiparticle dynamics
• Visualizing the evolution from the Mott insulator to a charge ordered insulator in lightly doped cuprates
• Incoherent transport across the strange metal regime of highly overdoped cuprates
• Competition between spin density wave order and superconductivity in the underdoped cuprates
• Collapse of the Fermi surface and fingerprints of order in the pseudogap state of cuprate superconductors
• First direct observation of the Van Hove singularity in the tunneling spectra of cuprates
• Observation of small Fermi pockets protected by clean CuO2 sheets of a high-Tc superconductor
• Local inhomogeneity and filamentary superconductivity in Pr-doped CaFe${}_2$As${}_2$
• Quasiparticles in the Pseudogap Phase of Underdoped Cuprate
• STM imaging of symmetry-breaking structural distortion in the Bi-based cuprate superconductors
• Pairing, Pseudogap and Fermi Arcs in Cuprates
• Magnetic excitations and phonons simultaneously studied by resonant inelastic x-ray scattering in optimally doped Bi${}_{1.5}$Pb${}_{0.55}$Sr${}_{1.6}$La${}_{0.4}$CuO${}_{6+\delta }$
• Universal Disorder in Bi2Sr2CaCu2O8+x
• Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed
• Modulated superconductivity due to vacancy and magnetic order in $A_x$Fe${}_{2-x/2}$Se${}_2$ [$A=$Cs, K, (Tl,Rb), (Tl,K)] iron-selenide superconductors
• Evolution of Charge and Pair Density Modulations in Overdoped Bi2Sr2CuO6+delta
• Origin of the Pseudogap in High-Temperature Cuprate Superconductors
• The n_s - T_c correlations in granular superconductors
• Reaffirming the $d_{x^2-y^2}$ superconducting gap using the auto-correlation angle-resolved photoemission spectroscopy of Bi${}_{1.5}$Pb${}_{0.55}$Sr${}_{1.6}$La${}_{0.4}$CuO${}_{6+\delta }$
• Theory of the Fermi Arcs, the Pseudogap, $T_c$ and the Anisotropy in k-space of Cuprate Superconductors
• Gossamer bulk high-temperature superconductivity in FeSe
• Typical-Medium Theory of Mott-Anderson Localization
• Improving quantum-transition temperatures in BaFe2As2-based crystals by removing local-lattice strain & electronic-structure disorder
• Real-space pairing through a confined local nematic state in cuprate superconductors
• Density wave probes cuprate quantum phase transition
• Conductivity of anisotropic inhomogeneous superconductors above critical temperature
• Single-parameter scaling in the magnetoresistance of optimally doped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Universal Properties of Cuprate Superconductors: Tc Phase Diagram, Room-Temperature Thermopower, Neutron Spin Resonance, and STM Incommensurability Explained in Terms of Chiral Plaquette Pairing
• Superconductivity in strongly repulsive fermions: the role of kinetic-energy frustration
• Scattering from incipient stripe order in the high-temperature superconductor Bi2Sr2CaCu2O8+d
• Quasiparticle interference and charge order in a heavily overdoped non-superconducting cuprate
• Disappearance of zinc impurity resonance in large gap region on Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ probed by scanning tunneling spectroscopy
• Electron-like Fermi surface and in-plane anisotropy due to chain states in YBa${}_2$Cu${}_3$O${}_{7-\delta }$ superconductors
• Nanoscale phase separation in deep underdoped Bi${}_2$Sr${}_2$CuO${}_{6+\delta }$ and Ca${}_2$CuO${}_2$Cl${}_2$
• Anisotropic zero-resistance onset in organic superconductors
• A picture of pseudogap phase related to charge fluxes
• Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates
• On the Origin of the Checkerboard Pattern in Scanning Tunneling Microscopy Maps of Underdoped Cuprate Superconductors
• Superconducting correlations induced by charge ordering in cuprate superconductors and Fermi arc formation
• Superatom Representation of High-TC Superconductivity Revisited
• Visualizing the charge order and topological defects in an overdoped (Bi,Pb)${}_2$Sr${}_2$CuO${}_{6+x}$ superconductor
• On the size of superconducting islands on the density-wave background in organic metals
• Particle-hole symmetry breaking in the pseudogap state of Pb0.55Bi1.5Sr1.6La0.4CuO6+d: A quantum-chemical perspective
• Inhomogeneous superconductivity onset in FeSe studied by transport properties
• Probing Local Variations of Superconductivity on the Surface of Ba(Fe1-xCox)2As2 Single Crystals
• Evidence that cuprate superconductors form an array of nanoscopic Josephson junctions
• Spin-wave excitations in presence of nanoclusters of magnetic impurities
• Origin of the pseudogap and its influence on superconducting state
• In-plane and Out-of-plane Plasma Resonances in Optimally Doped La1.84Sr0.16CuO4
• Implications of Charge Ordering in the High Tc Cuprate Superconductors in the Far-infrared Spectroscopy
• Nanoscale Interlayer Defects in Iron Arsenides
• Josephson scanning tunneling microscopy: A local and direct probe of the superconducting order parameter
• A first-principles-based study of the thermodynamics of competing low-energy states in correlated materials: Example of cuprates
• "Half-Bogoliubons" as the intermediate states for the phase coherence in underdoped cuprates