Imaging nanoscale Fermi-surface variations in an inhomogeneous superconductor (original) (raw)
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Charge-density-wave origin of cuprate checkerboard visualized by scanning tunnelling microscopy
Nature Physics, 2008
One of the main challenges in understanding high-T c superconductivity is to disentangle the rich variety of states of matter that may coexist, cooperate or compete with d-wave superconductivity. At centre stage is the pseudogap phase, which occupies a large portion of the cuprate phase diagram surrounding the superconducting dome 1. Using scanning tunnelling microscopy, we find that a static, non-dispersive, 'checkerboard'-like electronic modulation exists in a broad regime of the cuprate phase diagram and exhibits strong doping dependence. The continuous increase of checkerboard periodicity with hole density strongly suggests that the checkerboard originates from charge-density-wave formation in the antinodal region of the cuprate Fermi surface. These results reveal a coherent picture for static electronic orderings in the cuprates and shed important new light on the nature of the pseudogap phase. A great deal of current interest is focused on the 'checkerboard'like electronic lattices first discovered in cuprates by scanning tunnelling microscopy (STM) in vortex cores in optimally doped Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) (ref. 2). This ordering was found to have a roughly 4 unit-cell (4a 0) wavelength orientated along the Cu-O bond direction. Subsequent STM investigations of the cuprates have revealed other checkerboard structures in the absence of a magnetic field. For example, in the superconducting state of Bi-2212, the first report of a checkerboard saw a roughly 4a 0 wavelength throughout the sample 3 , whereas a later study found the ordering (wavelength 4.5a 0) limited to regions with large-gap ('zero-temperature pseudogap') tunnelling spectra 4. A checkerboard was also found in slightly underdoped Bi-2212 above the superconducting transition temperature T c with wavelength 4.7a 0 ± 0.2a 0 (ref. 5). In Ca 2−x Na x CuO 2 Cl 2 (Na-CCOC), a commensurate electronic crystal phase with period 4a 0 was found at low temperatures in both superconducting and nonsuperconducting samples 6. Although it is not yet clear whether these checkerboards all represent the same electronic entities, many models have been proposed to explain the mechanisms of these novel electronic
Journal of the Physical Society of Japan, 2012
One of the key motivations for the development of atomically resolved spectroscopic imaging STM (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These are detected below a lower energy scale |E|=∆ 0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k=±(π/a 0 ,0) to k=±(0, π/a 0). Below optimal doping, this 'nodal' arc shrinks continuously with decreasing hole density. In both the dSC and PG phases, the only broken symmetries detected in the |E|≤∆ 0 states are those of a dwave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E|~∆ 1 which is associated conventionally with the 'antinodal' states near k=±(π/a 0 ,0) and k=±(0, π/a 0). We find that these states break the expected 90 o-rotational (C 4) symmetry of electronic structure within CuO 2 unit cells, at least down to 180 orotational (C 2) symmetry (nematic) but in a spatially disordered fashion. This intraunit-cell C 4 symmetry breaking coexists at |E|~ ∆ 1 with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The characteristic wavevector Q of the latter is determined, empirically, by the k-space points where Bogoliubov quasiparticle interference terminates, and therefore evolves continuously with doping. The properties of these two classes of |E|~∆ 1 states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their
2011
We survey the use of spectroscopic imaging STM to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E=Δ 0 . We find that the Bogoliubov quasiparticle interference signatures of delocalized Cooper pairing are restricted to a k-space arc which terminates near the lines connecting k=±(π/a 0 ,0) to k=±(0,π/a 0 ). This arc shrinks continuously with decreasing hole density such that Luttinger's theorem could be satisfied if it represents the front side of a hole-pocket which is bounded behind by the lines between k=±(π/a 0 ,0) and k=±(0,π/a 0 ). In both phases the only broken symmetries detected for the |E|<Δ 0 states are those of a d-wave superconductor. The second class of states occurs proximate to the pseudogap energy scale E=Δ 1 . Here the non-dispersive electronic structure breaks the expected 90 orotational symmetry of electronic structure within each unit cell, at least down to 180 o -rotational symmetry. This Q=0 electronic symmetry breaking was first detected as an electronic inequivalence at the two oxygen sites within each unit cell by using a measure of nematic (C 2 ) symmetry. Incommensurate non-dispersive conductance modulations, locally breaking both rotational and translational symmetries, coexist with this intra-unit-cell electronic symmetry breaking at E=Δ 1 . Their characteristic wavevector Q 2 is determined by the k-space points where Bogoliubov quasiparticle interference terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (Q=0 and finite Q) coexisting at E~Δ 1 are found to be indistinguishable in the dSC and PG phases. We propose that the next challenge for SI-STM studies is to determine the relationship of the E~Δ 1 broken symmetry electronic states to the pseudogap phase, and to the E<Δ 0 states associated with Cooper pairing. The electronic structure of the CuO 2 plane is dominated by Cu 3d and O 2p orbitals [1]. Energetically each Cu d x2-y2 orbital is split into singly and doubly occupied configurations by on-site Coulomb interactions, with the O p-states intervening. This is a 'charge-transfer' [1] Mott insulator which is strongly antiferromagnetic due to superexchange [2,3]. 'Hole-doping' is achieved by removing electrons from the O atoms [4]. It results in the highest temperature superconductivity available today. The phase diagram [5], with p the number of holes per CuO 2 , is shown schematically in .
Proceedings of the National Academy of Sciences, 2020
The defining characteristic of hole-doped cuprates is d-wave high temperature superconductivity. However, intense theoretical interest is now focused on whether a pair density wave state (PDW) could coexist with cuprate superconductivity [D. F. Agterberg et al., Annu. Rev. Condens. Matter Phys. 11, 231 (2020)]. Here, we use a strong-coupling mean-field theory of cuprates, to model the atomic-scale electronic structure of an eight-unit-cell periodic, d-symmetry form factor, pair density wave (PDW) state coexisting with d-wave superconductivity (DSC). From this PDW + DSC model, the atomically resolved density of Bogoliubov quasiparticle states Nr,E is predicted at the terminal BiO surface of Bi2Sr2CaCu2O8 and compared with high-precision electronic visualization experiments using spectroscopic imaging scanning tunneling microscopy (STM). The PDW + DSC model predictions include the intraunit-cell structure and periodic modulations of Nr,E, the modulations of the coherence peak energy Δ...
Journal of Physics-condensed Matter, 2008
Temperature, T , variations of the tunnel conductance G(V ) were calculated for junctions between a normal metal and a spatially inhomogeneous superconductor with a dielectric gap on the nested sections of the Fermi surface or between two such superconductors. The dielectric gapping was considered to be a consequence of the charge density wave (CDW) appearance due to the electron-phonon (for a Peierls insulator) or a Coulomb (for an excitonic insulator) interactions. Spatial averaging was carried out over random domains with varying parameters of the CDW superconductor (CDWS). The calculated tunnel spectra demonstrate a smooth transformation from asymmetric patterns with a pronounced dip-hump structure at low T into those with a pseudogap depletion of the electron densities of states at higher T in the vicinity or above the actual critical temperatures of the superconducting transition for any of the CDWS domains. Thus, it is demonstrated that both the dip-hump structure and pseudogapping are manifestations of the same phenomenon. A possible CDW-induced asymmetry of the background contribution to G(V ) is also touched upon. The results explain the peculiar features of G(V ) for Bi 2 Sr 2 CaCu 2 O 8+δ and other related high-T c cuprates.
Physical Review Letters, 2008
In two dimensions the non-interacting density of states displays a Van Hove singularity (VHS) which introduces an intrinsic electron-hole asymmetry, absent in three dimensions. We show that due to this VHS the strong-coupling analysis of tunneling spectra in high-Tc superconductors must be reconsidered. Based on a microscopic model which reproduces the experimental data with great accuracy, we elucidate the peculiar role played by the VHS in shaping the tunneling spectra, and show that more conventional analyses of strong-coupling effects can lead to severe errors. PACS numbers: 68.37.Ef, 74.72.Hs, 74.50.+r Scanning tunneling spectroscopy of Bi-based cuprate high-T c superconductors (HTS) shows a d-wave gap and a strong dip-hump feature which is nearly always stronger for occupied than for empty states. 1 It has been proposed that the dip-hump structure results from the interaction of electrons with a collective mode, 2 but the dip asymmetry has not received an explanation so far. Indeed such a coupling leads to electron-hole symmetric spectra in classical superconductors. 3,4,5 The dip-hump was also observed by photoemission, but in those experiments it is not possible to probe the electron-hole asymmetry. Sometimes photoemission spectra are even symmetrized, 6 thus ignoring the relevance of the asymmetry seen in tunneling. The fact that in two dimensions the density of states (DOS) has a prominent van-Hove singularity (VHS), unlike in 3D, introduces naturally an asymmetry and thereby modifies the strongcoupling analysis and the corresponding determination of the collective mode frequency in an essential way.
EPL (Europhysics Letters), 2010
We investigate the interplay between strong electron correlations and charge-lattice interaction in cuprates. The coupling between half breathing bond stretching phonons and doped holes in the t-t ′ -J model is studied by limited phonon basis exact diagonalization method. Nonadiabatic electronphonon interaction leads to the splitting of the phonon spectral function at half-way to the zone boundary at qs = {(±π/2, 0), (0, ±π/2)} and to low energy kink feature in the electron dispersion, in agreement with experimental observations. Another kink due to strong electron correlation effects is observed at higher energy, depending on the strength of the charge-lattice coupling.
Fermiology of cuprates from first principles: From small pockets to the Luttinger Fermi surface
Physical Review B, 2008
Fermiology, the shape and size of the Fermi surface, underpins the low-temperature physical properties of a metal. Recent investigations of the Fermi surface of high-T c superconductors, however, show a most unusual behavior: upon addition of carriers, "Fermi" pockets appear around nodal (hole doping) and antinodal (electron doping) regions of the Brillouin zone in the "pseudogap" state. With progressive doping, δ, these evolve into well-defined Fermi surfaces around optimal doping (δ opt ), with no pseudogap. Correspondingly, various physical responses, including d-wave superconductivity, evolve from highly anomalous, up to δ opt , to more conventional beyond. Describing this evolution holds the key to understanding high-temperature superconductivity. Here, we present ab initio quantum chemical results for cuprates, providing a quantitative description of the evolution of the Fermi surface with δ. Our results constitute an ab initio justification for several, hitherto proposed semiphenomenological theories, offering an unified basis for understanding of various, unusual physical responses of doped cuprates.