Spectroscopic Imaging Scanning Tunneling Microscopy Studies of Electronic Structure in the Superconducting and Pseudogap Phases of Cuprate High-T_cSuperconductors

Abstract

One of the key motivations for the development of atomically resolved spectroscopic imaging scanning tunneling microscopy (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 jEj ¼ Á 0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k ¼ AEð=a 0 ; 0Þ to k ¼ AEð0; =a 0 Þ. 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 jEj Á 0 states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale jEj $ Á 1 which is associated conventionally with the ''antinodal'' states near k ¼ AEð=a 0 ; 0Þ and k ¼ AEð0; =a 0 Þ. We find that these states break the expected 90 -rotational (C 4 ) symmetry of electronic structure within CuO 2 unit cells, at least down to 180 -rotational (C 2 ) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C 4 symmetry breaking coexists at jEj $ Á 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 jEj $ Á 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 energy scales jEj $ Á 1 and jEj Á 0 , and to understand how this impacts the electronic phase diagram and the mechanism of high-T c superconductivity, represents one of a key challenges for cuprate studies.

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

“…Moreover, we demonstrate that the dFF-DW modulations at E = −∆ 1 (filled states) occur with relative phase π compared to those at E = ∆ 1 (empty states). Finally, we show that the conventionally defined dFF-DW Q corresponds to scattering between the 'hot frontier' regions of momentum-space beyond which Bogoliubov quasiparticles cease to exist [30][31][32] . These data indicate that the cuprate dFF-DW state involves particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in momentum space where the pseudogap opens.…”

Staggered Flux State in Two-Dimensional Hubbard Models

“…1,2 Because the pseudogap phase appears in the proximity of half filling, it is probably related to Mott insulators 3,4 (precisely, charge-transfer insulators 5 ). Experimentally, the pseudogap phase presents various features distinct from an ordinary Fermi liquid.…”

“…(2) Rotational symmetry breaking (or nematic order) similar to the stripe phase is observed, and the oxygen sites between copper atoms are involved. 2,20 (3) Charge orders or charge density waves are observed in resonant X-ray scattering experiments. [21][22][23] (4) (π, π)-folded (shadow) bands appear in ARPES spectra, and so forth.…”

“…Besides cuprates, we consider a model for layered organic conductors, κ-(BEDT-TTF) 2 X, [henceforth, abbreviated as κ-(ET) 2 X] with X being a univalent anion. [73][74][75] In these compounds, SC arises for T c 12 K, and a pseudogap behavior similar to that of cuprates has been observed.…”

Quasiparticle interference and the interplay between superconductivity and density wave order in the cuprates

“…1,8,9 STS has revealed that the cuprates have a spatially inhomogeneous electronic structure, including modulations in the LDOS and superconducting gap magnitude. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] In the d-wave superconducting phase, the LDOS modulations can arise from quasiparticle interference (QPI), due to the scattering of wave-like quasiparticles off impurities. 12,15,22,[25][26][27] The wavevectors of the modulations can be determined from the Fourier transform of the LDOS.…”