Electronic structure of the cuprate superconducting and pseudogap phases from spectroscopic imaging STM

Abstract

Abstract. We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-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 = 0 . We find that the Bogoliubov quasiparticle interference (QPI) 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 that is bounded behind by the 8 Author to whom any correspondence should be addressed. New Journal of Physics 13 (2011) 0650141367-2630/11/065014+32$33.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 lines between k = ±(π/a 0 , 0) and k = ±(0, π/a 0 ). In both phases, the only broken symmetries detected for the |E| < 0 states are those of a d-wave superconductor. The second class of states occurs proximate to the PG energy scale E = 1 . Here the non-dispersive electronic structure breaks the expected 90• -rotational symmetry of electronic structure within each unit cell, at least down to 180• -rotational symmetry. This 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 = 1 . Their characteristic wavevector Q is determined by the k-space points where Bogoliubov QPI terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (intraunit-cell and finite Q) coexisting at E ∼ 1 are found to be indistinguishable in the dSC and PG phases. The next challenge for SI-STM studies is to determine the relationship of the E ∼ 1 broken symmetry electronic states with the PG phase, and with the E < 0 states associated with Cooper pairing.

Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ

“…We find that V CDW is neither equivalent to the Fermi velocity seen in ARPES nor the quasi-particle-interference dispersion seen in STM 21 (Supplementary Information), indicating that the weak-coupling fermiology may be irrelevant for describing the observed dispersion. Temperature-dependent measurements were conducted on another Bi2212 crystal with a similar T c (40 K), with results shown in Fig.…”

“…We choose the double-layer cuprate Bi 2.2 Sr 1.8 Ca 0.8 Dy 0.2 Cu 2 O 8+δ (Bi2212), whose electronic structure has been extensively studied by surface-sensitive spectroscopy, such as scanning tunnelling microscopy 21 and angle-resolved photoemission 22 , and in which a short-range CDW order was recently reported 7,8 . With improved energy resolution up to 40 meV, we see additional features in the previous quasi-elastic region (Fig.…”

Universal disorder in Bi2Sr2CaCu2OAlldredge1, Fujita2, Eisaki3 et al. 2013Phys. Rev. B

“…The low energy 'V-shaped' region of the LDOS(E) are the energies where the coherent excitations of the Bogoliubov quasiparticles from the superconducting condensate reside 10 . These excitations present themselves as the dispersive QPI, seven vectors in q-space that emanate from the eight ends of the superconducting band structure 1,4,15 .…”

“…Due to the short length scale of this disorder, the only method capable of directly probing it is spectroscopic imaging scanning tunneling microscopy (SI-STM). This technique produces data sets that contain detailed information about both the spatial and energy dependence of the quasiparticle interference (QPI) of Bogoliubov quasiparticles [1][2][3][4][5] , the checkerboard 3,6 and the pseudogap states [7][8][9][10] . It has been recently shown that the low energy empty states electronic structure (positive energies) can be classified into three energy scales using the Tripartite model 11 , which is a phenomenological model explaining from both q-space and r-space SI-STM data.…”

“…This paper is divided into seven sections, the introduction (1), background material (2), a definition of the Tripartite model (3), fitting procedure (4), fitting results (5), the relationship between the local fitting observables and the spatial modulations (6) and conclusions (7). Additional overviews of SI-STM phenomena in Bi 2 Sr 2 CaCu 2 O 8+x is available in several review publications 10,12 . The Tripartite model is also explained in detail and applied to mean LDOS(E) spectra and QPI gap structures in a recent publication 11 .…”