Direct phase-sensitive identification of a d -form factor density wave in underdoped cuprates

Abstract

The identity of the fundamental broken symmetry (if any) in the underdoped cuprates is unresolved. However, evidence has been accumulating that this state may be an unconventional density wave. Here we carry out site-specific measurements within each CuO 2 unit cell, segregating the results into three separate electronic structure images containing only the Cu sites [Cu(r)] and only the x/y axis O sites [O x (r) and O y (r)]. Phase-resolved Fourier analysis reveals directly that the modulations in the O x (r) and O y (r) sublattice images consistently exhibit a relative phase of π. We confirm this discovery on two highly distinct cuprate compounds, ruling out tunnel matrix-element and materials-specific systematics. These observations demonstrate by direct sublattice phaseresolved visualization that the density wave found in underdoped cuprates consists of modulations of the intraunit-cell states that exhibit a predominantly d-symmetry form factor.CuO 2 pseudogap | broken symmetry | density-wave form factor U nderstanding the microscopic electronic structure of the CuO 2 plane represents the essential challenge of cuprate studies. As the density of doped holes, p, increases from zero in this plane, the pseudogap state (1, 2) first emerges, followed by the high-temperature superconductivity. Within the elementary CuO 2 unit cell, the Cu atom resides at the symmetry point with an O atom adjacent along the x axis and the y axis (Fig. 1A, Inset). Intraunit-cell (IUC) degrees of freedom associated with these two O sites (3, 4), although often disregarded, may actually represent the key to understanding CuO 2 electronic structure. Among the proposals in this regard are valence-bond ordered phases having localized spin singlets whose wavefunctions are centered on O x or O y sites (5, 6), electronic nematic phases having a distinct spectrum of eigenstates at O x and O y sites (7,8), and orbital-current phases in which orbitals at O x and O y are distinguishable due to time-reversal symmetry breaking (9). A common element to these proposals is that, in the pseudogap state of lightly hole-doped cuprates, some form of electronic symmetry breaking renders the O x and O y sites of each CuO 2 unit cell electronically inequivalent.Electronic Inequivalence at the Oxygen Sites of the CuO 2 Plane in Pseudogap State Experimental electronic structure studies that discriminate the O x from O y sites do find a rich phenomenology in underdoped cuprates. Direct oxygen site-specific visualization of electronic structure reveals that even very light hole doping of the insulator produces local IUC symmetry breaking, rendering O x and O y inequivalent (10), that both Q ≠ 0 density wave (11) and Q = 0 C 4 -symmetry breaking (11, 12, 13) involve electronic inequivalence of the O x and O y sites, and that the Q ≠ 0 and Q = 0 broken symmetries weaken simultaneously with increasing p and disappear jointly near p c = 0.19 (13). For multiple cuprate compounds, neutron scattering reveals clear intraunit-cell breaking of rotational symmetry (14,15...

Intra-unit-cell nematic charge order in the titanium-oxypnictide family of superconductors

“…The earlier muon spin relaxation results 26,27 , together with the ED measurements, allow us to rule out the existing proposals of SDW formation 32,33 or a phonon-driven CDW 34 . Instead, an intra-unit-cell charge-nematic electronic symmetry breaking is implicated, similar to that proposed for doped cuprates 39 .…”

Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

“…Within a given "hot region" in the Brillouin zone, the spin-fluctuation exchange gives rise to CDW order with a small momentum, much like as the one due to small-Q phonon exchange 28 , Magnetically mediated CDW order also naturally gives rise to a sign change between CDW orders in different hot regions separated by (π, π). This is consistent with the observed d-wave formfactor of the CDW order parameter 11 .…”

“…An incommensurate CDW order has been observed in La-based cuprates a while ago 1,2 , and recently was found to be ubiquitous in the cuprates [3][4][5][6][7][8][9][10][11][12][13] . The CDW order is incommensurate, with momentum Q along X and/or Y directions, where Q ∼ (0.2 − 0.3) × 2π.…”

“…In a finite field a true long-range CDW order has been detected 14 . An incommensurate charge order parameter generally has both onsite and bond components (a true CDW and a bond order, respectively 8,11 . To simplify the presentation, we use the term CDW below for both on-site and bond orders.…”

Doping asymmetry and striping in a three-orbitalCuO2Hubbard model

“…Achkar et al 14 have reported resonant soft x-ray scattering measurements which show that the charge distribution on the oxygens of LBCO have an s -CDW orbital structure in which the charge modulations on the O px and O py sites in a unit cell are in phase. STM Studies of BSCCO (p ∼ 8%) and NaCCOC (p ∼ 12%) find that these materials have a predominantly d-CDW orbital form factor in which these O px and O py charge modulations are out of phase 15 . Finally, recent resonant x-ray scattering measurements of Nd 2−x Ce x CuO 4 near optimal doping 16 find charge order which occurs with a similar periodicity and Cu-O bond orientation to that of the charge stripes seen in LBCO.…”