4a×4aelectronic charge order enhanced in the inhomogeneous pseudogap state ofBi2Sr2<

Abstract

Scanning tunneling microscopy and spectroscopy are used to examine the 4a ϫ 4a electronic charge order ͑CO͒ and the spatial dependence of energy gap in the pseudogap ͑PG͒ state above T c on Bi 2 Sr 2 CaCu 2 O 8+␦ . We report the first observation on energy gap inhomogeneity in the PG state, together with the result that the static CO develops markedly in the inhomogeneous PG state, although it is very weak in the homogeneous PG state. This static CO, which is considered to be stabilized by the pinning of the dynamically fluctuating CO, can coexist with the superconductivity below T c .In high-T c cuprate superconductors, it has been established that an unusual electronic state, characterized by a gaplike structure around the Fermi level E F , the so-called "pseudogap ͑PG͒," develops in the normal state above T c , and it must be well understood to elucidate the mechanism of high-T c superconductivity. Recently, in the PG state of underdoped ͑UD͒ Bi 2 Sr 2 CaCu 2 O 8+␦ ͑Bi2212͒, Vershinin et al. found a charge order ͑CO͒ in two-dimensional ͑2D͒ maps of the local density of states ͑LDOS͒ at specified energies, which were obtained by scanning tunneling microscopy and spectroscopy ͑STM/STS͒. 1 This CO is oriented along the two Cu-O bond directions, intersecting at right angles; its period is independent of energy, 4.5a -4.8a along each Cu-O direction ͑a, the lattice constant or the Cu-O-Cu distance͒, which is called "nondispersive." Interestingly, the nondispersive CO develops markedly at low energies within the PG and tends to disappear outside the PG. On the other hand, in the superconducting ͑SC͒ state, they did not observe the nondispersive CO, but observed dispersive LDOS modulations due to quasiparticle interference effects, which were first reported by Hoffman et al. 2 This tempted many researchers to suppose that the nondispersive CO is a characteristic feature only for the PG state above T c .However, in the SC state of UD Bi2212, Howald et al. 3 and Momono et al. 4 observed a nondispersive CO, whose period, ϳ4a for each Cu-O direction, was smaller than that reported by Vershinin et al. in the PG state. Furthermore, it has recently been demonstrated in STM/STS experiments that the amplitude of 4a ϫ 4a CO at T Ӷ T c is strongly sample dependent; in samples exhibiting an intense 4a ϫ 4a CO at T Ӷ T c , the spatial dependence of the energy gap structure is inhomogeneous on the nanometer scale, and vice versa. 5 For elucidating the relation among the CO, PG, and high-T c superconductivity, it is of urgency to study the problem of whether the 4a ϫ 4a CO is a common feature in both the SC and PG states. In this paper, we report STM/STS experiments in the PG state above T c on two kinds of samples that exhibit strong and weak 4a ϫ 4a CO's at T Ӷ T c , as shown in Figs. 2͑d͒ and 2͑e͒ and suggest that the static 4a ϫ 4a CO, which develops markedly in the inhomogeneous PG state, will remain below T c , together with the inhomogeneous gap structure.Bi2212 crystals were grown by the traveling solvent floating zone metho...

Strong-Coupling Superconductivity in the Cuprate Oxide

“…The checkerboard has actually been observed above T c . 77 It will be interesting to examine whether or not and how the appearance of the checkerboard and the development of the pseudogap are correlated. Since the cuprate-oxide superconductor is in the vicinity of the Néel state, antiferromagnetic critical fluctuations are also so crucial that they are responsible for the so-called T -linear resistivity.…”

Extinction of quasiparticle interference in underdoped cuprates with coexisting order

“…FT-STS has also been used to probe the pseudogap state in the underdoped regime where non-dispersive (bias-independent) quasi-periodic conductance modulations has been identified both in BSCCO 4,[6][7][8]22 and Ca 2−x Na x CuO 2 Cl 2 (Na-CCOC). 23 The origin of these peaks remains unknown at present but may be caused by short-range charge order, possibly connected to the existence of nested segments of the Fermi surface near the antinodal regions of the Brillouin zone.…”

Pseudogap-Like Phenomena in Cuprates as a Manifestation of Charge-Density Waves

“…Unidirectional CDW-like modulations and checkerboard structures have been also found in a number of high-T c oxides [21][22][23], which provides a direct support for our viewpoint. At the same time, to explain the smeared character of DHSs and PG-driven shallow DOS depletions, a wide spread of the PG parameters was assumed in close agreement with the observations [12,[21][22][23][24].…”

“…At the same time, such a charge modulation does take place in high-T c oxides (see, e.g., Refs. [23,27]), which explains our choice in favor of the CDW scenario. Moreover, in hole-doped cuprates, the antiferromagnetic region of the phase diagram lies far away from the superconducting dome [4,5], contrary to that, which exhibits the PG phenomena, making the SDW scenario less probable.…”

“…CDW gaps) and SGs, the higher inhomogeneity of the former was noticed while analyzing the scanning tunnel microscopy (STM) data for BSCCO [22] (see also Ref. [23]). An ingenious renormalization method, used to process the results of STM measurements for an overdoped (Bi 1−y Pb y ) 2 Sr 2 CuO 6+x sample with T c = 15 K [12], allowed it to be seen more or less directly.…”