In the present work, scanning tunneling microscopy/spectroscopy ͑STM/STS͒ measurements were carried out on underdoped Bi 2 Sr 2−x La x CuO 6+␦ and Bi 2 Sr 2 CaCu 2 O 8+␦ to clarify the origin of the pseudogap, in particular, the inhomogeneous large pseudogap. The nodal part of a d-wave pairing gap, which is under no influence of the inhomogeneous large pseudogap, was also examined by relating the homogeneous bottom part of the STS gap to a nodal d-wave gap in momentum space. We report that the inhomogeneous large pseudogap in the antinodal region links to a two-dimensional electronic charge order, and that the gap size of the nodal d-wave part ⌬ sc scales with the superconducting critical temperature T c in the pseudogap regime.

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...

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