A ‘checkerboard’ electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2

Abstract

The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the 'pseudogap' regime 1 . This regime is rich in peculiar electronic phenomena 1 , prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca 2−x Na x CuO 2 Cl 2 . Tunnelling spectroscopy (at energies |E|>100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for |E|<100 meV, the spectrum exhibits a V-shaped energy gap centred on E=0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO 2 -unit-cell square 'checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca 2−x Na x CuO 2 Cl 2 .Scanning tunnelling microscopy (STM) has recently emerged as a suitable technique to search for 'hidden' electronic order in the copper oxides. Bi 2 Sr 2 CaCu 2 O 8+δ (Bi-2212) studies where high-transition-temperature (T c ) superconductivity (HTSC) was 2 suppressed to reveal the pseudogap have been especially fruitful. The prototypical study yielded a pseudogap-like conductance spectrum (V-shaped without coherence peaks) associated with a 'checkerboard' approximately four CuO 2 unit cells square of localdensity-of-states (LDOS) modulations surrounding vortex cores 2 . Similar phenomena were discovered throughout the sample above T c (ref.3), and within strongly underdoped nano-regions exhibiting pseudogap-like spectra 4 (see Fig. 1c). Underdoped Bi-2212 therefore shows a tendency towards checkerboard electronic modulations when HTSC is suppressed. However, it is unclear whether these checkerboard modulations in Bi-2212 represent a true electronic phase, because they exhibit [2][3][4] (1) a variety of dopingdependent incommensurate wavevectors, (2) very weak intensities, and (3) To search for electronic order hidden in the pseudogap while avoiding these uncertainties, we decided to study a simpler and less disordered copper oxide at lower doping and temperature. We chose Ca 2−x Na x CuO 2 Cl 2 (Na-CCOC), a material whose parent compound Ca 2 CuO 2 Cl 2 is a canonical Mott insulator 8 . Within its undistorted tetragonal crystal structure (Fig. 1b), all the CuO 2 planes are crystallographically identical. Sodium substitution for Ca destroys the Mott insulator state, producing first a nodal metal 9 in the zero-temperature pseudogap (ZTPG) regime, and eventually HTSC for x≥0. 10 (refs 10, 11). Crucially, Na-CCOC ...

Scanning tunneling microscopy and spectroscopy study of4a×4aelectronic charge order and the inhomogeneous pairing gap in superconductingBi2Hashimoto1, Momono2, Oda3 et al. 2006Phys. Rev. B371320View full textAdd to dashboardCite

“…9͑b͒, the spatially averaged spectrum over a distance of ϳ35 nm is shown together with the ZTPGs reported for lightly doped Na-CCOC and Bi2212. 1,2 The averaged gap structure is very similar to the ZTPGs of Na-CCOC and Bi2212. Width of the averaged gap ⌬ 0 , defined as the width between a shoulder on the positive bias side and zero bias V s =0, is ϳ80 meV.…”

“…11 The charge order is commensurate ͑4a ϫ 4a͒ and has an internal structure with a period of 4a /3ϫ 4a / 3, which is just like the electronic charge order reported by Hanaguri et al for lightly doped Na-CCOC. 1 The observation of almost the same charge order for both cuprates Na-CCOC and Bi2212 provides definite evidence that the nondispersive 4a ϫ 4a charge order develops on the Cu-O layer. The 4a ϫ 4a charge order is likely to be dynamical in itself, and pinned down over regions with effective pinning centers.…”

“…The present nondispersive 4a ϫ 4a superstructure observed in samples A and B is essentially the same as the nondispersive 4a ϫ 4a charge order with the internal structure of 4a /3ϫ 4a / 3 reported by Hanaguri et al for lightly doped Na-CCOC. 1 Shown in Fig. 5͑a͒ is part of a low-bias STM image taken on sample C at V s = 30 mV, which was cut from the single crystal ␤ ͑p ϳ 0.13, T c ϳ 78 K͒.…”

“…If the 4a ϫ 4a superstructure is due to some kind of lattice distortion, it is difficult to explain why the superstructure appears within a limited bias ͑energy͒ range, especially, associated with the gap size ⌬ 0 ; V s Շ⌬ 0 / e. Such a limitation of V s in observing the 4a ϫ 4a superstructure means that the superstructure is electronic in origin, that is, due to an electronic charge order, as has been claimed in many preceding studies. [1][2][3][9][10][11] The appearance of the 4a ϫ 4a charge order within the pairing gap implies that quasiparticles of the SC state and/or hole pairs will take part in causing the charge order.…”

“…4,5 Such charge orders have attracted much attention because the charge order can be a possible electronic hidden order in the pseudogap state. 1,3 In measurements of LDOS maps in the superconducting ͑SC͒ state of Bi2212, Hoffman et al and McElroy et al found a strongly dispersive 2D spatial structure, which has been successfully explained in terms of SC quasiparticle scattering interference. [6][7][8] Furthermore, Howald et al and Fang et al reported a nondispersive ϳ4a ϫ 4a charge order with anisotropy in the SC state of Bi2212 in addition to weakly dispersive ones, and claimed that the charge order was due to the stripe order and coexisted with the superconductivity.…”