Visualization of the emergence of the pseudogap state and the evolution to superconductivity in a lightly hole-doped Mott insulator

Abstract

Superconductivity emerges from the cuprate antiferromagnetic Mott state with hole doping. The resulting electronic structure 1 is not understood, although changes in the state of oxygen atoms seem paramount 2-5 . Hole doping first destroys the Mott state, yielding a weak insulator 6,7 where electrons localize only at low temperatures without a full energy gap. At higher doping levels, the 'pseudogap', a weakly conducting state with an anisotropic energy gap and intra-unit-cell breaking of 90 • rotational (C 4v ) symmetry, appears 3,4,8-10 . However, a direct visualization of the emergence of these phenomena with increasing hole density has never been achieved. Here we report atomic-scale imaging of electronic structure evolution from the weak insulator through the emergence of the pseudogap to the superconducting state in Ca 2− x Na x CuO 2 Cl 2 . The spectral signature of the pseudogap emerges at the lowest doping level from a weakly insulating but C 4v -symmetric matrix exhibiting a distinct spectral shape. At slightly higher hole density, nanoscale regions exhibiting pseudogap spectra and 180 • rotational (C 2v ) symmetry form unidirectional clusters within the C 4v -symmetric matrix. Thus, hole doping proceeds by the appearance of nanoscale clusters of localized holes within which the broken-symmetry pseudogap state is stabilized. A fundamentally two-component electronic structure 11 then exists in Ca 2− x Na x CuO 2 Cl 2 until the C 2v -symmetric clusters touch at higher doping levels, and the long-range superconductivity appears.To visualize at the atomic scale how the pseudogap and superconducting states are formed sequentially from the weak insulator state, we performed spectroscopic imaging scanning tunnelling microscopy (SI-STM) studies on Ca 2−x Na x CuO 2 Cl 2 (0.06 ≤ x ≤ 0.12; see also the Methods sections). The crystal structure is simple tetragonal (I 4/mmm) and thereby advantageous because the CuO 2 planes are unbuckled and free from orthorhombic distortion. More importantly Ca 2 CuO 2 Cl 2 can be doped from the Mott insulator to the superconductor by introduction of Na atoms. Figure 1c,d shows differential conductance images measured using SI-STM of bulk-insulating x = 0.06 and x = 0.08 samples taken in the field of views of the topographic images in Fig. 1a,b. The wavy, bright, arcs in Fig. 1c,d have never been observed in superconducting samples (x > 0.08) but appear only in such quasi-insulating samples (x ≤ 0.08). They are created by spectral peaks in differential conductance spectra whose energy is dependent on location (Fig. 1f). Consequently, the wavy arcs shrink with increasing bias voltages and finally disappear. This behaviour, due to tip-induced impurity charging [12][13][14] , is characteristic of poor electronic screening in a weakly insulating state.A wide variety of spectral shapes originating from electric heterogeneity were found in these samples. A typical example of the spectra is, as spectrum number 1 in Fig. 1e, the V-shaped pseudogap (∼0.2 eV) spectrum with a small dip (∼20...

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