Donghui Lu, Kyle Shen, and Zhi-Xun Shen

Departments of Applied Physics, Physics, and Stanford Synchrotron Radiation Laboratory, Stanford University, Stanford, CA 94305

High-temperature superconductors (HTSC's), following their remarkable discovery in 1986, continue to be at the center stage of modern condensed matter physics. Despite great efforts from both theoretical and experimental sides, the mechanism of HTSC still remains elusive. One of the most peculiar aspects of HTSC's is that their parent compounds are so-called Mott insulators and the superconductivity is achieved by doping carriers into the insulating parent compounds. It is generally believed that a comprehensive understanding of the doping evolution from Mott insulator to superconductor holds the key to the mystery of HTSC.

Angle-resolved photoemission spectroscopy, a method of probing the electronic states in momentum space, has played an indispensable role in advancing our understanding of the high-temperature cuprate superconductors over the last decade. With the state-of-the-art ARPES system at SSRL beamline 5-4, researchers Kyle Shen and Donghui Lu, along with their co-workers in Prof. Zhi-Xun Shen's group at Stanford University, have recently focused their attention on the doping evolution of the electronic structure in the lightly doped cuprate superconductor Ca_2-xNa_xCuO₂Cl₂ (Na-CCOC) [1]. In this intervening region between the Mott insulator and HTSC, the so-called pseudogap regime, the system exhibits many highly anomalous physical properties. Many attempts to explain these unusual properties have focused on the possibility of competing interactions in this regime. Recently, a distinct real-space pattern of 4a₀ x 4a₀ two-dimensional charge ordering (2DCO) in Na-CCOC has been discovered by scanning tunneling microscopy (STM) [2], a real-space probe that is complementary to ARPES. This finding calls attention to the importance of charge ordering and its connection to high-temperature superconductivity.

Detailed examinations of ARPES data reveal important aspects of the low energy excitations in Na-CCOC and provide insight to the 2DCO observed in STM. The highlight of this work is summarized in Figure 1. The left panel shows the momentum distribution of spectral weight around the Fermi energy, which is dominated by strong intensity diagonal to the copper-oxygen bond (along the (0,0) — (p,p) "nodal" direction) and drops off rapidly along a direction parallel to the copper-oxygen bond ((p,0), the "anti-node"). In conjunction to an analysis of the momentum distribution curves near the antinodes, a schematic of the Fermi surface is extracted, as shown in the middle panel. In addition to the well defined arc-like Fermi surface segments near the nodal directions, straight segments of Fermi surface near the antinodes (indicated in hatched regions) can be detected. These straight portions of the Fermi surface appear to be well nested and separated by approximately |q| ~ 2p/4a₀. Such a Fermi surface "nesting" behavior may be related to the 4a₀ x 4a₀ 2DCO pattern observed in STM, which is displayed in the right panel. This correspondence is exhibited not only in the agreement of the wave vectors, but also in the unusual weak energy (w) and doping dependence of this pattern.

Figure 1: (A) The integrated ARPES spectral weight within a ± 10 meV window around E_F in one quadrant of the first Brillouin zone for x = 0.10. (B) Schematic of the low-lying spectral intensity, which consists of well-defined Fermi arcs near the nodal region and very weak straight segments near the antinodes (hatched regions). (C) An STM dI/dV map taken at 24 meV, exhibiting the 4a₀ x 4a₀ ordering (after Ref. [2]).

Although the Fermi surface nesting behavior seen in ARPES seems to provide a natural explanation for the 2DCO pattern revealed by STM, the spectral weight in the nested portions of the Fermi surface that is representative of the charge ordering is extremely weak. This is very different from the conventional charge-density-wave systems, in which well-defined "quasiparticle" excitations still exist upon the formation of the charge-density-wave state. Therefore, the strongly suppressed spectral weight near the antinodal regions cannot be explained by simple Fermi surface nesting alone.

These surprising results also indicate a strong dichotomy between the real- and momentum-space probes, for which charge ordering is emphasized in the tunneling measurements, while photoemission is most sensitive to the excitations near the nodal direction. Irrespective of the microscopic model, the dichotomy between the sharp nodal quasiparticles and broad antinodal states emphasizes the important aspect of momentum anisotropy in the electronic structures of HTSC's and puts strong constraints on the theoretical models.

1. Kyle M. Shen, F. Ronning, D. H. Lu, F. Baumberger, N. J. C. Ingle, W. S. Lee, W. Meevasana, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, Z.-X. Shen, "Nodal Quasiparticles and Antinodal Charge Ordering in Ca_2-xNa_xCuO₂Cl₂", Science 307, 901 (2005).
   
2. T. Hanaguri, C. Lupien, Y. Kohsaka, D.-H. Lee, M. Azuma, M. Takano, H. Takagi, J. C. Davis, "A 'checkerboard' electronic crystal state in lightly hole-doped Ca_2-xNa_xCuO₂Cl₂", Nature 430, 1001 (2004).