In conventional superconductors, which operate at temperatures near absolute zero, the appearance of an energy gap in the electronic spectrum indicates pairing of electrons into Cooper pairs, global phase coherence, and a simultaneous transition into a macroscopic superconducting state. This gap is known as the superconducting gap. In contrast, in high-temperature superconductors (HTSCs) (which have nonsuperconductive, mixed, and superconductive matter states), an energy gap is already present at the Fermi surface in the normal, nonsuperconductive, state. This is known as a pseudogap, and its origin and relationship to superconductivity is one of the most important open issues in the physics of HTSCs and represents the focal point of current theoretical debate. According to one view, this pseudogap is really a pairing (superconducting) gap, reflecting the existence of Cooper pairs without global phase coherence. The superconducting transition then occurs at some lower temperature, when phase coherence is established. In an alternative view, the pseudogap represents another state of matter entirely that competes with superconductivity. However, the order associated with such a competing state has never been unambiguously detected.

Photoemission from LBCO at x = 1/8. Photoemission intensity from a narrow interval around the Fermi level (ω = 0 ± 10 meV) as a function of the in-plane momentum. High intensity represents the underlying Fermi surface. Lines represent fits to the positions of maxima in spectral intensity at the Fermi level for LBCO (x = 0.125) (solid line) and LSCO (x = 0.07) (dashed line).

Cuprates are well-known HTSCs, but in the cuprate compound LBCO, superconductivity is strongly suppressed and static spin and charge orders, or "stripes," develop near a low doping level of x = 1/8 (at a point when one-eighth of the electrons have been removed). Previous measurements have shown that these stripes, an alternating arrangement of electrons about four atoms wide, somehow inhibit superconductivity. This absence of superconductivity at x = 1/8 enabled the researchers to "peek" into the normal ground state of an HTSC material for the first time.

(A) Photoemission intensity from LBCO sample as a function of binding energy along the momentum lines indicated in Figure 1 by arrows. (B) Energy distribution curves of spectral intensity integrated over a small interval k_F ± Δk along the two lines in k-space shown in (A). The arrow represents the shift of the leading edge. The spectra were taken in the charge ordered state at T = 16 K.

The researchers measured the electronic excitations and detailed momentum dependence of the single-particle gap in the ordered state of LBCO. Using ARPES at ALS Beamline 12.0.1, they detected an energy gap at the Fermi surface in the nonsuperconducting LBCO that looks the same as the energy gap at the Fermi surface in superconducting cuprates. This pseudogap, like the superconducting gap, has magnitude consistent with d-wave symmetry (a form of electron pairing in which the electrons travel together in quantum waves shaped like a four-leaf clover), and vanishes at four nodal points on the Fermi surface. Using STM at the ultra-low vibration laboratory of Cornell University, they found that the density of states DOS(E) ∝ |E|, with zero-DOS falling exactly at the Fermi energy. Furthermore, the gap has a surprising doping dependence, with a maximum at x ≈ 1/8, precisely where T_c has a local minimum and the charge/spin order is established between two adjacent superconducting domes. These findings reveal the pairing origin of the pseudogap and imply that the most strongly bound Cooper pairs at x ≈ 1/8 are most susceptible to phase disorder and spatial ordering. Thus, the nonsuperconducting, "striped" state at x = 1/8 is consistent with a phase incoherent d-wave superconductor whose Cooper pairs form spin/charge ordered structures instead of becoming superconducting.

(A) Magnitude of single-particle gap for two LBCO samples (red and black triangles) as a function of an angle around the Fermi surface. The line represents a d-wave gap amplitude, Δ₀|cos(2f)| with Δ₀ = 20 meV. (B) Doping dependence of Δ₀ in LBCO (red triangles) and LSCO (blue circles). Red line represents doping dependence of T_c for LBCO.

Although with both ARPES and STM, low-energy electronic signatures were the same in both states, it is not yet clear how the superconducting state relates to the striped state. However, the fact remains that the same materials in two very different states appear to have identical energy-gap structures. 

Research conducted by T. Valla and G.D. Gu (Brookhaven National Laboratory), A. V. Fedorov (Berkeley Lab), and Jinho Lee and J.C. Davis (Cornell University).

Research funding: U.S. Department of Energy, Office of Basic Sciences (BES), the Office of Naval Research, and Cornell University. Operation of the ALS is supported by BES.

Publication about this research: T. Valla, A.V. Fedorov, J. Lee, J.C. Davis, and G.D. Gu, "The ground state of the pseudogap in cuprate superconductors," Science 314, 1914 (2006).