Evolution of the pseudogap from Fermi arcs to the nodal liquid

Abstract

T he response of a material to external stimuli depends on its low-energy excitations. In conventional metals, these excitations are electrons on the Fermi surface-a contour in momentum (k) space that encloses all of the occupied states for non-interacting electrons. The pseudogap phase in the copper oxide superconductors, however, is a most unusual state of matter 1 . It is metallic, but part of its Fermi surface is 'gapped out' (refs 2,3); low-energy electronic excitations occupy disconnected segments known as Fermi arcs 4 . Two main interpretations of its origin have been proposed: either the pseudogap is a precursor to superconductivity 5 , or it arises from another order competing with superconductivity 6 . Using angle-resolved photoemission spectroscopy, we show that the anisotropy of the pseudogap in k-space and the resulting arcs depend only on the ratio T/ T * (x), where T * (x) is the temperature below which the pseudogap first develops at a given hole doping x. The arcs collapse linearly with T/ T * (x) and extrapolate to zero extent as T → 0. This suggests that the T = 0 pseudogap state is a nodal liquid-a strange metallic state whose gapless excitations exist only at points in k-space, just as in a d-wave superconducting state.In Fig. 1a,b we show data for a slightly underdoped sample of Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) with a transition temperature T c = 90 K, for the superconducting state at 40 K, and the pseudogap phase at 140 K. The energy distribution curves (EDCs) at the Fermi momentum k F , which have been symmetrized 4 to remove the effects of the Fermi function on the spectra. k F is determined by the minimum separation between the peaks in the symmetrized spectra along each momentum cut. Fifteen momentum cuts were measured, as shown in Fig. 1e. Details of the symmetrization procedure are explained in the Methods section. The difference between the spectra in the two states is apparent: sharp spectral peaks are present in the superconducting state, indicating longlived excitations, and the superconducting gap vanishes only at points in the Brillouin zone, known as nodes; on the other hand, the spectra in the pseudogap phase are much broader, indicating short-lived excitations. Although a pseudogap is seen in cuts 1-7, substantial parts of the Fermi surface, cuts 8-15, show spectra peaked at the Fermi energy, indicating a Fermi arc of gapless excitations.The gap size can be estimated as half the peak-to-peak separation in energy. A more quantitative estimate is obtained by using a simple phenomenological function to describe the spectral lineshapes 7

Energy gaps in the failed high-Tc superconductor La1.875Ba0.125CuO4

“…In contrast to the notion of a simple d-wave nodal liquid as the pseudogap ground state that is directly derived from the antinodal pseudogap 15,16 , our observation of an apparent break-up in the gap function suggests a very different picture. It reveals a much richer pseudogap physics with its two aspects manifesting differently in distinct momentum regions, that is, the nodal precursor pairing and the antinodal pseudogap of different but unknown origin.…”

“…Despite persistent efforts, theoretical ideas for the pseudogap evolve around fluctuating superconductivity 2 , competing order 3-8 and spectral weight suppression due to many-body effects 9 . Recently, although some experiments in the superconducting state indicate a distinction between the superconducting gap and pseudogap 10-14 , others in the normal state, either by extrapolation from high-temperature data 15 The first high-T c superconductor discovered, La 2−x Ba x CuO 4 (LBCO), holds a unique position in the field because of an anomalously strong bulk T c suppression near x = 1/8. Right around this 'magic' doping level, scattering experiments by neutrons 18,19 and X-rays 20 find a static spin and charge (stripe) order.…”

Electronic structure of cuprate superconductors in a full charge-spin recombination scheme

“…In particular, as a direct method for probing the electron Fermi surface, the early ARPES measurements indicate that in the entire doping range, the underlying electron Fermi surface satisfies Luttinger's theorem [24][25][26][27] , i.e., the electron Fermi surface with the area is proportional to 1 − δ. Later, the ARPES experimental studies show that in the underdoped and optimally doped regimes, although the antinodal region of the electron Fermi surface is gapped out, leading to the notion that only part of the electron Fermi surface survives as the disconnected Fermi arcs around the nodes [28][29][30][31][32] , the underlying electron Fermi surface determined from the low-energy spectral weight still fulfills Luttinger's theorem in the entire doping range 32 . These ARPES experimental facts [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] on the other hand provide strong evidences supporting the notion of the charge-spin recombination 13,14 .…”

Compositional evolution of the anti-phase stripe superstructure in Bi2Sr2−xLaxCuO6(0 <x≤ 1.1) revealed by transmission electron microscopy

“…In the La and Pb co-doped Bi 2−y Pb y Sr 2−z La z CuO 6+x samples, STM found a static, no-dispersive and strong doping dependence 'checkerboard'-like electronic modulation in a broad doping regime which was suggested to originate from charge-density-wave formation [7]. Novel Fermi surface topologies, such as Fermi arcs in pseudogap state, signatures of particle-hole symmetry breaking in the pseudogap state [8][9][10] and hints of a "pseudogap phase transition" in Bi2201 [4] have been observed by ARPES. Recently, Fermi pocket has been revealed in underdoped Bi 2 Sr 2-x La x CuO 6 (La-Bi2201), which coexists with the Fermi arcs [1].…”