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
Angle resolved photoemission data in the pseudogap phase of underdoped cuprates have revealed the presence of a truncated Fermi surface consisting of Fermi arcs. We compare a number of proposed models for the arcs and find that the one that best models the data is a d-wave energy gap with a lifetime broadening whose temperature dependence is suggestive of fluctuating pairs.
Angle resolved photoemission on underdoped Bi 2 Sr 2 CaCu 2 O 8 reveals that the magnitude and d-wave anisotropy of the superconducting state energy gap are independent of temperature all the way up to T c . This lack of T variation of the entire k-dependent gap is in marked contrast to mean field theory. At T c the point nodes of the d-wave gap abruptly expand into finite length ''Fermi arcs.'' This change occurs within the width of the resistive transition, and thus the Fermi arcs are not simply thermally broadened nodes but rather a unique signature of the pseudogap phase. DOI: 10.1103/PhysRevLett.99.157001 PACS numbers: 74.25.Jb, 74.72.Hs, 79.60.Bm We present in this Letter angle resolved photoemission spectroscopy (ARPES) data on the energy gap in the superconducting (SC) and pseudogap phases of the underdoped high T c superconductor Bi 2 Sr 2 CaCu 2 O 8 (Bi2212). Reduced T c samples which lie in between the optimally doped, highest T c material and the undoped Mott insulator are called ''underdoped.'' Such samples exhibit an unusual normal-state pseudogap, whose signature in ARPES [1,2] is a loss of spectral weight in parts of k space, leading to low-energy electronic excitations which live on disconnected ''Fermi arcs '' [3]. Both the SC gap below T c and the pseudogap above T c are anisotropic gaps in the singleparticle excitation spectrum, but their relationship is not well understood. Our goal is to gain insight into how the SC gap, with its d-wave anisotropy [1,2] at low T, changes as a function of temperature and evolves into the anisotropic pseudogap upon heating through T c .Our first result is that the magnitude and anisotropy of the d-wave SC energy gap is essentially T independent for all T T c . This behavior is completely different from a mean field description of a d-wave superconductor. Within mean field theory the anisotropy would be T independent, but the gap magnitude, proportional to the order parameter, would be suppressed with increasing T and vanish at T c . Remarkably, our data show that the k-dependent SC gap in underdoped cuprates does not even know about the scale of T c .Second, there are four point nodes at which the energy gap vanishes for all T < T c , but above T c each point node abruptly expands into a gapless Fermi arc of finite extent. We show that this remarkable change occurs within the width of the resistive transition at T c . The abrupt change from point nodes to gapless arcs is not just thermal smearing, but rather it is closely connected with the loss of superconducting order.We present ARPES data on two underdoped Bi2212 films, one near optimality (T c 80 K) and the other more underdoped (T c 67 K), both of which exhibit a significant pseudogap. The films, prepared by RF sputtering on a SrTiO 3 substrate [4], exhibit only very weak superstructure replicas which simplifies the data analysis. The measurements were carried out at the Synchrotron Radiation Center, Wisconsin, using a Scienta R4000 analyzer with 22 eV photons, and momentum cuts and polarization para...
A charge-density wave (CDW) state has a broken symmetry described by a complex order parameter with an amplitude and a phase. The conventional view, based on clean, weak-coupling systems, is that a finite amplitude and long-range phase coherence set in simultaneously at the CDW transition temperature Tcdw. Here we investigate, using photoemission, X-ray scattering and scanning tunnelling microscopy, the canonical CDW compound 2H-NbSe2 intercalated with Mn and Co, and show that the conventional view is untenable. We find that, either at high temperature or at large intercalation, CDW order becomes short-ranged with a well-defined amplitude, which has impacts on the electronic dispersion, giving rise to an energy gap. The phase transition at Tcdw marks the onset of long-range order with global phase coherence, leading to sharp electronic excitations. Our observations emphasize the importance of phase fluctuations in strongly coupled CDW systems and provide insights into the significance of phase incoherence in ‘pseudogap’ states.
In the underdoped high temperature superconductors, instead of a complete Fermi surface above Tc, only disconnected Fermi arcs appear, separated by regions that still exhibit an energy gap. We show that in this pseudogap phase, the energy-momentum relation of electronic excitations near EF behaves like the dispersion of a normal metal on the Fermi arcs, but like that of a superconductor in the gapped regions. We argue that this dichotomy in the dispersion is difficult to reconcile with a competing order parameter, but is consistent with pairing without condensation.
We examine the momentum and energy dependence of the scattering rate of the high-temperature cuprate superconductors using angle-resolved photoemission spectroscopy. The scattering rate is of the form a + b around the Fermi surface for under-and optimal doping. The inelastic coefficient b is found to be isotropic. The elastic term a, however, is found to be highly anisotropic for under-and optimally doped samples, with an anisotropy which correlates with that of the pseudogap. This is contrasted with heavily overdoped samples, which show an isotropic scattering rate and an absence of the pseudogap above T c . We find this to be a generic property for both single-and double-layer compounds.
Cuprates possess a large pseudogap that spans much of their phase diagram 1,2 . The origin of this pseudogap is as debated as the mechanism for high-temperature superconductivity. In one class of theories, the pseudogap arises from some instability not related to pairing, typically charge, spin or orbital current ordering. Evidence of this has come from a variety of measurements indicating symmetry breaking [3][4][5][6] . On the other side are theories where the pseudogap is associated with pairing. This ranges from preformed pairs 7 to resonating valence bond theories where spin singlets become charge coherent 8 . Here, we study pairing in the cuprates by constructing the pair vertex using spectral functions derived from angle-resolved photoemission data. Assuming that the pseudogap is not due to pairing, we find that the superconducting instability is strongly suppressed, in stark contrast to what is actually observed. We trace this suppression to the destruction of the BCS logarithmic singularity from a combination of the pseudogap and lifetime broadening. Our findings strongly support those theories of the cuprates where the pseudogap is instead due to pairing.To construct the pair vertex, we must first know the singleparticle Green's function. An issue is that angle-resolved photoemission spectroscopy (ARPES) measures only occupied states. As in earlier work, we surmount this difficulty under the assumption of particle-hole symmetry with respect to the Fermi energy and Fermi surface (k F )where I is the photoemission intensity and ω is measured relative to the chemical potential. Relaxing this approximation should lead to only quantitative differences in the results (particle-hole asymmetry will act to suppress pairing). The assumption that the left-hand side of the equation can be equated to the spectral function (imaginary part of the single-particle Green's function) requires subtracting any background from the intensity (obtained from data for unoccupied momenta well beyond k F ), and then normalizing by requiring the integrated weight over frequency to be equal to unity. A similar method has been successfully employed by us in several works, most recently 9 to construct the dynamic susceptibility in cuprates, which was found to be in good agreement with inelastic neutron scattering (INS) data. In fact, the data set we employ here, from a near-optimal doped Bi 2 Sr 2 CaCu 2 O 8+δ sample with a T c of 90 K, was used in that work to reproduce the momentum and energy dependence of the INS data in the superconducting state, in particular the unique hourglass-like dispersion observed in a variety of cuprates. In our case, though, we will use normal-state data above T c . For this sample, a relatively complete momentum sweep was done in an octant of the Brillouin zone at a temperature of 140 K (ref. 10) and exhibits a pronounced pseudogap with a gapless arc. The data were obtained on a 2 meV energy grid down to 322 meV below the Fermi energy, with the background intensity adjusted to match each spectrum at th...
The autocorrelation of angle resolved photoemission data from the high temperature superconductor Bi(2)Sr(2)CaCu(2)O(8+delta) shows distinct peaks in momentum space which disperse with binding energy in the superconducting state, but not in the pseudogap phase. Although it is tempting to attribute a nondispersive behavior in momentum space to charge ordering, a deconstruction of the autocorrelation reveals that the nondispersive peaks arise from the tips of the Fermi arcs, which themselves do not change with binding energy.
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