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Register a new userSuperconducting correlations induced by charge ordering in cuprate superconductors and Fermi arc formation
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Evandro V. L. de Mello
Publication date
2017
fields
Physics
and research's language is
English
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We have developed a generalized electronic phase separation model of high-temperature cuprate superconductors that links the two distinct energy scales of the superconducting (SC) and pseudogap (PG) phases via a charge-density-wave (CDW) state. We show that simulated electronic-density modulations resembling the charge order (CO) modulations detected in cuprates intertwine the SC and charge orders by localizing charge and providing the energy scale for a spatially periodic SC attractive potential. Bulk superconductivity is achieved with the inclusion of Josephson coupling between nanoscale domains of intertwined fluctuating CDW and SC orders, and local SC phase fluctuations give rise to the Fermi arcs along the nodal directions of the SC gap. We demonstrate the validity of the model by reproducing the hole-doping dependence of the PG onset temperature $T^*$, and the SC transition temperature $T_c$ of ${rm YBa_2Cu_3O_y}$ and ${rm Bi_{2-y}Pb_ySr_{2-z}La_zCuO_{6+delta}}$. The results show that the periodicity of the CDW order is controlled by the PG energy scale, and the hole-doping dependence of the SC energy gap is controlled by the charge ordering free energy.
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The properties of cuprate high-temperature superconductors are largely shaped by competing phases whose nature is often a mystery. Chiefly among them is the pseudogap phase, which sets in at a doping $p^*$ that is material-dependent. What determines $p^*$ is currently an open question. Here we show that the pseudogap cannot open on an electron-like Fermi surface, and can only exist below the doping $p_{FS}$ at which the large Fermi surface goes from hole-like to electron-like, so that $p^*$ $leq$ $p_{FS}$. We derive this result from high-magnetic-field transport measurements in La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ under pressure, which reveal a large and unexpected shift of $p^*$ with pressure, driven by a corresponding shift in $p_{FS}$. This necessary condition for pseudogap formation, imposed by details of the Fermi surface, is a strong constraint for theories of the pseudogap phase. Our finding that $p^*$ can be tuned with a modest pressure opens a new route for experimental studies of the pseudogap.
One of the central issues in the recent study of cuprate superconductors is the interplay of charge order with superconductivity. Here the interplay of charge order with superconductivity in cuprate superconductors is studied based on the kinetic-energy-driven superconducting (SC) mechanism by taking into account the intertwining between the pseudogap and SC gap. It is shown that the appearance of the Fermi pockets is closely associated with the emergence of the pseudogap. However, the distribution of the spectral weight of the SC-state quasiparticle spectrum on the Fermi arc, or equivalently the front side of the Fermi pocket, and back side of Fermi pocket is extremely anisotropic, where the most part of the spectral weight is located around the tips of the Fermi arcs, which in this case coincide with the hot spots on the electron Fermi surface (EFS). In particular, as charge order in the normal-state, this EFS instability drives charge order in the SC-state, with the charge-order wave vector that is well consistent with the wave vector connecting the hot spots on the straight Fermi arcs. Furthermore, this charge-order state is doping dependent, with the charge-order wave vector that decreases in magnitude with the increase of doping. Although there is a coexistence of charge order and superconductivity, this charge order antagonizes superconductivity. The results from the SC-state dynamical charge structure factor indicate the existence of a quantitative connection between the low-energy electronic structure and collective response of the electron density. The theory also shows that the pseudogap and charge order have a root in common, they and superconductivity are a natural consequence of the strong electron correlation.
Despite immense efforts, the cuprate Fermi surface (FS) has been unambiguously determined in only two distinct, low-temperature regions of the phase diagram: a large hole-like FS at high doping, and a small electron-like pocket associated with charge-density-wave driven FS reconstruction at moderate doping. Moreover, there exists incomplete understanding of the reconstructed state, which is stabilized by high magnetic fields, and its connection with the normal state that consists of arc-like remnants of the large underlying FS. Part of the problem is that compound-specific idiosyncrasies, such as disorder effects and low structural symmetry, can obscure the fundamental properties of the quintessential CuO$_2$ planes. Here we present planar magnetotransport measurements for moderately-doped HgBa$_2$CuO$_{4+{delta}}$ that enable a quantitative understanding of the phase transition between the normal and reconstructed states and of the charge transport in the latter, and that demonstrate that the quasiparticle scattering rate in both states is due to Umklapp scattering. Building on prior insights, we furthermore arrive at a comprehensive understanding of the evolution of the planar transport properties throughout the entire cuprate phase diagram.
The presence of different electronic orders other than superconductivity populating the phase diagram of cuprates suggests that they might be the key to disclose the mysteries of this class of materials. In particular charge order in the form of charge density waves (CDW), i.e., the incommensurate modulation of electron density in the CuO$_2$ planes, is ubiquitous across different families and presents a clear interplay with superconductivity. Until recently, CDW had been found to be confined inside a rather small region of the phase diagram, below the pseudogap temperature and the optimal doping. This occurrence might shed doubts on the possibility that such low temperature phenomenon actually rules the properties of cuprates either in the normal or in the superconducting states. However, recent resonant X-ray scattering (RXS) experiments are overturning this paradigm. It results that very short-ranged charge modulations permeate a much wider region of the phase diagram, coexisting with CDW at lower temperatures and persisting up to temperatures well above the pseudogap opening. Here we review the characteristics of these high temperature charge modulations, which are present in several cuprate families, with similarities and differences. A particular emphasis is put on their dynamical character and on their coupling to lattice and magnetic excitations, properties that can be determined with high resolution resonant inelastic x-ray scattering (RIXS).
Charge-density-wave (CDW) correlations within the quintessential CuO$_2$ planes have been argued to either cause [1] or compete with [2] the superconductivity in the cuprates, and they might furthermore drive the Fermi-surface reconstruction in high magnetic fields implied by quantum oscillation (QO) experiments for YBa$_2$Cu$_3$O$_{6+{delta}}$ (YBCO) [3] and HgBa$_2$CuO$_{4+{delta}}$ (Hg1201) [4]. Consequently, the observation of bulk CDW order in YBCO was a significant development [5,6,7]. Hg1201 features particularly high structural symmetry and recently has been demonstrated to exhibit Fermi-liquid charge transport in the relevant temperature-doping range of the phase diagram, whereas for YBCO and other cuprates this underlying property of the CuO$_2$ planes is partially or fully masked [8-10]. It therefore is imperative to establish if the pristine transport behavior of Hg1201 is compatible with CDW order. Here we investigate Hg1201 ($T_c$ = 72 K) via bulk Cu L-edge resonant X-ray scattering. We indeed observe CDW correlations in the absence of a magnetic field, although the correlations and competition with superconductivity are weaker than in YBCO. Interestingly, at the measured hole-doping level, both the short-range CDW and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which the CDW formation is preceded at the higher pseudogap temperature by $q$ = 0 magnetic order [11,12] and the build-up of significant dynamic antiferromagnetic correlations [13]. Furthermore, the smaller CDW modulation wave vector observed for Hg1201 is consistent with the larger electron pocket implied by both QO [4] and Hall-effect [14] measurements, which suggests that CDW correlations are indeed responsible for the low-temperature QO phenomenon.
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