An understanding of the nature of superconductivity in cuprates has been hindered by the apparent diversity of intertwining electronic orders in these materials. Here we combine resonant X-ray scattering (REXS), scanning-tunneling microscopy (STM), and angle-resolved photoemission spectroscopy (ARPES) to observe a charge order that appears consistently in surface and bulk, as well as momentum and real space, with the Bi2Sr2−xLaxCuO 6+δ cuprate family. The observed wavevector rules out simple antinodal nesting in the single particle limit, but matches well with a phenomenological model of a many-body instability of the Fermi arcs. Combined with earlier observations in other cuprate families, these findings suggest the existence of a generic charge-ordered state in underdoped cuprates, and uncover its connection to the pseudogap regime. PACS numbers:Since the discovery of cuprate high-temperature superconductors, several unconventional phenomena have been observed in the region of the phase diagram located between the strongly localized Mott insulator at zero doping and the itinerant Fermi-liquid state that emerges beyond optimal doping [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The so-called 'pseudogap' opens at the temperature T * and obliterates the Fermi surface at the antinodes (AN) of the d-wave superconducting gap function, leaving behind disconnected "Fermi arcs" centered around the nodes. In addition, charge order has been observed on the surface of Bi-and Clbased compounds [4][5][6][7][8], in the bulk of La-based compounds [9][10][11], and most recently in YBa 2 Cu 3 O 6+δ (YBCO) [17][18][19][20], indicating this might be the leading instability in underdoped cuprates. The similarity between the observed charge ordering wavevector and the antinodal nesting vector of the hightemperature Fermi surface has prompted suggestions that a conventional Peierls-like charge-density-wave (CDW) might be responsible for the opening of the pseudogap [7,8,12,19]. We use complementary bulk/surface techniques to examine the validity of this scenario, and explore the connection between charge ordering and fermiology.By applying a suite of complementary tools to a single cuprate material, Bi 2 Sr 2−x La x CuO 6+δ (Bi2201), we reveal that the charge order in this system emerges just below T * , and that its wavevector corresponds to the Fermi arc tips rather than the antinodal nesting vector. We quantify the Fermi surface using ARPES, and we look for charge modulations along the Cu-O bond directions in both real-and reciprocalspace, using STM and REXS. The single-layer Bi2201 is well suited to this purpose owing to: (i) its two-dimensionality and high degree of crystallinity [22,23], and (ii) the possibility of probing the temperature evolution across T * , which is bettercharacterized [15,16] and more accessible than in bilayer sys-
The nature of the pseudogap phase of cuprate high-temperature superconductors is one of the most important unsolved problems in condensed matter physics. We studied the commencement of the pseudogap state at temperature T * using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally-doped Bi2201 crystals. We observe the coincident onset at T * of a particle-hole asymmetric antinodal gap, a non-zero Kerr rotation, and a change in the relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (T c ), entangled in an energy-momentum dependent fashion with the pre-existing pseudogap features.As complex oxides, cuprate superconductors belong to a class of materials which exhibit many broken-symmetry states; unravelling the relationship between superconductivity in the cuprates and other possible broken-symmetry states has been a major challenge of condensed matter physics. A possibly related issue concerns the nature of the pseudogap in the cuprates and its relationship with superconductivity. Angle-resolved photoemission spectroscopy (ARPES) studies have shown that the pseudogap develops below a temperature T * near the Brillouin zone boundary while preserving a gapless Fermi arc near the zone diagonal (1). A key issue is the extent to which the pseudogap is a consequence of superconducting fluctuations (2-5), which should exhibit a rough particle-hole symmetry, or another form of (incipient) order (6-12), which typically should induce particle-hole asymmetric spectral changes. Candidate orders include various forms of density wave, nematic or unconventional magnetic orders that break different combinations of lattice translational (6-8, 13-19), rotational (6, 9, 15, 17, 20-22), and time-reversal (7, 9, 23-26) symmetries.We have focused on crystals of nearly optimally-doped (OP) Pb 0.55 Bi 1.5 Sr 1.6 La 0.4 CuO 6+δ (PbBi2201, T c = 38 K, T * = 132 ± 8 K) (27), and combined the ARPES measurements of the evolution of the band structure over a wide range of temperature, momentum and energy, with high-precision measurements of the polar Kerr effect (PKE) and time-resolved reflectivity (TRR).Bi2201 was chosen to avoid the complications resulting from bilayer splitting and strong antinodal bosonic mode coupling inherent to Bi 2 Sr 2 CaCu 2 O 8+δ (Bi2212) (1). Whereas ARPES is a surface probe, PKE enables us to monitor a bulk, thermodynamic (via the fluctuation-dissipation theorem) 2 property which has proven (28) to be a sensitive probe of the onset of a broken-symmetry state, and TRR gives complementary information on the bulk, near-equilibrium dynamics of the system. We will first analyze our ARPES data collected in different temperature regions. Above T * , PbBi2201 has a simple one-band band structure (right side of Fig. 1). For each cut in momentum space Fig. 1), the only distinct feature in the ...
A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials, such as the cuprate high-temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates, where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping-and temperaturedependence ARPES study of spectral gaps in Bi 2 Sr 2 CaCu 2 O 8+δ , covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p = 0.19 for the pseudogap phase and p = 0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T c and exists p > 0.19 at higher temperatures. Our data imply a revised phase diagram that reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome.quantum materials | correlated electrons | laser ARPES T he momentum-resolved nature of angle-resolved photoemission spectroscopy (ARPES) makes it a key probe of the cuprates, the interesting phases of which have anisotropic momentumspace structure (1-4): both the d-wave superconducting gap and the pseudogap above T c have a maximum at the antinode [AN, near (π, 0)] and are ungapped at the node, although the latter phase also exhibits an extended ungapped arc (5-8). Ordering phenomena often result in gapping of the quasiparticle spectrum, and distinct quantum states produce spectral gaps with characteristic temperature, doping, and momentum dependence. These phenomena were demonstrated by recent ARPES experiments that argued that the pseudogap is a distinct phase from superconductivity based on their unique phenomenology (8-15): the pseudogap dominates near the AN (8, 11), and its magnitude increases with underdoping (11, 12), whereas near-nodal (NN) gaps have a different doping dependence and can be attributed to superconductivity because they close at T c (8, 12). Previous measurements focused on AN or intermediate (IM) momenta, but laser-ARPES, with its superior resolution and enhanced statistics, allows for precise gap measurements near the node where the gap is smallest. Our work is unique in its attention to NN momenta using laser-ARPES, and we demonstrate, via a single technique, that three distinct quantum phases manifest in different NN phenomenology as a function of doping. ResultsGaps at parallel cuts were determined by fitting symmetrized energy distribution curves (EDCs) at k F to a minimal model (16).The Fermi wavevector, k F , is defined by the minimum gap locus. Example spectra, raw and symmetrized EDCs at k F , and fits are shown for UD92 (underdoped, T c = 92) ...
Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of stronglycorrelated states of matter. The recent discovery of charge order in various cuprate families fueled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T c superconductors.Here we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi 2 Sr 2−x La x CuO 6+δ (Bi2201) and YBa 2 Cu 3 O 6+y (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum-structure of charge order. We also resolve the intra-unit-cell symmetry of the charge ordered state, which is revealed to be best represented by a bond-order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights on the microscopic description of charge order in cuprates, and on its origin and interplay with superconductivity.Complex oxides exhibit a mosaic of exotic electronic phases with various symmetry-broken ground states that revolve around three main instabilities: antiferromagnetism, charge order, and superconductivity. In particular, charge order -the tendency of the valence electrons to segregate into periodically-modulated structures -is found in various classes of strongly-correlated 3d-oxides, such as manganites [1], nickelates [2], and cobaltates [3]. The original discovery of period-4 stripe-like charge correlations in the La-based materials [4][5][6][7] confirmed the central role played by chargeordered states in the physics of underdoped cuprates, as anticipated by earlier theoretical work [8][9][10][11][12]. Following further indications by surface-sensitive scanning tunnelling microscopy (STM) [13, 14], the field was recently revived by the detection of charge-modulated states in YBCO using nuclear magnetic resonance [15] and resonant X-ray scattering (RXS), with wavevector Q * ∼ 0.31 reciprocal lattice units (r.l.u., used hereafter) [16][17][18][19][20][21]. Even more recently, this phenomenology was confirmed in Bi-based materials (with Q * ∼ 0.26 and 0.3 in single-and double-layer compounds, respectively), following observations in both bulk/momentum space (with RXS) FIG. 1:Charge ordering patterns and wavevectors. a, Schematics of a RXS experiment. b, Low-temperature RXS (at photon energy hν = 931.5 eV) from an underdoped Bi2201-UD15K sample, mapping reciprocal-space features along the two high-symmetry directions: (H, 0), antinodal, green (reproduced from Ref. 22, the full line represents a Gaussian fit plus background); and (H, H), nodal, orange. c,e, Modulation of the charge density ∆ρ(x, y), with functional form given by a sum (c) and product (e) of cosines, and a wavevector magnitude Q * = 0.265 r.l.u. (black bars indicate the period and direction of the spatial modulation, expressed in terms of the lattice parameter a = 3.86Å). The blu...
Fe-based superconductors have attracted research interest because of their rich structural variety, which is due to their layered crystal structures. Here we report the new-structure-type Fe-based superconductors CaAFe4As4 (A = K, Rb, Cs) and SrAFe4As4 (A = Rb, Cs), which can be regarded as hybrid phases between AeFe2As2 (Ae = Ca, Sr) and AFe2As2. Unlike solid solutions such as (Ba(1-x)K(x))Fe2As2 and (Sr(1-x)Na(x))Fe2As2, Ae and A do not occupy crystallographically equivalent sites because of the large differences between their ionic radii. Rather, the Ae and A layers are inserted alternately between the Fe2As2 layers in the c-axis direction in AeAFe4As4 (AeA1144). The ordering of the Ae and A layers causes a change in the space group from I4/mmm to P4/mmm, which is clearly apparent in powder X-ray diffraction patterns. AeA1144 is the first known structure of this type among not only Fe-based superconductors but also other materials. AeA1144 is formed as a line compound, and therefore, each AeA1144 has its own superconducting transition temperature of approximately 31-36 K.
In conventional superconductors, a gap exists in the energy absorption spectrum only below the transition temperature (T c ), corresponding to the price to pay in energy for breaking a Cooper pair of electrons and creating two excited states. In high-T c cuprate superconductors above T c but below a temperature T * , an energy gap called the pseudogap 1 exists, and is controversially attributed either to pre-formed superconducting pairs, which would show particle-hole symmetry, or to competing phases that would typically break it. Scanning tunnelling microscopy (STM) studies suggest that the pseudogap stems from lattice translational symmetry breaking 2-9 and is associated with a different characteristic spectrum for adding or removing electrons (particle-hole asymmetry; refs 2,3). However, no signature of either energy or spatial symmetry breaking of the pseudogap has previously been observed by angle-resolved photoemission spectroscopy 9-18 (ARPES). Here we report ARPES data from Bi2201, which reveal both particle-hole symmetry breaking and pronounced spectral broadening-indicative of spatial symmetry breaking without long-range order at the opening of the pseudogap. Our finding supports the STM proposal that the pseudogap state is a broken-symmetry state that is distinct from homogeneous superconductivity.The nature of the pseudogap can be explored by examining the dispersion of the occupied electronic states measured by ARPES. As shown in Fig. 1m, when a particle-hole symmetric gap opens from the normal-state dispersion (red curve) because of homogeneous superconductivity, one always expects an alignment between the Fermi momentum k F and the 'back-bending' or saturation momentum (green arrows) of the dispersion in the gapped states (weighted blue curve). As a result of this strong constraint, the observation of a back-bending or dispersion saturation anomaly away from k F in a gapped state can be conclusive evidence of a broken particle-hole symmetry nature of the gap, even though the information about the unoccupied state is absent. Here we note that the dispersion of the spectral peak position, regardless of the spectral weight, is a simple and direct way to address the issue of particle-hole symmetry. Owing to suppressed spectral weight that makes it hard to discern from the experimental background, the back-bending may sometimes be subtle and show up as a dispersion saturation. Nevertheless, it can be distinguished from a smooth dispersion where no dispersion saturation occurs.
To clarify the superconducting gap structure of the spin-triplet superconductor Sr2RuO4, the in-plane thermal conductivity has been measured as a function of relative orientations of the thermal flow, the crystal axes, and a magnetic field rotating within the 2D RuO2 planes. The in-plane variation of the thermal conductivity is incompatible with any model with line nodes vertical to the 2D planes and indicates the existence of horizontal nodes. These results place strong constraints on models that attempt to explain the mechanism of the triplet superconductivity.
We investigated the optical spectrum of Ba(Fe1−xCox)2As2 single crystals with various doping levels. It is found that the low-energy optical conductivity spectrum of this system can be decomposed into two components: a sharp Drude term and a broad "incoherent" term. For the compounds showing magnetic order, a gap appears predominantly in the "incoherent" component, while an swave like superconducting gap opens in both components for highly doped compounds. The Drude weight steadily increases as doping proceeds, consistent with electron doping in this system. On the other hand, the "incoherent" spectral weight is almost doping independent, but its spectral feature is intimately connected with the magnetism. We demonstrate that the presence of two distinct components in the optical spectrum well explains the doping and temperature dependences of the dc resistivity.
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