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We use angle-resolved photoemission spectroscopy applied to deeplyto reveal the presence of two distinct energy gaps exhibiting different doping dependence. One gap, associated with the antinodal region where no coherent peak is observed, increases with underdopinga behavior known for more than a decade and considered as the general gap behavior in the underdoped regime. The other gap, 1

Nematicity, defined as broken rotational symmetry, has recently been observed in competing phases proximate to the superconducting phase in the cuprate high-temperature superconductors. Similarly, the new iron-based high-temperature superconductors exhibit a tetragonal-to-orthorhombic structural transition (i.e., a broken C 4 symmetry) that either precedes or is coincident with a collinear spin density wave (SDW) transition in undoped parent compounds, and superconductivity arises when both transitions are suppressed via doping. Evidence for strong in-plane anisotropy in the SDW state in this family of compounds has been reported by neutron scattering, scanning tunneling microscopy, and transport measurements. Here, we present an angle-resolved photoemission spectroscopy study of detwinned single crystals of a representative family of electron-doped iron-arsenide superconductors, BaðFe 1-x Co x Þ 2 As 2 in the underdoped region. The crystals were detwinned via application of in-plane uniaxial stress, enabling measurements of single domain electronic structure in the orthorhombic state. At low temperatures, our results clearly demonstrate an in-plane electronic anisotropy characterized by a large energy splitting of two orthogonal bands with dominant d xz and d yz character, which is consistent with anisotropy observed by other probes. For compositions x > 0, for which the structural transition (T S ) precedes the magnetic transition (T SDW ), an anisotropic splitting is observed to develop above T SDW , indicating that it is specifically associated with T S . For unstressed crystals, the band splitting is observed close to T S , whereas for stressed crystals, the splitting is observed to considerably higher temperatures, revealing the presence of a surprisingly large in-plane nematic susceptibility in the electronic structure.C orrelated electron systems owe their emergent phenomena to a complex array of competing electronic phases. Among these, a nematic phase is one where rotational symmetry is spontaneously broken without breaking translational symmetry (1, 2). Two well-established examples are found in certain quantum Hall states (3) and in the bilayer ruthenate Sr 3 Ru 2 O 7 (4), both of which exhibit a large transport anisotropy under the application of large magnetic fields, even though they seem to originate from apparently different physics. Recently, evidence of nematicity has also been reported in the pseudogap phase of cuprate high-temperature (high-T C ) superconductors, in both YBa 2 Cu 3 O y (5) and Bi 2 Sr 2 CaCu 2 O 8þδ (6). The proximity of the pseudogap phase to superconductivity raises the question of what role nematicity plays in relation to the mechanism of high-T C superconductivity. Intriguingly, the newly discovered iron pnictide high-T C superconductors also exhibit a nematic phase in the form of a tetragonal-to-orthorhombic structural transition that either precedes or accompanies the onset of long-range antiferromagnetic order (7,8), both of which are suppressed with doping leading to...

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) ...

Understanding the role of competing states in the cuprates is essential for developing a theory for high-temperature superconductivity. We report angle-resolved photoemission spectroscopy experiments which probe the 4a0 x 4a0 charge-ordered state discovered by scanning tunneling microscopy in the lightly doped cuprate superconductor Ca2-xNaxCuO2Cl2. Our measurements reveal a marked dichotomy between the real- and momentum-space probes, for which charge ordering is emphasized in the tunneling measurements and photoemission is most sensitive to excitations near the node of the d-wave superconducting gap. These results emphasize the importance of momentum anisotropy in determining the complex electronic properties of the cuprates and places strong constraints on theoretical models of the charge-ordered state.

The evolution of Ca2−xNaxCuO2Cl2 from Mott insulator to superconductor was studied using angle-resolved photoemission spectroscopy. By measuring both the excitations near the Fermi energy as well as non-bonding states, we tracked the doping dependence of the electronic structure and the chemical potential with unprecedented precision. Our work reveals failures in the conventional quasiparticle theory, including the broad lineshapes of the insulator and the apparently paradoxical shift of the chemical potential within the Mott gap. To resolve this, we develop a model where the quasiparticle is vanishingly small at half filling and grows upon doping, allowing us to unify properties such as the dispersion and Fermi wavevector with the behavior of the chemical potential.PACS numbers: 74.20. Rp, 74.25.Jb, A central intellectual issue in the field of hightemperature superconductivity is how an antiferromagnetic insulator evolves into a superconductor. In principle, the ideal tool to address this problem is angleresolved photoemission spectroscopy (ARPES), which can directly extract the single-particle excitations. Despite the interest in this doping induced crossover, there continues to be a lack of experimental consensus, perhaps the most prominent example being the controversy over the chemical potential, µ. Over the past fifteen years, there have been conflicting claims of µ either being pinned in mid-gap or shifting to the valence / conduction band upon carrier doping [1,2,3,4,5,6]. The inability of photoemission spectroscopy to provide a logically consistent understanding of this fundamental thermodynamic quantity has been a dramatic shortcoming in the field.In this paper, we present a new procedure to quantify µ with unprecedented precision by ARPES, while allowing simultaneous high resolution measurements on the low energy states. These measurements allow us to make major conceptual advances in addressing the doping evolution. We find that the long standing confusion over µ stems from the manner in which quasiparticle-like (QP) excitations in the doped samples emerge from the unusually broad features in the undoped insulator. Our work reveals inconsistencies in the conventional framework that considers the main peak in the insulator spectrum to represent the QP pole. On the one hand, we find that µ changes in a manner consistent with an approximate rigid band shift; on the other hand, this shift appears to occur within the apparent Mott gap of the parent insulator. We show that this ostensible paradox can be naturally explained if one uses a model based on Franck-Condon-like broadening (FCB) where the quasiparticle residue, Z, is vanishingly small near half filling. This also reconciles existing puzzles regarding the insulator and the lightly doped compounds, and naturally ties the behavior of µ to low energy features such as the Fermi wavevector, k F , and the quasiparticle velocity v F .Ca 2−x Na x CuO 2 Cl 2 is an ideal system to address the doping evolution of the cuprates. The stoichiometric parent compoun...

High-temperature superconductivity (HTSC) mysteriously emerges upon doping holes 1 or electrons 2 into insulating copper oxides with antiferromagnetic (AFM) order. It has been thought that the large energy scale of magnetic excitations, compared to phonon energies for example, lies at the heart of an electronically-driven superconducting phase with high transition temperatures (T c ) 3-5 . Comparison of high-energy magnetic excitations of hole-and electron-doped superconductors in connection with the respective T c provides an exceptional, yet un-capitalized opportunity to test this hypothesis 6-9 . Here, we use resonant inelastic x-ray scattering (RIXS) at the Cu L 3 -edge 10,11 to reveal high-energy collective excitations in the archetypical electron-doped cuprate Nd 2-x Ce x CuO 4 (NCCO) 2 . Surprisingly, despite the fact that the AFM correlations are short-ranged 12 , magnetic excitations harden significantly across the AFM-HTSC phase boundary, in stark contrast with the hole-doped cuprates 6,7 . Furthermore, we find an unexpected and highly dispersive branch of collective modes in superconducting NCCO that are absent in hole-doped compounds. These modes emanate from zone center and weaken with increasing temperature, which signal a quantum phase distinct from superconductivity. The asymmetry uncovered between electron-and hole-doped cuprates provides new, unexpected dimensions to collective excitations that are generally important to the mechanism of superconductivity in these materials. Hole-doped cuprates display compelling evidence for the surprising persistence of magnetic excitations beyond the AFM phase boundary 6,7 , as well as the existence of symmetrybroken phases, such as charge density waves 13,14,15 and orbital loop currents 16 , distinct from superconductivity. Whether these are universal and exist on the other side of the cuprate phase diagram, i.e. with electron-doping, remains an important open question. To address this issue,

Experimental evidence on high-T c cuprates reveals ubiquitous charge density wave (CDW) modulations 1-10 , which coexist with superconductivity. Although the CDW had been predicted by theory 11-13 , important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap 10,14 . Here, we use ultrahigh-resolution resonant inelastic X-ray scattering to reveal new CDW character in underdoped Bi 2.2 Sr 1.8 Ca 0.8 Dy 0.2 Cu 2 O 8+δ . At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T * , the CDW persists, but the associated excitations significantly weaken with an indication of CDW wavevector shift. The dispersive CDW excitations, phonon anomaly, and analysis of the CDW wavevector provide a comprehensive momentumspace picture of complex CDW behaviour and point to a closer relationship with the pseudogap state.With sufficient energy resolution, resonant inelastic X-ray scattering (RIXS) can be an ideal probe for revealing the CDW excitations in cuprates. By tuning the incident photon energy to the Cu L 3 -edge (Fig. 1a), the resonant absorption and emission processes can leave the system in excited final states, which couple to a variety of excitations arising from orbital, spin, charge, and lattice degrees of freedom 15 . Thus, information of these elementary excitations in energy and momentum space can be deduced from analysing the RIXS spectra as functions of the energy loss and the momentum transfer of the photons (Fig. 1a). This is highlighted by the pivotal role that RIXS has recently played in revealing orbital and magnetic excitations in cuprates [16][17][18][19][20] . In addition, RIXS provided the first X-ray scattering evidence for an incommensurate CDW in (Y,Nd)Ba 2 Cu 3 O 6+δ (ref. 4), owing to energy resolution that separated the quasi-elastic CDW signal (bright spot in Fig. 1b, limited by the instrumental resolution ∼130 meV) from other intense higher-energy excitations. Notably this quasi-elastic signal is asymmetric with respect to zero energy loss (Fig. 1c), which indicates the possible existence of additional low-energy excitations near the CDW wavevector (Q CDW ).In this work, we exploit the newly commissioned ultrahighresolution RIXS instrument at the European Synchrotron Radiation Facility to reveal these low-energy excitations near the CDW. We choose the double-layer cuprate Bi 2.2 Sr 1.8 Ca 0.8 Dy 0.2 Cu 2 O 8+δ (Bi2212), whose electronic structure has been extensively studied by surface-sensitive spectroscopy, such as scanning tunnelling microscopy 21 and angle-resolved photoemission 22 , and in which a short-range CDW order was recently reported 7,8 . With improved energy resolution up to 40 meV, we see additional features in the pre...