In the past decade, Resonant Inelastic X-ray Scattering (RIXS) has made remarkable progress as a spectroscopic technique. This is a direct result of the availability of highbrilliance synchrotron X-ray radiation sources and of advanced photon detection instrumentation. The technique's unique capability to probe elementary excitations in complex materials by measuring their energy-, momentum-, and polarization-dependence has brought RIXS to the forefront of experimental photon science. We review both the experimental and theoretical RIXS investigations of the past decade, focusing on those determining the low-energy charge, spin, orbital and lattice excitations of solids. We present the fundamentals of RIXS as an experimental method and then review the theoretical state of affairs, its recent developments and discuss the different (approximate) methods to compute the dynamical RIXS response. The last decade's body of experimental RIXS data and its interpretation is surveyed, with an emphasis on RIXS studies of correlated electron systems, especially transition metal compounds. Finally, we discuss the promise that RIXS holds for the near future, particularly in view of the advent of x-ray laser photon sources.

Films of iron selenide (FeSe) one unit cell thick grown on strontium titanate (SrTiO3 or STO) substrates have recently shown superconducting energy gaps opening at temperatures close to the boiling point of liquid nitrogen (77 kelvin), which is a record for the iron-based superconductors. The gap opening temperature usually sets the superconducting transition temperature Tc, as the gap signals the formation of Cooper pairs, the bound electron states responsible for superconductivity. To understand why Cooper pairs form at such high temperatures, we examine the role of the SrTiO3 substrate. Here we report high-resolution angle-resolved photoemission spectroscopy results that reveal an unexpected characteristic of the single-unit-cell FeSe/SrTiO3 system: shake-off bands suggesting the presence of bosonic modes, most probably oxygen optical phonons in SrTiO3 (refs 5, 6, 7), which couple to the FeSe electrons with only a small momentum transfer. Such interfacial coupling assists superconductivity in most channels, including those mediated by spin fluctuations. Our calculations suggest that this coupling is responsible for raising the superconducting gap opening temperature in single-unit-cell FeSe/SrTiO3.

Inelastic light scattering is an intensively used tool in the study of electronic properties of solids. Triggered by the discovery of high temperature superconductivity in the cuprates and by new developments in instrumentation, light scattering both in the visible (Raman effect) and the X-ray part of the electromagnetic spectrum has become a method complementary to optical (infrared) spectroscopy while providing additional and relevant information. The main purpose of the review is to position Raman scattering with regard to single-particle methods like angle-resolved photoemission spectroscopy (ARPES), and other transport and thermodynamic measurements in correlated materials. Particular focus will be placed on photon polarizations and the role of symmetry to elucidate the dynamics of electrons in different regions of the Brillouin zone. This advantage over conventional transport (usually measuring averaged properties) indeed provides new insights into anisotropic and complex many-body behavior of electrons in various systems. We review recent developments in the theory of electronic Raman scattering in correlated systems and experimental results in paradigmatic materials such as the A15 superconductors, magnetic and paramagnetic insulators, compounds with competing orders, as well as the cuprates with high superconducting transition temperatures. We present an overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders. In a variety of materials we discuss which observations may be understood and summarize important open questions that pave the way to a detailed understanding of correlated electron systems.

A quantum spin Hall (QSH) insulator is a novel twodimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin-orbit coupling 1,2 . By investigating the electronic structure of epitaxially grown monolayer 1T'-WTe 2 using angle-resolved photoemission (ARPES) and first-principles calculations, we observe clear signatures of topological band inversion and bandgap opening, which are the hallmarks of a QSH state. Scanning tunnelling microscopy measurements further confirm the correct crystal structure and the existence of a bulk bandgap, and provide evidence for a modified electronic structure near the edge that is consistent with the expectations for a QSH insulator. Our results establish monolayer 1T'-WTe 2 as a new class of QSH insulator with large bandgap in a robust two-dimensional materials family of transition metal dichalcogenides (TMDCs).A two-dimensional (2D) topological insulator (TI), or a quantum spin Hall insulator, is characterized by an insulating bulk and a conductive helical edge state, in which carriers with different spins counter-propagate to realize a geometry-independent edge conductance 2e 2 /h (refs 1,2). The only scattering channel for such helical edge current is back scattering, which is prohibited by time reversal symmetry, making QSH insulators a promising material candidate for spintronic and other applications.The prediction of the QSH effect in HgTe quantum wells sparked intense research efforts to realize the QSH state [3][4][5][6][7][8][9][10][11] . So far only a handful of QSH systems have been fabricated, mostly limited to quantum well structures of three-dimensional (3D) semiconductors such as HgTe/CdTe (ref.3) and InAs/GaSb (ref. 6). Edge conduction consistent with a QSH state has been observed 3,6,12 . However, the behaviour under a magnetic field, where time reversal symmetry is broken, cannot be explained within our current understanding of the QSH effect 13,14 . There have been continued efforts to predict and investigate other material systems to further advance the understanding of this novel quantum phenomenon 5,[7][8][9]15 . So far, it has been difficult to make a robust 2D material with a QSH state, a platform needed for widespread study and application. The small bandgaps exhibited by many candidate systems, as well as their vulnerability to strain, chemical adsorption, and element substitution, make them impractical for advanced spectroscopic studies or applications. For example, a QSH insulator candidate stanene, a monolayer analogue of graphene for tin, grown on Bi 2 Se 3 becomes topologically trivial due to the modification of its band structure by the underlying substrate 11,16 . Free-standing Bi film with 2D bonding on a cleaved surface has shown edge conduction 9 , but its topological nature is still debated 17 . It takes 3D out-of-plane bonding with the substrate and large stra...

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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...

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 ...