T. P. Devereaux

Inelastic light scattering from correlated electrons

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 in both the visible (Raman effect) and 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, 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) provides new insights into anisotropic and complex many-body behavior of electrons in various systems. 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 are reviewed. An overview of the manifestations of complexity in the Raman response due to the impact of correlations and developing competing orders is presented. In a variety of materials, observations which may be understood and a summary of important open questions that pave the way to a detailed understanding of correlated electron systems, are discussed.

Abrupt onset of a second energy gap at the superconducting transition of underdoped Bi2212

The superconducting gap—an energy scale tied to the superconducting phenomena—opens on the Fermi surface at the superconducting transition temperature (Tc) in conventional BCS superconductors. In underdoped high-Tc superconducting copper oxides, a pseudogap (whose relation to the superconducting gap remains a mystery) develops well above Tc (refs 1, 2). Whether the pseudogap is a distinct phenomenon or the incoherent continuation of the superconducting gap above Tc is one of the central questions in high-Tc research. Although some experimental evidence suggests that the two gaps are distinct, this issue is still under intense debate. A crucial piece of evidence to firmly establish this two-gap picture is still missing: a direct and unambiguous observation of a single-particle gap tied to the superconducting transition as function of temperature. Here we report the discovery of such an energy gap in underdoped Bi2Sr2CaCu2O8+δ in the momentum space region overlooked in previous measurements. Near the diagonal of Cu–O bond direction (nodal direction), we found a gap that opens at Tc and has a canonical (BCS-like) temperature dependence accompanied by the appearance of the so-called Bogoliubov quasi-particles, a classical signature of superconductivity. This is in sharp contrast to the pseudogap near the Cu–O bond direction (antinodal region) measured in earlier experiments.

Distinct Fermi-momentum dependent energy gaps in deeply underdoped Bi2212.

We used angle-resolved photoemission spectroscopy applied to deeply underdoped cuprate superconductors Bi2Sr2Ca(1–x)YxCu2O8 (Bi2212) to 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, increased with underdoping, a behavior known for more than a decade and considered as the general gap behavior in the underdoped regime. The other gap, associated with the near-nodal regime where a coherent peak in the spectrum can be observed, did not increase with less doping, a behavior not previously observed in the single particle spectra. We propose a two-gap scenario in momentum space that is consistent with other experiments and may contain important information on the mechanism of high–transition temperature superconductivity.

Symmetry-breaking orbital anisotropy observed for detwinned Ba(Fe1-xCox)2As2 above the spin density wave transition

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 C4 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, Ba(Fe1-xCox)2As2 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 dxz and dyz character, which is consistent with anisotropy observed by other probes. For compositions x > 0, for which the structural transition (TS) precedes the magnetic transition (TSDW), an anisotropic splitting is observed to develop above TSDW, indicating that it is specifically associated with TS. For unstressed crystals, the band splitting is observed close to TS, 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.

From a single-band metal to a high-temperature superconductor via two thermal phase transitions.

Three techniques are used to probe the pseudogap state of cuprate high-temperature superconductors. The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem 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 observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (Tc), entangled in an energy-momentum–dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.

Nodal quasiparticle in pseudogapped colossal magnetoresistive manganites

A characteristic feature of the copper oxide high-temperature superconductors is the dichotomy between the electronic excitations along the nodal (diagonal) and antinodal (parallel to the Cu–O bonds) directions in momentum space, generally assumed to be linked to the ‘d-wave’ symmetry of the superconducting state. Angle-resolved photoemission measurements in the superconducting state have revealed a quasiparticle spectrum with a d-wave gap structure that exhibits a maximum along the antinodal direction and vanishes along the nodal direction. Subsequent measurements have shown that, at low doping levels, this gap structure persists even in the high-temperature metallic state, although the nodal points of the superconducting state spread out in finite ‘Fermi arcs’. This is the so-called pseudogap phase, and it has been assumed that it is closely linked to the superconducting state, either by assigning it to fluctuating superconductivity or by invoking orders which are natural competitors of d-wave superconductors. Here we report experimental evidence that a very similar pseudogap state with a nodal–antinodal dichotomous character exists in a system that is markedly different from a superconductor: the ferromagnetic metallic groundstate of the colossal magnetoresistive bilayer manganite La1.2Sr1.8Mn2O7. Our findings therefore cast doubt on the assumption that the pseudogap state in the copper oxides and the nodal-antinodal dichotomy are hallmarks of the superconductivity state.

Anisotropic electron-phonon interaction in the cuprates

We explore manifestations of electron-phonon coupling on the electron spectral function for two phonon modes in the cuprates exhibiting strong renormalizations with temperature and doping. Applying simple symmetry considerations and kinematic constraints, we find that the out-of-plane, out-of-phase O buckling mode (B(1g)) involves small momentum transfers and couples strongly to electronic states near the antinode while the in-plane Cu-O breathing modes involve large momentum transfers and couples strongly to nodal electronic states. Band renormalization effects are found to be strongest in the superconducting state near the antinode, in full agreement with angle-resolved photoemission spectroscopy data.

Phase Competition in Trisected Superconducting Dome

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 temperature-dependence ARPES study of spectral gaps in Bi2Sr2CaCu2O8+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 Tc 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.

Energy gaps in high-transition-temperature cuprate superconductors

The superconducting energy gap is perhaps the best-known of the spectral gaps in a superconductor, but there are many other types, including density waves and the mysterious pseudogap. This Review Article surveys what angle-resolved photoemission spectroscopy has revealed about the various gaps.

Particle-hole symmetry breaking in the pseudogap state of Bi2201

Photoemission studies in the pseudogap state of a cuprate superconductor show differences depending on whether a particle is added or removed, revealing broken translational symmetry. Moreover, this particle–hole asymmetry coincides with the opening of the pseudogap.