Resonant Inelastic X-Ray Scattering as a Probe of the Phase and Excitations of the Order Parameter of Superconductors

Abstract

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic s-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.PACS numbers: 78.70. Ck, 74.20.Rp Introduction In the past decade, resonant inelastic x-ray scattering (RIXS) [1,2] has made remarkable progress as a spectroscopic technique, establishing itself as an experimental probe of elementary spin [3][4][5][6][7][8], orbital [9,10], and lattice excitations [11]. In quite a number of cases, theoretical considerations have preceded and stimulated these experimental advances, prominent examples being the theoretical demonstration of the presence of strong single-magnon scattering channels in cuprates [12,13] and iridates [14]. Being a photonin/photon-out spectroscopy, both the energy ω and the momentum change q of the scattered photon are measured. As the energy and momentum lost by the photon are transferred to intrinsic excitations of the material under study, direct information on the dispersion of those excitations becomes available. The resonant character of the technique is due to the energy of the incident photon being chosen such that it coincides, and hence resonates, with an x-ray absorption edge of the system [1,2]. This year the energy resolution of RIXS has reached ∼30 meV in the hard x-ray regime [7], will reach 50 meV in the soft x-ray regime by building on present instrumentation [15] and is designed to reach 11 meV at the Cu L-edges at the NSLS-II presently under construction [16]. This brings the RIXS energy resolution well into the regime of the energy gap of cuprate superconductors, which stretches out to 119 meV for mercury-based high T c systems [17]. Consequently the fundamental question arises of how the superconducting (SC) state leaves its fingerprints in RIXS spectra -in particular whether and how RIXS is sensitive to the phase and amplitude of the SC gap and to quasiparticle excitations.Probing the order parameter in unconventional superconductors is generally the first step for an investigation of the pairing mechanism and of the character of the SC state. Compared to the available spectroscopic methods, such as scanning-tunneling spectroscopy (STS), photoemission spectroscopy, optical spectroscopy or inelastic neutron scattering, RIXS uniquely combines the advantages of bulk-sensitivity and availability of momentum resolution while at the same time requiring only small sample volumes. Here we show how the sensitivity of the RIXS process to the dynamical structure factor (DSF) of the electron spin and density in the SC state...

Probing the energy gap of high-temperature cuprate superconductors by resonant inelastic x-ray scattering

“…Figure 1a, b shows the imaginary part of the calculated χ c (q, ω) for Bi2212 in the normal and SC states, respectively. Explicitly, it is expressed as 20 Imχ c ðq; ωÞ /…”

“…18,19 This versatile capability of RIXS leads to the possibility of measuring the modifications of charge and spin susceptibilities induced by the SC gap opening. Indeed, Marra et al 20 have theoretically proposed that RIXS can serve as a probe of the symmetry and phase of the SC order parameter, given that the coherence factors in the charge and spin susceptibilities in the SC state reflect not only the amplitude but also the phase of the order parameter. 21 However, this perspective has not been realized to date because of the limited energy resolution of the available instruments, combined with the small energy scales associated with superconductivity.…”

Spin-orbit coupled systems in the atomic limit: rhenates, osmates, iridates

“…Here, we discuss this step in the context of double perovskite materials using a theoretical analysis of resonant inelastic X-ray scattering (RIXS), exact diagonalization studies of the single-site problem with SOC at different electron fillings (d 2 , d 3 , d 4 ), and complementary ab initio electronic structure calculations. a RIXS has proven to be a particularly valuable tool to explore spin and orbital excitations, and there has been extensive experimental [29][30][31][32][33][34][35][36] and theoretical work [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51] in this area (see Ref. 52 for a review).…”

Insights into the high temperature superconducting cuprates from resonant inelastic X-ray scattering

“…Some possibilities for novel experiments are discussed below including experiments on stripe ordered cuprates and cuprate-containing heterostructures, as well as the possibility of measuring phonon excitations. This list is not meant to be comprehensive, for example we do not address the possibilities of observing the superconducting gap [114] and the likely expansion of soft RIXS studies to measuring magnetic excitations in non-cuprate materials such as the manganites.…”