Superconductivity and fractionalized magnetic excitations in CeCoIn5

Abstract

Recent experiments on CeCoIn5 -- a prototypical d-wave superconductor -- indicate that its normal state lies near an unconventional quantum critical point (QCP). One intriguing hypothesis is that quantum-critical fluctuations promote fractionalization of localized 4f moments into fermionic spinons. This fractionalized Fermi liquid (FL*) scenario provides a comprehensive framework for the unconventional QCP and superconductivity, and can reconcile a "missing" Fermi-surface volume relative to the Luttinger count in the normal state of CeCoIn5. To test this possibility, we performed inelastic neutron scattering (INS) measurements on CeCoIn5 across the superconducting transition and corresponding theoretical analysis. Our high-precision spectra reveal detailed momentum and temperature dependence of the spin resonance and a structured spin excitation continuum persisting even in the normal state, placing stringent constraints on the physical picture of pairing in a d-wave superconductor. We show that a Kondo-lattice framework incorporating proximity to FL* physics and d-wave pairing reproduces key features of the data. The model suggests that both the quasi-localized nature of the f-moments above Tc and the resonance below Tc arise from common underlying gauge dynamics, implying a unifying organizing principle linking spin fractionalization and unconventional superconductivity in strongly correlated metals.

Figures (4)

• Figure 1: Magnetic excitation spectra in the superconducting phase of CeCoIn$_{5}$ (T = 0.3 K).a, Field–temperature phase diagram of CeCoIn$_{5}$kenzelmann2008kenzelmann2010. The "Q-phase" corresponds to a spin-density wave order of Ce$^{3+}$ moments with modulation vector $\mathbf{Q}_{\delta} = (0.45, 0.45, 1/2)$ in reciprocal lattice units. b, Two constant-energy slices of the inelastic neutron scattering (INS) spectrum at $T = 0.3$ K, integrated over two different energy ranges. c--e, Energy--momentum slices along high-symmetry directions, revealing a well-defined magnetic excitation branch across broad momentum space as well as continuum scattering. Dashed grey lines mark regions where the spectrum is affected by unreliable background subtraction of quasi-elastic scattering signals (see Fig. S3). f Momentum-dependent intensity over the energy range $0.9 \leq \hbar\omega \leq 0.95$ meV at $T = 0.3$ K. The red and blue shaded regions indicate nominal peaks obtained by fitting each side of the dispersive mode with a pseudo-Voigt function. g--h Extracted dispersion relations of the observed excitation branch from panels d and e, obtained by fitting the peak positions of constant-energy/momentum cuts through the volumetric intensity data.
• Figure 2: Temperature dependence of the magnetic excitations in CeCoIn$_{5}$. Each panel shows energy-momentum slices along [1/2, 1/2, $L$] and [$H$, $H$, 1/2] measured at a$T= 0.3$ K, b 1.6 K, c 2 K, d 2.15 K, e 2.5 K, and f 4 K. They demonstrate the evolution of the gapped magnetic excitations into a gapless, structured continuum scattering signal above $T_{\mathrm{c}}$. Dashed grey lines mark regions where the spectrum is affected by unreliable background subtraction due to strong quasi-elastic background signals (see Fig. S3).
• Figure 3: Minimal theoretical model for CeCoIn$_5$.a, Schematic theoretical phase diagram of CeCoIn$_5$ in the temperature–doping plane. Upon doping (horizontal arrow), the system undergoes a delocalization transition, as reported in Ref. maksimovic2022. Upon cooling (vertical arrow), it enters a superconducting state through the condensation of chargons. b, The minimal model capturing the proposed scenario consists of conduction electrons and local $f$-moments, coupled via a Kondo-like interaction. A central assumption is that the $f$-moments fractionalize into fermionic spinons, giving rise to a fractionalized FL* phase above $T_c$. A bosonic chargon field emerges as a bound state of an electron and a spinon, and its condensation drives the onset of superconductivity. The corresponding chargon condensate order parameter, $B_1$, is shown in c as a function of temperature. d, Contour plot of the low-energy spectrum in the FL$^*$ and superconducting phases. The color scale of the contour plot represents energy of the single-particle excitations. The gray contours indicates that individual spinon in the FL* phase is invisible to physical probes.
• Figure 4: Calculated dynamical spin structure factor (DSSF).a, DSSF between local $f$-moments in the mean-field approximation, evaluated at a temperature below $T_c$. The spectrum is characterized by a broad continuum arising from particle-hole excitations. b, Interaction-renormalized DSSF between local $f$-moments, obtained by summing ladder-type Feynman diagrams. A bound state of spinon pairs (or electron pairs below $T_c$) emerges below the continuum, manifesting as bright, dispersive modes. As temperature increases, this bound state gets closer to the continuum and gradually fades out. c, Static magnetic susceptibility $\chi(\bm{q}, 0)$ of non-interacting conduction electrons, which exhibits a peak near $(\pi,\pi)$—coinciding with the minimum of the bound-state dispersion. d, Renormalized propagator of the chargon field captured by the RPA series of diagrams. Here we only show the results for $B_{j,1}$ field, whose amplitude is reduced by a factor about $0.6$ relative to the bare value $J_K$; similar result holds for the $B_{j,2}$ field.