Strange superconductivity near an antiferromagnetic heavy-fermion quantum critical point

Abstract

The heavy fermion CeM In5 family with M = Co, Rh, Ir provide a prototypical example of strange superconductors with unconventional d-wave pairing and strange metal normal state, emerged near an antiferromagnetic quantum critical point. The microscopic origin of strange superconductor and its link to antiferromagnetic quantum criticality and strange metal state are still open issues. We propose a microscopic mechanism for strange superconductor, based on the coexistence and competition between the Kondo correlation and the quasi-2d short-ranged antiferromagnetic resonating-valence-bond spin-liquid near the antiferromagnetic quantum critical point via a large-N Kondo-Heisenberg model and renormalization group analysis beyond the mean-field level. We find the coexistence (competition) between the two types of correlations well explains the overall features of superconducting and strange metal state. The interplay of these two effects provides a qualitative understanding on how superconductivity emerges from the SM state and the observed superconducting phase diagrams for CeM In5 near the AF QCP.

The scaled-invariant Planckian metal and quantum criticality in Ce1−xNdxCoIn5

“…At the edge of antiferromagnetism, the Kondo effect not only stablizes the RVB spin liquid against the magnetic long-ranged order by partially sharing the f -electron spins 33 , but also introduces hoping of the RVB bonds to the conduction band to form charged Cooper pairs. This leads to a Kondo-RVB coexisting heavy-electron superconducting state with estimated transition temperature T c ~ χ 2 Δ R V B , in quantitatively good agreement with the experimental observation 34 .…”

“…Via the competition between Kondo and RVB physics, an AF-KB QCP was predicted inside the superconducting dome, qualitatively describing the phase transition between AF-superconducting coexisting phase and a pure superconducting phase observed in CeRhIn 5 34 , similar to our case here. By analyzing the amplitude fluctuations of the Kondo and RVB correlations beyond mean-field level via renormalization group (RG) analysis 34 , 35 , this mechanism provides a qualitative and semi-quantitative understanding of the SM properties in CeCoIn 5 in fields and pressure near the AF-KB QCP 20 , 24 , 25 . In particular, it captures the observed T -linear resistivity in terms of critical Kondo (charge) fluctuations ( field) via the electron-phonon-like interaction, (see “Methods” section), and a power-law-in- T divergence in γ ( T ) via both Kondo and RVB fluctuations 34 , 35 .…”

Strange metal in paramagnetic heavy-fermion Kondo lattice: Dynamical large-N fermionic multi-channel approach

“…Under field and pressure, the system undergoes a KB transition from a paramagnetic SM state to a heavy Fermi liquid state. The J K /J H ratio is expected to increase with increasing field or pressure [44,49]. The calculated SM feature in T -matrix (κ = 1/2) and the fermionic spin-liquid dynamical spin susceptibility (κ < 1/2) are qualitatively consistent with the quasi-linear-in-T resistivity persistent to the lowest temperature, observed in its Nidoped form [7], as well as the susceptibility measurement for its pure form [6,8,9], respectively.…”

“…The RVB spinliquid metal phase exits for small values of J K /J H (∆ = 0, x = 0, regions I,II, III), while the Kondo screened paramagnetic heavy-electron phase prevails at large J K /J H (∆ = 0, x = 0, regions V, VI). A coexisting phase, an extended s-wave superconducting phase when electron baths are connected, is found at intermediate J K /J H (∆ = 0, x = 0, region IV) [44]. A high temperature decoupled phase is reached when ∆ = x = 0 (region I).…”

“…When the local electron baths are connected, this SM feature in T -matrix indicates a quasi-linear-in-T resistivity ρ via conductivity σ(T ) = 1/ρ(T ) ∼ τ (ω)∂ ω f (ω)dω with f (ω) being the Fermi function [44,49]; and we expect the Fermi liquid limit, −N T ′′ (ω = 0, T ) ∝ T 2 as T → 0, on the FL phase is recovered. Since the T -matrix is proportional to the local density of states, it can be directly compared to the lowtemperature STM measurement.…”