skip to main content

Title: Multi-atom quasiparticle scattering interference for superconductor energy-gap symmetry determination

Complete theoretical understanding of the most complex superconductors requires a detailed knowledge of the symmetry of the superconducting energy-gap$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$Δkα, for all momentakon the Fermi surface of every bandα. While there are a variety of techniques for determining$$|{\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha |$$Δkα, no general method existed to measure the signed values of$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$Δkα. Recently, however, a technique based on phase-resolved visualization of superconducting quasiparticle interference (QPI) patterns, centered on a single non-magnetic impurity atom, was introduced. In principle, energy-resolved and phase-resolved Fourier analysis of these images identifies wavevectors connecting allk-space regions where$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$Δkαhas the same or opposite sign. But use of a single isolated impurity atom, from whose precise location the spatial phase of the scattering interference pattern must be measured, is technically difficult. Here we introduce a generalization of this approach for use with multiple impurity atoms, and demonstrate its validity by comparing the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$Δkαit generates to the$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$Δkαdetermined from single-atom scattering in FeSe where s±energy-gap symmetry is established. Finally, to exemplify utility, we use the multi-atom technique on LiFeAs and find scattering interference between the hole-like and electron-like pockets as predicted for$${\mathrm{{\Delta}}}_{\mathbf{k}}^\alpha$$Δkαof opposite sign.

; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
Journal Name:
npj Quantum Materials
Nature Publishing Group
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Negative correlations in the sequential evolution of interspike intervals (ISIs) are a signature of memory in neuronal spike-trains. They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of ISI correlations: non-bursting units have negative correlations which remain negative but decay to zero with increasing lags (Type I ISI correlations), and bursting units have oscillatory (alternating sign) correlation which damp to zero with increasing lags (Type II ISI correlations). Here, we predict and match observed ISI correlations in these afferents using a stochastic dynamic threshold model. We determine the ISI correlation function as a function of an arbitrary discrete noise correlation function$${{\,\mathrm{\mathbf {R}}\,}}_k$$Rk, wherekis a multiple of the mean ISI. The function permits forward and inverse calculations of the correlation function. Both types of correlation functions can be generated by adding colored noise to the spike threshold with Type I correlations generated with slow noise and Type II correlations generated with fast noise. A first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent ISImore »correlation functions, with the type being determined by the sign of the AR parameter. The predicted and experimentally observed correlations are in geometric progression. The theory predicts that the limiting sum of ISI correlations is$$-0.5$$-0.5yielding a perfect DC-block in the power spectrum of the spike train. Observed ISI correlations from afferents have a limiting sum that is slightly larger at$$-0.475 \pm 0.04$$-0.475±0.04($$\text {mean} \pm \text {s.d.}$$mean±s.d.). We conclude that the underlying process for generating ISIs may be a simple combination of low-order AR and moving average processes and discuss the results from the perspective of optimal coding.

    « less
  2. Abstract

    We consider a model of electrons at zero temperature, with a repulsive interaction which is a function of the energy transfer. Such an interaction can arise from the combination of electron–electron repulsion at high energies and the weaker electron–phonon attraction at low energies. As shown in previous works, superconductivity can develop despite the overall repulsion due to the energy dependence of the interaction, but the gap Δ(ω) must change sign at some (imaginary) frequencyω0to counteract the repulsion. However, when the constant repulsive part of the interaction is increased, a quantum phase transition towards the normal state occurs. We show that, as the phase transition is approached, Δ andω0must vanish in a correlated way such that$$1/| \log [{{\Delta }}(0)]| \sim {\omega }_{0}^{2}$$1/log[Δ(0)]~ω02. We discuss the behavior of phase fluctuations near this transition and show that the correlation between Δ(0) andω0locks the phase stiffness to a non-zero value.

  3. Abstract

    The proximity of many strongly correlated superconductors to density-wave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantum-critical (QC) fluctuations of the corresponding order parameter. Here we study anisotropics-wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the non-linear gap equation for the pairing gap$$\Delta (\theta ,{\omega }_{m})$$Δ(θ,ωm)and show that its angular dependence strongly varies below$${T}_{{\rm{c}}}$$Tc. We show that this variation is a signature of QC pairing and comes about because there are multiples-wave pairing instabilities with closely spaced transition temperatures$${T}_{{\rm{c}},n}$$Tc,n. Taken alone, each instability would produce a gap$$\Delta (\theta ,{\omega }_{m})$$Δ(θ,ωm)that changes sign$$8n$$8ntimes along the Fermi surface. We show that the equilibrium gap$$\Delta (\theta ,{\omega }_{m})$$Δ(θ,ωm)is a superposition of multiple components that are nonlinearly induced below the actual$${T}_{{\rm{c}}}={T}_{{\rm{c}},0}$$Tc=Tc,0, and get resonantly enhanced at$$T={T}_{{\rm{c}},n}\ <\ {T}_{{\rm{c}}}$$T=Tc,n<Tc. This gives rise to strong temperature variation of the angular dependence of$$\Delta (\theta ,{\omega }_{m})$$Δ(θ,ωm). This variation progressively disappears away from a QC point.

  4. Abstract

    In this paper, we construct cataclysm deformations for$$\theta $$θ-Anosov representations into a semisimple non-compact connected real Lie groupGwith finite center, where$$\theta \subset \Delta $$θΔis a subset of the simple roots that is invariant under the opposition involution. These generalize Thurston’s cataclysms on Teichmüller space and Dreyer’s cataclysms for Borel-Anosov representations into$$\mathrm {PSL}(n, \mathbb {R})$$PSL(n,R). We express the deformation also in terms of the boundary map. Furthermore, we show that cataclysm deformations are additive and behave well with respect to composing a representation with a group homomorphism. Finally, we show that the deformation is injective for Hitchin representations, but not in general for$$\theta $$θ-Anosov representations.

  5. Abstract

    A method for modelling the prompt production of molecular states using the hadronic rescattering framework of the general-purpose Pythia event generator is introduced. Production cross sections of possible exotic hadronic molecules via hadronic rescattering at the LHC are calculated for the$$\chi _{c1}(3872)$$χc1(3872)resonance, a possible tetraquark state, as well as three possible pentaquark states,$$P_c^+(4312)$$Pc+(4312),$$P_c^+(4440)$$Pc+(4440), and$$P_c^+(4457)$$Pc+(4457). For the$$P_c^+$$Pc+states, the expected cross section from$$\Lambda _b$$Λbdecays is compared to the hadronic-rescattering production. The$$\chi _{c1}(3872)$$χc1(3872)cross section is compared to the fiducial$$\chi _{c1}(3872)$$χc1(3872)cross-section measurement by LHCb and found to contribute at a level of$${\mathcal {O}({1\%})}$$O(1%). Finally, the expected yields of$$\mathrm {P_c^{+}}$$Pc+production from hadronic rescattering during Run 3 of LHCb are estimated. The prompt background is found to be significantly larger than the prompt$$\mathrm {P_c^{+}}$$Pc+signal from hadronic rescattering.