skip to main content

Title: Multiple intertwined pairing states and temperature-sensitive gap anisotropy for superconductivity at a nematic quantum-critical point

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.

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

    Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the electron spin, yet the required strength of the magnetic field–typically of order 100 T–means that very little is known about this insulator-metal transition. Here we show that Ce$${}_{3}$$3Bi$${}_{4}$$4Pd$${}_{3}$$3, owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A metallic Fermi liquid state is established above a critical magnetic field of only$${B}_{{\rm{c}}}\approx$$Bc11 T. A peak in the strength of electronic correlations near$${B}_{{\rm{c}}}$$Bc, which is evidentmore »in transport and susceptibility measurements, suggests that Ce$${}_{3}$$3Bi$${}_{4}$$4Pd$${}_{3}$$3may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

    « less
  2. Abstract

    We study the singular set in the thin obstacle problem for degenerate parabolic equations with weight$$|y|^a$$|y|afor$$a \in (-1,1)$$a(-1,1). Such problem arises as the local extension of the obstacle problem for the fractional heat operator$$(\partial _t - \Delta _x)^s$$(t-Δx)sfor$$s \in (0,1)$$s(0,1). Our main result establishes the complete structure and regularity of the singular set of the free boundary. To achieve it, we prove Almgren-Poon, Weiss, and Monneau type monotonicity formulas which generalize those for the case of the heat equation ($$a=0$$a=0).

  3. Abstract

    We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000$$\hbox {cm}^2\,\hbox {V}^{-1}\,\hbox {s}^{-1}$$cm2V-1s-1), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of anin-planeelectric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from$$\lambda =3$$λ=3to 12$$\upmu$$μm by adjusting themore »size of and distance between the circular holes in a hexagonal or square lattice structure. Most importantly, the LSPs along with an optical cavity increase the emittance of graphene from about 2.3% for pristine graphene to 80% for NPG, thereby outperforming state-of-the-art pristine graphene light sources operating in the near-infrared by at least a factor of 100. According to our COMSOL calculations, a maximum emission power per area of$$11\times 10^3$$11×103W/$$\hbox {m}^2$$m2at$$T=2000$$T=2000K for a bias voltage of$$V=23$$V=23V is achieved by controlling the temperature of the hot electrons through the Joule heating. By generalizing Planck’s theory to any grey body and deriving the completely general nonlocal fluctuation-dissipation theorem with nonlocal response of surface plasmons in the random phase approximation, we show that the coherence length of the graphene plasmons and the thermally emitted photons can be as large as 13$$\upmu$$μm and 150$$\upmu$$μm, respectively, providing the opportunity to create phased arrays made of nanoantennas represented by the holes in NPG. The spatial phase variation of the coherence allows for beamsteering of the thermal emission in the range between$$12^\circ$$12and$$80^\circ$$80by tuning the Fermi energy between$$E_F=1.0$$EF=1.0eV and$$E_F=0.25$$EF=0.25eV through the gate voltage. Our analysis of the nonlocal hydrodynamic response leads to the conjecture that the diffusion length and viscosity in graphene are frequency-dependent. Using finite-difference time domain calculations, coupled mode theory, and RPA, we develop the model of a mid-IR light source based on NPG, which will pave the way to graphene-based optical mid-IR communication, mid-IR color displays, mid-IR spectroscopy, and virus detection.

    « less
  4. Abstract

    Efficient conversion of methane to value-added products such as olefins and aromatics has been in pursuit for the past few decades. The demand has increased further due to the recent discoveries of shale gas reserves. Oxidative and non-oxidative coupling of methane (OCM and NOCM) have been actively researched, although catalysts with commercially viable conversion rates are not yet available. Recently,$${{{{{{{\mathrm{Sr}}}}}}}}_2Fe_{1.5 + 0.075}Mo_{0.5}O_{6 - \delta }$$Sr2Fe1.5+0.075Mo0.5O6δ(SFMO-075Fe) has been reported to activate methane in an electrochemical OCM (EC-OCM) set up with a C2 selectivity of 82.2%1. However, alkaline earth metal-based materials are known to suffer chemical instability in carbon-rich environments. Hence,more »here we evaluated the chemical stability of SFMO in carbon-rich conditions with varying oxygen concentrations at temperatures relevant for EC-OCM. SFMO-075Fe showed good methane activation properties especially at low overpotentials but suffered poor chemical stability as observed via thermogravimetric, powder XRD, and XPS measurements where SrCO3was observed to be a major decomposition product along with SrMoO3and MoC. Nevertheless, our study demonstrates that electrochemical methods could be used to selectively activate methane towards partial oxidation products such as ethylene at low overpotentials while higher applied biases result in the complete oxidation of methane to carbon dioxide and water.

    « less
  5. Abstract

    Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$(107Re103). Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$Re=v0x0ν, wherev0corresponds to the maximum wetting speed on a flat, dry surface andx0is the extension length of the liquidmore »meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv0andx0measurements using Water$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v02m/s,25µmx028µm), viscous FC-70$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v00.3m/s,18.6µmx038.6µm)and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$(v01.2m/s,11.8µmx033.3µm).

    « less