Isotropic Gap Research Articles

Enhanced Coupling of Superconductivity and Evolution of Gap Structure in CsV3Sb5 through Ta Doping

Abstract In this study, we present a detailed investigation of kagome superconductors CsV3Sb5 single crystal and its Ta-doped variant, Cs(V0.86Ta0.14)3Sb5, through specific heat measurements. Our specific heat results show a clear suppression of the charge density wave (CDW) and notable increase in the superconducting transition temperature (Tc) from 2.8 K to 4.6 K upon Ta doping. The electronic specific heat of the pristine CsV3Sb5 sample can be fitted with a model comprising an s-wave gap and a highly anisotropic extended s-wave gap, where the ratio 2△/k B T c is smaller than the weak coupling limit of 3.5. For the doped sample Cs(V0.86Ta0.14)3Sb5, it exhibits two isotropic s-wave gaps, yielding the larger gap of 2△/k B T c = 5.04, which indicates a significant enhancement in superconducting coupling. This evolution is attributed to the increased density of states (DOS) near the Fermi level released through the suppression of the CDW gap. Our results demonstrate enhanced superconducting coupling and variation of gap structure in CsV3Sb5 due to Ta doping.

Stealthy and hyperuniform isotropic photonic band gap structure in 3D.

In photonic crystals, the propagation of light is governed by their photonic band structure, an ensemble of propagating states grouped into bands, separated by photonic band gaps. Due to discrete symmetries in spatially strictly periodic dielectric structures their photonic band structure is intrinsically anisotropic. However, for many applications, such as manufacturing artificial structural color materials or developing photonic computing devices, but also for the fundamental understanding of light-matter interactions, it is of major interest to seek materials with long range nonperiodic dielectric structures which allow the formation of isotropic photonic band gaps. Here, we report the first ever 3D isotropic photonic band gap for an optimized disordered stealthy hyperuniform structure for microwaves. The transmission spectra are directly compared to a diamond pattern and an amorphous structure with similar node density. The band structure is measured experimentally for all three microwave structures, manufactured by 3D laser printing for metamaterials with refractive index up to . Results agree well with finite-difference-time-domain numerical investigations and a priori calculations of the band gap for the hyperuniform structure: the diamond structure shows gaps but being anisotropic as expected, the stealthy hyperuniform pattern shows an isotropic gap of very similar magnitude, while the amorphous structure does not show a gap at all. Since they are more easily manufactured, prototyping centimeter scaled microwave structures may help optimizing structures in the technologically very interesting region of infrared.

Superconductivity of Co-Doped CaKFe4As4 Investigated via Point-Contact Spectroscopy and London Penetration Depth Measurements.

The iron-based superconductors (IBSs) of the recently discovered 1144 class, unlike many other IBSs, display superconductivity in their stoichiometric form and are intrinsically hole doped. The effects of chemical substitutions with electron donors are thus particularly interesting to investigate. Here, we study the effect of Co substitution in the Fe site of CaKFe4As4 single crystals on the critical temperature, on the energy gaps, and on the superfluid density by using transport, point-contact Andreev-reflection spectroscopy (PCARS), and London penetration depth measurements. The pristine compound (Tc≃36 K) shows two isotropic gaps whose amplitudes (Δ1 = 1.4-3.9 meV and Δ2 = 5.2-8.5 meV) are perfectly compatible with those reported in the literature. Upon Co doping (up to ≈7% Co), Tc decreases down to ≃20 K, the spin-vortex-crystal order appears, and the low-temperature superfluid density is gradually suppressed. PCARS and London penetration depth measurements perfectly agree in demonstrating that the nodeless multigap structure is robust upon Co doping, while the gap amplitudes decrease as a function of Tc in a linear way with almost constant values of the gap ratios 2Δi/kBTc.

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV3Sb5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV3-xTaxSb5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{2}}{{\\Delta }}$$\\end{document} and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

Effect of varying concentration of dichroic dye on textural, electro-optical, phase transition and band gap studies of zinc oxide nanoparticles induced vertically aligned liquid crystals

Vertically aligned liquid crystal (VALC) perpetually boosts the advancement for display devices and optoelectronics. Herein, initially, the nanoparticles (NPs) induced VALC (nVALC) cell was prepared via doping of 0.3 (wt./wt.%) of zinc oxide NPs in nematic liquid crystal (LC). After that, a series of orange azo dichroic dye doped nVALC cells were prepared with varying concentrations of dye such as 0.0625, 0.125, 0.25 and 0.5 wt.%. The effect of dye concentrations on LC textures, phase transition, electro-optical and band gap properties were investigated, as well as resulted in a significantly reduced value of the threshold and operating voltages as a function of dye concentrations. The contrast ratio was also enhanced up to 0.25 wt.% dye doped nVALC cells. Additionally, the transition temperature from nematic to isotropic phase and band gap studies were also performed. The present work provides improved properties of nVALC systems for next-generation display technologies.

Isotropic gap formation, localization, and waveguiding in mesoscale Yukawa-potential amorphous structures

Amorphous photonic structures are mesoscopic optical structures described by electrical permittivity distributions with underlying spatial randomness. They offer a unique platform for studying a broad set of electromagnetic phenomena, including transverse Anderson localization, enhanced wave transport, and suppressed diffusion in random media. Despite this, at a more practical level, there is insufficient work on both understanding the nature of optical transport and the conditions conducive to vector-wave localization in these planar structures, as well as their potential applications to photonic nanodevices. In this study, we fill this gap by investigating experimentally and theoretically the characteristics of optical transport in a class of amorphous photonic structures and by demonstrating their use to some basic waveguiding nanostructures. We demonstrate that these 2-D structures have unique isotropic and asymmetric band gaps for in-plane propagation, controlled from first principles by varying the scattering strength and whose properties are elucidated by establishing an analogy between photon and carrier transport in amorphous semiconductors. We further observe Urbach band tails in these random structures and uncover their relation to frequency- and disorder-dependent Anderson-like localized modes through the modified Ioffe-Regel criterion and their mean free path - localization length character. Finally, we illustrate that our amorphous structures can serve as a versatile platform in which photonic devices such as disorder-localized waveguides can be readily implemented.

Superconducting Gap Structure of the Noncentrosymmetric Topological Superconductor Candidate HfRuP

We investigate the gap symmetry of the topological superconductor candidate HfRuP, which crystallizes in a noncentrosymmetric hexagonal crystal structure, using muon spin rotation/relaxation (μSR) measurements in transverse-field (TF) geometry. The temperature and magnetic field dependencies of the superconducting relaxation rate derived from the TF-μSR spectra can be well described by an isotropic s-wave gap. The superconducting carrier density ns = 1.41(1) × 1026 m−3 and the magnetic penetration depth, λ(0) = 603(2) nm, were calculated from the TF-μSR data. Interestingly, the ratio between the superconducting transition temperature and the superfluid density, Tc/λ−2(0) ∼ 3.3, is very close to those of unconventional superconductors. Further, our zero-field (ZF) μSR results do not show any considerable change in the muon spin relaxation above and below the superconducting transition temperature, suggesting that time-reversal symmetry is preserved in the superconducting state of this superconductor.

Toward precision Fermi-liquid theory in two dimensions

The ultra-cold and weakly-coupled Fermi gas in two spatial dimensions is studied in an effective field theory framework. It has long been observed that universal corrections to the energy density to two orders in the interaction strength do not agree with Monte Carlo simulations in the weak-coupling regime. Here, universal corrections to three orders in the interaction strength are obtained for the first time, and are shown to provide agreement between theory and simulation. Special consideration is given to the scale ambiguity associated with the non-trivial renormalization of the singular contact interactions. The isotropic superfluid gap is obtained to next-to-leading order, and nonuniversal contributions to the energy density due to effective range effects, p-wave interactions and three-body forces are computed. Results are compared with precise Monte Carlo simulations of the energy density and the contact in the weakly-coupled attractive and repulsive Fermi liquid regimes. In addition, the known all-orders sum of ladder and ring diagrams is compared with Monte Carlo simulations at weak coupling and beyond.

Direct imaging of photonic band-edge states in golden Vogel spirals using photoemission electron microscopy

Golden Vogel spirals, as deterministic aperiodic structures, support isotropic photonic band gaps and have interesting applications. Localized modes, such as band-edge states, are essential for tailored light–matter interaction. Here we report imaging of such modes using photoemission electron microscopy (PEEM). Tunable ultrashort light pulses excite them in golden Vogel spirals that were fabricated by focused-ion-beam (FIB) milling of an a-Si:H layer. The local near-field leads to electron emission, which is detected spatially resolved. The demonstration of FIB-textured a-Si:H as photonic material and the ability of mode imaging by PEEM offers means to spatiotemporally resolve mode dynamics and to perform nanospectroscopy.

Experimental characterization of rigid-scatterer hyperuniform distributions for audible acoustics

Two-dimensional stealthy hyperuniform distributions of rigid scatterers embedded in a waveguide are experimentally characterized the wave transport properties for scalar waves in airborne audible acoustics. The non resonant nature of the scatterers allows us to directly links the these properties to the geometric distribution of points through the structure factor. The transport properties are analyzed as a function of the stealthiness $\chi$ of their hyperuniform point pattern and compared to those of a disordered material in the diffusive regime, which are characterized by the Ohm's law through the mean free path. Different scattering regimes are theoretically and numerically identified showing transparent regions, isotropic band gaps, and anisotropic scattering depending on $\chi$. The robustness of these scattering regimes to losses which are unavoidable in audible acoustics is experimentally unvealed.

Electron–phonon coupling and superconductivity in an alkaline earth hydride CaH6 at high pressures

Recently, an alkaline earth hydride CaH6 having a sodalitelike clathrate structure has been experimentally synthesized at megabar pressures with a maximum T c of 215 K, comparable to that of a rare earth hydride LaH10. Here, based on first-principles calculations, we find that CaH6 exhibits a huge peak in the Eliashberg spectral function α 2 F around the low-frequency region of H-derived phonon modes, in contrast to LaH10 having a widely spreading spectrum of α 2 F over the whole frequencies of H-derived phonon modes. It is revealed that the huge peak of α 2 F in CaH6 is associated with an effective electron–phonon coupling (EPC) between low-frequency optical phonons and hybridized H 1s and Ca 3d states near the Fermi energy. As pressure increases, the strengthened H–H covalent bonding not only induces a hardening of optical phonon modes but also reduces the electron–phonon matrix elements related to the low-frequency optical modes, thereby leading to a lowering of the EPC constant. It is thus demonstrated that H-derived low-frequency phonon modes play an important role in the pressure-induced variation of T c in CaH6. Furthermore, unlike the presence of two distinct superconducting gaps in LaH10, CaH6 is found to exhibit a single isotropic superconducting gap.

Possible unconventional pairing in (Ca,Sr)3(Ir,Rh)4Sn13 superconductors revealed by controlling disorder

We study the evolution of temperature-dependent resistivity with controlled point-like disorder induced by 2.5 MeV electron irradiation in stoichiometric compositions of the "3-4-13" stannides, $(\text{Ca,Sr})_{3}(\text{Ir,Rh})_{4}\text{Sn}_{13}$.Three of these cubic compounds exhibit a microscopic coexistence of charge-density wave (CDW) order and superconductivity (SC), while $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$ does not develop CDW order. As expected, the CDW transition temperature, $T_{\text{CDW}}$, is universally suppressed by irradiation in all three compositions. The superconducting transition temperature, $T_{c}$, behaves in a more complex manner. In $\text{Sr}_{3}\text{Rh}_{4}\text{Sn}_{13}$, it increases initially in a way consistent with a direct competition of CDW and SC, but quickly saturates at higher irradiation doses. In the other three compounds, $T_{c}$ is monotonically suppressed by irradiation. The strongest suppression is found in $\text{Ca}_{3}\text{Rh}_{4}\text{Sn}_{13}$, which does not have CDW order. We further examine this composition by measuring the London penetration depth, $\lambda(T)$, from which we derive the superfluid density. The result unambiguously points to a weak-coupling, full single gap, isotropic superconducting state. Therefore, we must explain two seemingly incompatible experimental observations: a single isotropic superconducting gap and a significant suppression of $T_{c}$ by non-magnetic disorder. We conduct a quantitative theoretical analysis based on a generalized Anderson theorem which points to an unconventional multiband $s^{+-}$-pairing state where the sign of the order parameter is different on one (or a small subset) of the smaller Fermi surface sheets, but remains overall fully-gapped.

Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV_{3}Sb_{5}.

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal AV_{3}Sb_{5} (A=K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV_{3}Sb_{5}. The spectra around K[over ¯] is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below E_{F}. The peak-dip-hump line shape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to E_{F} in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of ∼0.4 meV is observed on both the electron band around Γ[over ¯] and the flat band around K[over ¯], implying the multiband superconductivity. The finite density of states at E_{F} in the CDW phase is most likely in favor of the emergence of multiband superconductivity, particularly the enhanced density of states associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity.

Multiband superconductivity in V3Si determined from studying the response to controlled disorder

The London penetration depth, $\lambda(T)$, was measured in a single crystal V$_{3}$Si. The superfluid density obtained from this measurement shows a distinct signature of two almost decoupled superconducting gaps. This alone is insufficient to distinguish between $s_{\pm}$ and $s_{++}$ pairing states, but it can be achieved by studying the effect of a controlled non-magnetic disorder on the superconducting transition temperature, $T_{c}$. For this purpose, the same $\text{V}_{3}\text{Si}$ crystal was sequentially irradiated by 2.5 MeV electrons three times, repeating the measurement between the irradiation runs. A total dose of 10 C/cm$^{2}$ ($6.24\times10^{19}$ electrons/$\textrm{cm}^{2}$) was accumulated, for which $T_{c}$ has changed from 16.4 K in a pristine state to 14.7 K (9.3 $\%$). This substantial suppression is impossible for a single isotropic gap, but also it is not large enough for a sign-changing $s_{\pm}$ pairing state. Our electronic band-structure calculations show how five bands crossing the Fermi energy can be naturally grouped to support two effective gaps, not dissimilar from the iron pnictides physics. We analyze the results using two-gap models for both, $\lambda(T)$ and $T_{c}$, which describe the data very well. Thus, the experimental results and theoretical analysis provide strong support for an $s_{++}$ superconductivity with two unequal gaps, $\Delta_{1}\left(0\right)\approx2.53\;\textrm{meV}$ and $\Delta_{2}\left(0\right)\approx1.42\;\textrm{meV}$, and a very weak inter-band coupling in $\text{V}_{3}\text{Si}$ superconductor.

Superconducting order parameters in overdoped BaFe1.86Ni0.14As2 revealed by multiple Andreev reflection spectroscopy of planar break junctions

Using multiple Andreev reflection (MAR) spectroscopy, we studied superconductor - normal metal - superconductor (SnS) semiballistic contacts with incoherent transport in overdoped pnictide superconductors BaFe$_{1.86}$Ni$_{0.14}$As$_2$ with critical temperature $T_c \approx 12$ K. We directly determined an anisotropic large gap with the characteristic ratios $2\Delta_L^{\rm out}(0)/k_BT_c \approx 6$ and $2\Delta_L^{\rm in}(0)/k_BT_c \approx 4$, almost isotropic small gap with $2\Delta_S(0)/k_BT_c \approx 2$, and the temperature dependence of the resolved superconducting order parameters. Above the large gap position $2\Delta_L$, a fine dI(V)/dV structure fully vanishing at $T_c$ and possibly caused by a resonant coupling with a bosonic mode was observed.

Band-selective gap opening by a C4-symmetric order in a proximity-coupled heterostructure Sr2VO3FeAs

Complex electronic phases in strongly correlated electron systems are manifested by broken symmetries in the low-energy electronic states. Some mysterious phases, however, exhibit intriguing energy gap opening without an apparent signature of symmetry breaking (e.g., high-TC cuprates and heavy fermion superconductors). Here, we report an unconventional gap opening in a heterostructured, iron-based superconductor Sr2VO3FeAs across a phase transition at T 0 ∼150 K. Using angle-resolved photoemission spectroscopy, we identify that a fully isotropic gap opens selectively on one of the Fermi surfaces with finite warping along the interlayer direction. This band selectivity is incompatible with conventional gap opening mechanisms associated with symmetry breaking. These findings, together with the unusual field-dependent magnetoresistance, suggest that the Kondo-type proximity coupling of itinerant Fe electrons to localized V spin plays a role in stabilizing the exotic phase, which may serve as a distinct precursor state for unconventional superconductivity.

Probing the superconducting ground state of noncentrosymmetric high-entropy alloys using muon-spin rotation and relaxation

Recently, high entropy alloys (HEAs) have emerged as a new platform for discovering superconducting materials and offer avenues to explore exotic superconductivity. The highly disordered nature of HEA suggests regular phonon required for BCS superconductivity may be unlikely to occur. Therefore understanding the microscopic properties of these superconducting HEA is important. We report the first detailed characterization of the superconducting properties of the noncentrosymmetric ($\alpha$-Mn structure) HEA {(HfNb)}$_{0.10}${(MoReRu)}$_{0.90}$, and {(ZrNb)}$_{0.10}${(MoReRu)}$_{0.90}$ by using magnetization, specific heat, AC transport, and muon-spin relaxation/rotation ($\mu$SR). Despite the disordered nature, low temperature specific heat and transverse-field muon spin rotation measurements suggest nodeless isotropic superconducting gap and Zero-field $\mu$SR measurements confirm that time reversal symmetry is preserved in the superconducting ground state.

Hyperuniformity of expected equilibrium density distributions of Brownian particles via designer external potentials

Disordered hyperuniformity (DHU) is a recently discovered novel state of many-body systems that is characterized by vanishing normalized infinite-wavelength density fluctuations similar to a perfect crystal, yet possesses an amorphous structure like a liquid or glass. Due to their unique structural characteristics, DHU materials are typically endowed with unusual physical properties, such as large isotropic photonic band gaps, optimal transport properties and superior mechanical properties, enabling a wide spectrum of novel applications. Here we investigate hyperuniformity of expected equilibrium distributions of Brownian particles induced by external potentials. In particular, we analytically derive sufficient conditions on the external potentials in order to achieve distinct classes of DHU density distributions of Brownian particles in thermal equilibrium, based on the stationary-state solutions of the corresponding Smoluchowski equation. We show for a wide spectrum of tight-binding potentials, the desirable DHU distributions of Brownian particles can be controlled and achieved by imposing proper hyperuniformity conditions on the potentials. We also analyze the evolution dynamics of an initial density distribution (hyperuniform or non-hyperuniform) to the desirable equilibrium DHU distribution determined by the prescribed external potentials, which is shown to be coupled with the full spectra of the force fields associated with the imposed potentials. We find that although the transient density distribution can rapidly develop local patterns reminiscent of those in the equilibrium distribution, which is governed by the fast dynamics induced by the external potential, the overall distribution is still modulated by the initial density fluctuations which are relaxed through slow diffusive dynamics. Our study has implications for the fabrication of designer DHU materials.

Shear based gap control in 2D photonic quasicrystals of dielectric cylinders.

2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. In this work we study a quasiperiodic lattice made of silicon dielectric cylinders (ɛ = 12) arranged as periodic unit cell based on a decagonal approximant of a quasiperiodic Penrose lattice. We analyze the bulk properties of the resulting lattice as well as the bright states excited in the gap, which correspond to localized resonances of the electromagnetic field in specific cylinder clusters of the lattice. Then we introduce a controlled shear deformation γ which breaks the decagonal symmetry and evaluate the width reduction of the gap together with the evolution of the resonances, for all shear values compatible with physical constraints (cylinder contact). The gap width reduction reaches 18.5% while different states change their frequency in several ways. Realistic analysis of the actual transmission of the electromagnetic radiation, often missing in the literature, has been performed for a finite "slice" of the proposed quasicrystals structure. Two calculation procedures based on MIT Photonic Bands (MPB) and Finite Integration Technique (FIT) are used for the bulk and the finite structures showing an excellent agreement between them.

Superconductivity by hidden spin fluctuations in electron-doped iron selenide

Berg, Metlitski and Sachdev, Science 338, 1606 (2012), have shown that the exchange of hidden spin fluctuations by conduction electrons with two orbitals can result in high-temperature superconductivity in copper-oxide materials. We introduce a similar model for high-temperature iron-selenide superconductors that are electron doped. Conduction electrons carry the minimal 3d xz and 3d yz iron-atom orbitals. Low-energy hidden spin fluctuations at the checkerboard wavevector Q_AF result from nested Fermi surfaces at the center and at the corner of the unfolded (one-iron) Brillouin zone. Magnetic frustration from super-exchange interactions via the selenium atoms stabilize hidden spin fluctuations at Q_AF versus true spin fluctuations. At half filling, Eliashberg theory based purely on the exchange of hidden spin fluctuations reveals a Lifshitz transition to electron/hole Fermi surface pockets at the corner of the folded (two-iron) Brillouin zone, but with vanishing spectral weights. The underlying hidden spin-density wave groundstate is therefore a Mott insulator. Upon electron doping, Eliashberg theory finds that the spectral weights of the hole Fermi surface pockets remain vanishingly small, while the spectral weights of the larger electron Fermi surface pockets become appreciable. This prediction is therefore consistent with the observation of electron Fermi surface pockets alone in electron-doped iron selenide by angle-resolved photoemission spectroscopy (ARPES). Eliashberg theory also finds an instability to S+- superconductivity at electron doping, with isotropic Cooper pairs that alternate in sign between the visible electron Fermi surface pockets and the faint hole Fermi surface pockets. Comparison with the isotropic energy gaps observed in electron-doped iron selenide by ARPES and by scanning tunneling microscopy (STM) is consistent with short-range hidden magnetic order.