Two-band Superconductor Research Articles

Stability limits of flux states in two-band superconductor rings

Stability limits of flux states in two-band superconductor rings

Two-band superconductivity in Pt-intercalated ZrTe2, a Dirac semimetal

This study presents compelling evidence of superconductivity with 3.5 K onset and zero-resistance state at 2.25 K in the Dirac semimetal compound ZrTe2, upon intercalation with platinum in the van der Waals gap. The temperature dependence of the upper critical field and the normalized superfluid density can be modeled effectively using a two-gap model, consistent with the possibility of topological superconductivity.

Table-top laser-based terahertz high harmonic generation spectroscopy under magnetic fields and low temperatures.

We have developed a terahertz (THz) nonlinear spectrometer at low temperatures (1.5-300K) and under high magnetic fields (up to 10T) by combining the laser-driven table-top intense THz source with a superconducting magnet. The strong-field THz pump pulse was generated from LiNbO3 crystal using the tilted-pulse-front technique and tightly focused into the center of the magnet by an off-axis parabolic mirror and a THz lens. The electric fields at the focus can achieve 500kV/cm with a monocycle waveform and 30kV/cm with a multicycle waveform at 0.5THz. The sample was mounted on a low-temperature motorized rotation stage, which enables performing the polarization dependent measurements of the third harmonic generation (THG) intensity without rotating the incident THz pulses. The magnetic field direction can be rotated using a mechanical rotator, allowing for a convenient switch between Faraday and Voigt geometry. We demonstrate the excellent performance of our instrument by conducting THG measurements in the two-band superconductor MgB2 as a function of temperature, sample azimuth angle, as well as in-plane and out-of-plane magnetic fields. The successful combination of the strong field THz source with magnetic fields enables us to study a variety of materials with magnetic-field-dependent properties of interest.

Point-contact spectroscopy of Leggett modes in superconducting compounds with unconventional pairing

Proximity-coupled nanostructures of conventional superconductors (SCs) and half-metallic ferromagnets (hmFs) are promising candidates as materials with unconventional superconductivity. The interrelated superposition of spin singlet-triplet and frequency even-odd superconducting condensates characterizes the superconducting state in such heterostructures. In a multi-band SC, the collective modes associated with the excitations of the relative phase between superconducting bands without perturbation of the Cooper pairs symmetry (Leggett modes) are allowed. In this report, we present the results of experimental investigations via the point-contact transport measurements of the Leggett-like collective excitations in the superconducting state of the nanocomposite of s-wave two-band superconductor MgB2 and half-metallic ferromagnet (La,Sr)MnO3. Two types of point contacts (PCs) have been used: the nanocomposite-nonmagnetic metal PCs and the nanocomposite–hmF PCs. The conductance equidistant peaks against the background of the gap structure were observed in both types of high-quality point junctions. Their distinctive feature was their period: two times shorter for the nanocomposite–hmF contacts compared to the nonmagnetic metal PCs. We attribute these spin-selective conductance periodic peaks to the relative phase Leggett’s excitations between “parents” MgB2 even-frequency singlet condensates and proximity-induced triplet superconducting condensates. The data obtained on the hmF PCs also demonstrate the features that may indicate a dynamic coupling between even-frequency condensates and odd-frequency gapless superconducting condensates.

Infrared spectroscopic study on Nb-ion-irradiated MgB2 thin films

Magnesium diboride (MgB2) is a two-band superconductor with a high superconducting critical temperature (Tc) of approximately 39 K. Owing to the lack of vortex pinning centers, MgB2 exhibits an abrupt decline in the critical current density (Jc) in an applied magnetic field. Here, we prepared 1 MeV Nb ion-irradiated MgB2 thin-film samples with doses of 3×1013, 7×1013, and 9×1013 ions/cm2. Temperature-dependent magnetization and x-ray diffraction (XRD) measurements were performed to determine the Tc and c-axis lattice constant of each sample. Furthermore, a Fourier transform infrared (FTIR) spectroscopy was performed to obtain the infrared properties of the Nb-ion-irradiated MgB2 thin-film samples. The optical conductivity of each sample in the low-energy region was fitted with two (narrow and broad) Drude modes. We found that the spectral weight redistribution from the low-to high-frequency regions and the broadening of the narrow Drude mode caused by irradiation are closely related to the reduction in Tc.

Enhancement of superconductivity and phase diagram of Ta-doped Kagome superconductor CsV3Sb5

Kagome superconductors AV3Sb5 (A = K, Rb, and Cs) have attracted enormous interest due to the coexistence of charge density wave (CDW) order, unconventional superconductivity (SC) and anomalous Hall effect (AHE). In this paper, we reported an intensive investigation on Cs(V1−xTax)3Sb5 single crystals with systematic Ta doping. Ta was confirmed to be doped into V-site in the Kagome layer from both single crystal X-ray diffraction structural refinement and scanning transmission electron microscopy observation. The highest Ta doping level was found to be about 16%, which is more than twice as much as 7% in Nb-doped CsV3Sb5. With the increase of Ta doping, CDW order was gradually suppressed and finally vanished when the doping level reached to more than 8%. Meanwhile, superconductivity was enhanced with a maximum critical temperature (Tc) of 5.3 K, which is the highest Tc in the bulk crystal of this Kagome system at ambient pressure so far. The μ0Hc2(T) behavior demonstrates that the system is still a two-band superconductor after Ta doping. Based on the electrical transport measurement, a phase diagram was set up to exhibit the evolution of CDW and SC in the Cs(V1−xTax)3Sb5 system. These findings pave a new way to search for new superconductors with higher Tc in the AV3Sb5 family and establish a new platform for tuning and controlling the multiple orders and superconducting states.

Numerical Study on Monopole Production and Deconfinement Transition in Two-Condensate Charged Systems

The condensed matter Bose system may contain effective monopole quasiparticles in its excitation spectrum. In this paper, we first accomplish the mapping of the two-band Ginzburg–Landau theory to the extended CP1 model, and then perform the Monte Carlo simulations on the 50×50×50 cubic lattice with periodic boundary conditions. With the numerical data of monopole density and magnetic susceptibility, we indicate that there exists a monopole–antimonopole deconfinement transition for the two-band superconducting system with the critical temperature above 70 K. We also suggest the possible detection of this new monopole plasma phase in high-Tc iron-based superconductors.

Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasiflat band: Enhanced critical temperature evading particle-hole fluctuations

Emergent Fano-Feshbach resonance in two-band superconductors with an incipient quasiflat band: Enhanced critical temperature evading particle-hole fluctuations

Evolution from Bardeen–Cooper–Schrieffer to Bose–Einstein Condensation in Two Dimensions: Crossovers and Topological Quantum Phase Transitions

We review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.

Proximity Effect between a Two-Band Superconductor and a Ferromagnet

Proximity Effect between a Two-Band Superconductor and a Ferromagnet

Dissociation of composite Abrikosov vortices in two-band superconductors in a strong rf field

In several theoretical works, it was argued that under certain conditions Abrikosov vortices in multiband superconductors can split and exist in the form of fractional vortices, formed separately in superfluid condensates of different electron bands. Such vortices possess a fractional flux quantum, and these fractional vortices attract each other, trying to join into a composite vortex with the whole flux quantum ϕ0=h/2e. In the present work, we solve numerically the nonlinear dynamic equation for the composite vortex, settled in the pinning potential well of the columnar defect within a two-band superconductor, and exerted the rf Lorentz force action. We demonstrate that at high enough rf current amplitudes such composite Abrikosov vortices will dissociate into fractional ones and escape from the pinning potential well. The sequence of these events depends on the character of the pinning potential well, e.g., the radius of the pinning potential well. The possible manifestation of such kind transitions in rf electrodynamic characteristics, such as a complex rf resistivity and harmonics generation is calculated.

Impurity and hybridization effects on the symmetry classification and magnetic response function of a two-band superconductor with interband pairing order

Abstract The effects of hybridization and impurity (magnetic and nonmagnetic) potentials on the pairing symmetries and magnetic response of a two-band superconductor with an equal-time s-wave interband pairing order parameter in the framework of Green’s function technique are investigated theoretically. First, the effects of spin-independent and spin-dependent hybridization on the generation of even- or odd-frequency Cooper pairs which determines the symmetry classification and the response of the superconductor are studied. Next, the impurity effect on creating different symmetry classes and the kernel response function of a two-band superconductor are discussed. By separating the contributions of even- and odd-frequency pairing to the Meissner kernel, it is shown that the competition between these two terms determines the total Meissner effect of the superconductor. For a two-band spin-singlet superconductor, nonmagnetic impurity scatterings do not change transition temperature according to Anderson’s theorem, while both intra- and interband magnetic impurity scattering cause superconducting transition temperature suppression with the rate following the Abrikosov–Gor’kov theory. For spin-triplet pairing, interband magnetic scattering has no impact on pair breaking, whereas intraband magnetic scattering acts as a pair breaker and suppresses the transition temperature in the Born limit. In this case, the odd-frequency superconducting pairs can be induced in the simultaneous presence of both intra- and interband magnetic impurities. Thus, by controlling the concentration of magnetic impurities, it is possible to engineer triplet-pairing odd-frequency superconductors with a total diamagnetic Meissner response which stabilizes the superconducting state. This technique opens up an avenue for designing stable odd-frequency superconductors.

Multiple-q current states in a multicomponent superconducting channel

It is well-established that multicomponent superconductors can host different nonstandard phenomena such as broken-time reversal symmetry (BTRS) states, exotic Fulde–Ferrell–Larkin–Ovchinnikov phases, the fractional Josephson effect as well as plenty of topological defects like phase solitons, domain walls and unusual vortex structures. We show that in the case of a two-component superconducting quasi-one-dimensional channel this catalogue can be extended by a novel inhomogeneous current state, which we have termed as a multiple-q state, characterized by the coexistence of two different interpenetrating Cooper pair condensates with different total momenta. Within the Ginzburg–Landau formalism for a dirty two-band superconductor with sizable impurity scattering treated in the Born-approximation we reveal that under certain conditions, the occurrence of multiple-q states can induce a cascade of transitions involving switching between them and the homogeneous BTRS (non-BTRS) states and vice versa leading this way to a complex interplay of homogeneous and inhomogeneous current states. We find that hallmarks of such a multiple-q state within a thin wire or channel can be a saw-like dependence of the depairing current and the existence of two distinct stable branches on it (a bistable current state).

Band-resolved Caroli-de Gennes-Matricon states of multiple-flux-quanta vortices in a multiband superconductor.

Superconductors are of type I or II depending on whether they form an Abrikosov vortex lattice. Although bulk lead (Pb) is classified as a prototypical type-I superconductor, we show that its two-band superconductivity allows for single-flux-quantum and multiple-flux-quanta vortices in the intermediate state at millikelvin temperature. Using scanning tunneling microscopy, the winding number of individual vortices is determined from the real space wave function of its Caroli-de Gennes-Matricon bound states. This generalizes the topological index theorem put forward by Volovik for isotropic electronic states to realistic electronic structures. In addition, the bound states due to the two superconducting bands of Pb can be separately detected and the two gaps close independently inside vortices. This yields strong evidence for a low interband coupling.

Moiré Enhanced Two-Band Superconductivity in a MnTe/NbSe2 Heterojunction.

Recent advances in creating moiré periods of two-dimensional heterostructures enable diverse and compatible tunability to modulate the conventional proximity effect involving superconductivity, magnetism, and topology. Here, by constructing a MnTe/NbSe2 heterojunction via molecular beam epitaxy growth, we report on a moiré-enhanced multiband superconductivity by low-temperature scanning tunneling microscopy/spectroscopy measurements. We observe a distinct double-gap superconducting spectrum on monolayer MnTe that is absent on the NbSe2 substrate. The subgap character exhibits a moiré-related oscillation in real space, which can be well described by an effective two-band model. The restored two-gap feature and its rapid suppression under a small magnetic field are speculated to be mediated by the moiré superlattice, which is closely related to the enhanced interband coupling strength of quasiparticle scattering. Our work paves the way for engineering proximitized properties of heterostructures by a moiré landscape with spatial modulations.

High magnetic field superconductivity in a two-band superconductor

We present a mechanism allowing for superconductivity at high magnetic fields, beyond the Pauli-Chandrasekhar-Clogston limit. We consider spin splitting induced by an in-plane external magnetic field in a superconductor with two relevant bands close to the Fermi level. The magnetic field therefore controls which bands are available for Cooper pair formation. The presence of interband superconducting pairing, i.e., Cooper pairs formed by electrons with different band indices, produces high-field reentrant superconducting domains, whose critical magnetic field violates the Pauli-Chandrasekhar-Clogston limit. We analyze how the interband superconducting domains are influenced by the band parameters, and show that, for a certain range of parameters, the system presents two separate superconducting regions, for low and high magnetic field.

Sweeping across the BCS-BEC crossover, reentrant, and hidden quantum phase transitions in two-band superconductors by tuning the valence and conduction bands

Two-band electronic structures with a valence and a conduction band separated by a tunable energy gap and with pairing of electrons in different channels can be relevant to investigate the properties of two-dimensional multiband superconductors and electron-hole superfluids, as monolayer FeSe, recently discovered superconducting bilayer graphene, and double-bilayer graphene electron-hole systems. This electronic configuration allows also to study the coexistence of superconductivity and charge density waves in connection with underdoped cuprates and transition metal dichalcogenides. By using a mean-field approach to study the system above mentioned, we have obtained numerical results for superconducting gaps, chemical potential, condensate fractions, coherence lengths, and superconducting mean-field critical temperature, considering a tunable band gap and different filling of the conduction band, for parametric choice of the pairing interactions. By tuning these quantities, the electrons redistribute among valence and conduction band in a complex way, leading to a new physics with respect to single-band superconductors, such as density induced and band-selective BCS-BEC crossover, quantum phase transitions, and hidden criticalities. At finite temperature, this phenomenon is also responsible for the non-monotonic behavior of the superconducting gaps resulting in a superconducting-normal state reentrant transition, without the need of disorder or magnetic effects.

Temperature-Dependent Anisotropy and Two-Band Superconductivity Revealed by Lower Critical Field in Organic Superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br

Resistivity and magnetization have been measured at different temperatures and magnetic fields in organic superconductors κ-(BEDT-TTF)2Cu[N(CN)2]Br. The lower critical field and upper critical field are determined, which allow to depict a complete phase diagram. Through the comparison between the upper critical fields with magnetic field perpendicular and parallel to the conducting ac-planes, and the scaling of the in-plane resistivity with field along different directions, we find that the anisotropy Γ is strongly dependent on temperature. It is realized that Γ is quite large (above 20) near T c, which satisfies the 2D model, but approaches a small value in the low-temperature region. The 2D-Tinkham model can also be used to fit the data at high temperatures. This is explained as a crossover from the orbital depairing mechanism in high-temperature and low-field region to the paramagnetic depairing mechanism in the high-field and low-temperature region. The temperature dependence of lower critical field, H c1(T), shows a concave shape in wide temperature region. It is found that neither a single d-wave nor a single s-wave gap can fit the H c1(T), however a two-gap model containing an s-wave and a d-wave can fit the data rather well, suggesting two-band superconductivity and an unconventional pairing mechanism in this organic superconductor.

Theoretical Investigation of the Superconducting and Thermodynamic Properties of Two-Band Model High-Temperature Iron-Based Superconductor Ba1–xNaxFe2As2

This work presents the theoretical investigation of the superconducting and thermodynamic properties of the two-band model high-temperature iron-based superconductor Ba1-xNaxFe2As2. By developing a model Hamiltonian and by employing the well-knownvdouble-time temperature-dependent Green’s function formalism, we have computed the superconducting orderbparameters for the electron and hole intra- and inter-band transitions, superconducting transition temperature, densitiesbof states, and condensation energies. Furthermore, the electronic specific heat and the entropy for electron and hole intra-band transitions have been determined. By using appropriate experimental data and some credible approximations of the parameters in the computed expressions, we have found the phase diagrams of superconducting order parameters versus the temperature, superconducting critical temperature versus the inter-band interaction potential, temperature dependences of the electronic specific heat and entropy for electron and hole intra-band transitions, and densities of states for the electron and hole intra-band transitions as functions of the excitation energy at different values of the temperature. Finally, the phase diagrams of the condensation energy versus the temperature, inter-band pairing potential at T = 0 K versus the condensation energy, and condensation energy versus the superconducting transition temperature (TC) have been drawn. In some of the phase diagrams, the comparison between theoretical and experimental values has been made. The results are in a good agreement with previous findings.

Collective excitations in three-band superconductors

We investigate equilibrium states, magnetic response and the normal oscillations of internal degrees of freedom (Higgs modes and Goldstone modes) of three-band superconductors accounting the terms of both internal proximity effect and the ``drag'' effect (intergradient interaction) in the Lagrangian. Both the Goldstone mode and the Higgs mode are split into three branches each: common mode oscillations and two modes of anti-phase oscillations, which are analogous to the Leggett mode in two-band superconductors. It is demonstrated that the second and third branches are nonphysical, and they can be removed by special choice of coefficients at the ``drag'' terms in Lagrangian. As a result, three-band superconductors are characterized by only single coherence length. Spectrum of the common mode Higgs oscillations has been obtained. The magnetic penetration depth is determined with densities of superconducting electrons in each band, although the drag terms renormalize the carrier masses.