Clean Superconductors Research Articles

Optical and Raman selection rules for odd-parity clean superconductors

Optical and Raman selection rules for odd-parity clean superconductors

Vanishing of Resistivity upon Freezing of Vortex Liquid in Clean Superconductors

Vanishing of Resistivity upon Freezing of Vortex Liquid in Clean Superconductors

Tunability of Andreev levels in a spin-active Ising superconductor/half-metal Josephson junction

We study the Andreev levels, supercurrent and tunnelling conductance in a clean Ising superconductor (ISC)/half-metal (HM)/ISC Josephson junction (JJ) with spin-active interfaces using Bogoliubov–de Gennes equations. We theoretically demonstrate the effect of spin mixing, spin flipping processes and spin–orbit coupling (SOC) of the ISC on Andreev bound states spectra, the current phase relation and tunnelling conductance in a transparent and opaque barrier limit. We witness an additional splitting of the Andreev levels due to the SOC of the ISC and transition for different barrier magnetic moments. Also, different φ-junctions can be achieved by tuning the strength of the barrier magnetic moment and spin mismatch angle. Moreover, a possible transition can also be achieved for a SOC stronger than the chemical potential of the ISC using suitable control parameters. The tunnelling conductance is found to be dependent on the spin mismatch angle. A finite subgap conductance is also observed, indicating different probabilities of Andreev reflected electrons and holes in the presence of SOC. Furthermore, anomalous Andreev levels are observed for different HM length scales, signifying their role in the tunability of the φ-phase JJ.

Superconducting properties of pt-type and bct-type YRh4B4

YRh4B4, which exhibits high- superconductivity in the RRh4B4 system, has two types of crystal structures, CeCo4B4 type (pt-type) and LuRu4B4 type (bct-type). Both types of structure have similar (pt-type; = 10.6 K, bct-type; = 9.8 K), but the of both compounds is very different, pt-type; = 2.50 T and bct-type; = 9.85 T. From our results, one can see that the difference in between pt-YRh4B4 and bct-YRh4B4 is mainly caused from the difference of the density of state at Fermi energy. The high- in pt-YRh4B4 is derived from the high Debye temperature caused by vibrations of boron. In contrast, in bct-YRh4B4 it is caused by a stronger electron–phonon coupling than in pt-YRh4B4. Regarding the symmetry of superconductivity, it is suggested that pt-YRh4B4 is a clean limit superconductor and has basically a fully gapped superconducting gap, but is slightly anisotropic from the results of ) below and . However, bct-YRh4B4 is a dirty limit superconductor and has an anisotropic superconducting gap from the results of below and .

A new methodology for studying vortex dynamics based on point-contact spectroscopy

Vortex dynamics has attracted tremendous attention for both fundamental physics and applications of type-II superconductors. However, methods to detect local vortex motion or vortex jump with high sensitivity are still scarce. Here, we fabricated soft point contacts on the clean layered superconductor 2H–NbSe2, which are demonstrated to contain multiple parallel micro-constrictions by scanning electronic microscopy. Andreev reflection spectroscopy was then studied in detail for the contacts. Differential conductance taken at fixed bias voltages was discovered to vary spontaneously over time in various magnetic fields perpendicular to the sample surface. The conductance variations become invisible when the field is zero or large enough, or parallel to the sample surface, which can be identified as the immediate consequence of vortex motion across a finite number of micro-constrictions. These results demonstrate point contact Andreev reflection spectroscopy to be a new potential way with a high time resolution to study the vortex dynamics in type-II superconductors.

Current-enabled optical conductivity of superconductors

While optical techniques are fundamental in the investigation of the superconducting state, in many clean superconductors the combination of particle-hole and inversion symmetries prevents momentum-conserving transitions. Here, the authors show that by driving supercurrent through the sample optical transitions across the superconducting gap become allowed even in clean single-band systems. As the signal depends strongly on the superconducting pairing as well as on the underlying normal state, supercurrent-driven optical conductivity provides a new way of determining the superconducting state properties.

Contribution of collective excitations to third harmonic generation in two-band superconductors: The case of MgB2

Multiband superconductors can host collective excitations with marked differences with respect to their single-band counterpart. We first study the spectrum of collective amplitude fluctuations in a clean two-band superconductor, showing that the spectral weight of the Higgs mode rapidly deviates from the naive extension of the single band case as the interband coupling is turned on. These results are then used to critically analyze the nonlinear optical response in ${\mathrm{MgB}}_{2}$, providing an explanation for the apparently contradictory results of recent experiments, pointing towards a selective relevance either of the Leggett mode or of the amplitude fluctuations at twice the lower gap. By using exact numerical simulations and realistic estimates of disorder we compute the relative contribution of the quasiparticle, amplitude, and phase fluctuations to the nonlinear optical response. We show that at low pumping frequency only the resonance at twice the smaller gap emerges, as due to the BCS response, while the Leggett mode dominates only in a narrow range of higher pumping frequencies matching its low-temperature value. Our findings provide a fresh perspective on the potential of nonlinear THz spectroscopy to detect collective modes in other multiband systems, such as iron-based superconductors.

Nonlinear microwave response of clean superconducting films

We develop an explicitly gauge-invariant semiclassical approach to investigate nonlinear response of superconductors to monochromatic THz radiation. We demonstrate that in clean superconductors charge conservation forbids non-linear response to a uniform field. We apply our approach to quasi-two-dimensional films and obtain an explicit expression for the photoinduced current. We find that the photoinduced current exhibits a strong dependence on polarization and incidence angle of the radiation. Our predictions may be directly verified in experiments with quasi-two-dimensional superconducting films.

Proximity-induced superconductivity generated by thin films: Effects of Fermi surface mismatch and disorder in the superconductor

We investigate the effects of disorder characterising a superconducting thin film on the proximity-induced superconductivity generated by the film (in, e.g., a semiconductor) based on the exact numerical analysis of a three-dimensional microscopic model. To make the problem numerically tractable, we use a recursive Green's function method in combination with a patching approach that exploits the short-range nature of the interface Green's function in the presence of disorder. As a result of the Fermi surface mismatch between the superconductor (SC) and the semiconductor (SM) in combination with the confinement-induced quantization of the transverse SC modes, the proximity effect induced by a clean SC film is typically one to three orders of magnitude smaller that the corresponding quantity for a bulk SC and exhibits huge thickness-dependent variations. The presence of disorder has competing effects: on the one hand it enhances the proximity-induced superconductivity and suppresses its strong thickness dependence, on the other hand it generates proximity-induced effective disorder in the SM. The effect of proximity-induced disorder on the topological superconducting phase and the associated Majorana modes is studied nonperturbatively.

Angular dependence of the upper critical induction of clean s- and d x 2−y 2 -wave superconductors with self-consistent ellipsoidal effective mass and Zeeman anisotropies

We employ the Schrödinger-Dirac method generalized to an ellipsoidal effective mass anisotropy in order to treat the spin and orbital effective mass anisotropies self consistently, which is important when Pauli-limiting effects on the upper critical field characteristic of singlet superconductivity are present. By employing the Klemm–Clem transformations to map the equations of motion into isotropic form, we then calculate the upper critical magnetic induction at arbitrary directions and temperatures T for isotropic s-wave and for anisotropic -wave superconducting order parameters. As for anisotropic s-wave superconductors, is largest in the direction of the lowest effective mass, and is proportional to the universal orientation factor . However, for -wave pairing and vanishing planar effective mass anisotropy, exhibits a four-fold azimuthal pattern with C 4 symmetry the maxima of which are along the crystal axes just below the transition temperature T c , but these maxima are rotated by about the z axis as T is lowered to 0. However for -wave pairing with weak planar effective mass anisotropy, exhibits a two-fold pattern with C 2 symmetry for all , which also rotates by about the z axis as T is lowered to 0. These low planar effective mass anisotropy cases provide a new method to distinguish s-wave and -wave pairing symmetries in clean unconventional superconductors.

Quantum phase transition in a clean superconductor with repulsive dynamical interaction

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) frequency ω0 to 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 and ω0 must vanish in a correlated way such that 1/| log [{{Delta }}(0)]| sim {omega }_{0}^{2}. We discuss the behavior of phase fluctuations near this transition and show that the correlation between Δ(0) and ω0 locks the phase stiffness to a non-zero value.

Vortex core near planar defects in a clean layered superconductor

We investigate the structure of quasiparticle states localized in a core of an Abrikosov vortex in a clean layered superconductor in the presence of planar defects. It is shown that even a highly transparent defect opens a minigap at the Fermi energy. Its magnitude, $E_g\sim\Delta\sqrt{R}$, exceeds the mean level spacing for the chiral branch, $\omega_0\sim\Delta^2/E_F$, already for very small values of the reflection coefficient off the defect, $R\ll1$ ($\Delta$ is the bulk gap). For $R\gtrsim\sqrt{\Delta/E_F}$, formation of the minigap is accompanied by the appearance of subgap states localized along the defect, in accordance with [A. V. Samokhvalov \emph{et al.}, Phys.\ Rev.\ B \textbf{102}, 174501 (2020)]. The minigap takes its maximal value for the vortex located right at the defect, decreases with increasing the distance $b$ from the defect, and closes when $k_Fb\sim (\Delta/\omega_0)\sqrt{R}$. We also study various configurations of several planar defects (few crossing planes, stars, periodic structures). Although the minigap remains, a strong commensurability effect is observed. For two crossing planar defects, the magnitude of the minigap strongly depends on how close the intersection angle is to a rational fraction of $\pi$.

How repulsive can a pairing interaction be?

Quantum phase transition in a clean superconductor with repulsive dynamical interaction Authors: Dimitri Pimenov and Andrey V. Chubukov arXiv:2112.06273 Recommended with a commentary by Jörg Schmalian, Karlsruhe Institute of Technology |View Commentary (pdf)| This commentary may be cited as: DOI: 10.36471/JCCM_January_2022_01 https://doi.org/10.36471/JCCM_January_2022_01

Effects of Nonmagnetic Impurities and Subgap States on the Kinetic Inductance, Complex Conductivity, Quality Factor, and Depairing Current Density

We investigate how a combination of a nonmagnetic-impurity scattering rate $\gamma$ and finite subgap states parametrized by Dynes $\Gamma$ affects various physical quantities relevant to to superconducting devices: kinetic inductance $L_k$, complex conductivity $\sigma$, surface resistance $R_s$, quality factor $Q$, and depairing current density $J_d$. All the calculations are based on the Eilenberger formalism of the BCS theory. We assume the device materials are extreme type-II $s$-wave superconductors. It is well known that the optimum impurity concentration ($\gamma/\Delta_0 \sim 1$) minimizes $R_s$. Here, $\Delta_0$ is the pair potential for the idealized ($\Gamma\to 0$) superconductor for the temperature $T\to 0$. We find the optimum $\Gamma$ can also reduce $R_s$ by one order of magnitude for a clean superconductor ($\gamma/\Delta_0 < 1$) and a few tens $\%$ for a dirty superconductor ($\gamma/\Delta_0 > 1$). Also, we find a nearly-ideal ($\Gamma/\Delta_0 \ll 1$) clean-limit superconductor exhibits a frequency-independent $R_s$ for a broad range of frequency $\omega$, which can significantly improve $Q$ of a very compact cavity with a few tens of GHz frequency. As $\Gamma$ or $\gamma$ increases, the plateau disappears, and $R_s$ obeys the $\omega^2$ dependence. The subgap-state-induced residual surface resistance $R_{\rm res}$ is also studied, which can be detected by an SRF-grade high-$Q$ 3D resonator. We calculate $L_k(\gamma, \Gamma,T)$ and $J_d(\gamma, \Gamma,T)$, which are monotonic increasing and decreasing functions of $(\gamma, \Gamma,T)$, respectively. Measurements of $(\gamma, \Gamma)$ of device materials can give helpful information on engineering $(\gamma, \Gamma)$ via materials processing, by which it would be possible to improve $Q$, engineer $L_k$, and ameliorate $J_d$.

Microwave response of superconductors that obey local electrodynamics

Surface impedance of type-II superconductors is determined by their local optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$. Standard BCS-like theoretical descriptions of $\ensuremath{\sigma}(\ensuremath{\omega})$, due to Mattis and Bardeen [Phys. Rev. 111, 412 (1958)] or Zimmermann et al. [Physica C 183, 99 (1991)], do not take pair-breaking processes into account. Therefore they do not provide a quantitative explanation of the microwave response, and in particular, they cannot predict the magnitude of the coherence peak. Here, based on the recently developed concept of Dynes superconductors, which does take also the pair-breaking scattering into account, we provide a simple but complete description of the microwave response of type-II superconductors, concentrating on the unexpected properties of clean superconductors which are often used as cavity materials.

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

Origin of the anomalous Hall effect in two-band chiral superconductors

We consider the origin of the anomalous Hall effect in a general model of a clean two-band chiral superconductor. Within the Kubo formalism we derive an analytic expression for the high-frequency ac Hall conductivity valid close to the critical temperature. This expression involves two distinct gauge-invariant time-reversal-odd bilinear (TROB) functions involving the pairing potential and its Hermitian conjugate. We argue that the existence of at least one of these TROBs generically implies a nonzero ac Hall conductivity. The TROBs allow us to clarify the roles of intra- and interband pairing, and provide a straightforward criterion for a superconducting state to exhibit the anomalous Hall effect. We briefly exemplify our results with model calculations for a chiral $p$-wave pairing state in strontium ruthenate and a chiral $d$-wave pairing state on the honeycomb lattice.

The Zeeman, spin-orbit, and quantum spin Hall interactions in anisotropic and low-dimensional conductors

To construct a microscopic theory of electrons and holes in anisotropic conductors that self-consistently treats their band effective mass anisotropy with their interactions with applied electric and magnetic fields, the Dirac equation is extended for an electron or hole in an orthorhombically-anisotropic conduction band. Its covariance is established both by a modified version of the Klemm–Clem transformations to a space in which it is isotropic, and also in its fully anisotropic form by making the most general proper and improper Lorentz transformations, proving its validity in both the relativistic and non-relativistic limits. The appropriate Foldy–Wouthuysen transformations are extended to expand about the non-relativistic Hamiltonian limit to fourth order in the inverse of the particle’s Einstein rest energy. The results have important consequences for magnetic measurements of many classes of clean anisotropic semiconductors, metals, and superconductors. In all of these cases, the Zeeman interaction is found to depend strongly upon the effective mass anisotropy. When an electron or hole is traveling in an atomically thin one-dimensional conduction band, its Zeeman, spin–orbit, and quantum spin Hall interactions are vanishingly small. Accurate expressions for the Zeeman, spin–orbit and quantum spin Hall interactions for two-dimensional conductors are provided.

Conductivity of superconductors in the flux flow regime

We develop a theory of conductivity of type-II superconductors in the flux flow regime taking into account random spatial fluctuations of the system parameters, such as the gap magnitude $\Delta$(r) and the diffusion coefficient D(r). We find a contribution to the conductivity that is proportional to the inelastic relaxation time $\tau_{in}$, which is much longer than the elastic relaxation time. This new contribution is due to Debye-type relaxation, and it can be much larger than the conventional flux flow conductivity due to Bardeen and Stephen. The new contribution is expected to dominate in clean superconductors at low temperatures and in magnetic fields much smaller than $H_{c2}$.

Anomalous Hall effect in single-band chiral superconductors from impurity superlattices

Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effective theory whose Hall effect can be studied with ease. We demonstrate that the occurrence of the Hall effect depends on the superlattice geometry and on the parity of the chiral pairing. In particular, due to the mixed particle-hole character of the subgap states, the Hall conductance may arise at the one-loop level of the current-current correlator in our effective model. Our theory provides a new insight into the impurity-induced anomalous Hall effect in chiral superconductors.