Superconducting Density Of States Research Articles

Magnon influence on the superconducting density of states in superconductor–ferromagnetic-insulator bilayers

Magnon influence on the superconducting density of states in superconductor–ferromagnetic-insulator bilayers

Microwave Susceptibility Observation of Interacting Many-Body Andreev States.

Electrostatic charging affects the many-body spectrum of Andreev states, yet its influence on their microwave properties has not been elucidated. We developed a circuit quantum electrodynamics probe that, in addition to transition spectroscopy, measures the microwave susceptibility of different states of a semiconductor nanowire weak link with a single dominant (spin-degenerate) Andreev level. We found that the microwave susceptibility does not exhibit a particle-hole symmetry, which we qualitatively explain as an influence of Coulomb interaction. Moreover, our state-selective measurement reveals a large, π-phase shifted contribution to the response common to all many-body states which can be interpreted as arising from a phase-dependent continuum in the superconducting density of states.

Critical fields of superconductors with magnetic impurities

The upper critical field ${H}_{c2}$, the field ${H}_{c3}$ for nucleation of the surface superconductivity, and the thermodynamic field ${H}_{c}$ are evaluated within the weak-coupling theory for the isotropic s-wave case with arbitrary transport, and pair-breaking scattering. We find that, for the standard geometry of a half-space sample in a magnetic field parallel to the surface, the ratio $\mathcal{R}={H}_{c3}/{H}_{c2}$ is within the window $1.55\ensuremath{\lesssim}\mathcal{R}\ensuremath{\lesssim}2.34$, regardless of temperature or the scattering type. While the nonmagnetic impurities tend to flatten the $\mathcal{R}(T)$ variation, magnetic scattering merely shifts the maximum of $\mathcal{R}(T)$ to lower temperatures. Surprisingly, while reducing the transition temperature, magnetic scattering has a milder impact on $\mathcal{R}$ than nonmagnetic scattering. The surface superconductivity is quite robust; in fact, the ratio $\mathcal{R}\ensuremath{\approx}1.7$ even in the gapless state. We used Eilenberger's energy functional to evaluate the condensation energy ${F}_{c}$ and the thermodynamic critical field ${H}_{c}$ for any temperature and scattering parameters. By comparing ${H}_{c2}$ and ${H}_{c}$, we find that, unlike transport scattering, the pair-breaking pushes materials toward type-I behavior. We find a peculiar behavior of ${F}_{c}$ as a function of the pair-breaking scattering parameter at the low-$T$ transition from gapped to gapless phases, which has recently been associated with the topological transition in the superconducting density of states.

Very large thermal rectification in ferromagnetic insulator-based superconducting tunnel junctions

We investigate electronic thermal rectification in ferromagnetic insulator-based superconducting tunnel junctions. Ferromagnetic insulators coupled to superconductors are known to induce sizable spin splitting in the superconducting density of states and also lead to efficient spin filtering if used as tunnel barriers. The combination of spin splitting and spin filtering is shown to yield a substantial amount of self-amplification of the electronic heat diode effect due to breaking of the electron-hole symmetry in the system, which is added to the thermal asymmetry of the junction. Large spin splitting and large spin polarization (≳90%) can potentially lead to thermal rectification efficiencies exceeding ∼5×104% for realistic parameters in a suitable temperature range, thereby outperforming up to a factor of ∼250, the heat diode effect achievable with conventional superconducting tunnel junctions. These results are relevant for improved control of heat currents in innovative phase-coherent caloritronic nanodevices and for enhanced thermal management of quantum circuits at the nanoscale.

Giant microwave absorption in [formula omitted]- and [formula omitted]- wave superconductors

We discuss a new mechanism of microwave absorption in s- and d-wave superconductors, which arises in the presence of a dc supercurrent in the system. It produces a contribution to the ac conductivity that is proportional to the inelastic quasiparticle relaxation time. This contribution also determines the supercurrent dependence of the conductivity. It may significantly exceed the conventional contribution because in typical superconductors the inelastic relaxation time is several orders of magnitude longer than the elastic one. We show that the aforementioned contribution to the conductivity may be expressed in terms of the single particle density of states in superconductors in the presence of a dc supercurrent. Our results may enable determination of the inelastic relaxation time in superconductors from microwave absorption measurements.

Surface density of states in superconductors with inhomogeneous pairing constant: Analytical results

We consider a superconductor with surface suppression of the BCS pairing constant $\lambda(x)$. We analytically find the gap in the surface density of states (DOS), behavior of the DOS $\nu(E)$ above the gap, a "vertical" peculiarity of the DOS around an energy equal to the bulk order parameter $\Delta_0$, and a perturbative correction to the DOS at higher energies. The surface gap in the DOS is parametrically different from the surface value of the order parameter due to a difference between the spatial scale $r_c$, at which $\lambda(x)$ is suppressed, and the coherence length. The vertical peculiarity implies an infinite-derivative inflection point of the DOS curve at $E=\Delta_0$ with square-root behavior as $E$ deviates from $\Delta_0$. The coefficients of this dependence are different at $E<\Delta_0$ and $E>\Delta_0$, so the peculiarity is asymmetric.

Design and performance of hafnium optical and near-IR kinetic inductance detectors

We report on the design and performance of microwave kinetic inductance detectors (MKIDs) sensitive to single photons in the optical to near-infrared range using hafnium as the sensor material. Our test device had a superconducting transition temperature of 395 mK and a room temperature normal state resistivity of 97 μΩ cm with RRR=1.6. Resonators on the device displayed internal quality factors of around 200 000. Similar to the analysis of MKIDs made from other highly resistive superconductors, we find that modeling the temperature response of the detector requires an extra broadening parameter in the superconducting density of states. Finally, we show that this material and design is compatible with a full-array fabrication process, which resulted in pixels with decay times of about 40 μs and resolving powers of ∼9 at 800 nm.

RECONSTRUCTION OF THE DOS AT THE END OF A S/F BILAYER

Influence of a nonmagnetic surface on the density of states in a spin-split superconductor, which is realized on the basis of a S/F bilayer, is investigated. It is demonstrated that if the ferromagnet magnetization has a defect in the form of a domain wall in the vicinity of the surface, the superconducting density of states is reconstructed manifesting the spin-split Andreev resonances. Formation of these resonances is not connected to any superconducting order parameter inhomogeneities. Andreev reflection processes forming the resonances occur at the inhomogeneity of the spin-split gap generated by the domain wall. These resonances can be used as a spectroscopic probe of a domain wall presence and motion.

Reconstruction of the Density of States at the End of an S/F Bilayer

Influence of a nonmagnetic surface on the density of states in a spin-split superconductor, which is realized on the basis of a S/F bilayer, is investigated. It is demonstrated that if the ferromagnet magnetization has a defect in the form of a domain wall in the vicinity of the surface, the superconducting density of states is reconstructed manifesting the spin-split Andreev resonances. Formation of these resonances is not connected to any superconducting order parameter inhomogeneities. Andreev reflection processes forming the resonances occur at the inhomogeneity of the spin-split gap generated by the domain wall. These resonances can be used as a spectroscopic probe of a domain wall presence and motion.

Revisiting the vortex-core tunnelling spectroscopy in YBa2Cu3O7-δ.

The observation by scanning tunnelling spectroscopy of Abrikosov vortex cores in the high-temperature superconductor YBa2Cu3O7−δ (Y123) has revealed a robust pair of electron-hole symmetric states at finite subgap energy. Their interpretation remains an open question because theory predicts a different signature in the vortex cores, characterized by a strong zero-bias conductance peak. Here, we present scanning tunnelling spectroscopy data on very homogeneous Y123 at 0.4 K revealing that the subgap features do not belong to vortices: they are actually observed everywhere along the surface with high spatial and energy reproducibility, even in the absence of magnetic field. Detailed analysis and modelling show that these states remain unpaired in the superconducting phase and belong to an incoherent channel, which contributes to the tunnelling signal in parallel with the superconducting density of states.

Optical observation of superconducting density of states in luminescence spectra of InAs quantum dots

We study luminescence spectra observed from InAs quantum dots (QDs) embedded in an $n$-type InGaAs-based heterostructure, where electron Cooper pairs penetrate from an adjacent niobium (Nb) superconductor with the proximity effect. Below the superconducting (SC) critical temperature of Nb, we observe substantial luminescence intensity enhancement and a sharp edge in luminescence spectra of InAs QDs. We explain the observed sharp edge in the luminescence spectra with the proximity effect, that is, with the consideration of opening of SC gap and modification of density of states (DOS) near the electron Fermi level in the $n$-type semiconductor heterostructure. We demonstrate that the sharp edge luminescence spectra are well reproduced by the SC DOS, with quasiparticle lifetime broadening and a Gaussian distribution of lowest QD state emission lines. We discuss the reason why it has been difficult to observe the sharp edge luminescence spectra in the previous quantum well-based SC light emitting diodes.

Nonequilibrium spin transport in Zeeman-split superconductors

We investigate theoretically the non-local conductance through a superconducting wire in tunnel contact with normal and ferromagnetic leads. In the presence of an in-plane magnetic field, the superconducting density of states is spin-split, and the current injected from the normal lead is spin-polarized. A non-local conductance that is antisymmetric with the applied voltage can be measured with a ferromagnetic lead. It persists for a distance between the contacts that is larger than both the charge-imbalance relaxation length and the normal-state spin relaxation length. We determine its amplitude by considering two extreme models of weak and strong internal equilibration of the superconducting quasiparticles due to electron-electron interactions. We find that the non-local signal, which was measured in recent experiments and discussed as a spin-imbalance effect, can be interpreted alternatively as the signature of a thermoelectric effect.

Magnetic Pair Breaking in Superconducting SrPd2Ge2 Investigated by Scanning Tunnelling Spectroscopy

SrPd2Ge2 has been structurally identical with the 122-type iron pnictide compounds with iron completely replaced by Pd and pnictogen replaced by Ge yielding the superconducting transition below 3 K. Our previous works showed that in contrast to iron pnictides this system is electronically fully three-dimensional and revealed conventional superconductivity, even of type I. Here, by means of sub-Kelvin STM spectroscopy, we show that the dirty limit occurs in the sample driving it to type-II superconductivity. STM also proves that in magnetic field the sample undergoes the phase transition to the Abrikosov vortex-lattice state. The de Gennes–Maki theory of gapless superconductivity for dirty superconductors is successfully applied to model the tunnelling spectra of the superconducting density of states in magnetic field. We show that this theory is applicable in a wide range of magnetic fields starting from 60 % of the upper critical field Hc2.

Effect of Phase Fluctuations on the Superconducting Properties of Strongly Disordered 3D NbN Thin Films

We present transport, Hall effect, electronic tunnelling and penetration depth studies in 3D homogeneously disordered epitaxial NbN thin films with disorder ranging from the moderately clean limit (KFl~10.12) to the very dirty limit (KFl~1.24). The superconducting transition temperature (Tc) decreases from ~17K to less than 350mK with increasing disorder. The Tc and conductivity at the lowest temperature (σ0) both asymptotically approach zero as KFl →l indicating a coincidence of the metal-insulator transition (MIT) and the superconductor-insulator transition (SIT). Close to critical disorder there is spatial inhomogeneity in the superconducting density of states (DOS) and the superconducting state is governed by quantum phase fluctuations. This results in suppression of the superfluid density (ns) and a pseudogap state where the resistance is no longer zero but the energy gap (Δ) remains finite.

Precision microwave electrodynamic measurements of K- and Co-dopedBaFe2As2

We have studied the microwave electrodynamics of single crystal iron-based superconductors Ba$_{0.72}$K$_{0.28}$Fe$_2$As$_2$ (hole-doped, $T_\mathrm{c}$ $\approx $30 K) and Ba(Fe$_{0.95}$Co$_{0.05}$)$_2$As$_2$ (electron-doped, $T_\mathrm{c}$ $\approx$20 K), by cavity perturbation and broadband spectroscopy. SQUID magnetometry was used to confirm the quality and homogeneity of the samples under study. Through cavity perturbation techniques, the temperature dependence of the in-plane London penetration depth $\Delta\lambda(T)$, and therefore the superfluid phase stiffness $\lambda^2(0)/\lambda^2(T)$ was measured. Down to 0.4 K, the data do not show the exponential saturation at low temperatures expected from a singly-, fully-gapped superconductor. Rather, both the electron- and the hole-doped systems seem to be best described by a power law behavior, with $\lambda^2(0)/\lambda^2(T)$ $\sim$ $T^n$ and \emph{n} $\approx$ 2.5. In the three samples we studied, a weak feature near the sensitivity limit of our measurements appears near $T/T_\mathrm{c}$ =~0.04, hinting at a corresponding low energy feature in the superconducting density of states. The data can also be relatively well-described by a simple two-gap s-wave model of the order parameter, but this yields parameters which seem unrealistic and dependent on the fit range. Broadband surface resistance measurements reveal a sample dependent residual loss whose origin is unclear. The data from the \FeAs samples can be made to scale as $\omega^2$ if the extrinsic loss is treated as an additive component, indicating large scattering rates. Finally, the temperature dependence of the surface resistance at 13 GHz obeys a power law very similar to those observed for $\Delta\lambda(T)$.

Fulde–Ferrell–Larkin–Ovchinnikov states in quasi-two-dimensional d + s-wave superconductors: Enhancement of the upper critical field

We investigate the spatially nonuniform Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting state in a quasi-two-dimensional (Q2D) d+s-wave superconductor. In the d+s-wave superconductor, the shape of the superconducting gap function and the nature of FFLO state depend on the degree of s-wave (or d-wave) admixture. The magnetic field versus temperature phase diagrams for the d+s-wave states with different shape of gap function are studied systematically. We find in particular that, a slight deviation of gap function from that of d-wave state may lead to significant change of FFLO state and remarkable enhancement of the upper critical magnetic field. The superconducting density of states (DOS) for d+s-wave superconductor is also calculated and found to be strikingly different from that for pure s-wave and pure d-wave superconductors.

Tunneling spectroscopy of persistent currents in superconducting microrings

It is shown that in a structure consisting of a superconducting ring-shaped electrode overlapped by a normal metal contact through a thin oxide barrier, measurements of the tunnel current in magnetic field can probe persistent currents in the ring. The effect manifests itself as periodic oscillations of the tunnel current through the junction at a fixed bias voltage as function of perpendicular magnetic field. The magnitude of oscillations depends on bias point. It reaches maximum at energy eV which is close to the superconducting gap and decreases with increase of temperature. The period of oscillations Δ Φ in units of magnetic flux is equal neither to h/e nor to h/2 e, but significantly exceeds these values for larger loop circumferences. The phenomenon is explained by formation of metastable states with large vorticity. The pairing potential and the superconducting density of states are periodically modulated by the persistent currents at sub-critical values resulting in corresponding variations of the measured tunnel current.

Modeling study of the dip-hump feature inBi2Sr2CaCu2O8+δtunneling spectroscopy

The tunneling spectra of high temperature superconductors on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212) reproducibly show a high bias structure in the form of a dip-hump at voltages higher than the gap voltage. Of central concern is whether this feature originates from the normal state background or is intrinsic to the superconducting mechanism. We address this issue by generating a set of model conductance curves - a ''normal state'' conductance that takes into account effects such as the band structure and a possible pseudogap, and a pure superconducting state conductance. When combined, the result shows that the dip-hump feature present in the experimental conductance curves cannot be naively attributed to a normal state effect. In particular, strong dip features found in superconductor-insulator-superconductor data on optimally-doped Bi-2212, including negative dI/dV, cannot be a consequence of an extrinsic pseudogap. However, such features can easily arise from states-conserving deviations in the superconducting density of states, e.g., from strong-coupling effects.

Conductance in normal-metal/PrOs 4Sb 12

The tunnel conductance in normal-metal/insulator/PrOs 4Sb 12 junctions is theoretically studied, where skutterudite PrOs 4Sb 12 is considered to be an unconventional superconductor. The conductance is calculated for several pair potentials which have been proposed in recent papers. The results show that the conductance spectra are sensitive to the relation between the direction of electric currents and the position of point nodes. Generally speaking, the tunnel spectra are believed to reflect the density of states in superconductor. The calculated results, however, often deviate from the shape of bulk density of states.

Effects of interband impurity scattering on superconducting density of states in a two-band superconductor

We investigate interband impurity scattering effects on a double gap structure in the superconducting density of states (SDOS) in a two-band superconductor. Using the self-consistent t-matrix theory, we show how the double gap structure gradually disappears/revives when impurity concentration and the magnitude of impurity potential are varied. The increase of impurity concentration leads to an averaged single gap SDOS due to the mixing of two bands by interband scattering. However, this mixing effect is shown to disappear in the strong interband scattering limit. We also show that the intraband impurity scattering suppresses the interband scattering effect because it tends to exclude electrons away from impurity sites.