Subgap Conductance Research Articles

Andreev Current and Subgap Conductance of Spin-Valve SFF Structures

The Andreev current and the subgap conductance in a superconductor/insulator/ferromagnet (SIF) structure in the presence of a small spin-splitting field show novel interesting features (Ozaeta et al. in Phys. Rev. B 86:060509(R), 2012). For example, the Andreev current at zero temperature can be enhanced by a spin-splitting field h, smaller than the superconducting gap Δ, as has been recently reported by the authors. Also at finite temperatures, the Andreev current has a peak for values of the spin-splitting field close to the superconducting gap, h≈Δ. Finally, the differential subgap conductance at low temperatures shows a peak at the bias voltage eV=h. In this paper, we investigate the Andreev current and the subgap conductance in SFF structures with arbitrary direction of magnetization of the F layers. We show that all the aforementioned features occur now at the value of the “effective field”, which is the field acting on the Cooper pairs in the multi-domain ferromagnetic region, averaged over the decay length of the superconducting condensate into a ferromagnet. We also briefly discuss the heat transport and electron cooling in the considered structures.

Electronic transport through ferromagnetic and superconducting junctions with spin-filter tunneling barriers

We present a theoretical study of the quasiparticle and subgap conductance of generic $X/{I}_{\text{sf}}/{S}_{M}$ junctions with a spin-filter barrier ${I}_{\text{sf}}$, where $X$ is either a normal $N$ or a ferromagnetic metal $F$ and ${S}_{M}$ is a superconductor with a built-in exchange field. Our study is based on the tunneling Hamiltonian and the Green's-function technique. First, we focus on the quasiparticle transport, both above and below the superconducting critical temperature. We obtain a general expression for the tunneling conductance which is valid for arbitrary values of the exchange field and arbitrary magnetization directions in the electrodes and in the spin-filter barrier. In the second part, we consider the subgap conductance of a $N/{I}_{\text{sf}}/S$ junction, where $S$ is a conventional superconductor. In order to account for the spin-filter effect at interfaces, we heuristically derive boundary conditions for the quasiclassical Green's functions. With the help of these boundary conditions, we show that the proximity effect and the subgap conductance are suppressed by spin filtering in a $N/{I}_{\text{sf}}/S$ junction. Our work provides useful tools for the study of spin-polarized transport in hybrid structures both in the normal and in the superconducting state.

FIRST-PRINCIPLES CALCULATIONS OF SPIN-TRIPLET ANDREEV REFLECTION SPECTRA AT HALF-METALLIC FERROMAGNET/SUPERCONDUCTOR INTERFACE

Combining the first-principles noncollinear calculations of scattering matrices with Andreev approximation, we investigated the spin-triplet Andreev reflection (AR) spectra for the interface between half-metallic ferromagnet Co 2 MnSi and s-wave BCS superconductor Al with and without interfacial roughness, where the orientations of magnetic moments near the interface are randomly distributed. The calculated results show that the AR spectra have peak structures near zero bias for the clean interface with relative weak magnetic disorder. With the increasing degree of interfacial roughness or magnetic disorder, these subgap peaks of conductance spectra will be washed out. The results also show that the value of subgap conductance spectrum can be raised significantly by the magnetic disorder. Finally, our calculations reveal that the long-range spin-triplet AR in Co 2 MnSi / Al (001) interface can be enhanced by a small amount of interfacial roughness.

Dephasing of Cooper pairs and subgap electron transport in superconducting hybrids

We argue that electron-electron interactions fundamentally restrict the penetration length of Cooper pairs into a diffusive normal metal (N) from a superconductor (S). At low temperatures this Cooper pair dephasing length $L_\varphi$ remains finite and does not diverge at $T \to 0$. We evaluate the subgap conductance of NS hybrids in the presence of electron-electron interactions and demonstrate that this new length $L_\varphi$ can be directly extracted from conductance measurements in such structures.

Sub-micron normal-metal/insulator/superconductor tunnel junction thermometer and cooler using Nb

We have fabricated Cu/AlOx-Al/Nb normal-metal/insulator/superconductor tunnel junction devices with a high value of the superconducting gap (up to ∼1 mV), using electron-beam lithography and angle evaporation techniques in the sub-micron scale. The subgap conductance of these junctions shows the expected strong temperature dependence, rendering them suitable for thermometry all the way from 100 mK to 6 K. In addition, some direct electronic cooling of the normal metal was also seen at bias values near the gap edge. The device performance was strongly influenced by the details of the Al layer geometry, with lateral spilling of the aluminium giving rise to strong extra subgap features, and the thickness of Al layer affecting the proximised superconducting gap value of the superconducting Al/Nb bilayer.

Observation of Andreev Bound States at Spin-active Interfaces

We report on high-resolution differential conductance experiments on nanoscale superconductor-ferromagnet tunnel junctions with ultrathin oxide tunnel barriers. We observe subgap conductance features that are symmetric with respect to bias and shift according to the Zeeman energy with an applied magnetic field. These features can be explained by resonant transport via Andreev bound states induced by spin-active scattering at the interface. From the energy and Zeeman shift of the bound states, both the magnitude and sign of the spin-dependent interfacial phase shifts between spin-up and spin-down electrons can be determined. These results contribute to the microscopic insight into the triplet proximity effect at spin-active interfaces.

Topological origin of subgap conductance in insulating bilayer graphene

Graphene has a random edge structure. According to theory, this dirty and random edge affects the topological nature of bilayer graphene, which accounts for measurement discrepancies across different experimental probes. The edges of graphene-based systems possess unusual electronic properties, originating from the non-trivial topological structure associated with the pseudospinorial character of the electron wavefunctions. These properties, which have no analogue for electrons described by the Schrödinger equation in conventional systems, have led to the prediction of many striking phenomena, such as gate-tunable ferromagnetism and valley-selective transport1,2,3. In most cases, however, the predicted phenomena are not expected to survive the strong structural and chemical disorder that unavoidably affects the edges of real graphene devices. Here, we present a theoretical investigation of the intrinsic low-energy states at the edges of electrostatically gapped bilayer graphene, and find that the contribution of edge modes to the linear conductance of realistic devices remains sizable even for highly imperfect edges. This contribution may dominate over that of the bulk for sufficiently clean devices, such as those based on suspended bilayer graphene samples. Our results illustrate the robustness of those phenomena whose origin is rooted in the topology of the electronic band structure, even in the absence of specific protection mechanisms.

Effects of interface spin-orbit coupling on tunneling between normal metal and chiralp-wave superconductor

We study the tunneling conductance of a clean normal metal/chiral p-wave superconductor junction using the extended Blonder-Tinkham-Klapwijk formalism. It is shown that the spin-orbit coupling of the Rashba type that is present near the interface causes the subgap conductance peaks associated with the Andreev surface bound states to shift to a nonzero bias. We also investigate the effect of the Fermi wavevector mismatch between the normal metal and the superconductor.

Tunneling conductance of ferromagnet/noncentrosymmetric superconductor junctions

Based on the extended Blonder-Tinkham-Klapwijk formalism, the tunneling conductance characteristics of a planar junction between a ferromagnet and a noncentrosymmetric superconductor are studied. The effects of the Rashba spin-orbit coupling (RSOC), the exchange energy, and the Fermi wave-vector mismatch (FWM) on the conductance are all taken into account. In the absence of the FWM, it is found that far away from the gap edge the conductance is suppressed by the RSOC, while around the gap edge it is almost independent of RSOC. The interplay of the RSOC and the exchange energy causes an enhancement of the subgap conductance, which is more pronounced when the RSOC is small. When the FWM is introduced, it is shown that the conductance is monotonically enhanced as the FWM parameter decreases.

Effect of Electrical Stress on Josephson Tunneling Characteristics of ${\rm Nb/Al/AlO}_{x}/{\rm Nb}$ Junctions

Fabrication-induced variations in the critical currents of Josephson junctions significantly affect the performance and yield of complex superconducting integrated circuits. Electrical stress that may develop during plasma processing steps in the fabrication process was initially suggested as a possible cause of these variations. The effect on the Josephson and quasiparticle tunneling properties of Nb/Al/AlOx/Nb junctions with ultrathin AlOx barriers by the application of dc electrical stress was investigated. Current ramps with increasing amplitude corresponding to voltages across the barrier up to ~ 0.65 V were used to apply electrical stress. Junction conductance and current-voltage (I-V) characteristics were measured after each stress application at room temperature. As the stressing progresses, a dramatic increase in subgap conductance of the junctions, the appearance of subharmonic current steps, and a gradual increase in both the critical and the excess currents as well as a decrease in the normal-state resistance have been observed. A model is proposed wherein a progressively increasing number of defects and associated additional conduction channels (superconducting quantum point contacts (SQPCs)) are induced by the applied electric field in the tunnel barrier. The dependence of the stress effect on the polarity is also investigated and the results are presented. It is found that the magnitude of stress current needed for junction breakdown is unlikely to be supplied during plasma processing and as such, potential differences that can develop during plasma processing appear to be an unlikely cause of fabrication-induced, circuit pattern-dependent variations of Josephson junctions' critical currents in superconductor integrated circuits.

Ferromagnet/superconductor heterostructures in graphene

We investigate the unusual features of the proximity effect in graphene-based ferromagnet/super-conductor (F/S) heterostructures. We show that, for a weakly doped ferromagnetic graphene with an exchange energy h exceeding its Fermi energy E F , the Andreev reflection of massless Dirac fermions at the FS interface is accompanied with a Klein tunneling through an exchange field p–n barrier between two spin-split conduction and valence subbands. This spin Andreev–Klein process leads to an anomalous exchange-field-induced increase of the amplitude of Andreev reflection which has significant consequences for the subgap conductance and the shot noise power of an SF junction. For h > E F , we find that the exchange field enhances the subgap conductance to reach a maximum value which is greater than the corresponding value for non-ferromagnetic structure at bias voltages e V < Δ / 2 . We further demonstrate that, due to the spin Andreev–Klein process, the Josephson coupling in a ferromagnetic graphene Josephson junction can be long-ranged, and that it survives at very large exchange fields h ≫ E F . The possibility for transitions between 0 and π Josephson coupling by varying the doping of the ferromagnetic contact is also demonstrated.

Point-contact spectroscopy of competing/coexisting orders in Cd-doped CeCoIn5

Differential conductance spectra are taken from metallic point-contact junctions on Cd-doped CeCoIn5. For (100) junctions with nominal 10% doping, we observe signatures for subsequent antiferromagnetic and superconducting transitions in qualitative agreement with bulk measurements. In the superconducting state, two conductance channels compete, both with enhanced subgap conductance, one due to superconductivity and the other antiferromagnetism. The conductance data exhibit variances for different doping levels and crystallographic orientations and junction to junction. This issue will be addressed further in terms of surface inhomogeneity or intrinsic nonuniform phase formation.

Andreev-Klein reflection in graphene ferromagnet-superconductor junctions

We show that Andreev reflection in a junction between ferromagnetic (F) and superconducting (S) graphene regions is fundamentally different from the common FS junctions. For a weakly doped F graphene with an exchange field $h$ larger than its Fermi energy ${E}_{F}$, Andreev reflection of massless Dirac fermions is associated with a Klein tunneling through an exchange field $p\text{\ensuremath{-}}n$ barrier between two spin-split conduction and valence subbands. We find that this Andreev-Klein process results in an enhancement of the subgap conductance of a graphene FS junction by $h$ up to the point at which the conductance at low voltages $eVl\ensuremath{\Delta}/\sqrt{2}$ is greater than its value for the corresponding nonferromagnetic junction. We also demonstrate that the Andreev reflection can be of retro or specular types in both convergent and divergent ways with the reflection direction aligned, respectively, closer to and farther from the normal to the junction as compared to the incidence direction.

Electrical stress effect on Josephson tunneling through ultrathin AlOx barrier in Nb/Al/AlOx/Nb junctions

The effect of dc electrical stress and breakdown on Josephson and quasiparticle tunneling in Nb/Al/AlOx/Nb junctions with ultrathin AlOx barriers typical for applications in superconductor digital electronics has been investigated. The junctions’ conductance at room temperature and current-voltage (I-V) characteristics at 4.2 K have been measured after the consecutive stressing of the tunnel barrier at room temperature. Electrical stress was applied using current ramps with increasing amplitude ranging from 0 to ∼1000Ic corresponding to voltages across the barrier up to ∼0.65 V, where Ic is the Josephson critical current. A very soft breakdown has been observed with polarity-dependent breakdown current (voltage). As the stressing progresses, a dramatic increase in subgap conductance of the junctions, the appearance of subharmonic current steps, and a gradual increase in both the critical and the excess currents as well as a decrease in the normal-state resistance have been observed. The observed changes in superconducting tunneling suggest a model in which a progressively increasing number of defects and associated additional conduction channels [superconducting quantum point contacts (SQPCs)] are induced by electric field in the tunnel barrier. By comparing the I-V characteristics of these conduction channels with the nonstationary theory of current transport in SQPCs based on multiple Andreev reflections by Averin and Bardas, the typical transparency D of the induced SQPCs was estimated as D∼0.7. The number of induced SQPCs was found to grow with voltage across the barrier as sinh(V/V0) with V0=0.045 V, in good agreement with the proposed model of defect formation by ion electromigration. The observed polarity dependence of the breakdown current (voltage) is also consistent with the model. Based on the observed magnitude of breakdown currents, electric breakdown of AlOx barrier during plasma processing was considered to be an unlikely cause of fabrication-induced, circuit pattern-dependent nonuniformities of Josephson junctions’ critical currents in superconductor integrated circuits.

Andreev reflection spectroscopy of the pure and Cd-doped heavy-fermion superconductor CeCoIn 5: Detecting order parameter symmetry and competing phases

Andreev reflection conductance spectra are obtained on nanoscale ballistic junctions between Au tips and single crystals of the pure and Cd-doped heavy-fermion superconductor CeCoIn 5. Background conductance asymmetry starting at the heavy-fermion coherence temperature T* (∼45 K) and increasing with decreasing temperature down to T c (2.3 K) signifies the emerging heavy-fermion liquid in CeCoIn 5. Below T c, enhancement of the sub-gap conductance arises from Andreev reflection, but the Blonder–Tinkham–Klapwijk theory dictates that the Fermi velocity mismatch should yield no Andreev reflection. The signal we do observe is several times weaker than that observed in conventional superconductors, but consistent with other heavy-fermion superconductor data reported. Data taken in the (0 0 1), (1 1 0), and (1 0 0) orientations provide consistent and reliable spectroscopic evidence for d x 2 - y 2 symmetry of the superconducting order parameter. Conductance spectra on the (1 0 0) surface of 10% Cd-doped CeCoIn 5 show intriguing behaviors following antiferromagnetic and subsequent superconducting transitions.

Additional sub-gap conductance enhancement in nanoscale Andreev point contactjunctions

We demonstrate an enhancement in the sub-gap conductance in Nb/Al/Cu nanoscalepinhole junctions, significantly larger than the conductance doubling expected from thepoint contact Andreev reflection process. Such an enhancement is not observed in standardmicrometre-driven NbTi/Cu wire-tipped junctions where the expected sub-gapconductance is regained. This additional sub-gap conductance arises due to regions of thepinhole junction being driven into the normal state due to current-induced pairbreaking, causing the Andreev reflection process to occur at different interfaceswithin the contact structure as the bias is increased. This work demonstrates,again, that a great deal of care must be taken in interpreting Andreev reflectionmeasurements in nanoscale junctions, in particular with regard to extracting accurate spinpolarization.

Subgap conductivity in SIN-junctions of high barrier transparency

We investigate the current–voltage characteristics of high-transparency superconductor–insulator–normal metal (SIN) junctions with the specific tunnel resistance ρ≲30Ωμm2. The junctions were fabricated from different superconducting and normal conducting materials, including Nb, Al, AuPd and Cu. The subgap leakage currents were found to be appreciably larger than those given by the standard tunnelling model. We explain our results using the model of two-electron tunnelling in the coherent diffusive transport regime. We demonstrate that even in the high-transparency SIN-junctions, a noticeable reduction of the subgap current can be achieved by splitting a junction into several submicron sub-junctions. These structures can be used as nonlinear low-noise shunts in rapid-single-flux-quantum (RSFQ) circuitry for controlling Josephson qubits.

Specular Andreev Reflection in Graphene

By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal incidence the electron-hole conversion happens with unit efficiency in spite of the large mismatch in Fermi wavelengths at the two sides of the interface; and, most fundamentally: (3) away from normal incidence the reflection angle may be the same as the angle of incidence (retroreflection) or it may be inverted (specular reflection). Specular Andreev reflection dominates in weakly doped graphene, when the Fermi wavelength in the normal region is large compared to the superconducting coherence length.

Point-contact spectroscopy of CeCoIn 5: Andreev reflection studies of the normal-metal–heavy-fermion superconductor interface

Point-contact spectroscopy (PCS) results are obtained with normal-metal (N) Au tips on single crystals of the heavy-fermion superconductor (HFS) CeCoIn 5. Our exceptionally clean, reproducible data are taken over a temperature range of 60 K to 400 mK. Contacts are shown to be in the Sharvin limit. Asymmetry observed in the background conductance starting at T* (∼45 K), increasing with decreasing temperature to T c (2.3 K), signifies the emerging heavy-fermion liquid. Below T c, the enhancement of the subgap conductance (∼13.3% at 400 mK) arises from Andreev reflection (AR). According to standard Blonder–Tinkham–Klapwijk (BTK) theory, the Fermi velocity mismatch between an N and a HFS should yield no AR. The AR we do observe is several times lower than that observed in N/conventional superconductor PCS, but consistent with other N–HFS data reported. Our zero-bias conductance data are best fit with an extended d-wave BTK model. A fit to the full conductance curve at 400 mK indicates strong coupling (2Δ/ k B T c=4.6), but the suppression of both the AR signal and the energy gap cannot be accounted for with existing models.

Andreev reflection at the normal-metal/heavy-fermion superconductorCeCoIn5interface

The dynamic conductance of the heavy-fermion superconductor CeCoIn$_5$ is measured by point-contact spectroscopy as a function of temperature from 60 K down to 400 mK. The contact between the gold tip and the single-crystal is shown to be in the Sharvin limit with the enhanced sub-gap conductance arising from Andreev reflection. The zero-bias conductance data are best fit using the extended Blonder-Tinkham-Klapwijk model with a d-wave superconducting order parameter. A fit to the full conductance curve at 400 mK indicates strong coupling ($2\Delta(0)/k_\textrm{B}T_\textrm{c} = 4.6$) and quantifies the suppressed Andreev reflection signal, which is a signature of normal-metal/heavy-fermion superconductor junctions. Possibilites for theoretical modeling to account for the suppressed Andreev conductance are suggested.