Subharmonic Gap Structure Research Articles

Multiple Andreev reflections in diffusive SINIS and SIFIS junctions

We study Multiple Andreev Reflections in long diffusive superconductor(S)-normal metal(N)-superconductor junctions with low-transparency interfaces. Assuming strong thermalization in the weak link, we calculate the current-voltage dependence I(V)I(V). At intermediate temperatures, \varepsilon_\mathrm{Th}\ll T\ll\DeltaεTh≪T≪Δ, the current is dominated by noncoherent multiple Andreev reflections and is obtained analytically. The results are generalized to a ferromagnetic junction. We find that the exchange field produces a non-trivial splitting of the subharmonic gap structure. This effect relies on thermalization and vanishes in SFS junctions with no energy relaxation in the weak link.

Phase-tunable multiple Andreev reflections in a quantum spin Hall strip

A quantum spin Hall strip where different edges are contacted by s-wave superconductors with a phase difference φ supports Majorana bound states protected by time-reversal symmetry. We study signatures of these states in a four-terminal setup where two Josephson junctions are built on opposite edges of the strip and the phase difference between superconductors can be controlled by an external flux. Applying a voltage bias across the quantum spin Hall strip results in a sequence of conductance peaks from multiple Andreev reflections (MARs). We find that this so-called subharmonic gap structure is very sensitive to the phase difference and displays a phase-controlled even–odd effect, where all odd spikes disappear when the Majorana states are formed for . Moreover, the remaining even spikes split when the superconductors forming the junction have different gap size. We explain these features by showing that any midgap bound states enhance the transmission of the even order MARs, while the reduced density of states at the gap edges suppresses the odd order ones.

Fabrication of Josephson junctions by single line etching of Nb thin films utilizing nitrogen-gas-field ion-source focused ion beam

We focused on a focused ion beam (FIB) technology, called nitrogen gas field ion source FIB (N2 GFIS-FIB), which can etch directly at the 10 nm level or finer. We performed single line etching of Nb thin film microbridges deposited by N2 GFIS-FIB and fabricated Josephson junction (JJ) devices. The microbridge area was separated into two parts by the processing line, whose width was around 20 nm. We performed electrical characterizations of the devices at low temperature and observed typical behaviors of JJ devices, such as a superconducting current region and current jumping to the normal current region in some of the deeply etched devices. We also observed an AC resistance oscillation in some of the shallowly etched devices. The oscillation may be due to a sub-harmonic gap structure that originates from Andreev reflection. These results indicate that simple single line etching of Nb by N2 GFIS-FIB can form JJ devices.

Multiple andreev reflections in topological insulator nanoribbons

Superconducting proximity junctions made of topological insulator (TI) nanoribbons (NRs) provide a useful platform for studying topological superconductivity. We report on the fabrication and measurement of Josephson junctions (JJs) using Sb-doped Bi2Se3 NRs in contact with Al electrodes. Aharonov–Bohm and Altshuler–Aronov–Spivak oscillations of the axial magneto-conductance of TI NR were observed, indicating the existence of metallic surface states along the circumference of the TI NR. We observed the supercurrent in the TI NR JJ and subharmonic gap structures of the differential conductance due to multiple Andreev reflections. The interface transparency of the TI NR JJs estimated based on the excess current reaches τ = 0.83, which is among the highest values reported for TI JJs. The temperature dependence of critical current is consistent with the short and ballistic junction model confirming the formation of highly transparent superconducting contacts on the TI NR. Our observations would be useful for exploring topological Josephson effects in TI NRs.

Gate-controlled supercurrent in ballistic InSb nanoflag Josephson junctions

High-quality III–V narrow bandgap semiconductor materials with strong spin–orbit coupling and large Landé g-factor provide a promising platform for next-generation applications in the field of high-speed electronics, spintronics, and quantum computing. Indium antimonide (InSb) offers a narrow bandgap, high carrier mobility, and small effective mass and, thus, is very appealing in this context. In fact, this material has attracted tremendous attention in recent years for the implementation of topological superconducting states supporting Majorana zero modes. However, high-quality heteroepitaxial two-dimensional (2D) InSb layers are very difficult to realize owing to the large lattice mismatch with all commonly available semiconductor substrates. An alternative pathway is the growth of free-standing single-crystalline 2D InSb nanostructures, the so-called nanoflags. Here, we demonstrate fabrication of ballistic Josephson-junction devices based on InSb nanoflags with Ti/Nb contacts that show a gate-tunable proximity-induced supercurrent up to 50 nA at 250 mK and a sizable excess current. The devices show clear signatures of subharmonic gap structures, indicating phase-coherent transport in the junction and a high transparency of the interfaces. This places InSb nanoflags in the spotlight as a versatile and convenient 2D platform for advanced quantum technologies.

Spin-polarized multiple Andreev reflections in spin-split superconductors

We study the transport properties of a voltage biased contact between two spin-split superconductors separated by an insulating barrier of arbitrary transparency. At low transparency, the contribution of multiple Andreev reflections leads to a subharmonic gap structure that crucially depends on the amplitude and relative angle of the spin-splitting fields of each superconductor. For non-collinear fields, we find an interesting even-odd effect on the bound states within the gap, where the odd order multiple Andreev reflections split, but the even order ones remain at their expected positions. By computing the current-voltage characteristics, we determine the transparency required for the emergence of a subharmonic gap structure and show that the splitting of the odd bound states is associated with different threshold energies of spin-polarized Andreev processes. Our findings provide a tool to experimentally determine the amplitude and orientation of Zeeman fields in spin-split superconductors.

Andreev reflections and magnetotransport in 2D Josephson junctions

In this paper, the subharmonic energy gap structures (SGS) and induced superconductivity, due to multiple Andreev reflections, in indium gallium arsenide (In0.75Ga0.25As) two-dimensional electron gas (2DEG) are discussed at different temperatures and magnetic fields. Strong suppression of both SGS and induced gap are observed as a function of temperature and magnetic field. The differential conductance of the Josephson junctions (JJs) as a function of external in-plane magnetic fields shows an asymmetric response to positive and negative magnetic field sweeps with a conductance maximum at close to zero. Our approach to quantum transport studies of the ballistic 2D JJs may open a new road towards scalable and integrated quantum processing and help pave the way for the development of topological circuits for the realization of the next generation of quantum processors.

Non-equilibrium charge and spin transport in superconducting-ferromagnetic-superconducting point contacts.

The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi-particles and where the precession produces spin-flip scattering processes. As a result, the Andreev states develop sidebands and a non-equilibrium population that depend on the details of the spin precession. The Andreev states carry a steady-state Josephson charge current and a time-dependent spin current, whose current-phase relations could be used to characterize the precessing spin. The spin current is supported by spin-triplet correlations induced by the spin precession and creates a feedback effect on the classical spin in the form of a torque that shifts the precession frequency. By applying a bias voltage, the Josephson frequency adds another complexity to the situation and may create resonances together with the Larmor frequency. These Shapiro resonances manifest as torques and, under suitable conditions, are able to reverse the direction of the classical spin in sub-nanosecond time. Another characteristic feature is the subharmonic gap structure in the DC charge current displaying an even-odd effect attributable to precession-assisted multiple Andreev reflections.This article is part of the theme issue 'Andreev bound states'.

Magnetic, superconducting and electron-boson properties of GdO(F)FeAs oxypnictides

We performed comprehensive studies of nearly optimal fluorine-substituted GdO1−xFx FeAs oxypnictide superconductors with TC=48−53K. Specific heat measurements revealed a sharp peak at T=3.5K that shifts to lower temperatures with magnetic field increase. This peak corresponds to an antiferromagnetic ordering in Gd3+ ion sublattice and may indicate coexistence between superconducting and magnetic orderings. Andreev transport through artificially made constriction demonstrated two channels for the carriers from the band(s) with the large superconducting gap as well as from those with the small gap. As expected, the presence of a transport channel with the bands mixing (ΔL+ΔS) was not detected. Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we determined two superconducting gaps, ΔS≈2.7meV, and ΔL≈11.6meV. The reproducible fine structure in the dI(V)/dV spectra of the Andreev contacts (satellites of the main subharmonic gap structure for ΔL) was interpreted as caused by a resonant emission of bosons with the energy ε0=12−15meV≈ΔL+ΔS during the process of multiple Andreev reflections (MAR) for normal carriers in ΔL-band(s) transport channel.

Proximity induced superconductivity in indium gallium arsenide quantum wells

We report on the experimental observation of the proximity induced superconductivity in an indium gallium arsenide (In0.75Ga0.25As) quantum well. The Josephson junction was fabricated by several photo-lithographic processes on an InGaAs heterojunction and Niobium (Nb) was used as superconducting electrodes. Owing to the Andreev reflections and Andreev bound states at the Nb-In0.75Ga0.25As quantum well-Nb interfaces, the subharmonic energy gap structures (SGS) are observed at the differential conductance (dI/dV) versus voltage (V) plots when the applied source-drain bias voltages satisfy the expression VSD = 2Δ/ne. The dI/dV as a function of applied magnetic field B shows a maximum at zero B which decreases by increasing B. When decreasing B to below ±0.4 T, a hysteresis and shift of the conductance maxima close to B = 0 T are observed. Our results help to pave the way to the development of integrated coherent quantum circuitry.

Transport in superconductor–normal metal–superconductor tunneling structures: Spinful p -wave and spin-orbit-coupled topological wires

We theoretically study transport properties of voltage-biased one-dimensional superconductor--normal metal--superconductor tunnel junctions with arbitrary junction transparency where the superconductors can have trivial or nontrivial topology. Motivated by recent experimental efforts on Majorana properties of superconductor-semiconductor hybrid systems, we consider two explicit models for topological superconductors: (i) spinful p-wave, and (ii) spin-split spin-orbit-coupled s-wave. We provide a comprehensive analysis of the zero-temperature dc current $I$ and differential conductance $dI/dV$ of voltage-biased junctions with or without Majorana zero modes (MZMs). The presence of an MZM necessarily gives rise to two tunneling conductance peaks at voltages $eV = \pm \Delta_{\mathrm{lead}}$, i.e., the voltage at which the superconducting gap edge of the lead aligns with the MZM. We find that the MZM conductance peak probed by a superconducting lead $without$ a BCS singularity has a non-universal value which decreases with decreasing junction transparency. This is in contrast to the MZM tunneling conductance measured by a superconducting lead $with$ a BCS singularity, where the conductance peak in the tunneling limit takes the quantized value $G_M = (4-\pi)2e^2/h$ independent of the junction transparency. We also discuss the "subharmonic gap structure", a consequence of multiple Andreev reflections, in the presence and absence of MZMs. Finally, we show that for finite-energy Andreev bound states (ABSs), the conductance peaks shift away from the gap bias voltage $eV = \pm \Delta_{\mathrm{lead}}$ to a larger value set by the ABSs energy. Our work should have important implications for the extensive current experimental efforts toward creating topological superconductivity and MZMs in semiconductor nanowires proximity coupled to ordinary s-wave superconductors.

Critical analysis of soft point contact Andreev reflection spectra between superconducting films and pressed In

We present a critical analysis of an alternative technique of point contact Andreev reflection (PCAR) spectroscopy used to extract energy resolved information of superconductors which is based on making ‘soft-contacts’ between superconductors and indium. This technique is not sensitive to mechanical vibrations and hence can be used in a cryogen free platform increasing its accessibility to users having no access to cryogenic liquids. Through our experiments on large number of superconducting films we show that the PCAR spectra below the Tc of In show sub-harmonic gap structures consistent with the theory of multiple Andreev reflection (MAR) and a zero bias conductance (ZBC) anomaly associated with the Josephson supercurrent. Furthermore, we demonstrate that large contact resistance with low transparency ballistic contacts in the PCAR regime are required to obtain reliable spectroscopic data. One limitation of the technique arises for low contact resistance junctions where the superconducting proximity effect (SPE) reduces the value of the superconducting energy gap.

Resonant subgap current transport in Josephson field effect transistor

We study theoretically the current-voltage characteristics (IVCs) of the Josephson field effect transistor - a ballistic SNINS junction with superconducting (S) electrodes confining a planar normal metal region (N), which is controlled by the gate induced potential barrier (I). The calculations were performed using the computation technique developed earlier for long single-channel junctions in the coherent multiple Andreev reflections (MAR) regime. We find significant difference of the subgap current structure in these junctions compared to the subharmonic gap structure in tunnel junctions and atomic-size point contacts. For long junctions, whose length significantly exceeds the coherence length, the IVC exhibits current peaks at multiples (harmonics) of the difference $\delta_m$ between the static Andreev levels, $eV_n = n\delta_m$. Moreover, the averaged IVC follows the power rather than exponential behavior, and has a universal scaling with the junction transparency. This result is qualitatively understood using an analytical approach based on the concept of resonant MAR trajectories. In shorter junctions whose length is comparable to the coherence length, the IVC has an exponential form common for point contacts, however the current structures appear at the subharmonics of the Andreev interlevel distance, $eV_n = \delta_m/n$ rather than the gap subharmonics $2\Delta/n$.

Signatures of evanescent transport in ballistic suspended graphene-superconductor junctions.

In Dirac materials, the low energy excitations behave like ultra-relativistic massless particles with linear energy dispersion. A particularly intriguing phenomenon arises with the intrinsic charge transport behavior at the Dirac point where the charge density approaches zero. In graphene, a 2-D Dirac fermion gas system, it was predicted that charge transport near the Dirac point is carried by evanescent modes, resulting in unconventional “pseudo-diffusive” charge transport even in the absence of disorder. In the past decade, experimental observation of this phenomenon remained challenging due to the presence of strong disorder in graphene devices which limits the accessibility of the low carrier density regime close enough to the Dirac point. Here we report transport measurements on ballistic suspended graphene-Niobium Josephson weak links that demonstrate a transition from ballistic to pseudo-diffusive like evanescent transport below a carrier density of ~1010 cm−2. Approaching the Dirac point, the sub-harmonic gap structures due to multiple Andreev reflections display a strong Fermi energy-dependence and become increasingly pronounced, while the normalized excess current through the superconductor-graphene interface decreases sharply. Our observations are in qualitative agreement with the long standing theoretical prediction for the emergence of evanescent transport mediated pseudo-diffusive transport in graphene.

Induced Superconductivity and Engineered Josephson Tunneling Devices in Epitaxial (111)-Oriented Gold/Vanadium Heterostructures.

We report a unique experimental approach to create topological superconductors by inducing superconductivity into epitaxial metallic thin film with strong spin-orbit coupling. Utilizing molecular beam epitaxy technique under ultrahigh vacuum conditions, we are able to achieve (111) oriented single phase of gold (Au) thin film grown on a well-oriented vanadium (V) s-wave superconductor film with clean interface. We obtained atomically smooth Au thin films with thicknesses even down to below a nanometer showing near-ideal surface quality. The as-grown V/Au bilayer heterostructure exhibits superconducting transition at around 3.9 K. Clear Josephson tunneling and Andreev reflection are observed in S-I-S tunnel junctions fabricated from the epitaxial bilayers. The barrier thickness dependent tunneling and the associated subharmonic gap structures (SGS) confirmed the induced superconductivity in Au (111), paving the way for engineering thin film heterostructures based on p-wave superconductivity and nano devices exploiting Majorana Fermions for quantum computing.

Intrinsic Multiple Andreev Reflections in Layered Th-Doped Sm1−x Th x OFeAs

Layered oxypnictide Sm$_{1-x}$Th$_x$OFeAs (Sm-1111) is an ideal candidate to be probed by intrinsic multiple Andreev reflections effect (IMARE) spectroscopy. Using the classical "break-junction" technique, we formed ballistic Andreev arrays of identical S--n--S-contacts, where $S$ is superconductor, and $n$ is a layer of normal metal. For $T < T_C$, the I(V) curve shows an excess-current and a subharmonic gap structure (SGS): a set of sharp dI(V)/dV-dips at positions which depend on the superconducting gap value, the number of junctions in the array, and the natural subharmonic order, thus manifesting the effect of intrinsic multiple Andreev reflections. Here we present the I(V) and dI(V)/dV with up to 4 SGS dips for Andreev arrays formed in optimally doped Sm-1111 with critical temperatures $T_C \approx 49$\,K, as well as in underdoped samples with $T_C \approx 37$\,K. We show that a number of Andreev subharmonics facilitates the determination of the superconducting gap with a better accuracy.

Fabrication of sandwich-type MgB2/Boron/MgB2 Josephson junctions with rapid annealing method

Sandwich-type MgB2/Boron/MgB2 Josephson junctions were fabricated using magnetron sputtering system. The rapid-anneal process was adopted to replace traditional way of annealing, trying to solve the problem of interdiffusion and oxidation with multilayer films. The boron film was used as barrier layer to avoid the introduction of impurities and improve reproducibility of the junctions. The bottom MgB2 thin films deposited on c-plane sapphire substrate exhibits a critical temperature TC of 37.5 K and critical current density JC at 5 K of 8.7 × 106 A cm−2. From the XRD pattern, the bottom MgB2 thin film shows c-axis orientation, whereas the top MgB2 became polycrystalline as Boron barrier layer grown thicker. Therefore, all junction samples show lower TC than single MgB2 thin film. The junctions exhibit excellent quasiparticle characteristics with ideal dependence on temperature and Boron barrier thickness. Subharmonic gap structure was appeared in conductance characteristics, which was attributed to the multiple Andreev reflections (MAR). The result demonstrates great promise of this new fabrication technology for MgB2 Josephson junction fabrication.

Crossover from Josephson effect to single interface Andreev reflection in asymmetric superconductor/nanowire junctions.

We report on the fabrication and characterization of symmetric nanowire-based Josephson junctions, that is, Al- and Nb-based junctions, and asymmetric junctions employing superconducting Al and Nb. In the symmetric junctions, a clear and pronounced Josephson supercurrent is observed. These samples also show clear signatures of subharmonic gap structures. At zero magnetic field, a Josephson coupling is found for the asymmetric Al/InAs-nanowire/Nb junctions as well. By applying a magnetic field above the critical field of Al or by raising the temperature above the critical temperature of Al the junction can be switched to an effective single-interface superconductor/nanowire structure. In this regime, a pronounced zero-bias conductance peak due to reflectionless tunneling has been observed.

Spin-polarized Shapiro steps and spin-precession-assisted multiple Andreev reflection

We investigate the charge and spin transport of a voltage-biased superconducting point contact coupled to a nanomagnet. The magnetization of the nanomagnet is assumed to precess with the Larmor frequency, $\omega_L$, due to ferromagnetic resonance. The interplay between the ac Josephson current and the magnetization dynamics leads to spin-polarized Shapiro steps at voltages $|V|=\hbar \omega_L/2en$ for $n=1,2,...$ and the subharmonic steps with $n>1$ are a consequence of multiple Andreev reflection (MAR). Moreover, the spin-precession-assisted MAR generates quasiparticle scattering amplitudes that, due to interference, lead to current-voltage characteristics of the dc charge and spin currents with subharmonic gap structures displaying an even-odd effect.

Charge transport in InAs nanowire Josephson junctions

We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30 nm, exhibits a record high magnitude of 800 nA at low temperature that comes close to the theoretically expected value. The critical current in all other devices is typically reduced compared to the theoretical values. The excess current is consistent with the normal resistance data and agrees well with the theory. The subgap current shows a large number of structures; some of them are identified as subharmonic gap structures generated by multiple Andreev reflection. The other structures, detected in both suspended and nonsuspended devices, have the form of voltage steps at voltages that are independent of either the superconducting gap or length of the wire. By varying the gate voltage in suspended devices, we are able to observe a crossover from typical tunneling transport at large negative gate voltage, with suppressed subgap current and negative excess current, to pronounced proximity junction behavior at large positive gate voltage, with enhanced Josephson current and subgap conductance as well as a large positive excess current.