Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4$π$ periodic current phase relation. The experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. Here, we report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is found to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4$π$ periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4$π$ Josephson junctions in relationship to topological superconductivity.
We report on half-integer Shapiro steps observed in an InAs nanowire Josephson junction. We observed the Shapiro steps of the short ballistic InAs nanowire Josephson junction and found anomalous half-integer steps in addition to the conventional integer steps. The half-integer steps disappear as the temperature increases or transmission of the junction decreases. These experimental results agree closely with numerical calculation of the Shapiro response for the skewed current phase relation in a short ballistic Josephson junction.
Two-particle backscattering in time-reversal invariant interacting helical electron systems can lead to the formation of quasiparticles with charge $e/2$. We propose a way to detect such states by means of the Josephson effect in the presence of proximity-induced superconductivity. In this case, the existence of $e/2$ charges leads to an $8 π$-periodic component of the Josephson current which can be identified through measurement of Shapiro steps in Josephson junctions. In particular, we show that even when there is weak explicit time-reversal symmetry breaking, which causes the two-particle b…
We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor (S-QSHI-S) hybrid system in the presence of a microwave radiation. Instead of adiabatic analysis or using the resistively shunted junction model, we start from the microscopic Hamiltonian and calculate the DC current directly with the help of the non-equilibrium Green's Functions method. The numerical results show that (i) the I-V curves of background current due to multiple Andreev reflections (MAR) exhibit a different structure with that in the conventional junctions, (ii) all Shapiro steps are v…
The demonstration of the non-Abelian properties of Majorana bound states (MBS) is a crucial step toward topological quantum computing. We theoretically investigate how Majorana fusion rules manifest themselves in the current-voltage characteristics of a topological Josephson junction. The junction is built on U-shaped quantum spin Hall edges and hosts a Majorana qubit formed by four MBS. Owing to Majorana fusion rules, inter- and intra-edge couplings among adjacent MBS provide two orthogonal components in the rotation axis of the Majorana qubit. We show that the interplay of the dynamics of th…
The superconducting proximity effect is probed experimentally in Josephson junctions fabricated with InAs nanowires contacted by Nb leads. Contact transparencies $t \sim 0.7$ are observed. The electronic phase coherence length at low temperatures exceeds the channel length. However, the elastic scattering length is a few times shorter than the channel length. Electrical measurements reveal two regimes of quantum transport: (i) the Josephson regime, characterized by a dissipationless current up to $\sim 100$ nA, and (ii) the quantum dot regime, characterized by the formation of Andreev Bound St…
The AC Josephson effect manifests itself in the form of "Shapiro steps" of quantized voltage in Josephson junctions subject to RF radiation. This effect presents an early example of a driven-dissipative quantum phenomenon and is presently utilized in primary voltage standards. Shapiro steps have also become one of the standard tools to probe junctions made in a variety of novel materials. Here, we study Shapiro steps in a widely tunable graphene-based Josephson junction. We investigate the variety of patterns that can be obtained in this well-understood system depending on the carrier density,…
We present an accurate way to detect spin dynamics of a nutating molecular nanomagnet by inserting it in a tunnel Josephson junction and studying the current voltage (I-V) characteristic. The spin nutation of the molecular nanomagnet is generated by applying two circularly polarized magnetic fields. We demonstrate that modulation of the Josephson current by the nutation of the molecular nanomagnet's spin appears as a stepwise structure like Shapiro steps in the I-V characteristic of the junction. Width and heights of these Shapiro-like steps are determined by two parameters of the spin nutatio…
We present a Josephson junction based on a Ge-Si core-shell nanowire with transparent superconducting Al contacts, a building block which could be of considerable interest for investigating Majorana bound states, superconducting qubits and Andreev (spin) qubits. We demonstrate the dc Josephson effect in the form of a finite supercurrent through the junction, and establish the ac Josephson effect by showing up to 23 Shapiro steps. We observe multiple Andreev reflections up to the sixth order, indicating that charges can scatter elastically many times inside our junction, and that our interfaces…
Topological Josephson junctions designed on the surface of a 3D-topological insulator (TI) harbor Majorana bound states (MBS's) among a continuum of conventional Andreev bound states. The distinct feature of these MBS's lies in the $4π$-periodicity of their energy-phase relation that yields a fractional ac Josephson effect and a suppression of odd Shapiro steps under $r\!f$ irradiation. Yet, recent experiments showed that a few, or only the first, odd Shapiro steps are missing, casting doubts on the interpretation. Here, we show that Josephson junctions tailored on the large bandgap 3D TI Bi$_…
We have studied the effects of optical-frequency light on proximitized InAs/Al Josephson junctions based on highly n-doped InAs nanowires at varying incident photon flux and at three different photon wavelengths. The experimentally obtained IV curves were modeled using a shunted junction model which takes scattering at the contact interfaces into account. The Josephson junctions were found to be surprisingly robust, interacting with the incident radiation only through heating, whereas above the critical current our devices showed non-thermal effects resulting from photon exposure. Our work pro…
A superconducting quantum interference device (SQUID) comprising 0- and $π$-Josephson junctions (JJs), called $π$-SQUID, is studied by the resistively shunted junction model. The $π$-SQUID shows half-integer Shapiro-steps (SS) under microwave irradiation at the voltage $V$ = $(\hbar/2e)Ω(n/2)$, with angular frequency $Ω$ and half-integer $n$/2 in addition to integer $n$. We show that the $π$-SQUID can be a $π$-qubit with spontaneous loop currents by which the half-integer SS are induced. Making the 0- and $π$-JJs equivalent is a key for the half-integer SS and realizing the $π$-qubit.
We present a novel technique for the realization of suspended Josephson junctions based on InAs semiconductor nanowires. The devices are assembled using a technique of drop-casting guided by dielectrophoresis that allows to finely align the nanostructures on top of the electrodes. The proposed architecture removes the interaction between the nanowire and the substrate which is known to influence disorder and the orientation of the Rashba vector. The relevance of this approach in view of the implementation of Josephson junctions based on High-Temperature Superconductors is discussed.
The fractional Josephson effect has been observed in many instances as a signature of a topological superconducting state containing zero-energy Majorana modes. We present a nontopological scenario which can produce a fractional Josephson effect generically in semiconductor-based Josephson junctions, namely, a resonant impurity bound state weakly coupled to a highly transparent channel. We show that the fractional ac Josephson effect can be generated by the Landau-Zener processes which flip the electron occupancy of the impurity bound state. The Josephson effect signature for Majorana modes be…
The Majorana zero-energy modes (MZMs) residing at the boundary of topological superconductors have attracted a great deal of interest recently, as they provide a platform to explore fundamental physics such as non-Abelian statistics, as well as fault-tolerant quantum computation. Period doubling of Shapiro steps in a Josephson junction under microwave irradiation has been regarded as strong evidence for the emergence of the MZMs at the junction edges. However, questions remain as to how the Shapiro steps respond to the presence of a 4π-periodic Josephson current. In this study, we investigated…
Superconductor-semiconductor nanowire hybrid structures are useful in fabricating devices for quantum information processing. While selective area growth (SAG) offers the flexibility to grow semiconductor nanowires in arbitrary geometries, in-situ evaporation of superconductors ensures pristine superconductor-semiconductor interfaces, resulting in strong induced superconductivity in the semiconducting nanowire. In this work, we evaporated islands of superconductor tin on InAs SAG nanowires, by using in-situ shadowing with high aspect-ratio pre-fabricated SiOx dielectric walls. Our technique al…
We present a quantitative characterization of an electrically tunable Josephson junction defined in an InAs nanowire proximitized by an epitax-ially-grown superconducting Al shell. The gate-dependence of the number of conduction channels and of the set of transmission coefficients are extracted from the highly nonlinear current-voltage characteristics. Although the transmissions evolve non-monotonically, the number of independent channels can be tuned, and configurations with a single quasi-ballistic channel achieved.
Superconductor/semiconductor-nanowire hybrid structures can serve as versatile building blocks to realize Majorana circuits or superconducting qubits based on quantized levels such as Andreev qubits. For all these applications it is essential that the superconductor-semiconductor interface is as clean as possible. Furthermore, the shape and dimensions of the superconducting electrodes needs to be precisely controlled. We fabricated self-defined InAs/Al core/shell nanowire junctions by a fully in-situ approach, which meet all these criteria. Transmission electron microscopy measurements confirm…
Josephson junctions defined in strong spin orbit semiconductors are highly interesting for the search for topological systems. However, next to topological edge states that emerge in a sufficient magnetic field, trivial edge states can also occur. We study the trivial edge states with superconducting quantum interference measurements on non-topological InAs Josephson junctions. We observe a SQUID pattern, an indication of superconducting edge transport. Also, a remarkable $h/e$ SQUID signal is observed that, as we find, stems from crossed Andreev states.
In a standard Josephson junction the current is zero when the phase difference between the superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin-orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect -- the hallmark effect of superconducting spintronics --and can be characterized by the corresponding anomalous phase shift ($ϕ_0$). We report the observation of a tunable anomalous Jose…
Josephson junctions based on InAs semiconducting nanowires and Nb superconducting electrodes are fabricated in-situ by a special shadow evaporation scheme for the superconductor electrode. Compared to other metallic superconductors such as Al, Nb has the advantage of a larger superconducting gap which allows operation at higher temperatures and magnetic fields. Our junctions are fabricated by shadow evaporation of Nb on pairs of InAs nanowires grown selectively on two adjacent tilted Si (111) facets and crossing each other at a small distance. The upper wire relative to the deposition source a…
Semiconductor-based Josephson junctions provide a platform for studying proximity effect due to the possibility of tuning junction properties by gate voltage and large-scale fabrication of complex Josephson circuits. Recently Josephson junctions using InAs weak link with epitaxial aluminum contact have improved the product of normal resistance and critical current, $I_cR_N$, in addition to fabrication process reliability. Here we study similar devices with epitaxial contact and find large supercurrent and substantial product of $I_cR_N$ in our junctions. However we find a striking difference w…
All fractional Shapiro steps in the RSJ model with two Josephson harmonics
L. D. Landau Institute for Theoretical Physics RAS（朗道理论物理研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Laboratory for Condensed Matter Physics, HSE University（高等经济大学凝聚态物理实验室）
We combine electron beam lithography and masked anodization of epitaxial aluminium to define tunnel junctions via selective oxidation, alleviating the need for wet-etch processing or direct deposition of dielectric materials. Applying this technique to define Josephson junctions in proximity induced superconducting Al-InAs heterostructures, we observe multiple Andreev reflections in transport experiments, indicative of a high quality junction. We further compare the mobility and density of Hall-bars defined via wet etching and anodization. These results may find utility in uncovering new fabri…
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$π$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evid…
The transparent interface in epitaxial Al-InAs heterostructures provides an excellent platform for potential advances in mesoscopic and topological superconductivity. Semiconductor-based Josephson Junction Field Effect Transistors (JJ-FETs) fabricated on these heterostructures have a metallic gate that tunes the supercurrent. Here we report the fabrication and measurement of gate-tunable Al-InAs JJ-FETs in which the gate dielectric in contact with the InAs is produced by mechanically exfoliated hexagonal boron nitride (h-BN) followed by dry transfer using a van der Waals-mediated pick up proce…
One-dimensional (1D) electronic transport and induced superconductivity in semiconductor nano-structures are crucial ingredients to realize topological superconductivity. Our approach for topological superconductivity employs a two-dimensional electron gas (2DEG) formed by an InAs quantum well, cleanly interfaced with a superconductor (epitaxial Al). This epi-Al/InAs quantum well heterostructure is advantageous for fabricating large-scale nano-structures consisting of multiple Majorana zero modes. Here, we demonstrate building-block transport studies using a high-quality epi-Al/InAs 2DEG heter…
The Josephson effect is a fundamental quantum phenomenon consisting in the appearance of a dissipationless supercurrent in a weak link between two superconducting (S) electrodes. While the mechanism leading to the Josephson effect is quite general, i.e., Andreev reflections at the interface between the S electrodes and the weak link, the precise physical details and topology of the junction drastically modify the properties of the supercurrent. Specifically, a strong enhancement of the critical supercurrent $I_C$ is expected to occur when the topology of the junction allows the emergence of Ma…
We investigate theoretically the dynamics of a Josephson junction in the framework of the RSJ model. We consider a junction that hosts two supercurrrent contributions: a $2π$- and a $4π$-periodic in phase, with intensities $I_{2π}$ and $I_{4π}$ respectively. We study the size of the Shapiro steps as a function of the ratio of the intensity of the mentioned contributions, i.e. $I_{4π}/I_{2π}$. We provide detailed explanations where to expect clear signatures of the presence of the $4π$-periodic contribution as a function of the external parameters: the intensity AC-bias $I_\text{ac}$ and freque…
Gate-tunable semiconductor-superconductor nanowires with superconducting leads form exotic Josephson junctions that are a highly desirable platform for two types of qubits: those with topological superconductivity (Majorana qubits) and those based on tunable anharmonicity (gatemon qubits). Controlling their behavior, however, requires understanding their electrostatic environment and electronic structure. Here we study gated InAs nanowires with epitaxial aluminum shells. By measuring current-phase relations (CPR) and comparing them with analytical and numerical calculations, we show that we ca…
