Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4$pi$ periodic current phase relation. The experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, mis
sing 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$pi$ 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$pi$ Josephson junctions in relationship to topological superconductivity.
We demonstrate robust superconducting proximity effect in InAs$_{0.5}$Sb$_{0.5}$ quantum wells grown with epitaxial Al contact, which has important implications for mesoscopic and topological superconductivity. Unlike more commonly studied InAs and I
nSb semiconductors, bulk InAs$_{0.5}$Sb$_{0.5}$ supports stronger spin-orbit coupling and larger $g$-factor. However, these potentially desirable properties have not been previously measured in epitaxial heterostructures with superconductors, which could serve as a platform for fault-tolerant topological quantum computing. Through structural and transport characterization we observe high-quality interfaces and strong spin-orbit coupling. We fabricate Josephson junctions based on InAs$_{0.5}$Sb$_{0.5}$ quantum wells and observe strong proximity effect. These junctions exhibit product of normal resistance and critical current, $I_{c}R_{N} = SI{270}{micro V}$, and excess current, $I_{ex}R_{N} = SI{200}{micro V}$ at contact separations of 500~nm. Both of these quantities demonstrate a robust and long-range proximity effect with highly-transparent contacts.
Topological superconductivity supports exotic Majorana bound states (MBS) which are chargeless zero-energy emergent quasiparticles. With their non-Abelian exchange statistics and fractionalization of a single electron stored nonlocally as a spatially
separated MBS, they are particularly suitable for implementing fault-tolerant topological quantum computing. While the main efforts to realize MBS have focused on one-dimensional systems, the onset of topological superconductivity requires delicate parameter tuning and geometric constraints pose significant challenges for their control and demonstration of non-Abelian statistics. To overcome these challenges, building on recent experimental advances in planar Josephson junctions (JJs), we propose a MBS platform of X-shaped JJs. This versatile implementation reveals how external flux control of the superconducting phase difference can generate and manipulate multiple MBS pairs to probe non-Abelian statistics. The underlying topological superconductivity exists over a large parameter space, consistent with materials used in our fabrication of such X junctions, as an important step towards scalable topological quantum computing.
Topological superconductivity holds promise for fault-tolerant quantum computing. While planar Josephson junctions are attractive candidates to realize this exotic state, direct phase-measurements as the fingerprint of the topological transition are
missing. By embedding two gate-tunable Al/InAs Josephson junctions in a loop geometry, we measure a $pi$-jump in the junction phase with increasing in-plane magnetic field, ${bf B}_|$. This jump is accompanied by a minimum of the critical current, indicating a closing and reopening of the superconducting gap, strongly anisotropic in ${bf B}_|$. Our theory confirms that these signatures of a topological transition are compatible with the emergence of Majorana 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 ma
gnetic 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 ($phi_0$). We report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device (SQUID). By gate controlling the density of InAs we are able to tune the spin-orbit coupling of the Josephson junction by more than one order of magnitude. This gives us the ability to tune $phi_0$, and opens several new opportunities for superconducting spintronics, and new possibilities for realizing and characterizing topological superconductivity.
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 usin
g 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 when we compare these samples with higher mobility samples in terms of product of excess current and normal resistance, $I_{ex}R_N$. The excess current is negligible in lower mobility devices while it is substantial and independent of gate voltage and junction length in high mobility samples. This indicates that even though both sample types have epitaxial contacts only the high-mobility one has a high transparency interface. In the high mobility short junctions, we observe values of $I_cR_N/Delta sim 2.2$ and $I_{ex}R_N/Delta sim 1.5$ in semiconductor weak links.
Transport properties of highly mobile 2D electrons are studied in symmetric GaAs quantum wells placed in titled magnetic fields. Quantum positive magnetoresistance (QPMR) is observed in magnetic fields perpendicular to the 2D layer. Application of in
-plane magnetic field produces a dramatic decrease of the QPMR. This decrease correlates strongly with the reduction of the amplitude of Shubnikov de Haas resistance oscillations due to modification of the electron spectrum via enhanced Zeeman splitting. Surprisingly no quantization of the spectrum is detected when the Zeeman energy exceeds the half of the cyclotron energy suggesting an abrupt transformation of the electron dynamics. Observed angular evolution of QPMR implies strong mixing between spin subbands. Theoretical estimations indicate that in the presence of spin-orbital interaction the elastic impurity scattering provides significant contribution to the spin mixing in GaAs quantum wells at high filling factors.
Effect of dc electric field on transport of highly mobile 2D electrons is studied in wide GaAs single quantum wells placed in titled magnetic fields. The study shows that in perpendicular magnetic field resistance oscillates due to electric field ind
uced Landau-Zener transitions between quantum levels that corresponds to geometric resonances between cyclotron orbits and periodic modulation of electron density of states. Magnetic field tilt inverts these oscillations. Surprisingly the strongest inverted oscillations are observed at a tilt corresponding to nearly absent modulation of the electron density of states in regime of magnetic breakdown of semiclassical electron orbits. This phenomenon establishes an example of quantum resistance oscillations due to Landau quantization, which occur in electron systems with a constant density of states.
The magnetotransport of highly mobile 2D electrons in wide GaAs single quantum wells with three populated subbands placed in titled magnetic fields is studied. The bottoms of the lower two subbands have nearly the same energy while the bottom of the
third subband has a much higher energy ($E_1approx E_2<<E_3$). At zero in-plane magnetic fields magneto-intersubband oscillations (MISO) between the $i^{th}$ and $j^{th}$ subbands are observed and obey the relation $Delta_{ij}=E_j-E_i=kcdothbaromega_c$, where $omega_c$ is the cyclotron frequency and $k$ is an integer. An application of in-plane magnetic field produces dramatic changes in MISO and the corresponding electron spectrum. Three regimes are identified. At $hbaromega_c ll Delta_{12}$ the in-plane magnetic field increases considerably the gap $Delta_{12}$, which is consistent with the semi-classical regime of electron propagation. In contrast at strong magnetic fields $hbaromega_c gg Delta_{12}$ relatively weak oscillating variations of the electron spectrum with the in-plane magnetic field are observed. At $hbaromega_c approx Delta_{12}$ the electron spectrum undergoes a transition between these two regimes through magnetic breakdown. In this transition regime MISO with odd quantum number $k$ terminate, while MISO corresponding to even $k$ evolve $continuously$ into the high field regime corresponding to $hbaromega_c gg Delta_{12}$
The effects of microwave radiation on the transport properties of atomically thin $La_{2-x}Sr_xCuO_4$ films were studied in the 0.1-13 GHz frequency range. Resistance changes induced by microwaves were investigated at different temperatures near the
superconducting transition. The nonlinear response decreases by several orders of magnitude within a few GHz of a cutoff frequency $ u_{cut} approx$ 2 GHz. Numerical simulations that assume an ac response to follow the dc V-I characteristics of the films reproduce well the low frequency behavior, but fail above $ u_{cut}$. The results indicate that two-dimensional superconductivity is resilient against high-frequency microwave radiation, because vortex-antivortex dissociation is dramatically suppressed in two-dimensional superconducting condensates oscillating at high frequencies.
