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.
A superconducting quantum interference device (SQUID) comprising 0- and $pi$-Josephson junctions (JJs), called $pi$-SQUID, is studied by the resistively shunted junction model. The $pi$-SQUID shows half-integer Shapiro-steps (SS) under microwave irra
diation at the voltage $V$ = $(hbar/2e)Omega (n/2)$, with angular frequency $Omega$ and half-integer $n$/2 in addition to integer $n$. We show that the $pi$-SQUID can be a $pi$-qubit with spontaneous loop currents by which the half-integer SS are induced. Making the 0- and $pi$-JJs equivalent is a key for the half-integer SS and realizing the $pi$-qubit.
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 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 star
t from the microscopic Hamiltonian and calculate the DC current directly with the help of the non-equilibrium Greens 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 visible and appear one by one at high frequency, while at low frequency, the steps evolve exactly as the Bessel functions and the odd steps are completely suppressed, implying a fractional Josephson effect.
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 (s
pin) 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 between superconductor and semiconductor are transparent and have low disorder.
We investigate the current-phase relation of S/F/S junctions near the crossover between the 0 and the pi ground states. We use Nb/CuNi/Nb junctions where this crossover is driven both by thickness and temperature. For a certain thickness a non-zero m
inimum of critical current is observed at the crossover temperature. We analyze this residual supercurrent by applying a high frequency excitation and observe the formation of half-integer Shapiro steps. We attribute these fractional steps to a doubling of the Josephson frequency due to a sin(2*phi) current-phase relation. This phase dependence is explained by the splitting of the energy levels in the ferromagnetic exchange field.