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Register a new userTwo-dimensional Josephson vortex lattice and anomalously slow decay of the Fraunhofer oscillations in a ballistic SNS junction with a warped Fermi surface
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$ $The critical current of a Josephson junction is an oscillatory function of the enclosed magnetic flux $Phi$, because of quantum interference modulated with periodicity $h/2e$. We calculate these Fraunhofer oscillations in a two-dimensional (2D) ballistic superconductor--normal-metal--superconductor (SNS) junction. For a Fermi circle the amplitude of the oscillations decays as $1/Phi$ or faster. If the Fermi circle is strongly warped, as it is on a square lattice near the band center, we find that the amplitude decays slower $propto 1/sqrtPhi$ when the magnetic length $l_m=sqrt{hbar/eB}$ drops below the separation $L$ of the NS interfaces. The crossover to the slow decay of the critical current is accompanied by the appearance of a 2D array of current vortices and antivortices in the normal region, which form a bipartite rectangular lattice with lattice constant $simeq l_m^2/L$. The 2D lattice vanishes for a circular Fermi surface, when only the usual single row of Josephson vortices remains.
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We investigate the Josephson critical current $I_c(Phi)$ of a wide superconductor-normal metal-superconductor (SNS) junction as a function of the magnetic flux $Phi$ threading it. Electronic trajectories reflected from the side edges alter the function $I_c(Phi)$ as compared to the conventional Fraunhofer-type dependence. At weak magnetic fields, $Blesssim Phi_0/d^2$, the edge effect lifts zeros in $I_c(Phi)$ and gradually shifts the minima of that function toward half-integer multiples of the flux quantum. At $B>Phi_0/d^2$, the edge effect leads to an accelerated decay of the critical current $I_c(Phi)$ with increasing $Phi$. At larger fields, eventually, the system is expected to cross into a regime of classical mesoscopic fluctuations that is specific for wide ballistic SNS junctions with rough edges.
We calculate the beating of $h/2e$ and $h/e$ periodic oscillations of the flux-dependent critical supercurrent $I_c(Phi)$ through a quantum spin-Hall insulator between two superconducting electrodes. A conducting pathway along the superconductor connects the helical edge channels via a non-helical channel, allowing an electron incident on the superconductor along one edge to be Andreev reflected along the opposite edge. In the limit of small Andreev reflection probability the resulting even-odd effect is described by $I_cpropto|cos(ePhi/hbar)+f|$, with $|f|ll 1$ proportional to the probability for phase-coherent inter-edge transmission. Because the sign of $f$ depends on microscopic details, a sample-dependent inversion of the alternation of large and small peaks is a distinctive feature of the beating mechanism for the even-odd effect.
Using tunneling spectroscopy, we have measured the local electron energy distribution function in the normal part of a superconductor-normal metal-superconductor (SNS) Josephson junction containing an extra lead to a normal reservoir. In the presence of simultaneous supercurrent and injected quasiparticle current, the distribution function exhibits a sharp feature at very low energy. The feature is odd in energy, and odd under reversal of either the supercurrent or the quasiparticle current direction. The feature represents an effective temperature gradient across the SNS Josephson junction that is controllable by the supercurrent.
The fractional Josephson effect is known to be a characteristic phenomenon of topological Josephson junctions hosting Majorana zero modes (MZMs), where the Josephson current has a $4pi$ (rather than a $2pi$) periodicity in the phase difference between the two topological superconductors. We introduce a one-dimensional model of a topological superconductor/normal-metal/superconductor (SNS) junction with the normal-metal (N) region of finite length, which is intermediate regime between the short- and long-junction limits. Assuming weak tunneling at the SN interfaces, we investigate resonance and finite-size effects on the fractional Josephson effect due to the existence of several discrete energy levels in the N region in which wavefunctions have oscillating nodal structure. Through careful analysis of the sign change in the transmission amplitudes through the junction and the fermion parity of the two MZMs, we find that the fractional Josephson current is proportional to the parity of total fermion numbers including both filled normal levels and two MZMs. Furthermore, we elucidate drastic enhancement of the Josephson current due to the resonance between a discrete level in the N region and MZMs.
We report the realization and investigation of a ballistic Andreev interferometer based on an InAs two dimensional electron gas coupled to a superconducting Nb loop. We observe strong magnetic modulations in the voltage drop across the device due to quasiparticle interference within the weak-link. The interferometer exhibits flux noise down to $sim 80, muPhi_0/sqrt{textrm{Hz}}$, and a robust behavior in temperature with voltage oscillations surviving up to $sim7,$K. Besides this remarkable performance, the device represents a crucial first step for the realization of a fully-tunable ballistic superconducting magnetometer and embodies a potential new platform for the investigation of Majorana bound states as well as non-local entanglement of Cooper pairs.
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