Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userChiral current-phase relation of topological Josephson junctions: A signature of the $4pi$-periodic Josephson effect
88
0
0.0
(
0
)
Authors
G. Tkachov
Ask ChatGPT about the research
No Arabic abstract
The $4pi$-periodic Josephson effect is an indicator of Majorana zero modes and a ground-state degeneracy which are central to topological quantum computation. However, the observability of a $4pi$-periodic Josephson current-phase relation (CPR) is hindered by the necessity to fix the fermionic parity. As an alternative to a $4pi$-periodic CPR, this paper proposes a chiral CPR for the $4pi$-periodic Josephson effect. This is a CPR of the form $J(phi) propto C , |sin(phi/2)|$, describing a unidirectional supercurrent with the chirality $C= pm 1$. Its non-analytic dependence on the Josephson phase difference $phi$ translates into the $4pi$-periodic CPR $J(phi) propto sin(phi/2)$. The proposal requires a spin-polarized topological Josephson junction which is modeled here as a short link between spin-split superconducting channels at the edge of a two-dimensional topological insulator. In this case, $C$ coincides with the Chern number of the occupied spin band of the topological insulator. The paper details three scenarios of achieving a chiral CPR: By only Zeeman-like splitting, by Zeeman splitting combined with bias currents, and by an external out-of-plane magnetic field.
rate research
Read More
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.
The current-phase relation (CPR) of a Josephson junction (JJ) determines how the supercurrent evolves with the superconducting phase difference across the junction. Knowledge of the CPR is essential in order to understand the response of a JJ to various external parameters. Despite the rising interest in ultra-clean encapsulated graphene JJs, the CPR of such junctions remains unknown. Here, we use a fully gate-tunable graphene superconducting quantum intereference device (SQUID) to determine the CPR of ballistic graphene JJs. Each of the two JJs in the SQUID is made with graphene encapsulated in hexagonal boron nitride. By independently controlling the critical current of the JJs, we can operate the SQUID either in a symmetric or asymmetric configuration. The highly asymmetric SQUID allows us to phase-bias one of the JJs and thereby directly obtain its CPR. The CPR is found to be skewed, deviating significantly from a sinusoidal form. The skewness can be tuned with the gate voltage and oscillates in anti-phase with Fabry-P{e}rot resistance oscillations of the ballistic graphene cavity. We compare our experiments with tight-binding calculations which include realistic graphene-superconductor interfaces and find a good qualitative agreement.
Josephson junctions with topological insulator weak links can host low energy Andreev bound states giving rise to a current phase relation that deviates from sinusoidal behaviour. Of particular interest are zero energy Majorana bound states that form at a phase difference of $pi$. Here we report on interferometry studies of Josephson junctions and superconducting quantum interference devices (SQUIDs) incorporating topological insulator weak links. We find that the nodes in single junction diffraction patterns and SQUID oscillations are lifted and independent of chemical potential. At high temperatures, the SQUID oscillations revert to conventional behaviour, ruling out asymmetry. The node lifting of the SQUID oscillations is consistent with low energy Andreev bound states exhibiting a nonsinusoidal current phase relation, coexisting with states possessing a conventional sinusoidal current phase relation. However, the finite nodal currents in the single junction diffraction pattern suggest an anomalous contribution to the supercurrent possibly carried by Majorana bound states, although we also consider the possibility of inhomogeneity.
The Josephson energy of two superconducting islands containing Majorana fermions is a 4pi-periodic function of the superconducting phase difference. If the islands have a small capacitance, their ground state energy is governed by the competition of Josephson and charging energies. We calculate this ground state energy in a ring geometry, as a function of the flux -Phi- enclosed by the ring, and show that the dependence on the Aharonov-Bohm phase 2ePhi/hbar remains 4pi-periodic regardless of the ratio of charging and Josephson energies - provided that the entire ring is in a topologically nontrivial state. If part of the ring is topologically trivial, then the charging energy induces quantum phase slips that restore the usual 2pi-periodicity.
Recently, much research has been dedicated to understanding topological superconductivity and Majorana zero modes induced by a magnetic field in hybrid proximity structures. This paper proposes a realization of topological superconductivity in a short Josephson junction at an edge of a 2D topological insulator subject to a perpendicular magnetic field. The magnetic field effect is entirely orbital, coming from a gradient of the order parameter phase at the edge, which results in a soliton defect at the junction with a pair of gapless Andreev bound states. The latter are reducible to Majorana zero modes by a unitary rotation and protected by a chiral symmetry. Furthermore, both ground state and excitations are quasiperiodic in the magnetic flux enclosed in the junction, with the period equal to the double flux quantum $2Phi_0 = h/e$. This behaviour follows from the gauge invariance of the $4pi$ - phase periodicity of the Majorana states and manifests itself as $2Phi_0$ - spaced magnetic oscillations of the critical current. Another proposed observable is a persistent current occurring in the absence of an external phase bias. Beside the oscillations, it shows a sign reversal prompted by the neutral Majorana zero modes. These findings offer the possibility to access topological superconductivity through low-field dc magnetotransport measurements.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
