Effects of the Spatial Extension of the Edge Channels on the Interference Pattern of a Helical Josephson Junction

Abstract

Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ${\varphi }_0$ (where ${\varphi }_0=h/2e$) as a fundamental period. If CPs' splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches $2{\varphi }_0$.

arXiv comment13 pages, 5 figures

References in corpus (29)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• Induced Superconductivity in the Quantum Spin Hall Edge
• Gapless Andreev bound states in the quantum spin Hall insulator HgTe
• Edge-mode Superconductivity in a Two Dimensional Topological Insulator
• Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions
• Topological Josephson ${\varphi }_0$-junctions
• Superconductor coupled to two Luttinger liquids as an entangler for electron spins
• Evidence for an anomalous current phase relation in topological insulator Josephson junctions
• Anomalous Fraunhofer Interference in Epitaxial Superconductor-Semiconductor Josephson Junctions
• Interacting topological edge channels
• Quantum interference of edge supercurrents in a two-dimensional topological insulator
• Coherent transport and nonlocality in mesoscopic SNS junctions: anomalous magnetic interference patterns
• Cooper-Pair Injection into Quantum Spin Hall Insulators
• $h/e$ superconducting quantum interference through trivial edge states in InAs
• Double path interference and magnetic oscillations in Cooper pair transport through a single nanowire
• Nonlocality in mesoscopic Josephson junctions with strip geometry
• Even-odd flux quanta effect in the Fraunhofer oscillations of an edge-channel Josephson junction
• Crossed Andreev Reflection in InSb Flake Josephson Junctions
• Manipulation of Cooper pair entanglement in hybrid topological Josephson junctions
• Superconducting Quantum Interference in Edge State Josephson Junctions
• Theory of anomalous magnetic interference pattern in mesoscopic SNS Josephson junctions
• 2${\Phi }_0$-periodic magnetic interference in ballistic graphene Josephson junctions

Cited by in corpus (4)

• Anomalous supercurrent and diode effect in locally perturbed topological Josephson junctions
• Emerging topological bound states in Haldane model zigzag nanoribbons
• Reconstruction-Induced ${\phi }_0$ Josephson Effect in Quantum Spin Hall Constrictions
• Interedge backscattering in time-reversal symmetric quantum spin Hall Josephson junctions