Combined Zeeman and orbital effect on the Josephson effect in rippled graphene

Abstract

The two-dimensional nature of graphene Josephson junctions offers the possibility of creating effective superconductor-ferromagnet-superconductor junctions with tunable Zeeman splitting caused by an in-plane magnetic field. Such junctions would be able to alternate between a conventional superconducting ground state and a ground state with an intrinsic phase difference, making them controllable 0-π Josephson junctions. However, in addition to the Zeeman splitting, an in-plane magnetic field will in general also produce an orbital effect because of height variations in graphene, colloquially known as ripples. Both the Zeeman and orbital effect will thus affect the critical current, so to be able to identify 0-π transitions it is necessary to understand their combined effect. From both analytical and numerical solutions of the Usadel equation we find that ripples can in fact produce a current response similar to that which is characteristic of a 0-π transition. Hence, additional analysis is required in order to reveal the presence of a 0-π transition caused by spin splitting in graphene with ripples. We provide a closed form analytical expression for the critical current in the presence of exchange field and ripple effects as well as an expression for the scaling of critical current zeros with junction parameters.

Planar graphene- NbSe2 Josephson junctions in a parallel magnetic field

“…For the typical short wavelength ripple seen in graphene on SiO 2 , parallel fields of order 50 T are required to obtain an entire flux quantum within a ripple. However the cumulative effect of many such ripples causes a faster decay of the critical current which can create exponential-like behavior, similar to the Zeeman effect [19].…”

“…This effect can lead to critical current decay with parallel field, a non-Fraunhofer interference pattern, and suppression and recovery of the critical current mimicking a 0-π transition. The effect of ripples changes depending on ripple amplitude and wavelength, and junction dimensions [19]. Thus in any experiment involving graphene in parallel field, or indeed, we believe -any 2D conductor in parallel field -this effect should be considered.…”

“…The salient features of the data are therefore (a) exponential decay of the critical current at low field (b) saturation of the critical current at intermediate fields (c) lobe structure transition from Fraunhoferlike to SQUID-like, and (d) vanishing and reappearing of the central lobe critical current in Device A. In what follows, we discuss the physics in our 2DJJ by considering both the parallel field-tunable Zeeman splitting of the graphene band structure, and the orbital effect of out-of-plane ripples in the graphene [19].…”

“…Lacking an intrinsic spin-orbit coupling, graphene dispersion is affected by magnetic field only through Zeeman splitting, where the Zeeman energy is analogous to the exchange interaction in SFS JJs [19,44].…”

“…Using the same model discussed previously, we distinguish between the effects of short and long wavelength ripples [19]. Short ripples as seen in microscopy studies of graphene on SiO 2 are typically ≈ 0.3 nm peak-to-peak with a correlation length of 10-30 nm [49][50][51][52].…”