Thin transition metal dichalcogenides (TMDs) sustain superconductivity at large in-plane magnetic fields due to Ising spin-orbit protection which locks their spins in an out-of-plane orientation. Here we use thin NbSe2 as superconducting electrodes laterally coupled to graphene -making a planar, all van der Waals (vdW) two-dimensional Josephson junction (2DJJ). We map out the behavior of these novel devices with respect to temperature, gate voltage, and both out-of-plane and in-plane magnetic fields.Notably, the 2DJJs sustain supercurrent up to parallel fields as high as 8.5 T, where the Zeeman energy EZ rivals the Thouless energy E T h , a regime hitherto inaccessible in graphene. As the parallel magnetic field H increases, the 2DJJ's critical current is suppressed, and in a few cases undergoes a suppression and recovery. We explore the behavior in H by considering theoretically two effects: A 0-π transition induced by tuning of the Zeeman energy, and the unique effect of ripples in an atomically thin layer which create a small spatially varying perpendicular component of the field. 2DJJs have potential utility as flexible probes for two-dimensional superconductivity in a variety of materials, and introduce high H as a newly accessible experimental knob.By coupling graphene to exfoliated superconductors such as NbSe 2 [1-3] it is possible to realize Josephson junctions where both the normal and superconductor materials are two-dimensional (2D).Such junctions should sustain high in-plane magnetic fields. Thin NbSe 2 retains superconductivity at very high in-plane fields due to a combination of suppressed orbital depairing and Ising protection against pair-breaking [4, 5], and can sustain magnetic fields above 8 T without any measureable effect on the gap * Equal contribution 1

When the impurity mean free path is short, only spin-polarized Cooper pairs which are non-locally and antisymmetrically correlated in time may exist in a half-metallic ferromagnet. As a consequence, the half-metal acts as an odd-frequency superconducting condensate. We demonstrate both analytically and numerically that quantum vortices can emerge in half-metals despite the complete absence of conventional superconducting correlations. Because these metals are conducting in only one spin band, we show that a circulating spin supercurrent accompanies these vortices. Moreover, we demonstrate that magnetic disorder at the interfaces with the superconductor influences the position at which the vortices nucleate. This insight can be used to help determine the effective interfacial misalignment angles for the magnetization in hybrid structures, since the vortex position is experimentally observable via STM-measurements. We also give a brief discussion regarding which superconducting order parameter to use for odd-frequency triplet Cooper pairs in the quasiclassical theory. arXiv:1904.04846v4 [cond-mat.supr-con] 5 Jan 2020

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.

The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. These phenomena are commonly described by the two-layer shallow-water equations (SWE). When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer SWE. It has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions to correct the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly captures the behaviour of shocks and contact discontinuities without additional closure relations. The result shows that simplification to an effective one-layer model is justified mathematically and can be made without additional knowledge of the shock behaviour. The shock speed in the proposed model is consistent with empirical models and identical to front conditions that have been found theoretically by e.g. von Kármán and by Benjamin. This suggests that the breakdown of the SWE in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the SW framework to shocks by studying one-dimensional lock-exchange/-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. The equations are solved numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer SWE. We also compare numerical results from the model with results from experiments, and find good agreement. arXiv:1902.04648v3 [physics.flu-dyn]

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