We investigate the superconducting proximity effect through graphene in the long diffusive junction limit, at low and high magnetic field. The interface quality and sample phase coherence lead to a zero-resistance state at low temperature, zero magnetic field, and high doping. We find a striking suppression of the critical current near graphene's charge neutrality point, which we attribute to specular reflection of Andreev pairs at the interface of charge puddles. This type of reflection, specific to the Dirac band structure, had up to now remained elusive. At high magnetic field, the use of superconducting electrodes with high critical field enables the investigation of the proximity effect in the quantum Hall regime. Although the supercurrent is not directly detectable in our two-wire configuration, interference effects are visible which may be attributed to the injection of Cooper pairs into edge states.

The notion of topological phases has been extended to higher-order and has been generalized to different dimensions. As a paradigm, ${\mathrm{Cd}}_3{\mathrm{As}}_2$ is predicted to be a higher-order topological semimetal, possessing three-dimensional bulk Dirac fermions, two-dimensional Fermi arcs, and one-dimensional hinge states. These topological states have different characteristic length scales in electronic transport, allowing one to distinguish their properties when changing sample size. Here, we report an anomalous dimensional reduction of supercurrent transport by increasing the size of Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$-based Josephson junctions. An evolution of the supercurrent quantum interferences from a standard Fraunhofer pattern to a superconducting quantum interference device (SQUID)-like one is observed when the junction channel length is increased. The SQUID-like interference pattern indicates the supercurrent flowing through the 1D hinges. The identification of 1D hinge states should be valuable for deeper understanding of the higher-order topological phase in a 3D Dirac semimetal.

The high tunability of the density of states of graphene makes it an ideal probe of quantum transport in different regimes. In particular, the supercurrent that can flow through a nonsuperconducting (N) material connected to two superconducting (S) electrodes, crucially depends on the length of the N relative to the superconducting coherence length. Using graphene as the N material we have investigated the full range of the superconducting proximity effect, from short to long diffusive junctions. By combining several S/graphene/S samples with different contacts and lengths, and measuring their gate-dependent critical currents $\left(I_c\right)$ and normal state resistance $R_N$, we compare the product $e{R}_N{I}_c$ to the relevant energies, the Thouless energy in long junctions and the superconducting gap of the contacts in short junctions, over three orders of magnitude of Thouless energy. The experimental variations strikingly follow a universal law, close to the predictions of the proximity effect both in the long and short junction regime, as well as in the crossover region, thereby revealing the interplay of the different energy scales. Differences in the numerical coefficients reveal the crucial role played by the interfacial barrier between graphene and the superconducting electrodes, which reduces the supercurrent in both short and long junctions. Surprisingly, the reduction of supercurrent is independent of the gate voltage and of the nature of the electrodes. A reduced induced gap and Thouless energy are extracted, revealing the role played by the dwell time in the barrier in the short junction, and an effective increased diffusion time in the long junction. We compare our results to the theoretical predictions of Usadel equations and numerical simulations, which better reproduce experiments with imperfect NS interfaces.

Superconducting nanowires can be fabricated by decomposition of an organometallic gas using a focused beam of Ga ions. However, physical damage and unintentional doping often result from the exposure to the ion beam, motivating the search for a means to achieve similar structures with a beam of electrons instead of ions. This has so far remained an experimental challenge. We report the fabrication of superconducting tungsten nanowires by electron-beam-induced-deposition, with critical temperature of 2.0 K and critical magnetic field of 3.7 T, and compare them with superconducting wires made with ions. This work is an important development for the template-free realization of nanoscale superconducting devices, without the requirement of an ion beam column.

One of the consequences of Cooper pairs having a finite momentum in the interlayer of a Josephson junction is $\pi$-junction behavior. The finite momentum can either be due to an exchange field in ferromagnetic Josephson junctions, or due to the Zeeman effect. Here, we report the observation of Zeeman-effect-induced $0\text{−}\pi$ transitions in ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$, three-dimensional Dirac semimetal-based Josephson junctions. The large in-plane $g$ factor allows tuning of the Josephson junctions from 0 to $\pi$ regimes. This is revealed by measuring a $\pi$ phase shift in the current-phase relation measured with an asymmetric superconducting quantum interference device (SQUID). Additionally, we directly measure a nonsinusoidal current-phase relation in the asymmetric SQUID, consistent with models for ballistic Josephson transport.