Disordered graphene Josephson junctions

A tight-binding approach based on the Chebyshev-Bogoliubov-de Gennes method is used to describe disordered single-layer graphene Josephson junctions. Scattering by vacancies, ripples, or charged impurities is included. We compute the Josephson current and investigate the nature of multiple Andreev reflections, which induce bound states appearing as peaks in the density of states for energies below the superconducting gap. In the presence of single-atom vacancies, we observe a strong suppression of the supercurrent, which is a consequence of strong intervalley scattering. Although lattice deformations should not induce intervalley scattering, we find that the supercurrent is still suppressed, which is due to the presence of pseudomagnetic barriers. For charged impurities, we consider two cases depending on whether the average doping is zero, i.e., existence of electron-hole puddles, or finite. In both cases, short-range impurities strongly affect the supercurrent, similar to the vacancies scenario.

Figure 1

Layout of graphene Josephson junction considered in this work. Disordered and superconducting regions are separated by clean interface strips where Andreev reflection takes place.

Figure 2

DOS for a graphene Josephson junction considering different concentration of vacancies $x_{\mathrm{vac}}=N_{\mathrm{vac}}/N=0,0.1\%,0.2\%,0.3\%,0.4\%,0.5\%,1\%,$ and $5\%$ from bottom to top. Curves are progressively shifted in the vertical axis. Two cases are considered, according to the compensation in the distribution between the two sublattices: (a) completely compensated where vacancies are distributed equally in the two sublattices and (b) completely uncompensated where vacancies are randomly present only in one of the sublattices.

Figure 3

Average critical current density in a graphene Josephson junction for different concentrations of vacancies, diluted randomly over both sublattices (compensated), over a single sublattice (uncompesated), or over two-coupled sublattices (bivacancy). The continuous lines correspond to a least squares fit to $f\left(x\right)=a{(x+b)}^c$ and $g\left(x\right)=ax+b$.

Figure 4

Strained graphene Josephson junction with different configurations of Gaussian bumps. (a)–(c) show isolated Gaussian bumps, while (d) corresponds to an arrangement of four Gaussian bumps in a triangular configuration.

Figure 5

DOS for a graphene Josephson junction for the different strain configurations shown in Fig. 4. Panels from left to right correspond to cases from top to bottom shown in Fig. 4, respectively. Andreev peaks are shown for deformations with the maximum strain increasing from 0% to 5%, 10%, and 20% (bottom to top). Curves are progressively shifted in the vertical axis inside each panel.

Figure 6

Average critical current density in strained Josephson junctions as a function of maximal strain for the strain configurations depicted in Figs. 4–4.

Figure 7

Average DOS for disordered graphene Josephson junctions, considering impurity scattering potentials with different ranges, $\varepsilon /a_0=0.1$, 0.5, and 4.0. Different values of the impurity concentration considered inside the panels are $x_{\mathrm{imp}}=0$%, 1%, 2%, 3%, and 5%, from bottom to top, where the curves are progressively shifted in the vertical axis inside each panel.

Figure 8

Average critical current density in a graphene Josephson junction as a function of the impurity concentration $x_{\mathrm{imp}}$ for different widths of the Gaussian potential induced by isolated impurities. Equal number of electron and holelike potentials are considered in (a), while only electronlike potentials are assumed in (b) leading to an inhomogeneous but finitely doped junction.