Light-modulated Josephson effect in Kekulé patterned graphene

Abstract

We theoretically study the Josephson effect in a superconductor/normal metal/superconductor junction based on Kekulé patterned graphene. For the Kekulé-O patterned junctions, a Fermi momentum-splitting Andreev reflection at the interface can be induced by the off-resonant circularly polarized light applied in the normal region, which results in the possible π-state. In contrast, for the Kekulé-Y patterned junctions, the Fermi momentum-splitting Andreev reflection is strongly suppressed due to the valley-momentum locking and the junction always exhibits the 0-state. The dependence of the critical current on the junction length and the illumination parameter of the light field is also presented in detail. I. INTRODUCTIONKekulé (Kek) patterned graphene is a two-dimensional superlattice consisting of periodic thin and thick atomic bonds [1][2][3][4]. These alternating bonds form a √ 3 × √ 3 supercell, where the K and K valleys of the pristine graphene are folded on top of each other [5][6][7]. Recent experiments demonstrated that a carbon atom-centered bond texture can be realized in the graphene sheet grown on Cu(111) [4,8], which is known as the Kek-Y patterned graphene. The valley-momentum locking[5] predicted in this system leads to many peculiar properties, such as the enhanced Andreev reflection[9], the valley precession effect[10], the resonant transport [11], and the tunable optical absorption [12]. However, the pattern in which the C-C bond strength is altered as in a benzene ring is known as the Kek-O bond texture with a gap opened at the Dirac point[5]. Recently, in the Kek-O patterned graphene, Beenakker et al. predicted a valley switch effect by use of the Andreev-like reflection[13] and Wang et al. subsequently reported the valley supercurrent[14].The Josephson effect is an example of a macroscopic quantum phenomenon first predicted by B. D Josephson in 1962[15, 16]. A Josephson junction consists of two superconductors coupled by a weak link [17][18][19][20][21]. The current flowing continuously across the junction without any voltage applied is called the dc Josephson current [22][23][24][25], which is driven by the superconducting phase difference φ and can be expressed as I ∼ sin(φ + φ 0 ) with φ 0 representing the additional phase shift. The ground state of the junction usually has a zero phase shift at φ 0 = 0 due to the time-reversal symmetry [26][27][28]. With a ferromagnetic link, an extra π phase shift can appear in the junction leading to the π-state junctions with the supercurrent reversals [29][30][31][32][33]. As an analogy to the spin polarization, several studies have revealed that the valley isospin polarizations in graphene-like materials can also result in the π-state junctions, such as the irradiated graphene-and silicene-based Josephson junctions [34,35].