Charge transport of graphene ferromagnetic-insulator-superconductor junction with pairing state of broken time reversal symmetry

Abstract

We investigate the charge transport through a graphene-based ferromagnetic-insulator-superconductor junction with a broken time reversal symmetry (BTRS) of dx2−y2 + is and dx2−y2 + idxy superconductor using the extended Blonder-Tinkham-Klapwijk formalism. Our analysis have shown several charateristics in this junction, providing a useful probe to understand the role of the order parameter symmetry in the superconductivity. We find that the presence of the BTRS (X) state in the superconductor region has a strong effect on the tunneling conductance curves which leads to a decrease in the height of the zero-bias conductance peak (ZBCP). In particular, we show that the magnitude of the superconducting proximity effect depends to a great extent on X and by increasing X, the zero-bias charge conductance oscillations with respect to the rotation angle β are suppressed. In addition, we find that at the maximum rotation angle β = π/4, introducing BTRS in the FIS junction causes oscillatory behavior of the zero-bias charge conductance with the barrier strength (χG) by a period of π and by approaching the X to 1, the amplitude of charge conductance oscillations increases. This behavior is drastically different from none BTRS similar graphene junctions. At last, we suggest an experimental setup for verifying our predicted effects.

Identifying the graphene d-wave superconducting symmetry by an anomalous splitting zero-bias conductance peak

“…And not only the subpeaks but also the ZBCDs are widened with the enhancement of h, companied by the gradual decrease of the zero-bias conductance for the ZBCD up to zero at h=E F . This is thoroughly different from that without RSOC in [14][15][16][17], where the ZBCPs always exist with its peak height modulated by h. It follows therefore that the splitting ZBCP is originated from the interplay between h and RSOC, which induces triplet equal-spin AR or novel AR between the FM and SC with the incident electrons and the reflected holes coming from the same spin subband. The property of splitting for the ZBCP with the exchange field h increased is a little similar with that in the FM/FM/d-wave SC junctions with noncollinear magnetizations [11].…”

“…It is obvious that the zero-bias conductance is insensitive to any increase in χ due to the zero energy state formed at the junction interface [2,3]. However, the variation of the non-zero bias conductance is non-monotonic with increasing χ from 0 to π/2 and is thoroughly different from the results of [13][14][15][16][17] for the absence of RSOC, where the conductance monotonously decreases. In order to unveil such a non-monotonic property, in figure 5(b), we give the plot of the conductance under the situation of eV/Δ 0 =0.5 as a function of χ, which is corresponding to figure 5(a).…”

“…The experimental observation of the splitting of ZBCP with varied h, particularly for h>E F , will provide direct evidence for the existence of not only the RSOC but also the d-wave pairing symmetry both combined with the nodal relativistic low-energy Dirac fermions. Here, for h/E F =0, the FM region is reduced to a normal one without spinsplitting, and due to the formation of zero-energy states in the graphene-based d-wave SC junction, the perfect AR is produced at eV/Δ 0 =0, as a result, one can observe a ZBCP with twice the normal-state conductance as shown in figures 2(a) and 3(b), which normally appears in relative d-wave SC junctions [10][11][12][13][14][15][16][17].…”

“…Linder and Sudbø theoretically investigated the influence of an anisotropic order parameter induced in graphene on the tunneling conductance in graphene-based normal metal (NM)/insulator (I)/d-wave SC junction, which owes line nodes that always cross the Fermi surface in the gap, thus featuring not only Andreev bound states but also nodal relativistic low-energy Dirac fermions [13]. The graphene-based FM/I/d-wave SC junctions with or without a BTRS in SC region have also been investigated theoretically, which reveals that the exchange filed h only decreases the height of the ZBCP and the split is absent [14][15][16][17]. This is very different from that for the conventional FM/I/d-wave SC junctions [6,10,11].…”

“…It has been demonstrated that, the anisotropic d-wave pair symmetry could be merged with the relativistic nodal fermions of graphene and the anomaly of the ZBCP as an experimental signature of the high-T c superconducting proximity effect in graphene was also exhibited [20,13]. Since tunneling conductance spectra of the graphene-based FM/I/d-wave SC junctions have been investigated [14][15][16][17], it is highly desirable to study the ZBCP of graphene-based FM/RSOC/I/d-wave SC multilayered structure so as to find whether or not the triplet states induced by the interplay between RSOC and FM possess some new features on the ZBCP compared with the one without RSOC? And thus, the features may be an experimental signature for demonstrating the existence of proximity-induced RSOC and d-wave pair symmetry combined with the spin-triplet pairing states in graphene layers.…”