Electron And Spin Transport In The Graphene And Superconductor Junctions

Investigating the exotic transport properties of newly discovered materials as well as exploiting the novel microscopic devices has always been an exciting arena in the community of condensed matter physics and promised numerous industrial applications. Recently, the countless theoretical and experimental studies have been dedicated to graphene, a single atomic layer of carbon with honeycomb lattice, due to the extraordinary electronic structure. Simultaneously, the interest also extends to the combined systems with other popular phases and interactions, such as superconductivity, spin-orbit coupling and exchange interaction. Actually, the superconductivity is an equivalently thriving field which has been enhanced by the emersion of various unconventional superconductors. Therefore, we conducted, in this thesis, several theoretical studies on the electron and spin transport in the graphene and superconductor junctions and explored the potential applications.In chapter1, we introduce the typical features of graphene and triplet superconductivity and present the main numerical methods, such as lattice Green’s function. Moreover, some paragraphs also are also dedicated to the introduction of spin-orbit coupling and exchange interaction.In chapter2, the dynamical conductances of graphene tunneling structures were numerically calculated using the scattering matrix method with the interaction effect included in a phenomenological approach. The overall single barrier dynamical conductance is capacitative. Transmission resonances in the single barrier structure lead to dips in the capacitative imaginary part of the response. This is different from the ac responses of typical semiconductor nanostructures, where transmission resonances usually lead to inductive peaks. The features of the dips depend on the Fermi energy. When the Fermi energy is below half of the barrier height, the dips are sharper. When the Fermi energy is higher than half of the barrier height, the dips are broader. Inductive behaviors can be observed in a double barrier structure due to the resonances formed by reflection between the two barriers. In chapter3, the Andreev reflection is investigated theoretically in the hybrid junctions consisting of a triplet p-wave superconductor and a zigzag edged graphene nanoribbon within the single energy-mode region. The Andreev reflection coefficient as well as the conductance spectrum is calculated from the Landauer-Buttiker formula. For the junction with px-wave symmetry, the conductance peak is absent at even Nz due to the prohibition of the Andreev reflection, a manifestation of parity conservation rule. For the junction with py-or (px+ipy)-wave symmetry, the prohibition of Andreev reflection disappears because the paring potential does not possess the reflection symmetry and the parity is not a good quantum number. When the ferromagnet is applied, the prohibition of Andreev reflection can be manipulated via the orientation of the d-vector. Moreover, the configuration of the ferromagnet also influences the prohibition. Those findings are helpful for understanding the tunneling process from triplet superconductor to ZGNR.In chapter4, we report a theoretical study on spin transports in the hybrid Josephson junction composed of the singlet s-wave and triplet p-wave superconductor. The node of the triplet pair potential is considered perpendicular to the interface of the junction. Based on a symmetry analysis, we predict that there is no net spin density at the interface of the junction but instead, a transverse mode-resolved spin density can exist and a nonzero spin current can flow transversely along the interface of the junction. The predictions are numerically demonstrated by means of the lattice Matsubara Green’s function method. It is also shown when a normal metal is sandwiched in between two superconductors, both spin current and transverse mode-resolved spin density are only residing at two interfaces due to the smearing effect of the multimode transport. Those findings are useful for identifying the pairing symmetry of the p-wave superconductor and generating spin current.In chapter5, we investigate theoretically the equilibrium transverse charge and spin currents flowing in a hybrid Josephson junction composed of two triplet p-wave superconductors and a Rashba spin-orbit coupling (RSOC) layer in between. Through a symmetry analysis, we show that the transverse currents originate from the breaking of mirror symmetries due to the misalignment of d-vectors in the two triplet superconductor leads. Besides, the mirror symmetries strongly constrain the dependence of the transverse currents on both the absolute and relative angles of the d-vectors. The symmetry analysis is confirmed by the numerical calculations based on the lattice Matsubara Green’s function method. The dependence of the transverse currents on the RSOC strength as well as the middle layer length is also addressed. These findings shed new light on the equilibrium spintronics device design and are useful for identifying the order parameter symmetries of p-wave superconductors.In chapter6, we investigate the Josephson Hall current flowing transversely in a hybrid s-wave/p-wave Josephson junction by considering the Dresselhaus-type (DSOC) and Rashba-type spin-orbit coupling (RSOC). Based on both analytic symmetry analysis and numerical calculations, we found that nonzero charge and spin Hall currents can flow in the junction and the driving force is the spin polarization induced by the interplay of singlet and triplet Cooper pairs. Due to different symmetries between DSOC and RSOC, the charge and spin Hall currents display different phase-dependence and d-vector dependence of the triplet superconductor lead. These findings are useful for designing the equilibrium spintronics device and identifying the type of SOC.In chapter7, a summary is drawn for the whole thesis.