Spin-resolved Quantum Transport Properties Of Relativistic Fermion

Since graphene was first reported in 2004,the novel behavior of relativistic fermions in condensed matter systems has drawn a lot of interest of researchers.As a consequence of their linear energy dispersion,the transport properties in the diverse set of materials can exhibit a significant number of novel phenomena,such as,unconventional quantum Hall effect,Klein paradox,specular Andreev reflection,1/3 sub-Poissonian shot noise,chiral anomaly,and so on.Moreover,due to the outstanding electronical and optical properties,those materials will draw much attention not only in therortical study on the novel quantum transport properties,but also in experimental study on the applications in semiconductor engineering.In this thesis,we focus on the quantum transport of relativistic fermions in graphene-and Weyl semimetal-based heterojunction.(1)Based on the DBdG equation,we have theoretically investigated the chirality-resolved transport properties through a superconducting heterojunction in the presence of both the RSOI and the DSOI.Our results show that,if only the RSOI is present,the chirality-resolved Andreev tunneling conductance can be enhanced in the superconducting gap,while it always shows a suppression effect for the case of the DSOI alone.Moreover,the zero-bias tunneling conductances for the RAR and the SAR also show a qualitative difference with respect to the barrier parameters.When the RSOI and the DSOI are finite,three orders of magnitude enhancement of specular Andreev tunneling conductance is revealed.Furthermore,by analyzing the balanced SOI case,we find that the RAR is in favor of a parabolic dispersion,while a linear dispersion is highly desired for the SAR.These results shed light on the diagnosing of the SAR in graphene when subjected to both kinds of SOI.(2)Based on the DBdG equation and the FTK formula,we have studied the current-phase relation,the skewness,and the critical supercurrent characteristics of a ballistic graphene Josephson junction.The numerical results indicate that the propagating Andreev mode and the quasilocalized Andreev level can not only be greatly modulated by the strength of the SOI,but also exhibit a strikingly different dependence on the SOI.In particular,the supercurrent for the pristine case,in sharp contrast to its counterpart in conventional junction,becomes non-monotonic and gives rise to a maximum or a single singularity at certain SOI(the DSOI equates to half of the RSOI).We also analyze the stability of these features to the barrier and the doping level,and we find that they are expected to persist with the SOI.Besides,they can lead to the enhancement and the suppression features in junction with the certain values.In particular,the propagating Andreev mode gives rise to a ?/2 periodic oscillatory behavior with the barrier,while the quasilocalized Andreev level induces a ? periodic oscillatory.Therefore,the results could contribute to the diagnosing of the SAR and the exploring of the quantum devices based on graphene with the SOI.(3)By using the Landauer formula and the non-equilibrium Green's function method,we have studied the spin-resolved transport properties through a patterned graphene nanoribbon with a straight zigzag edge.The top and the bottom edge states of nanoribbon can be merged with each other by the patterned edge states,thereby the tunneling conductance exhibits a large suppression.In contrast to ferromagnetic graphene nanoribbon,a pure spin current can be obtained in antiferromagnetic graphene nanoribbon with special patterned structure and incident energy.Moreover,the intrinsic magnetic transport properties of patterned zigzag graphene nanoribbon can be easily tuned by the patterned size and the incident energy.Thus,we suggest that the proposed patterned operation can be regarded as a new and effective route for the spintronics devices based on a zigzag graphene nanoribbon.(4)Based on the transfer matrix method,we have combined analytical formula with numerical calculation to explore the shot noise of massless Weyl fermions in the Weyl semimetal resonant junction.The shot noise can be tuned efficiently by varying barrier strength,structure of the junction,Fermi energy and crystallographic angle.For a quasiperiodic supperlattice,in complete contrast to conventional junction case,the effect of the disorder strength on the shot noise depends on the competition of the classical tunneling and the Klein tunneling.Moreover,the delta barrier structure is also vital in determining the shot noise.In particular,a universal Fano factor has been found in a single delta potential case,whereas the resonant structure of the Fano factor perfectly matches with the number of the barrier in a delta potential supperlattice.These results are crucial for nanoelectronic devices design based on this topological semimetal material.