External Field-manipulated Thermoelectric And Supercurrent Transport In Two-dimensional Hexagonal Materials

In 2004,Novesolov and Geim firstly fabricated the stable graphene by using mi-cromechanical cleavage method.This creative work overturns the statement that a true two-dimensional lattice material can not exist at finite temperatures due to thermody-namic fluctuations,and attracts many researchers to study two-dimensional lattice mate-rials.Owing to its simple structure,effective external field modulation,and great potential value in both theory and application,this not only stimulates researcher's interest on new physical properties about two-dimensional lattice materials,but also motivates them to study new two-dimensional lattice materials such as silicene,germanene,and molybde-num disulfide.In the past dozen years,two-dimensional lattice materials greatly promote the progress of condensed matter physics,and even bring a new industrial revolution.This thesis mainly focuses on the thermoelectric and supercurrent transport properties in graphene and silicene system.In this thesis,we study the anomalous thermomagnetic and Josephson effects in graphene and silicene,respectively.In graphene,we mainly pay attention to the tem-perature gradient-driven valley-dependent electric transport and the relation between the anomalous thermomagnetic effect and topological phase transition.In silicene,we study valley-dependent ? Josephson junction and ?0 Josephson junction arised from the topo-logical edge states.These results can provide the basis for designing quantum devices in future.The detailed arrangements of our paper are as following:In chapter one,we first introduce the basic properties and research progress of graphene and silicene,respectively.Then we introduce three basic effects in physics,i.e.,thermomagnetic effect,Andreev reflection,and Josephson effect.At last,the theoretical methods used in our thesis are described.In chapter two,we study the valley-dependent anomalous thermomagnetic effects,including the Nernst and Ettingshausen effects,in a graphene monolayer which is sub-jected to a staggered sublattice potential and an off-resonant circularly polarized light.It is found that a topological phase transition in this system can significantly affect the signs of the Nernst conductivity as well as the Ettingshausen thermal conductivity,which pro-vides a new method to characterize the phase transition between the band and topological insulators.At the topological phase transition point,the pure valley polarized electric and heat currents are generated.In contrast to the traditional thermomagnetism,the anoma-lous thermomagnetic figure of merit is formulated and used to characterize the conversion efficiency.This theoretical approach including the analytical treatment and numerical cal-culations can also be used to study the same properties of other graphene-like materials.In chapter three,we investigate the Andreev bound states(ABSs)and Josephson current in a silicene-based superconductor-normal-superconductor junction modulated by a perpendicular electric field and an off-resonant circularly polarized light.Based on the Dirac-Bogoliubov-de Gennes equation,we analytically derive the ABS levels,and show they have different phase-difference dependences,which will remarkably influence the velocity of Cooper pairs and then the Josephson current.In the pristine or gated silicene,the ABS levels always show negative slope,which means that the Josephson current is unreversable because of the time-reversal symmetry.When an off-resonant circularly polarized light is applied,whether or not there is a perpendicular electric field,the ABS levels will have positive slope,leading to the emergence of reversed Josephson current,due to the nonzero center of mass wavevector of Cooper pairs.In this light-modulated silicene-based Josephson junction,valley polarization provides an alternative mechanism for 0-? transition,very different from that for the conventional ferromagnetic Josephson junctions where the spin polarization is essential.In chapter four,we investigate the supercurrent in a silicene-based Josephson junc-tion under external-field modulations.Employing the qualitative analysis and solving the Dirac-Bogoliubov-de Gennes equation,it is found that,for the bulk states,a ? junction is generated by applying an antiferromagnetic exchange magnetization due to valley po-larization;in contrast,for the topologically protected edge states,a ? as well as ?0 junction can be obtained by adjusting ferromagnetic exchange field or antiferromagnetic exchange magnetization to shift the edge states in wavevector space;or alternatively by modulating electric and light fields to modify the Fermi velocity of the edge states.It is proposed that a direct current superconducting quantum interference devices can be used to observe these ? and ?0 junctions in experiment.In the last chapter,we make a brief summary of our thesis and give an outlook about our future study.