Study On Valley Current Of Monolayer Graphene

In the last two decades,the monolayer graphene has attracted much attention of researcher-s in both the condensed matter physics and material science fields,because it not only has the significance of basic theory research,but also has the value of practical application.As a mat-ter of fact,it has become one of the core research subjects in many research fields.Besides the electron charge and spin degrees of freedom,low energy Dirac electrons of the monolayer graphene have an extra valley degree of freedom.It has the advantages of the low energy dis-sipation,long coherence time in comparison with the other two degrees of freedom.Therefore,the valley degree of freedom has been proposed to be an ideal carrier of the next generation of electron devices.In this thesis,we have studied the valley-related electron transport properties of the monolayer graphene,and the obtained results are helpful for fabricating the valley-based device.According to the current theoretical research progress,this paper mainly does the following aspects of the work:We first proposed a theoretical method to generate the valley-polarized electron in the monolayer graphene system by introducing a strong static potential barrier in a tunneling device.We showed that the single strong potential barrier can be employed to filtrate the valley degree of freedom and permit one of valleys K or K^′travelling but prohibit the opposite valley K^′or K.In the case of the multilayer potential barriers,the valley filtration was further enhanced and the efficiency will be 100%,the filtrated valley electron depends on the polarization of the static barrier as well as the transport direction.Furthermore,we have also studied the valley-valve effect by considering the two opposite polarization of potential barrier like the Giant Magneto Resistance effect in the spin-based device.We showed the multilayer potential barrier can realize a perfect valley-valve effect and can produce higher valley filtration efficiency.The physics origin is from the strong static potential that makes the transport in the high-energy region of the graphene but not near the Dirac point,in other words,which only allows the preferential valley transport.In order to manupilate the valley degree of freedom in graphene,we have studied the valley-related transport in the Y-Kekul（?）lattice distorted graphene system,which is actually a graphene superlattice composed of a 3-fold enlargement of the original cell in comparison with the pristine graphene.So the K and K^′valleys are coupled together.Based on numerical calculations,we showed that the mere hopping-energy modification of Y-Kekul（?）structure can remain the Klein tunneling effect of the original Dirac electrons in graphene,however,the K-lein tunneling effect will appear when a site-energy modification is considered in the distorted superlattice system,the mirror inversion symmetry of the system will be destroyed,the electron tunneling transmission with all-angle injections will approach to the unit 1.More importantly,we found that the valley coupling effect in the Y-Kekul（?）structure can manupilate the valley degree to realize the valley superposition state and it can be controlled in a purely electric way.Besides the Y-Kekul（?）lattice distortion in the monolayer graphene,there is another type of lattice distortion,the O-Kekul（?）structure and both of them are observed in experiment.The difference between them is that the C-C distortions show different patterns in the hexagonal lattice structure of the original graphene,but the same is that the unit cell is expanded to 3 times of the original graphene.O-Kekul（?）structure can not only make the valley coupling together like the Y-Kekul（?）structure,but also lead to generation of a energy gap around the Dirac point.We showed that the system is actully a valley-version superconductor since the opposite K and K^′valley are coupled together like a Cooper pair,resulting in valley contraction,and opening of the energy gap.We studied the possible valley-version Josephson effect and found that a valley supercurrent is producted,such a valley current respects the time-reversal symmetry and can be modulated by a gate voltage for both its direction and magnitude.We also investigate the quantum Hall effect in theα-T₃lattice under strong magnetic field,focusing on the electronic properties related to valley degrees of freedom.Theα-T₃lattice can be used to link graphene lattices to Dice lattices,by changing the parameterα.One of the most novel features of theα-T₃model is the integer quantum Hall effect due to the existence of a nondispersive flat band.We investigate the effect of the disordered or staggered lattice potential in theα-T₃model on the integer quantum Hall conductance after the nondispersive flat band is destroyed.It is found that the zero hall conductance platform inα-T₃structure is very unstable and easily destroyed by weak disorder even the adjacent Hall conductance platform is affected.When theα-T₃structure only has the staggered lattice potential without the disorder,a new integer quantum Hall conductance platformσ_xy=νe²/h（ν=±2,±4,···）appears near the original zero Hall conductance platform.The emerging integer quantum Hall conductance is independent of strong magnetic fields and is even fully valley polarized.The Hall coefficients of electron and hole are respectively from the K and K^′valley electrons.In summary,we have proposed seveal reasonable methods to produce the valley current in the monolayer graphene through studying the valley-related transport properties and they in-cludes the selective effect due to the strong static potential barrier,the valley-versioned Joseph-son effect in the O-Kekul（?）structure,as well as the quantum Hall effect of theα-T₃model under strong magnetic field.Besides,we also found the Y-Kekul（?）structure can be employed to con-trol the valley precession due to the valley coupling effect in the studied graphene superlattice structure.Our findings in the thesis are helpful and will render some feasible methods to exploit and devise valley-based devices in experiments.