Thermoelectric Properties Of Graphene And Transport Properties Of Topological Insulator

By using the nonequilibrium Green’s function method combined with the tight-bindingHamiltonian, we have studied topological Anderson insulator phenomena induced bydifferent-cell hopping disorder in HgTe/CdTe quantum wells and thermoelectric properties ofthe zigzag monolayer and bilayer graphene nanoribbons.Firstly, we have studied in detail the influence of same-orbit and different-orbit hoppingdisorders in HgTe/CdTe quantum wells. Intriguingly, similar to the behavior of the on-siteAnderson disorder, a phase transition from a topologically trivial phase to a topological phaseis induced at a proper strength of the same-orbit hopping disorder. For different-orbit hoppingdisorder, however, the phase transition does not occur. The results have been analyticallyverified by using effective medium theory. A consistent conclusion can be obtained bycomparing phase diagrams, conductance, and conductance fluctuations. In addition, theinfluence of Rashba spin-orbit interaction （RSOI） on the system has been studied for differenttypes of disorder. It has been found that a RSOI greater than a certain of strength can destroythe topological phase. The topological phase induced by same-orbit hopping disorder is morerobust against the RSOI than that induced by on-site Anderson disorder. For different-orbithopping disorder, no matter whether the RSOI is included or not, the phase transition does notoccur. The results indicate, whether or not the topological Anderson insulator can be observeddepends on a competition between the different types of the disorder as well as the strength ofthe RSOI in a system.Secondly, the thermopower and conductance in a zigzag graphene p-njunction arestudied. The conductance and thermopower of the junction can be affected by its width, thepotential drop, the applied perpendicular magnetic fields, and the edge vacancy defects. Anarrow graphene p-njunction shows insulating characteristics, and its thermopower ismuch larger than that of the wider one around the Dirac point. The insulating characteristic ofthe junction decreases as the width increases. With increasing junction width or the potentialdrop, the conductance plateau is strongly enhanced and the thermopower is inverted aroundthe Dirac point. In particular, a perpendicular magnetic field strongly suppresses the conductance and enhances the thermopower in the p-nregion. The edge lattice vacancydefects result in the decreasing of the conductance and the increasing of the thermopower.Since a one-atom vacancy, i.e. the removal of one atom, is a high energy defect that leavesthree carbon atoms two-coordinated, effectively breaking thesp2character of the locallattice, the effect of the one-atom vacancy is larger than that of the two-atom vacancy andthree-atom vacancy for the thermopower and conductance.Finally, we have studied the effects of the edge states on the conductance and thethermopower for zigzag monolayer graphene nanoribbons （zMGNs） and bilayer graphenenanoribbons （zBGNs）. It is shows that the band structure, conductance, and thermopower canbe modulated by the boundary potentials. For the zMGNs, under a staggered sublatticepotential, by adjusting the boundary potentials, the system can be conveniently modulatedfrom metal state to nonmetal state. The thermopower of a gapped zMGNs can be very largerthan that of a perfect zMGNs around Dirac point. There is a remarkable case the chargecarriers can be changed from electron-like to hole-like and vice versa by adjusting boundarypotentials. Though the increasing width leads to dense subbands and diminishing band gap forthe gapped zMGNs, the thermopower is nearly unchanged for the modulated zMGNs. For thezBGNs under a bias voltage to the layers, when the boundary potentials are adjusted to thenearest neighbor hopping energy, there are gapless edge-modes with opposite velocitiesappear in the vicinity of the two Dirac points, and the quantized conductance has a transitionfrom2（n+1）G₀to2（n+1/2）G₀withG₀being the conductance unit and n an integer.Particularly, under the strong bias voltage, compare to the gapless perfect zBGNs, thethermopower can be enhanced more than twice for the gapless edge modes with oppositevelocities. Combining the reduced thermal conductivity in few-layer graphene, our resultsshow that the modulated zBGNs are more reliable in thermoelectric application.