锯齿型石墨烯纳米窄带中量子霍尔体系的电场调控

Electrically controlled quantum spin Hall in narrow zigzag graphene nanoribbon

应用含自洽格点在位库仑作用的Kane-Mele模型,研究锯齿型石墨烯纳米窄带平面内横向电场对边界带能带结构和量子自旋霍尔(QSH)体系的影响.研究结果显示,当电场强度较弱时,外加电场的方向可以调控自旋向下的两个边界带一起朝不同方向移动,导致波矢q=0.5处自旋向下的两个纯边界态的能量简并劈裂方向可由电场调控;当电场强度进一步增强到超过0.69 V/nm,自旋向下的两个边界带出现较大带隙,能带反转,而自旋向上的电子结构无能隙,系统呈现半金属性,同时QSH体系不再是B类.特别当电场强度为1.17 V/nm时,在自旋向下能带的能隙中,q=0.5处存在自旋向上的纯边界态,意味着在8格点边界处可以产生自旋向上的纯边界电流.当电场强度持续增加时,QSH系统从B类到C类经历3个阶段的变化.当电场强度超过1.42 V/nm后,自旋向上的两个边界带也出现能带反转,分别成为导带和价带,系统成为C类的普通量子霍尔体系.

Using the tight binding Kane-Mele model including the self-consistent on-site Coulomb interactions （O-CIs）, we study the influence of transverse electric field in the narrow zigzag graphene nanoribbon （ZGNR） plane on the edge band structure in order to investigate the way to control the type of quantum spin Hall （QSH） system in the ZGNR. The theoretical results show that when applying weak electric field intensity, the direction of electric field can adjust these two spin-down edge bands moving along the different directions in one-dimensional q space, which leads to the two different types of degenerative breakdown of two pure spin-down edge states at q = 0.5. When applying positive electric field the energy of spin-down edge band at edge site 1 is higher than that at edge site 8. On the contrary, when applying negative electric field the energy of spin-down edge band at edge site 8 is higher than that at edge site 1. It shows that we can use the direction of electric field to control the two spin-down edge currents occurring at two different energies. Further, when the electric field intensity increases above 0.69 V/nm, the increased large band gap between the two spin-down edge bands leads to the inversion of these two spin-down edge bands. That is to say, there is a spin-down band gap, however, there is not a band gap for spin-up edge band in the region of spin-down band gap. Thus the system becomes half-metallic, and the QSH does not belong in the type B any longer. Specially, when the electric field intensity reaches 1.17 V/nm in the region of spin-down band gap, the pure spin-up edge state appears at q = 0.5, which shows that the strong pure spin-up edge current along the edge site 8 can occur. With increasing the intensity of electric field, the QSH system undergoes three processes from the type B to the type C. When the electric field intensity is more than 1.42 V/nm, the two spin-up edge bands also present band inversion and turn into the conduction band and the valence band, respectively. Thus the system becomes semiconducting and the QSH system does not belong in the type C, ordinary quantum Hall system. Finally, according to the results discussed above, we can expect that using the direction and the intensity of the transverse electric field in plane we can adjust the properties of edge current, and control the type of QSH system varying from the type B to the type C.