Uddin Salah, Hussain Altaf, Rashid Amin Ur, Ullah Kefayat, Oh Won-Chun
Department of Applied Physical and Material Sciences, University of Swat 19120 KPK Pakistan.
Department of Mathematics & Statistics, University of Swat 19120 KPK Pakistan.
RSC Adv. 2024 Aug 27;14(37):27162-27173. doi: 10.1039/d4ra05553e. eCollection 2024 Aug 22.
We have theoretically investigated the impact of both periodic electric and vector potentials on the low energy spectrum of ABA-trilayer graphene superlattice. Finite energy Dirac points appear in the energy spectrum due to the application of the vector potential. These extra Dirac points are symmetric about = 0 plane for equal barrier and well widths. For different barriers and well widths, one Dirac point shifts away and the second Dirac point shifts towards the = 0 plane. The extra Dirac points are not only generated from the original Dirac point but also emerge from the valleys developed in the energy spectrum. The application of both electric and vector potentials with identical barrier and well widths breaks the symmetry of the spectrum about the Fermi level. When the electric and vector potentials are asymmetric with all three layers having the same electric potentials, the energy spectrum becomes asymmetric about the Fermi level, and this asymmetric behavior of both potentials annihilates the original Dirac point from the spectrum. When all the layers have different electric potentials and both electric and vector potentials are asymmetric, the spectrum becomes asymmetric again, but this time the asymmetry of the spectrum occurs across the = 0 plane.
我们从理论上研究了周期性电场和矢量势对ABA三层石墨烯超晶格低能谱的影响。由于矢量势的作用，能谱中出现了有限能量的狄拉克点。对于相等的势垒和阱宽度，这些额外的狄拉克点关于( = 0)平面是对称的。对于不同的势垒和阱宽度，一个狄拉克点远离，另一个狄拉克点向( = 0)平面移动。额外的狄拉克点不仅从原始狄拉克点产生，也从能谱中形成的能谷中出现。具有相同势垒和阱宽度的电场和矢量势的应用打破了能谱关于费米能级的对称性。当电场和矢量势不对称且所有三层具有相同电势时，能谱关于费米能级变得不对称，并且这两种势的这种不对称行为从能谱中消除了原始狄拉克点。当所有层具有不同电势且电场和矢量势都不对称时，能谱再次变得不对称，但这次能谱的不对称发生在( = 0)平面上。
