论文标题
为$α-\ Mathcal {t} _3 $模型开发一种半经典的温泽尔 - kramer-brillouin理论
Developing a semiclassical Wentzel-Kramers-Brillouin theory for $α-\mathcal{T}_3$ model
论文作者
论文摘要
我们已经为$α-\ Mathcal {t} _3 $模型开发了一个完整的半经典温ZEL-KRAMER-BRILLOUIN（WKB）理论，该理论描述了一系列现有的Pseudospin-1 Dirac锥体材料。通过在普朗克常数$ \ hbar $的范围内扩展所寻求的波函数，我们获得了领先的订单扩展项，这是计算$α-\ Mathcal {t} {t} _3 $的半经典电子的电子和传输属性所需的关键数量。我们得出了连接波函数的每两个连续阶的传输方程，并将它们求解以获得一阶WKB波函数。我们还讨论了所获得的近似值的适用性，以及如何使用这些结果来研究$α-\ Mathcal {t} _3 $具有非平凡势能曲线的材料的各种隧道和运输特性。我们的结果也可能有助于基于创新的平板狄拉克材料来构建电子设备和晶体管。
We have developed a complete semiclassical Wentzel-Kramers-Brillouin (WKB) theory for $α-\mathcal{T}_3$ model which describes a wide class of existing pseudospin-1 Dirac cone materials. By expanding the sought wave functions in a series over the powers of Planck constant $\hbar$, we have obtained the leading order expansion term which is the key quantity required for calculating the electronic and transport properties of a semiclassical electron in $α-\mathcal{T}_3$. We have derived the transport equations connecting each two consecutive orders of the wave function expansion and solved them to obtained the first order WKB wavefunction. We have also discussed the applicability of the obtained approximation and how these results could be used to investigate various tunneling and transport properties of $α-\mathcal{T}_3$ materials with non-trivial potential profiles. Our results could be also helpful for constructing electronics devices and transistors based on innovative flat-band Dirac materials.
