Using the tight-binding BHZ model and Landauer-Büttiker formalism, the topological invariant of the finite width of ribbons of HgTe/CdTe quantum well is studied in the absence and presence of an external transverse electric field. It will be recognized that a critical current changes topological invariant of ribbons of quantum well. This topological phase transition, which occurred by adjustment of the bias voltage, depends on the width of the sample and the gate voltage. The profound effects of an external transverse electric field are considered to the separation of spin-up and spin-down band structures, decreasing band gap and tuning the topological phase transition between ordinary and quantum spin Hall regime. These declares the transverse electric field amplifies the quantum spin Hall regime and causes inducing the topological phase transition in ribbons of quantum well. Our finding may instantly clear some practical aspects of the study in the field of spintronic for employment in spin-based devices.

使用紧密结合的BHZ模型和Landauer-Büttiker形式主义，研究了在不存在和存在外部横向电场的情况下，HgTe / CdTe量子阱带的有限宽度的拓扑不变性。将会认识到，临界电流改变了量子阱带的拓扑不变性。通过调整偏置电压而发生的这种拓扑相变取决于样品的宽度和栅极电压。外部横向电场的深远影响被认为是分离了自旋向上和自旋向下的能带结构，减小了带隙并调节了普通自旋和量子自旋霍尔机制之间的拓扑相变。这些声明了横向电场放大了量子自旋霍尔机制，并引起了量子阱带中的拓扑相变。我们的发现可能会立即清除自旋电子学领域中用于基于自旋器件的研究的一些实际方面。