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Using the tight-binding BHZ model and Landauer-B\"uttiker formalism, thetopological invariant of the finite width of ribbons of HgTe/CdTe quantum wellis studied in the absence and presence of an external transverse electricfield. It will be recognized that a critical current changes topologicalinvariant of ribbons of quantum well. This topological phase transition, whichoccurred by adjustment of the bias voltage, depends on the width of the sampleand the gate voltage. The profound effects of an external transverse electricfield are considered to the separation of spin-up and spin-down bandstructures, decreasing band gap and tuning the topological phase transitionbetween ordinary and quantum spin Hall regime. These declares the transverseelectric field amplifies the quantum spin Hall regime and causes inducing thetopological phase transition in ribbons of quantum well. Our finding mayinstantly clear some practical aspects of the study in the field of spintronicfor employment in spin-based devices.

Bias-Voltage-Induced Topological Phase Transition in Finite Size Quantum Spin Hall Systems in the Presence of a Transverse Electric Field