Quantum spin Hall effect in nanostructures based on cadmium fluoride

Tunneling current-voltage (I-V) characteristics and temperature dependences of static magnetic susceptibility and specific heat of the CdB x F2 − x /p-CdF2-QW/CdB x F2 − x planar sandwich structures formed on the surface of an n-CdF2 crystal have been studied in order to identify superconducting properties of the CdB x F2 − x δ barriers confining the p-type CdF2 ultranarrow quantum well. Comparative analysis of current-voltage (I-V) characteristics and conductance-voltage dependences (measured at the temperatures, respectively, below and above the critical temperature of superconducting transition) indicates that there is an interrelation between quantization of supercurrent and dimensional quantization of holes in the p-CdF2 ultranarrow quantum well. It is noteworthy that detection of the Josephson peak of current in each hole subband is accompanied by the appearance of the spectrum of the multiple Andreev reflection (MAR). A high degree of spin polarization of holes in the edge channels along the perimeter of the p-CdF2 ultranarrow quantum well appears as a result of MAR and makes it possible to identify the quantum spin Hall effect I-V characteristics; this effect becomes pronounced in the case of detection of nonzero conductance at the zero voltage applied to the vertical gate in the Hall geometry of the experiment. Within the energy range of superconducting gap, the I-V characteristics of the spin transistor and quantum spin Hall effect are controlled by the MAR spectrum appearing as the voltage applied to the vertical gate is varied. Beyond the range of the superconducting gap, the observed I-V characteristic of the quantum spin Hall effect is represented by a quantum conductance staircase with a height of the steps equal to e 2/h; this height is interrelated with the Aharonov-Casher oscillations of longitudinal and depends on the voltage applied to the vertical gate.

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