SHAPE EFFECT OF QUANTUM BALLISTIC TRANSPORT THROUGH A MICROSCOPIC CONSTRICTION IN A 2-DIMENSIONAL ELECTRON-GAS

The hyperbolic model is used to understand the shape effect in the qua ntized conductance of a microscopic constriction in a two-dimensional electron gas with high mobility. To obtain the conductance G as a func tion of the constriction slope and width, we have solved the Schroding er equation in the elliptic coordinates. The results have revealed a s ystematic trend in the value and quantization of G with respect to the shape. It is found that a certain degree of the smoothness and length of the constriction is necessary for a number of quantized steps of G . We have also calculated G of the same hyperbolic constriction using the Glazman scheme (JETP Lett. 48, 238 (1988)). The results of G have shown that the Glazman scheme cannot take into account the shape effec t because of the inherent assumption of the constriction smoothness. T hus we compare two results to find a more apparent shape effect in the quantum ballistic transport through a narrow constriction.