Quantized conductance of point contacts in a two-dimensional electron gas

Quantized conductance of point contacts in a two-dimensional electron gas

1988 | Wees, B.J. van; Houten, H. van; Beenakker, C.W.J.; Williamson, J.G.; Kouwenhoven, L.P.; Marel, D. van der; Foxon, C.T.
The quantized conductance of point contacts in a two-dimensional electron gas (2DEG) was experimentally studied. Ballistic point contacts in GaAs-AlGaAs heterostructures were examined in zero magnetic field. The conductance changed in quantized steps of $ e^2/\pi\hbar $ as the width of the point contact, controlled by a gate, was varied. Up to sixteen steps were observed when the width was increased from 0 to 360 nm. The results suggest that quantized transverse momentum in the point-contact region explains the observed quantization. The study used high-mobility 2DEG in GaAs-AlGaAs heterostructures. The point contacts were defined by electrostatic depletion of the 2DEG under a gate. The conductance of the point contact was found to be quantized in units of $ e^2/\pi\hbar $, consistent with the classical expression for conductance. The quantization was attributed to the discrete transverse wave vectors in the contact constriction. The conductance of a ballistic point contact is given by $ G = e^2 N_0 W (\hbar/2m) \langle |k_x| \rangle $, where $ N_0 $ is the density of states in the 2DEG, $ W $ is the width of the constriction, and $ \langle |k_x| \rangle $ is the average longitudinal wave vector. The number of channels $ N_c $ is the largest integer smaller than $ k_F W/\pi $, and the conductance is quantized in units of $ e^2/\pi\hbar $. The findings suggest that the experimental system closely approximates the behavior of idealized mesoscopic systems. The study reports the first measurements of the conductance of single ballistic point contacts in a 2DEG and demonstrates a novel quantum effect: the conductance is quantized in units of $ e^2/\pi\hbar $.The quantized conductance of point contacts in a two-dimensional electron gas (2DEG) was experimentally studied. Ballistic point contacts in GaAs-AlGaAs heterostructures were examined in zero magnetic field. The conductance changed in quantized steps of $ e^2/\pi\hbar $ as the width of the point contact, controlled by a gate, was varied. Up to sixteen steps were observed when the width was increased from 0 to 360 nm. The results suggest that quantized transverse momentum in the point-contact region explains the observed quantization. The study used high-mobility 2DEG in GaAs-AlGaAs heterostructures. The point contacts were defined by electrostatic depletion of the 2DEG under a gate. The conductance of the point contact was found to be quantized in units of $ e^2/\pi\hbar $, consistent with the classical expression for conductance. The quantization was attributed to the discrete transverse wave vectors in the contact constriction. The conductance of a ballistic point contact is given by $ G = e^2 N_0 W (\hbar/2m) \langle |k_x| \rangle $, where $ N_0 $ is the density of states in the 2DEG, $ W $ is the width of the constriction, and $ \langle |k_x| \rangle $ is the average longitudinal wave vector. The number of channels $ N_c $ is the largest integer smaller than $ k_F W/\pi $, and the conductance is quantized in units of $ e^2/\pi\hbar $. The findings suggest that the experimental system closely approximates the behavior of idealized mesoscopic systems. The study reports the first measurements of the conductance of single ballistic point contacts in a 2DEG and demonstrates a novel quantum effect: the conductance is quantized in units of $ e^2/\pi\hbar $.
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