Novel features of quantum conduction in a constriction

Abstract

The effects of the geometry and temperature on the quantum conductance for one-dimensional (1D) ballistic transport through a constriction in a 2D electron gas are investigated by use of a refined formalism. As the length of the constriction increases, weak oscillations around the classical conductance evolve into a steplike structure and the resonances on the plateaus become pronounced. Quantization at integer multiples of 2e2/h occurs only for uniform constriction of finite length. At finite temperature of 0.6 K significantly long uniform constriction is necessary to observe plateaus devoid of resonance structure. © 1989 The American Physical Society

Quantum heat transfer through an atomic wire

“…The total thermal conductance becomes expects that each subband in the wire having Ω i,min = 0, that formed by increasing the cross section, leads to a jump in K as in the electrical conduction. However, the amplitude of steps decreases exponentially with increasing Ω i,min at given low temperature T. Furthermore, an important difference between the electrical and thermal conductance is that all the modes of a given branch i contribute to K o , whereas the quantum ballistic electrical conduction in the 1D channels 8,25 is governed by the Fermi-Dirac distribution.…”

“…shows novel features [1][2][3][4][5][6][7][8] owing to two facts: (1) The electronic states confined in directions which are perpendicular to the one for the current flow are quantized. The level spacings 9 , ∆ǫ i = ǫ i+1 − ǫ i , of the quantized states of the nanoparticle are finite but strongly size and geometry dependent.…”

Quantum Transport in Semiconductor Nanostructures

“…The different spatial extension of edge channels and magnetoelectnc subbands leads to an entirely different sensitivity to scattermg processes in weak and strong magnetic fields Firstly, the zero-field conductance quantization is destroyed by a small amount of elastic scattermg (due to impunties or roughness of the channel boundanes, cf Refs 313,316,317,407,and 408), while the QHE is robust to scattermg 97 This difference is a consequence of the suppression ofbackscattenng by a magnetic field discussed m Section 13b, which itself follows from the spatial Separation at opposite edges of edge channels moving m opposite directions Second, the spatial Separation of edge channels at the same edge in the case of a smooth confinmg Potential opens up the possibihty of adiabatic transport (i e, the füll suppression of interedge channel scattermg) In weak magnetic fields, adiabaticity is of importance within a pomt contact, but not on longer length scales (cf Sections 13 a and 15 a) In a wide 2DEG region, scattermg among the modes in weak fields estabhshes local equilibnum on a length scale given by the melastic scattermg length (which m a high-mobility GaAs-AlGaAs heterostructure is presumably not much longer than the elastic scattermg length /~10μηι) The Situation is stnkmgly different m a strong magnetic field, where the selectwe population and detection of edge channels observed by van Wees et al 426 has demonstrated the persistence of adiabaticity outside the pomt contact…”

Atomic-scale tip-sample interactions and contact phenomena

“…Having the parameterized form of the potential and treating tip and sample in the free-electron approximation, ~ is obtained by evaluating the expectation value of the current operator in terms of current-carrying states, and integrating it over the Fermi sphere. The current-carrying states, in turn, are calculated by a transfer matrix method [15]. This method has a wide range of applications covering tunneling as well as ballistic transport, even including the field emission of electrons.…”