A potential-well based formulation to calculate the quantized conductance of a one-atom constriction

A simple method to find the electron conductance of a one-atom metallic wire

“…This relationship agrees with ref. [2] and is consistent with that conductance quantization in a metallic nanowire takes place if the diameter of the wire is on the same order of magnitude of the de Broglie wavelength of the conduction electrons, whose associated waves propagate in the transverse direction of the wire so that they constitute a well-defined quantum mode consisting of standing waves. Given that the contributions to the total conductance of all the modes are the same, then the total conductance is directly proportional to the number of modes so it is quantized.…”

“…(2) is consistent with the fact that the magnitude of the corresponding quantized Fermi velocity reads (see, for example, ref. [2]):…”

“…Key aspects relative to conductance quantization in nanowires should be fully investigated. Within this context, conductance quantization due to a single electron in a quasi-one-dimensional potential well presents notorious interest [1,2]. This fact will be exploited in the following to calculate the linear conductance of a one-atom metallic wire.…”

Calculation of the electrical conductance in multi-atom nanoconstrictions — A new quantitative theory

“…This can be inferred from the so-called Landauer model but there are other approaches, for example that of Ref. [17], for deriving the same result.…”

“…[14,15]). This result can be obtained from the fact that the width of the wire is of the same order of magnitude as the de Broglie wavelength associated with the conduction electrons [2,16], from considering standing waves in a quantum box as well as extended Hückel theory [17]. As a matter of fact, the electron waves which propagate along the transverse direction of the wire constitute well-defined quantum modes, so we may speak of standing waves.…”