Beyond Wave-Nature Signatures: h-Independent Transport in Strongly-Scattering 2D Quantum Channels

The Landauer-Büttiker formalism provides a fundamental framework for mesoscopic transport, typically expressing conductance in units of the quantum of conductance, e2/h. Here, we present a theoretical study of electron transport in a two-dimensional (2D) quantum wire. This system features a wide transverse confinement and a longitudinal, high-energy, narrow potential barrier. The derivation, performed within the Landauer framework, yields an analytical expression for the total conductance that is explicitly independent of Planck's constant (h). Instead, the conductance is found to depend solely on the Fermi energy, the electron effective mass, the wire width, and the effective barrier strength. We interpret this as an emergent phenomenon where the explicit signature of the electron's wave-like nature, commonly manifest through Planck's constant (h) in the overall scaling of conductance, is effectively absorbed within the energy- and geometry-dependent sum of transmission probabilities. This allows the conductance to be primarily governed by the Fermi energy, representing a 'state-counting' quantum parameter rather than more wave-like characteristic.