Detailed numerical results are presented for the calculated conductance of quantum point contacts, or, narrow constrictions between high mobility two-dimensional electron systems fabricated on semiconductor nanostructures. The conductance is calculated from the two-terminal multichannel transmission matrix formalism using the recursive single-particle Green’s function technique. The Green’s functions are obtained recursively for a tight-binding two-dimensional disordered Anderson lattice model representing the constriction. The conductance is calculated as a function of the shape and the size of the constriction (i.e., its geometry), the temperature, and, the elastic disorder in the system. Our main results, which are consistent with experimental findings, are: (1) increase of elastic scattering destroys the quantization; (2) for a fixed amount of disorder (i.e., for a given value of the elastic mean free path), the conductance quantization is poorer for longer constrictions; (3) in general, the quantization is poorer for higher quantum numbers or subbands; (4) constrictions with sharper geometry have sharper quantization, but may have quantum resonances associated with their sharp corners; (5) the quantum resonances (in sharp constrictions) are suppressed for shorter constriction lengths and at higher temperatures; (6) in general, higher temperatures lower the quantization quality by smoothening out the conductance except for sharp constrictions where at the lowest temperatures the quantum resonances show up, adversely affecting the quantization; (7) in smooth or adiabatic constrictions, the conductance quantization is smooth (but not extremely accurate) but, adiabaticity is not a necessary requirement for conductance quantization; (8) in general, geometry, finite temperature, and finite disorder effects do not allow better than 1% type accuracy in the quantization (compared with integral multiples of 2e2/h) even in the best of circumstances; (9) increase of elastic disorder smoothly takes the system from a conductance quantized regime to the regime of universal conductance fluctuations; and, (10) inelastic scattering, which we treat only in a very crude phenomenological model, behaves similar to thermal effects in broadening and smearing the sharpness of the conductance quantization. We also discuss the effect of an external magnetic field on the conductance quantization phenomenon. Some results are given for the conductance of two constrictions in series.
Indirect to Direct Gap Crossover in Two-Dimensional InSe Revealed by Angle-Resolved Photoemission Spectroscopy