Conductance of a ballistic electron billiard in a magnetic field: does the semiclassical approach apply?

Abstract

We utilize a semi-classical approach to calculate conductance and weak localization corrections in a triangular billiard in non-zero magnetic field. Results of the calculations and comparison to numerical quantum mechanical simulations suggest that applicability of the standard semiclassical method for description of the geometry-specific features in the conductance of such systems is not obvious as the unitarity of the semiclassical scattering matrix is violated as well as the symmetry of the conductance/reflectance with respect to the magnetic field and the direction of the current is not satisfied. The reason for this is given. Our findings raise the question to what extent one can rely on numerous predictions for statistical properties of the conductance oscillations of ballistic cavities including the WL lineshapes and fractal conductance which were essentially based on the standard SC approach.