MESOSCOPIC DESCRIPTION OF HETEROJUNCTIONS

Starting from the microscopic current associated with the single-elect ron wave functions and using Wannier functions suitably generalized fo r nonperiodic heterostructures we construct mesoscopic (either discret e or continuous) conserved currents associated with states having comp onents only in the considered band. This provides a rigorous basis to the approximate envelope function approaches. As an application we ana lyze general one-dimensional heterojunctions, mapping explicitly the m icroscopic asymptotic states onto mesoscopic (one-band envelope) ones. This proves that, apart from the effective masses and the band offset s, the connection rules are characterized in general by three paramete rs, the values of which are unconstrained, confirming the results of p henomenological analyses.