Real-space multiband envelope-function approach without spurious solutions

The envelope-function approach for mesoscopic electronic structure calculations is plagued by spurious solutions that originate in the ill representation of first-order derivatives in real-space bases. We present a symmetry-adapted finite element approach for multiband (k) over right arrow . (p) over right arrow envelope-function Hamiltonians that is manifestly free from spurious solutions, numerically efficient, and easy to implement. In addition, a gauge-invariant extension to this method is developed for problems involving magnetic fields. We predict the electrical exciton g-factor tuning in single InAs/GaAs embedded quantum dots to be significantly larger than previously found.