  Stimulated by the recent realization of three dimensional topological
insulator nanowire interfer- ometers, a theoretical analysis of quantum
interference effects on the low energy spectrum of Bi2Se3 nanowires is
presented. The electronic properties are analyzed in nanowires with circular,
square and rectangular cross-sections starting from a continuum three
dimensional model with particular emphasis on magnetic and geometrical effects.
The theoretical study is based on numerically exact diagonalizations of the
discretized model for all the geometries. In the case of the cylindrical wire,
an approximate analytical solution of the continuum model is also discussed.
Although a magnetic field corresponding to half quantum flux is expected to
close the band gap induced by Berry phase, in all the studied geometries with
finite area cross-sections, the gap closes for magnetic fields typically larger
than those expected. Furthermore, unexpectedly, due to geometrical quantum
interference effects, for a rectangular wire with a sufficiently large aspect
ratio and smaller side ranging from 50{\deg}A and 100{\deg}A, the gap closes
for a specific finite area cross-section without the application of a magnetic
field.
