  It is well-known that helical surface states of a three-dimensional
topological insulator (TI) do not respond to a static in-plane magnetic field.
Formally this occurs because the in-plane magnetic field appears as a vector
potential in the Dirac Hamiltonian of the surface states and can thus be
removed by a gauge transformation of the surface electron wavefunctions. Here
we show that when the top and bottom surfaces of a thin film of TI are
hybridized and the Fermi level is in the hybridization gap, a nonzero
diamagnetic response appears. Moreover, a quantum phase transition occurs at a
finite critical value of the parallel field from an insulator with a
diamagnetic response to a semimetal with a vanishing response to the parallel
field.
