  The vibrational modes of Jahn-Teller molecules are affected by a Berry phase
that is associated with a conical intersection of the adiabatic potentials. We
investigate theoretically how this Berry phase affects transport through a
single $E \otimes e$ Jahn-Teller molecule when the tunneling electrons
continually switch the molecule between a symmetric and a Jahn-Teller distorted
charge state. We find that the Berry phase in conjunction with a spectral
trapping mechanism leads to a current blockade even in regions outside the
Coulomb blockade. The blockade is strongly asymmetric in the gate voltage and
induces pronounced negative differential conductance.
