Topological quantization of current in quantum tunnel contacts

It is shown that an account of the Berry phase (a topological $\theta$-term) together with a dissipative term in the effective action $S[\phi]$ of the tunnel contacts induces a strong quantization of the tunnel current at low temperatures. This phenomenon like the Coulomb blockade reflects a discrete charge structure of the quantum shot noise and can ensure a quantization of the tunnel current without a capacitive charging energy $E_C$, when the latter is strongly suppressed by quantum fluctuations. Since a value of the $\theta$-parameter is determined by the gate voltage, this effect allows to control a current through the contact. A possible physical application of this effect is proposed.