Topological quantization of current in quantum tunnel contacts

It is shown that an account of the Berry phase (a topological θ-term), together with a dissipative term in the effective action S[ϕ] of the tunnel contacts, induces a strong quantization of the tunnel current at low temperatures. This phenomenon, as 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 the value of the θ parameter is determined by the gate voltage, this effect allows us to control the current through the contact. A possible physical application of this effect is proposed.