Proposal on Tunneling Effect between Quantum Hall States

Abstract

In the integer and fractional quantum Hall effects, the electric current flows through a thin layer under the strong magnetic field. The diagonal resistance becomes very small at integer and specific fractional filling factors where the electron scatterings are very few. Accordingly the coherent length is large and therefore a tunneling effect of electrons may be observed. We consider a new type of a quantum Hall device which has a narrow potential barrier in the thin layer. Then the electrons flow with tunneling effect through the potential barrier. When the oscillating magnetic field is applied in addition to the constant field, the voltage steps may appear in the curve of voltage V versus electric current I . If the voltage steps are found in the experiment, it is confirmed that the 2D electron system yields the same phenomenon as that of the ac-Josephson effect in a superconducting system. Furthermore the step V is related to the transfer charge Q as V = ( hf )/ Q where f is the frequency of the oscillating field and h is the Planck constant. Then the detection of the step V determines the transfer charge Q . The ratio Q / e ( e is the elementary charge) clarifies the origin of the transfer charge. Many conditions are required for us to observe the tunneling phenomenon. The conditions are examined in details in this article.