Frequency Dependence of Diagonal Resistance in Fractional Quantum Hall Effect via Periodic.pdf

Frequency Dependence of Diagonal Resistance in Fractional Quantum Hall Effect via Periodic Modulation of Magnetic Field Shosuke Sasaki Shizuoka Institute of Science and Technology, 2200-2 Toyosawa, Fukuroi, 437-8555, Japan E-mail: sasaki @ns.sist.ac.jp Energy spectrum of fractional quantum Hall (FQH) states is composed of single electron energy (Landau energy) neglecting the Coulomb interactions between electrons, classical Coulomb energy and the quantum energy via quantum transitions. Herein, the sum of the Landau energy and the classical Coulomb energy depends upon the value of the filling factor continuously. However, the quantum transition energy discontinuously depends upon the value of the filling factor . This discontinuity yields energy gaps in many stable FQH states. The energy gaps for specific filling factors produce the precise confinement of Hall resistance. A new experiment is considered as follows; the magnetic strength is fixed to the value to confine the Hall resistance at the filling factor of 2/3 as an example. Moreover the magnetic modulation with frequencyf is applied to the system. The frequency dependence of the diagonal resistance is measured. Then, it is shown in this paper that the diagonal resistance varies drastically at some frequency valuef 0 . We clarify the following relation between this value f 0 and the magnetic strength width dB of Hall plateaus as f 0 = e dB / (4 Pi m), where -e is the charge of electron, Pi =3.14 1592, and m is the mass of electron. 1. Introduction Precise experiments have been carried out in ultra-high-mobility samples [1, 2], and then many local minima of diagonal resistivity xx were discovered at filling factors ν=3