Movement of diagonal resistivity in fractional quantum hall effect via periodic modulation of magnetic field strength

Abstract

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 frequency f 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 value f 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 =3.141592, and m is the mass of electron.for the Hall device used in reference [1]. Drastic increment of diagonal resistanceWe consider a new experiment as:(1) The magnetic field strength is fixed to maintain the FQH state with ! " = 2 3.(2) A periodic magnetic modulation is added to the system. The frequency value is ! f . (3) The diagonal resistance ! R xx is measured. Then the value of ! R xx depends upon the oscillation frequency ! f . The behaviour of ! R xx versus ! f is predicted as shown in figure 3.

Gap Structure and Gapless Structure in Fractional Quantum Hall Effect

“…We have used the term "energy gap" for the gap in the spectrum of energy versus filling factor in the previous sections. This gap produces the plateau in the Hall resistance curve [18][19][20][21][22][23]. There is another gap which indicates the minimum value of all excitation energies from the ground state to excited states with the same filling factor ν.…”

Fractional Quantum Hall States for Filling Factors 2/3 < <i>ν</i> < 2

“…These energy gaps can explain the fractional quantum Hall effect in the region 1 2 ν < < as clarified in the following sections. (We have already succeeded to obtain the energy gaps for the specific filling factors in the regions 1 ν < and 2 ν > in the previous articles [20]- [30].) Figure 1 shows a quantum Hall device where the electric current flows along the x-axis and the Hall voltage appears along the y-axis.…”

Proposal on Tunneling Effect between Quantum Hall States

“…The present author has developed a theory based on the electron pair to explain the fractional quantum Hall effect [15][16][17][18][19][20][21]. The Coulomb interaction acts between electron pair and depends upon only the relative coordinate.…”

“…Therefore the total momentum of the interacting electron pair conserves along the x-direction of Figures 2-4 via the Coulomb transition. The electron pair has a large binding energy at the specific filling factors where the number of the allowed Coulomb transitions becomes maximum [15][16][17][18][19][20][21]. Then the binding of the electron pairs is so strong that the pairing is expected to be held in the tunneling process.…”