Quantum hall effect in a wide parabolic quantum well

Abstract

We i n vestigate the activated conductivity for Landau levels at lling factors =1,2 in a parabolic AlxGa1,xAs well down to 30 mK. We obtain a very small activation energy 0.02 meV, which i s almost 1-2 orders of magnitude smaller than the expected values for energy gaps in a wide quantum well. The resistivity minima vanish completely when a parallel component of magnetic eld is applied. The collapse of the energy gaps in the wide parabolic well occurs due to the new electron correlated state, probably the charge density w ave state predicted for a uniform wide electron slab in high magnetic eld. I IntroductionThe Quantum Hall e ect QHE is characterized by narrow resistivity peaks separated by deep minima 1 . These resistivity minima arise due to the localization of the electron states at the Fermi energy, when it lies in the gaps between Landau or spin split levels. In this regime the resistivity is determined by the electron thermal activation with an energy gap h! c where ! c =eB m c -cyclotron frequency for Landau levels and g B 2 for spin split levels. Here is the Bohr magneton, g is the e ective Lande factor, which is strongly enhanced in a two-dimensional electron gas due to the electron-electron interactions. The temperature dependence of the resistivity minima can therefore be used to study energy gaps in the quantum Hall e ect. Several experiments have been performed to study the exchange enhanced Landau and spin splitting 2 , composite Fermions cyclotron energy 3 and skyrmions 4 . In a conventional picture the quantum Hall e ect is predicted to disappear for a su ciently wide quantum well. Fig.1 shows the energy spectrum as a function of magnetic eld B for a wide square quantum well. At su ciently high B the Fermi energy crosses the energy levels corresponding to the lowest Landau level of each subband. Therefore, it is expected that for a wide quantum well the last resistivity minima could be due to the energy gap between electric subbands, and not to Landau levels. In a real system the energy levels will have nite widths because of the disorder, therefore the last resistivity minima disappear for a su ciently thick l a yer, when corresponding electric subbands overlap. However, the magnetoresistance should show oscillations as the Fermi energy crosses degenerated Landau subbands. A three dimensional electron gas 3DEG in the presence of a strong magnetic eld is also expected to show i n teresting properties. It has been predicted a charge-density w ave or a Wigner crystal at high magnetic elds for such a system 5 . However, in doped three dimensional semiconductors the electron impurity i n teraction is very strong and can destroy these exotic ground states. The system which can be used in order to study the evolution of states of a quasi-two-dimensional toward a three dimensional behavior is a wide partially lled parabolic quantum well. Considerably larger mobility in comparison with conventional bulk three dimensional electron gas has been achieved by removing the dopant atoms from the quantum well ...

Coexistence of a two- and three-dimensional Landau states in a wide parabolic quantum well

“…6͑a͒, which leads to the recovery of the 2D Landau levels at strong field and, finally, to the formation of the quantum Hall effect in a parabolic quantum well. 15 The Landau fan chart shows that one should observe exactly six minima after the last spin-up 3D level, and the last minima correspond to the gap between the lowest and second subbands at zero magnetic field. 15 It is worth noting that the positions of the minima and maxima in a strong magnetic field do not reflect the separation of the levels but their degeneracy; 1 therefore, the positions of the gaps in the Landau fan chart do not correspond to positions of the minima in R xx shown in Fig.…”

“…The parallel magnetic field leads to a shifting of the electron wave function from the center of the well and, consequently, to a bending of the well bottom at the edge of the well. Taking into account the first-order correction to the energy we can obtain the following expression for the energy of each subband in the symmetric square quantum well: 12 E͑k x ,k y ͒ϭ…”