Quantum Hall effect and cyclotron resonance in intentionally disordered two-dimensional electron systems of GaAs/GaAlAs heterostructures

Katrin Buth

The physics of two-dimensional electron systems in semiconductors is an interesting research field with fascinating phenomena like the integer and the fractional quantum Hall effect discovered in 1980 by von Klitzing et. al. and 1982 by Tsui et al., respectively. In the integer quantum Hall effect the Hall resistance exhibits so-called Hall plateaus in certain regions of the magnetic field at low temperatures. The plateaus correspond to quantized values h/ne² that depend only on natural constants, namely Planck's constant h and the elementary charge e, with an integer n. The fractional quantum Hall effect is characterized by Hall plateaus belonging to fractional filling factors n. The importance of the quantum Hall effects is underlined by two nobel prizes (1985 for von Klitzing, 1998 for Laughlin, Störmer and Tsui). Although there still exists no comprehensive theory for the two quantum Hall effects, it is certain that the integer quantum Hall effect is due to disorder, whereas the fractional quantum Hall effect arises from electron-electron interactions and can only be observed in high-mobility samples.

Fig. 1: Integer quantum Hall effect in a Be-d -doped GaAs/GaAlAs heterostructure. The dashed line is the classical Hall line.

Our samples are specifically designed modulation doped GaAs/GaAlAs heterostructures in which strong intentional disorder is provided by a d-doped layer of negatively charged beryllium acceptors. They have been grown by K. Eberl at the Max-Planck-Institut für Festkörperforschung in Stuttgart. In order to vary the electron density, gated Hall geometries are prepared by optical lithography and chemical wet etching. Magnetotransport experiments are performed at low temperatures down to 30 mK and in high magnetic fields up to 16 T in a ³He/⁴He dilution refrigerator. Spectroscopic experiments are carried out in a Fourier-transform spectrometer at liquid helium temperatures of 2 to 4 K.

The results of the magnetotransport experiments in Be-d-doped samples can be summarized as follows: In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic-field-induced delocalization. For low electron densities this effect is more pronounced. At increased magnetic fields the integer quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around n_c = 0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials.The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance.

The magnetotransport experiments are complemented with far-infrared spectroscopy. Especially investigations in the insulating phase of quantum Hall droplets profit by spectroscopy because the breakdown of the current limits transport measurements. Since Kohn's theorem is no longer valid in disordered samples we observe three distinct shapes of cyclotron resonance in different regimes of the magnetic field or filling factor (Fig. 2). In low magnetic fields, i.e. at high filling factors, an undisturbed cyclotron resonance occurs. The resonance is relatively broad due to the high degree of disorder. In intermediate fields the resonance line is split into at least two peaks: one at the cyclotron frequency w_c and a second one at a higher frequency. In high magnetic fields only the shifted resonance persists and becomes exceptionally narrow in the extreme quantum limit. The strong narrowing of the shifted resonance can be explained by the localization of electrons in quantum Hall droplets and strong electron-electron interaction that couples the individual cyclotron transitions to one hybridized line.

Fig. 2: Cyclotron resonances in a Be-d-doped sample in different regimes of the magnetic field.

The experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths.

Fig. 3: Calculated symmetric potential landscape with equal amounts of positively and negatively charged Coulomb scatterers.

Fig. 4: Situation at the percolation threshold. In order to determine the percolation threshold the electrons are poured as water into the potential landscape.

• K. Buth, M. Widmann, A. Thieme, and U. Merkt,
  Electrons in Potential Landscapes of Random and Correlated Distributions of Repulsive Scatterers,
  Semicond. Sci. Technol. 18, 434-441 (2003)
  

• K. Buth and U. Merkt,
  Quantum Hall Effect in Intentionally Disordered Two-Dimensional Electron Systems,
  Ann. Phys. (Leipzig) 11, 843-891 (2002)
  

• K. Buth,
  PhD Thesis: Quantum Hall effect in intentionally disordered two-dimensional electron systems of GaAs/GaAlAs heterostructures
  Shaker Verlag, Aachen 2002
  

• K. Buth, M. Widmann, U. Merkt, E. Batke, and K. Eberl,
  Percolation of quantum Hall droplets in intentionally disordered GaAs/GaAlAs heterojunctions,
  Physica E 12, 662-665 (2002)
  

• K. Buth, M. Widmann, U. Merkt, and K. Eberl,
  Quantum Hall effect and cyclotron resonance in disordered d -doped GaAs/AlGaAs-heterojunctions,
  Ann. Phys. (Leipzig) 8, SI 29-SI 32 (1999)
  

• M. Widmann, U. Merkt, M. Cortés, W. Häusler, and K. Eberl,
  Cyclotron resonance of interacting quantum Hall droplets,
  Physica B 249-251, 762 (1998)
  

• U. Merkt,
  Cyclotron Resonance of Localized Electron Systems in the Magnetic Quantum Limit,
  Phys. Rev. Lett. 76, 1134 (1996)