Quantum Hall Effect in GaAs/AlGaAs Semiconductor Superlattice
Minoru Kawamura
Doctoral Thesis, University of Tokyo (2001)
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Note: Doctoral Thesis, University of Tokyo
A two-dimensional electron gas (2DEG) exhibits the quantum Hall effect (QHE) when it is placed under a strong perpendicular magnetic field. As two-dimensionality is a prerequisite for the occurrence of the QHE, it is interesting to ask what happens when a degree of freedom for the motion perpendicular to the two-dimensional plane is introduced. This issue has been addressed theoretically and experimentally since the early stage of QHE research. Experimentally, St\"{o}rmer {\it et al.} first demonstrated that the quantized Hall resistance and the vanishing diagonal resistivity is observed
in a semiconductor superlattice.
In a quantum Hall phase, electronic states at the Fermi energy are Anderson localized. The localization length diverges as the Fermi energy approaches the center of the Landau subband. The exponent of the diverging localization length
depends on the dimension of the system. In the case of semiconductor superlattice, the electronic states at the center of Landau level have a certain degree of three-dimensionality because of the dispersion relation along the growth direction. Therefore, in the semiconductor superlattice, the critical behavior near the center of Landau level is expected to differ from that in a single layer 2DEG.
The QHE in semiconductor superlattice has recently attracted renewed interest triggered by the theoretical prediction of the chiral surface state. In an isolated 2DEG in the quantum Hall state, all the bulk states at the Fermi level
are localized so that the Hall current is carried by the edge channels. These edge channels are free from backscattering because of their chirality. For the integer quantum Hall state, the edge states are described in terms of chiral Fermi liquid. When the interlayer transfer is introduced, the edge states in different layers are coupled to form a conducting surface state. The existence of the chiral surface state was first demonstrated experimentally by Druist {\it et al.}
The experimental attempt to explore some aspects of the QHE in GaAs/AlGaAs semiconductor superlattice is described in this thesis. The paper is organized as follows. After a brief introduction of QHE, theoretical backgrounds of QHE in three-dimensional systems and related experiments are reviewed in chapter 1.
In chapter 2, the experimental procedure for sample fabrication and low-temperature measurement is described. Our experimental attempt to investigate the critical behavior in semiconductor superlattice is described in chapter 3.
The vertical transport of semiconductor superlattice in the quantum Hall regime
is described in chapter 4. A distinct non-Ohmicity and a large transverse magnetoresistance of the chiral surface state are discussed there.
Finally, concluding remarks are described in chapter 5.