TY - JOUR

T1 - Microscopic analytical theory of a correlated, two-dimensional N-electron gas in a magnetic field

AU - Johnson, Neil F.

AU - Quiroga, Luis

PY - 1997/7/7

Y1 - 1997/7/7

N2 - We present a microscopic, analytical theory describing a confined N-electron gas in two dimensions subject to an external magnetic field. The number of electrons N and strength of the electron-electron interaction can be arbitrarily large, and all Landau levels are included implicitly. For any value of the magnetic field B, the correlated N-electron states are determined by the solution to a universal effective problem which resembles that of a fictitious particle moving in a multi-dimensional space, without a magnetic field, occupied by potential minima corresponding to the classical N-electron equilibrium configurations. Introducing the requirement of total wavefunction antisymmetry selects out the allowed minimum-energy N-electron states. It is shown that low-energy minima can exist at filling factors v = p/(2n + 1) where p and n are any positive integers. These filling factors correspond to the experimentally observed fractional (FQHE) and integer (IQHE) quantum Hall effects. The energy gaps calculated analytically at v = p/3 aie found to be consistent with experimental data as a function of magnetic field, over a range of samples.

AB - We present a microscopic, analytical theory describing a confined N-electron gas in two dimensions subject to an external magnetic field. The number of electrons N and strength of the electron-electron interaction can be arbitrarily large, and all Landau levels are included implicitly. For any value of the magnetic field B, the correlated N-electron states are determined by the solution to a universal effective problem which resembles that of a fictitious particle moving in a multi-dimensional space, without a magnetic field, occupied by potential minima corresponding to the classical N-electron equilibrium configurations. Introducing the requirement of total wavefunction antisymmetry selects out the allowed minimum-energy N-electron states. It is shown that low-energy minima can exist at filling factors v = p/(2n + 1) where p and n are any positive integers. These filling factors correspond to the experimentally observed fractional (FQHE) and integer (IQHE) quantum Hall effects. The energy gaps calculated analytically at v = p/3 aie found to be consistent with experimental data as a function of magnetic field, over a range of samples.

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U2 - 10.1088/0953-8984/9/27/018

DO - 10.1088/0953-8984/9/27/018

M3 - Article

AN - SCOPUS:0342984105

VL - 9

SP - 5889

EP - 5920

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 27

ER -