Article

# Density modulation and electrostatic self-consistency in a two-dimensional electron gas subject to a periodic quantizing magnetic field

Physical Review B (Impact Factor: 3.74). 10/1997; 57(3). DOI: 10.1103/PhysRevB.57.1680

Source: arXiv

**ABSTRACT**

We calculate the single-particle states of a two-dimensional electron gas (2DEG) in a perpendicular quantizing magnetic field, which is periodic in one direction of the electron layer. We discuss the modulation of the electron density in this system and compare it with that of a 2DEG in a periodic electrostatic potential. We take account of the induced potential within the Hartree approximation, and calculate self-consistently the density fluctuations and effective energy bands. The electrostatic effects on the spectrum depend strongly on the temperature and on the ratio between the cyclotron radius $R_c$ and the length scale $a_{\delta\rho}$ of the density variations. We find that $a_{\delta\rho}$ can be equal to the modulation period $a$, but also much smaller. For $R_c \sim a_{\delta\rho}$ the spectrum in the vicinity of the chemical potential remains essentially the same as in the noninteracting system, while for $R_c \ll a_{\delta\rho}$ it may be drastically changed by the Hartree potential: For noninteger filling factors the energy dispersion is reduced, like in the case of an electrostatic modulation, whereas for even-integer filling factors, on the contrary, the dispersion may be amplified. Comment: 9 pages, 6 figures, Revtex, to appear in Phys. Rev. B

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**ABSTRACT:**The energy spectra of spin-1/2 electrons under two-dimensional magnetic field modulations are calculated beyond the one-band approximation. Our formulation is generally applicable to a modulation field with a rectangular lattice symmetry. The field distribution within a plaquette is otherwise arbitrary. The spectra being obtained are qualitatively different from their electric-modulated counterparts. Peculiar features of the spectra are that, for an electron with a g factor precisely equal to 2, no matter how strong the modulation is, the zero-energy level seems to be unaffected by the modulation and is separated from higher energy levels with a nonzero energy gap. Moreover, there is a twofold degenerancy for all states with positive energies with respect to spin flip. These features agree with earlier analytical studies of the periodically magnetic-modulated systems. - [Show abstract] [Hide abstract]

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**ABSTRACT:**We calculate the quantum states corresponding to the drifting and channeled classical orbits in a two-dimensional electron gas (2DEG) with strong magnetic and electric modulations along one spatial direction, $x$. The channeled states carry high, concentrated currents along the $y$ axis, and are confined in an effective potential well. The quantum and the classical states are compared. Comment: 8 pages with 4 included ps figures, contribution to "SemiMag 13" Nijmegen, August 1998, to appear in Physica B