Abstract
Herein, the collective effects of spin polarization in a degenerate electron gas of an arbitrary space dimension are discussed. We consider these low-dimensional systems in light of potential wells (rectangular or cylindrical), and as a two- or one-dimensional oscillator system with the second (and third) spatial dimension proportional to the oscillator’s length. The concept of “intermediate” sizes ν = 6, 5, 4 corresponding to the quasi-low dimensions ν* = 0, 1, 2, contrary to “pure” space dimensions ν = 1, 2 is introduced. A general effect of the space dimension upon the spontaneous polarization in electron Fermi gas is detected.
Highlights
During the last decade, the ground state of a low-dimensional electron system has been the object of intensive study [1,2,3]
The establishment of an equilibrium spin polarization is a result of the competition of two main contributions: (i) Non-force exchange, which is a consequence of the Pauli exclusive principle, due to which the kinetic energy of a Fermi gas increase when spins are unpaired because free particles should occupy higher single-particle states; (ii) a Coulomb exchange interaction directly causing a decrease of unpaired spins energy
A system of electrons whose motion is free only in two spatial dimension and whose motion in the second and third dimensions corresponds to a discrete energy spectrum is called the
Summary
The ground state of a low-dimensional electron system has been the object of intensive study [1,2,3]. A high mobility spin-polarized two-dimensional electron gas has been obtained in dilute magnetic semiconductor heterostructures such as Cd1−x Mnx Te/Cd1−y Mgy Te n-type modulation doped quantum wells [24] It has been investigated by electron Raman spectroscopy [25,26,27,28]. The oscillator’s length corresponds to the real width of the sample in the experiment, whereas the frequency ω is a mean value, determined by the size of the sample Such an electron-trapping model allows us to manipulate with the space dimension by changing the external field frequency ω in the case of cluster systems or by varying the depth aosc of nanowire or nanofilms used for nanosensors. Such a representation of these main parameters will be useful for consideration of polarized states of the electron Fermi gas accounting for particle interaction
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