It is rigorously proved that the Green's function of a uniform two-dimensional interacting electron gas in a perpendicular magnetic field is diagonal with respect to single-particle states in the Landau gauge. The implication of this theorem is briefly discussed. \textcopyright{} 1996 The American Physical Society.
In this work we introduce a bosonization scheme for the low-energy excitations of a two-dimensional interacting electron gas in the presence of a uniform magnetic field under conditions where a large integral number of Landau levels are filled. We give an explicit construction for the electron operator in terms of the bosons. We show that the elementary neutral excitations, known as the magnetic excitons or magnetoplasma modes, can be described within a bosonic language and that it provides a quadratic bosonic Hamiltonian for the interacting electron system that can be easily diagonalized.
This chapter presents the microscopic theory of a two-dimensional (2D) electron gas based on an ab initio functional approach to the many-body problem developed by V. A. Khodel et al. and V. R. Shaginyan. It discusses the detailed structure of the theory and scheme of the numerical solution of relevant equations. The chapter also discusses the method of evaluation of the single-particle spectrum of a 2D electron gas. It examines the behavior of a 2D electron gas in external magnetic fields. The chapter focuses on the disappearance of magnetic oscillations in electron systems of metal-oxide-semiconductor field-effect transistors due to merging of spin- and valley-split Landau levels in silicon, being the topological rearrangement of the Landau state, analogous to the formation of the fermion condensate. It explores the impact of the violation of the equidistance of electron spectra in strong magnetic fields on the structure of magnetic oscillations near the critical density.
Abstract Understanding the quantum problem of a free charged particle undergoing two-dimensional motion in a perpendicular uniform, constant magnetic field is necessary to the comprehension of some very important phenomena in physics. In particular, a grasp of the nature of the Landau states in a symmetric gauge is crucial to explain the underlying principles of quantum Hall effects. In this work we provide a step-by-step solution of this quantum problem in a pedagogical fashion that is easy to follow by an audience of undergraduate students and prospective physics teachers. This approach should enable undergraduate students to comprehend all the technical mathematical details involved in the process. Such details are routinely missing from mainstream quantum mechanics textbooks. In particular, this study allows a broad audience of students and teachers to gradually absorb knowledge not only on basic principles of quantum mechanics, but also on various special mathematical functions that are encountered in the process.
Using a path integral approach and bosonization, we calculate the low-energy asymptotics of the one particle Green's function for a "magnetically incoherent" one dimensional strongly interacting electron gas at temperatures much greater than the typical exchange energy but much lower than the Fermi energy. The Green's function exhibits features reminiscent of spin-charge separation, with exponential spatial decay and scaling behavior with interaction dependent anomalous exponents inconsistent with any unitary conformal field theory. We compute the tunneling density of states at low energies and find that it is a power law in energy with exponent 1/(4g)-1, where g is the Luttinger interaction parameter in the charge sector. The underlying physics is made transparent by the simplicity of the approach. Our results generalize those of Cheianov and Zvonarev [Phys. Rev. Lett. 92, 176401 (2004)]].
This is a mathematical study of certain aspects of the interacting electron system in very high perpendicular magnetic field.\nWe analyse restrictions imposed upon the density correlation functions of this system and propose a set of sum rules which they must obey.\nWe study the possibility of building a bosonisation scheme for the projected density operators in the lowest Landau level. We suggest a second order bosonisation, along with an approximation scheme, which may be useful for carrying out calculations in the lowest Landau level.\nWe analyse the possible ground states of the system. We suggest a set of variational wavefunctions which can have lower energy than the Laughlin state for sufficiently soft interaction potentials.\nWe study the collective excitations of the system, paying particular attention to its symmetries. We suggest a set of variational excited states and discuss their applicability to finite as well as infinite systems.