Publication

The nature of the spectrum for a Landau hamiltonian with delta impurities

Nicolas Macris
1997
Journal Articles

Abstract

We consider a single-band approximation to the random Schr6dinger operator in an external magnetic field. The random potential consists of delta functions of random strengths situated on the sites of a regular two-dimensional lattice. We characterize the entire spectrum of this Hamiltonian when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level in the absence of a random potential being infinitely degenerate, while the eigenfunctions corresponding to energies in the rest of the spectrum are localized.

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https://infoscience.epfl.ch/entities/publication/838dcffd-a02c-4d68-b253-ada86f21b329

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Nicolas Macris
1997
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/838dcffd-a02c-4d68-b253-ada86f21b329

About this result

Related concepts (32)

Magnetic field

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets.

Landau quantization

In quantum mechanics, Landau quantization refers to the quantization of the cyclotron orbits of charged particles in a uniform magnetic field. As a result, the charged particles can only occupy orbits with discrete, equidistant energy values, called Landau levels. These levels are degenerate, with the number of electrons per level directly proportional to the strength of the applied magnetic field. It is named after the Soviet physicist Lev Landau. Landau quantization is directly responsible for the electronic susceptibility of metals, known as Landau diamagnetism.

Magnetic moment

In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets), permanent magnets, elementary particles (such as electrons), composite particles (such as protons and neutrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc).

Related publications (5)

The nature of the spectrum for a Landau hamiltonian with delta impurities

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Two-dimensional magnetic materials from first principles

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