The Theory Group

Physics in High Magnetic Fields

I.D.Vagner

Grenoble High Magnetic Field Laboratory (CNRS-MPI)
166X, F-48042, Grenoble, Cedex 9, France.
Tel: +33-4-76-88-11-27; Fax: +33-4-76-85-56-10.
E-Mail: vagner@labs.polycnrs-gre.fr

Physics and Engineering Research Institute (P.E.R.I.)
Ruppin Instutute for Higher Education
Emek Hefer 40250, Israel.
Tel: (+972)-9898-1340, (+972)-9898-3042;
Fax: (+972)-9898-6848
E-mail: perinst@netvision.net.il


2D de Haas-van Alphen effect

An analytical theory for the magnetisation and susceptibility of the electron gas in two-dimensional systems is developed in series of papers [1],[2],[5]. This theory is aimed to replace the standard Landau -Lifshitz - Kosevich theory, applicable only for the three-dimensional electron systems. This theory has stimulated recent experimental studies of 2D dHvA in synthetic metals (see and references therein).

  1. Magnetization of a two-dimensional electron gas
  2. Strong Coulomb Correlations and Lattice Effect on dHvA Oscillations

1. Magnetization of a two-dimensional electron gas

The great success of the de Haas-van Alphen effect in three dimensional conductors is due to the existence of a well developed theory, which provides a quantitative basis (the Lifshitz-Kosevich formula (LK)) for the determination of complicated Fermi surfaces of metals. In the two dimensional case we still do not have such a general and useful formula to analyse the experimental data. The qualitative difference between the 3D- and 2D- dHvA effect follows from the fact, that in the isotropic case the Fermi surface crosses a large number of Landau tubes. In a 2D electron gas, however, the Landau levels just below and just above the Fermi energy dominate the magnetic field dependence of the chemical potential which "jumps", periodically, between the adjacent Landau levels. The LK-theory is based on the assumption of the field-independent chemical potential and is not operative, therefore, in 2D electronic systems.

1.1 Magnetization oscillation envelope

As a step toward the theory of the 2D- dHvA we have obtained an analytical expression for the magnetization oscillations envelope in the limiting case of sharp Landau levels and made a detailed comparison with the numerical calculation, presented in Fig. 2.2.

Unlike in the LK theory we have not used the Poisson summation formula, which is not operative in the two-dimensional case at low enough temperatures hwc>> kBT. In the high field limit the agreement is very good. In the low field limit the Landau level broadening can not be neglected, and one may use the Shoenberg theory to calculate the magnetization envelope. Inclusion of the Landau level width, finite density of states between the Landau levels and of the kz - dispersion is in progress.

1.2 The reservoir model

According to the Peierls theory, the de Haas-van Alphen oscillations should have a saw-tooth form in an ideal two-dimensional electron gas when the chemical potential is pinned to a Landau level during the entire de Haas-van Alphen period (constant number of carriers) or when an infinite reservoir of carriers exists (fixed chemical potential). Recent experiments indicate that neither of these conditions are fulfilled, during a single period in AsF5, intercalated graphite.

Motivated by these experimental observations we have designed a model where the intercalant acts as a finite reservoir. In our model, AsF5-GIC can be thought of as a set of capacitors with positively charged graphite layers and negatively charged intercalant layers, which allows relatively free charge transfer when the chemical potential is within the Landau gap. This results in a triangular form of the magnetization oscillations. In realistic experimental conditions the triangular shape of the magnetization should smear out into an almost harmonic form, which is close to the experimental observations on As5-GIC. Numerical solution of the transcendental equation, describing this model, is presented in Fig. 2.3.

2. Strong Coulomb Correlations and Lattice Effect on dHvA Oscillations

The combined effect of strong Coulomb correlations and lattice effect on dHvA oscillations is studied. These effect enhance the effective mass and may strongly influence the amplitude and the frequency of magnetizaition oscillation.

Lattice effects

When the electron motion in the magnetic field is restricted by an underlying lattice, the electronic states in a band may split, under sufficiently strong fields, into a series of magnetic subbands called Hofstadter spectrum ,Fig.4.7.

Coulomb interactions

Coulomb correlations renormalize the Hofstadter specturm by narrowing the overall width of the specturm and by shifting the band center upward in energy as the filling fraction is increased, Fig. 4.8. The effective mass, therefore, increases as half filling is approached.

Both the srong Coulomb correlations and the lattice effect enhance the electron mass as function of the filling fraction. Strong Coulomb correlations, for example, lead to the Mott-Hubbard insulator at half filling, where the effective mass diverges via Brinkman-Rice localization. The lattice effect, on the other hand, enhances the effective mass as the van Hove singularity is approached.

Magnetization oscillations

In two dimensions, oscillation in thermodynamic properties have a sharp, saw-tooth, magnetic field behavior. In the absence of the underlying lattice, the oscillation are periodic with the inverse of magnetic field, as a consequence of the equidistant Landau levels. For a series of magnetic subbands (Hofstadter spectrum) one should include the uneven energy gap between neighboring subbands, Fig. 4.9.

Electron- phonon intractions

Coulomb correlation tend to suppres charge fluctuations, thereby reducing the electron-phonon coupling constant as the metal-insulator transition is approached. We have studied the influence of electron phonon interactions, in presence of both: the correlation and the lattice effects, on dHvA. Our approach is based on almost localized Fermi liquid theory. For simplicity, we use the one-band Hubbard Hamiltonian on a square lattice. Strong Coulomb correlations are treated in the infinite U limit by the slave boson technique (see figure 4.10).

Inclusion of the spin dependent interactions and the electron-electron self energy effects into the theory of the dHvA effect is in progress, as well as the study the effects of the coherent and the incohnerent quasiparticle spectal weights on the Fermi surface.


  1. I.D. Vagner, T.Maniv and E. Ehrenfreund ''Ideally Conducting Phases in Quasi Two-Dimensional Conductors.'' Phys. Rev. Lett. 51, 1700 (1983).
  2. I.D. Vagner and T. Maniv ''Spikes in the Orbital Magnetic Susceptibility of a 2D Electron Gas''. Phys. Rev. B, 32, 8398 (1985).
  3. I. D. Vagner, T. Maniv, W. Joss, J.M. van Ruitenbeek et K. Jauregui ''Theory of the de Haas-van Alphen Effect in Quasi-Two-Dimensional Conductors'', Synth. Met. 34, 393 (1989).
  4. W. Joss, J.M. van Ruitenbeek, I.D. Vagner, F.Jost, F.Rachdi and S. Roth ''Electronic Structure of AsF5 Intercalated Graphite From De Haas-van Alphen Measurements'' Synth. Met. 34, 381 (1989).
  5. K. Jauregui, V.I. Marchenko and I.D. Vagner ''Magnetization of Two-Dimensional Electron Gas.'' Phys. Rev. B.41, 129222 (1990).
  6. K. Jauregui, W. Joss, V.I. Marchenko, S.V. Meshkov and I.D. Vagner ''Magnetization of a two-dimensional electron gas with broadened Landau levels'', In: High Magnetic Fields in Semiconductor Physics III, 101, 668 (1992); Ed. G. Landwehr, Springer-Verlag Berlin Heidelberg.
  7. Ju H. Kim and I.D. Vagner ''Strong Coulomb Correlation and Lattice Effects on the de Haas - van Alphen Oscillations.'' Phys. Rev. B 48, 16564 (1993).
  8. A.M. Dyugaev, I.D. Vagner and P. Wyder ''Theory of the de Haas-van Alphen effect in dopped semiconductors.'' JETP Lett. 63, 195 (1996).
  9. M. Itskovsky, T. Maniv and I.D. Vagner ''De Haas van Alphen effect in two-dimensional conductors: Susceptibility oscillations.'' Zeitschrift für Physik, B101, 13 (1996).



Main Page Visitors Projects Links




Last updated 19-Jan-01.
WebMaster AK