J. Phys. I France
Volume 7, Numéro 6, June 1997
Page(s) 807 - 820
DOI: 10.1051/jp1:1997194
J. Phys. I France 7 (1997) 807-820

Orbital Maghetism in Two-Dimensional Integrable Systems

E. Gurevich and B. Shapiro

Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel

(Received 5 January 1997, received in final form 11 February 1997, accepted 19 February 1997)

We study orbital magnetism of a degenerate electron gas in a number of two-dimensional integrable systems, within linear response theory. There are three relevant energy scales: typical level spacing $\Delta$, the energy $\Gamma$, related to the inverse time of flight across the system, and the Fermi energy $\varepsilon_{\rm F}$. correspondingly, there are three distinct temperature regimes: microscopic ( $T\ll \Delta$), mesoscopic ( $\Delta \ll T\lesssim \Gamma$)and macroscopic ( $\Gamma \ll T \ll \varepsilon_{\rm F}$). In the first two regimes there are large finite-size effects in the magnetic susceptibility $\chi$, whereas in the third regime $\chi$ approaches its macroscopic value. In some cases, such as a quasi-one-dimensional strip or a harmonic confining potential, it is possible to obtain analytic expressions for $\chi$ in the entire temperature range.

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