Application of High Magnetic Fields in Semiconductor Physics by G. Landwehr

By G. Landwehr

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The ∆χor (T )/χor (T ) clearly shows the dependence given by Eq. (2) at low magnetic field and one given by Eq. 5 T the temperature dependence of χor (T )/χor (T ) differs from those two limits. As seen from Fig. , 1983). 5 T a crossover from the two-dimensional IE correction to the three-dimensional one takes place. At lower magnetic field the interaction length LIE (T ) is much shorter than the magnetic length LB , which in turn becomes dominant at high field. 5 T. A similar dependence of ∆χor (T )/χor (T ) was observed for arc-MWNTs after bromination (Fig.

The solid lines are fits for (d) by Eq. 1. 1983). , 1981): ∆σ(B) = ∆σWL (B) + ∆σIE (B). (5) Here ∆σWL (B) is the quantum correction to magnetoconductance for noninteracting electrons; ∆σIE (B) - the quantum correction to the magnetoconductance for interacting electrons. Both corrections have the logarithmic asymptotic in high magnetic fields (∆σWL (B) ≈ ln(Lϕ /LB ); ∆σInt (B) ≈ ln(LIE / LB ) at Lϕ /lB ; LIE /LB >> 1), and the quadratic asymptotic in low magnetic fields (∆σWL (B) ≈ B2 ; ∆σIE (B) ≈ B2 when Lϕ /LB ; LIE /LB << 1).

Besides, the summation involves the electron–vibrational molecular states Mα. Based on the Eqs. (1) and (15), one obtains P˙ Lkσk (t) = − NLkσk NLkσk × [Ka→b Pa (t) − Kb→a Pb (t)] . {NLk σ k (17) } NLkσk {NRqσq } Mα Similarly, one derives a kinetic equation for the molecular occupancy P(M, t). The equation reads ˙ P(M, t) = − [Ka→b Pa (t) − Kb→a Pb (t)] . {NLkσk } {NRqσq } (18) α The precise form of kinetic equations (17) and (18) can be obtained if one specifies the form of the multi–electron distribution function Pa (t).

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