Quantum magneto-optics of graphite with trigonal warping

The optical conductivity of graphite in quantizing magnetic fields is studied. Both the dynamical conductivities, longitudinal as well as Hall's, are analytically evaluated. The conductivity peaks are explained in terms of electron transitions. We have shown that the trigonal warping in graphite can be considered within the perturbation theory at strong magnetic fields larger than approximately 1 T. The main optical transitions obey the selection rule with $\Delta n=1$ for the Landau number $n$, however, the $\Delta n=2$ transitions due to the trigonal warping with small probability are also essential. The Kerr rotation and reflectivity in graphite in the quantizing magnetic fields are calculated. Parameters of the Slonczewski-Weiss-McClure model are used in the fit taking into account the previous dHvA measurements and correcting some of them for the case of strong magnetic fields.

Figure 1

LLs ${\varepsilon }_{sn}$ for $n=$ 0–4 in four bands $s=1,2,3,4$ (in dotted, solid, dashed, and dash-dotted lines, correspondingly) as functions of momentum $k_z$ along the $KH$ line in the brillouin zone ($K=0,H=\pi /2d_0$) at the magnetic field $B=$ 7 T with the SWMC model parameters given in Table . The main electron transitions shown in the right panel below 100 meV are possible between the levels with the selection rule $\Delta n=\pm 1$ ; see text.

Figure 2

Diagrams for the second iteration of the perturbation theory; corrections to the Green's function (a) and corrections to the vertex in conductivity (b).

Figure 3

Real (a) and imaginary (b) parts of the longitudinal ($xx$, solid line) and Hall ($xy$, dashed line) dynamical conductivities; Kerr angle (c) and reflectivity (d). The magnetic field $B=$ 7 T; the temperature T = 0.1 meV is less than the level broadening $\Gamma =3.5$ meV.

Figure 4

Kerr angle and reflectivity at 10, 15, and 25 T.