Pseudospin in Optical and Transport Properties of Graphene

We show that the pseudospin, being an additional degree of freedom for carriers in graphene, can be efficiently controlled by means of the electron-electron interactions which, in turn, can be manipulated by changing the substrate. In particular, an out-of-plane pseudospin component can occur leading to a zero-field Hall current as well as to polarization-sensitive interband optical absorption.

Figure 1

The pseudospin out-of-plane angle $\vartheta (k)$ for different environments numerically calculated from Eq. (3). The corresponding values of the substrate-dependent effective fine structure constant ${\alpha }^{*}$ are taken from Ref. 6. The inset shows the total ground state energy difference (4) between the in-plane and out-of-plane phases for different effective fine structure constants ${\alpha }^{*}=e^2/\epsilon \hslash v_0$. Increasing ${\alpha }^{*}$ makes the out-of-plane phase preferable.

Figure 2

The dispersion law $E_{\kappa }(k)$ in the in-plane (dashed curves) and out-of-plane (solid curves) phases for ${\alpha }^{*}=0.8$ corresponding to the ${\mathrm{SiO}}_2$ substrate [6]. The curves for both phases coincide for momenta larger than a certain critical value where ${\vartheta }_k=\pi /2$ becomes independent of $k$; see Fig. 1. The inset shows the gap region in detail.