Interplay between real and pseudomagnetic field in graphene with strain

We investigate electric and magnetic properties of graphene with rotationally symmetric strain. The strain generates a large pseudomagnetic field with alternating sign in space, which forms a strongly confined quantum dot connected to six chiral channels. The orbital magnetism, degeneracy, and channel opening can be understood from the interplay between the real and pseudomagnetic fields which have different parities under time reversal and mirror reflection. While the orbital magnetic response of the confined state is diamagnetic, it can be paramagnetic if there is an accidental degeneracy with opposite mirror reflection parity.

Figure 1

The vertical displacement of our considered systems in the text (a) and the pseudomagnetic fields (b). The radius is $R=100$ nm and the height is $h_0=20$ nm.

Figure 2

The eigenenergies as a function of the system size $L$. We set $R=100$ nm and $h_0=20$ nm. Note that at a certain energy (marked by an arrow), the eigenenergy becomes insensitive to the system size $L$.

Figure 3

(a) Probability densities of the localized wave functions $|{\psi }_{A,K}{\left(\mathbf{r}\right)|}^2$ and (b) $|{\psi }_{B,K}{\left(\mathbf{r}\right)|}^2$. We set $R=100$ nm, $h_0=20$ nm. (c) Classical closed orbits of a charged particle in the inhomogeneous magnetic field given by $B_{\mathit{ps}}$ which resemble the probability density of the localized states shown in (a) and (b). (d) Classical paths describing three outgoing channels.

Figure 4

(a) A detailed energy spectra as a function of the system size $L$ which shows crossing and avoided crossing. (b) The orbital magnetic response $-\frac{\partial E}{\partial B}$ of localized states. Mostly the magnetic response is diamagnetic $-\frac{\partial E}{\partial B}<0$ but the response for a level crossing point (indicated by the dotted line) shows a paramagnetic response (positive value). We set $R=100$ nm and $h_0=20$ nm.