Fluctuation phenomena in chaotic Dirac quantum dots: Artificial atoms on graphene flakes

We develop the stub model for the Dirac quantum dot, an electron confining device on a grapheme surface. Analytical results for the average conductance and the correlation functions are obtained and found in agreement with those found previously using semiclassical calculation. Comparison with available data is presented. The results reported here demonstrate the applicability of random matrix theory in the case of Dirac electrons confined in a stadium.

Figure 1

Diffuson (left) and cooperon (right) diagrams for the average of conductance [Eq. (7)].

Figure 2

(a) Equation (16) is plotted as a function of the magnetic flux for ${\mathcal{W}}_{st}=0,0.5,1,3$ (from top to bottom). (b) Equation (17) is plotted as a function of the magnetic flux for ${\mathcal{W}}_{ac}=0,1,\infty$ (from bottom to top). (c) Equation (18) is plotted as a function of the magnetic flux for $\mathcal{M}=0,1,\infty$ (from top to bottom) and ${\mathcal{W}}_{zz}={\mathcal{W}}_{st}=0$.

Figure 3

(a) Equation (19) was plotted (top to down) for ${\mathcal{W}}_{st}=0,0.5,\infty \left({\mathcal{W}}_{ac}={\mathcal{W}}_{zz}=\mathcal{M}=0\right)$ beyond Eq. (20) for ${\mathcal{W}}_{ac}=0.5,\infty$. (b) Equation (19) is plotted (top to down) for $\mathcal{M}=0.5,\infty \left({\mathcal{W}}_{st}={\mathcal{W}}_{ac}={\mathcal{W}}_{zz}=0\right)$ and Eq. (21) for ${\mathcal{W}}_{ac}=0.5,\infty \left({\mathcal{W}}_{st}=0\right)$. (c) Equation (19) was plotted (top to down) for ${\mathcal{W}}_{ac}=0.5,\infty \left({\mathcal{W}}_{st}=\mathcal{M}={\mathcal{W}}_{zz}=0\right)$ beyond Eq. (22) for $\mathcal{M},{\mathcal{W}}_{zz}=0.5,\infty \left({\mathcal{W}}_{st}=0\right)$.

Figure 4

Typical Lorentzian (left) and quadratic Lorentzian correlation function from Eq. (23) for (top to down) all parameters null, $\{\mathcal{X},\mathcal{M},{\mathcal{W}}_{ac},{\mathcal{W}}_{zz}\to \infty \}$ and ${\mathcal{W}}_{st}\to \infty$.