Electronic states in a bilayer graphene quantum ripple

Abstract

In this paper, we investigate the influence of the geometry in the electronic states of a quantum ripple surface. We have considered an electron governed by the spinless stationary Schrödinger equation constrained to move on the ripple surface due to a confining potential from which the Da Costa potential emerges. We investigate the role played by the geometry and orbital angular momentum on the electronic states of the system.

Figures (7)

• Figure 1: Quantum ripple coordinate system and some configurations
• Figure 2: Plots of the da Costa potencial for the quantum Gaussian ripple. In the left panel we have considered $b=1$ and three values of $A$, namely $A=1$, $A=2$ and $A=3$. In the right panel we have considered $A=1$ and three values of $b$, namely, $b=1$, $b=2$ and $b=3$.
• Figure 3: Plots of the effective mass of the electron on the quantum Gaussian ripple. In the left panel we have considered $b=1$ and three values of $A$, namely $A=1$, $A=2$ and $A=3$. In the right panel we have considered $A=1$ and three values of $b$, namely, $b=1$, $b=2$ and $b=3$.
• Figure 4: Gaussian curvature for the Gaussian-like ripple. In the left panel we have considered $b=1$ and three values of $A$, namely $A=1$, $A=2$ and $A=3$. In the right panel we have considered $A=1$ and three values of $b$, namely, $b=1$, $b=2$ and $b=3$.
• Figure 5: Plots of the effective potential $\bar{V}_{eff}$ for the electron on the quantum Gaussian ripple orbital angular momentum $\ell=0$. In the left panel we have considered $b=1$ and three values of $A$, namely $A=1$, $A=2$ and $A=3$. In the right panel we have considered $A=1$ and three values of $b$, namely, $b=1$, $b=2$ and $b=3$.