Electronic properties of bilayer graphene catenoid bridge

Abstract

We study the properties of an electron on a catenoid surface. The catenoid is understood as a realization of a bridge connecting two graphene layer by a smooth surface. The curvature induces a symmetrical reflectionless potential well around the bridge with one bound-state for m = 0. For m = 0, a centrifugal potential barrier arises controlling the tunnelling between the layers. An external electric field breaks the parity symmetry and provides a barrier that controls the conductance from one layer to another. By applying a constant magnetic field the effective potential exhibits a confining double-well potential nearby the bridge. We obtain the corresponding bound states and study the effects of the curvature on the Landau levels.

Position-dependent mass effects on a bilayer graphene catenoid bridge

“…The electric field creates a difference between the asymptotic values of the effective potential on the upper to the lower layer. This effect suggests that the catenoid bilayer bridge could be used as a diode [27].…”

“…In Ref. [27], we explored the effects of the geometry and of external electric and magnetic fields upon the graphene catenoid bridge. The da Costa potential provides a reflectionless attractive potential, whereas the symmetry with respect to the z axis yields to a centrifugal repulsive term [27].…”

“…[27], we explored the effects of the geometry and of external electric and magnetic fields upon the graphene catenoid bridge. The da Costa potential provides a reflectionless attractive potential, whereas the symmetry with respect to the z axis yields to a centrifugal repulsive term [27]. The geometric potential exhibits a parity and time reversal symmetry * Electronic address: euclides.silva@ufca.edu.br which holds under the action of the magnetic field but it is broken by the external electric field [27].…”

“…The da Costa potential provides a reflectionless attractive potential, whereas the symmetry with respect to the z axis yields to a centrifugal repulsive term [27]. The geometric potential exhibits a parity and time reversal symmetry * Electronic address: euclides.silva@ufca.edu.br which holds under the action of the magnetic field but it is broken by the external electric field [27]. The magnetic field produces a double-well potential which leads to bound states located at symmetric rings around the catendoid throat.…”

3D Hollow Xerogels with Ordered Cellulose Nanocrystals for Tailored Mechanical Properties

“…Catenoid, arising by rotating a catenary curve around an axis, has the remarkable property of be a minimal surface, i.e., a surface of the least area. [19] One typical case of catenoid in our daily life is the soap bubble between two open rings (Figure 1a). If the gravity could be ignored compared to the surface tension, this shape can be regarded as ideal catenoid, which is dominantly driven by the surface tension of liquid system.…”