Geometry-induced potential on a two-dimensional section of a wormhole: Catenoid

Abstract

We show that a two dimensional wormhole geometry is equivalent to a catenoid, a minimal surface. We then obtain the curvature induced geometric potential and show that the ground state with zero energy corresponds to a reflectionless potential. By introducing an appropriate coordinate system we also obtain bound states for different angular momentum channels. Our findings can be realized in suitably bent bilayer graphene sheets with a neck or in a honeycomb lattice with an array of dislocations or in nanoscale waveguides in the shape of a catenoid.

Analogies in electronic properties of graphene wormhole and perturbed nanocylinder

“…Both methods provided much different results, but in the case of the difference n − m of the components of the chiral vector of the wormhole bridge not being a multiple of 3, each of the methods confirmed similarity of both structures from the perspective of the electronic properties. In a different way, the equivalence of both structures was proven in [17]. The value of the perturbation in the investigated structures was not very large and that is why we can compare our results with the calculations in some earlier works [18,19].…”

Modeling the Electron Transport in Nanostructures by Using the Concept of BIons in M-theory

“…The observation as well as synthesization of the graphitic wormhole should have enormous effect for the future electronic nanodevices. The deformation induced additional geometric potential which through shift of the Fermi energy influence crucially electronic properties of such exotic bilayer structures [37][38][39]. We will focus on all these questions in our next research.…”

Two-dimensional electron gas under the effect of constrained potential and magnetic field in curved space

“…Two-dimensional electron gas (2DEG) in the planar heterostructures has been investigated greatly, which lead to in finding a number of remarkable quantum phenomena such as integer and fractional quantum Hall effects, and the Berry quantum phase. Non-planar low-dimensional structures are fundamentally new physical objects that have attracted the attention of the researchers during last recent years [8,[10][11][12][13][14][15][16][17][18][19][20].…”