Position-dependent mass effects on a bilayer graphene catenoid bridge

TL;DR

This paper investigates how a position-dependent effective mass influences the electronic properties of electrons on a bilayer graphene catenoid bridge, revealing transitions in potential and bound states due to curvature effects.

Contribution

It introduces a curvature-dependent position-dependent mass model and analyzes its impact on electronic states in a bilayer graphene catenoid bridge.

Findings

PDM causes a transition from reflectionless to double-well potential.

Bound states shift from a single state to two states around the bridge.

Degeneracy is restored at high PDM coupling due to tunneling resonance.

Abstract

We study the electronic properties of a position-dependent effective mass electron on a bilayer graphene catenoid bridge. We propose a position-dependent mass (PDM) as a function of both gaussian and mean curvature. The hamiltonian exhibits parity and time-reversal steaming from the bridge symmetry. The effective potential contains the da Costa, centrifugal and PDM terms which are concentrated around the catenoid bridge. For zero angular momentum states, the PDM term provides a transition between a reflectionless to a double-well potential. As a result, the bound states undergo a transition from a single state around the bridge throat into two states each one located at rings around the bridge. Above some critical value of the PDM coupling constant, the degeneracy is restored due to double-well tunneling resonance.