Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field

Abstract

We analytically calculate the energy spectrum of a circular graphene quantum dot with radius R subjected to a perpendicular magnetic field B by applying the infinite-mass boundary condition. We can retrieve well-known limits for the cases R, B → ∞ and B → 0. Our model is capable of capturing the essential details of recent experiments. Quantitative agreement between theory and experiment is limited due to the fact that a circular dot deviates from the actual experimental geometry, that disorder plays a significant role, and that interaction effects may be relevant.

Robustness of edge states in graphene quantum dots

“…We also study the magnetic field dependence of edge states in quantum dots. Whereas magnetic field spectroscopy of energy levels has up to now mainly been a useful tool to probe bulk states in graphene quantum dots, 28,29,50 we show how to employ this technique also to identify edge states. In addition, we study the level statistics of edge states.…”

Electric control of tunneling energy in graphene double dots

“…Landau levels tend to form [42]. For our dot parameters the magnetic length l B = √ /(eB) is of the order of the dot radius R for reasonable magnetic fields [26]. More precisely, l B is 81, 26, and 8 nm for a magnetic field of 0.1, 1, and 10 T, respectively, to be compared to a dot radius of R = 25 nm.…”

“…Graphene single dots have been intensively investigated during the last years [4,9,13,14,[25][26][27][28][29]. We extend those works by theoretical investigations of the dot-dot coupling, an essential ingredient for quantum computation [30,31].…”

Edge scattering of electrons in graphene: Boltzmann equation approach to the transport in graphene nanoribbons and nanodisks

“…Therefore, we do not include into consideration the size quantization of energy spectrum, which is important for graphene quantum dots. [41][42][43][44][45] Numerous experiments on the graphene nanoribbons revealed the peculiarities of conductivity due to the edge scattering and/or existence of the edge states. [46][47][48][49][50][51][52] These experiments also demonstrate that a localization "transport"gap can be induced by disorder related to the edges.…”