Erratum: Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field [Phys. Rev. B 78, 195427 (2008)]

Abstract

The use of the parameter m in Eq. (11) of our publication is incorrect. Rather, it should read E = ±v F 2e B(m + 1 + p), (1) where m is the previously defined quantum number and p is an integer with p > −(m + 1). This follows from the fact that Eq. (6) in our publication can be simplified to [ (α) (−α)] −1 = 0 in the limit R/ l B → ∞ with α := k 2 l 2 B /2 − m − 1. This is fulfilled for α = ±p and p being an integer. The later restriction of p > −(m+) is then required to make the radicand non-negative. The mathematical derivation based on our ansatz as described in our original publication is correct.

Modeling charge relaxation in graphene quantum dots induced by electron-phonon interaction

“…The Dirac equation (H τ v − E)ψ(r,ϕ) = 0 has been solved for both models in previous works [6,31]. In both cases, the above ansatz results in a simple Bessel-type differential equation for χ (1,2) m (r).…”

“…1(a) and 1(b)]. In the first model, which we will refer to as the "infinite mass boundary" (IM) model, the electron behaves like a free electron inside the dot, while being confined by an infinitely large masslike potential [31] at the boundary that might be realized by etching the dot. The second model, which will be referred to as the "electrostatic confinement" (EC) model, uses a finite electrostatic potential to achieve confinement [6].…”

“…To prevent Klein tunneling, we account for a finite mass term that might be induced by an underlying substrate. Within the nearest-neighbor tight-binding scheme in the low-energy approximation, both models can be described by a similar Hamiltonian in the valley isotropic form [6,31]:…”

“…In particular, we compare two simple models of QDs that have recently been discussed in the literature [6,12,31]. These studies focused on spin-relaxation processes and assumed a ratio of QD radius-to-phonon wavelength much smaller than the one reported in Ref.…”

Induced fermionic charge and current densities in two-dimensional rings

“…For example, the geometry with a single boundary at r = a corresponds to a circular graphene dot if the region r < a is considered and to a single circular nanohorn (or nanopore) for the region r > a. The influence of boundaries on the electronic properties of a circular graphene quantum dot in a magnetic field has been discussed in [37]. Comparing the analytical results obtained within the continuum model to those obtained from the tight-binding model, the authors conclude that the Dirac model with the infinite-mass boundary condition describes rather well its tight-binding analog and is in good qualitative agreement with experiments.…”