Scaling properties of induced density of chiral and nonchiral Dirac fermions in magnetic fields

Abstract

We find that a repulsive potential of graphene in the presence of a magnetic field has bound states that are peaked inside the barrier with tails extending over ℓ(N + 1), where ℓ and N are the magnetic length and Landau level(LL) index. We have investigated how these bound states affect scaling properties of the induced density of filled Landau levels of massless Dirac fermions. For chiral fermions we find, in strong coupling regime, that the density inside the repulsive potential can be greater than the value in the absence of the potential while in the weak coupling regime we find negative induced density. Similar results hold also for non-chiral fermions. As one moves from weak to strong coupling regimes the effective coupling constant between the potential and electrons becomes more repulsive, and then it changes sign and becomes attractive. Different power-laws of induced density are found for chiral and non-chiral fermions.PACS numbers:

Confinement and deconfinement in the potential of antidot arrays of a massless Dirac electron in magnetic fields

“…In contrast to the case of zero magnetic field the eigenstates are real bound states and no resonant quasi-bound states exist [22]. In addition, anomalous bound states with a sharp peak of probability density inside the repulsive potential and broad peak outside the potential can form [23]. However, there are also eigenstates whose probability densities are localized near the edge of the antidot.…”

“…The magnitudes of the individual parameters R and are not important; it is the ratio R/ that determines the relevant physics of confinement and deconfinement. The ratio R/ is actually a scaling variable [23]. In experiments the range of R is 100 Å < R < 1000 Å and can be varied from 100 Å to 1000 Å by changing magnetic fields.…”

Error Estimation for Eigenvalues of Unbounded Linear Operators and an Application to Energy Levels in Graphene Quantum Dots

“…For example, when designing a new electronic device, the analysis of electron dynamics in the underlying material is required. It is especially important to investigate the possibility of electron localisation and its energy spectrum by solving the eigenvalue problem within the used model [6,9,10,11,13,14,18]. Knowledge of the accuracy in the computed eigenvalues allows us to draw conclusions about which effects to incorporate in our models and which effects that can safely be neglected.…”

Impurity cyclotron resonance of anomalous Dirac electrons in graphene

“…They can form true boundstates with real energies [6][7][8] in contrast to the case of no magnetic field. Moreover, in addition to the magnetic length, ℓ = 25.66(B[T]) −1/2 [nm], a new length scale R is introduced in the wavefunction: boundstates with a s-channel angular momentum component can become anomalous and develop a sharp peak of a width R inside the potential and a broad peak of size magnetic length ℓ outside the potential [9]. Although the effect of the potential is strong it is partly mitigated by Klein tunneling and there is a competition between the two length scales R and ℓ: the peak is strong in the regime R/ℓ < 1, but small in the regime R/ℓ > 1 (in the limit R/ℓ → 0 it diverges).…”

“…Although the effect of the potential is strong it is partly mitigated by Klein tunneling and there is a competition between the two length scales R and ℓ: the peak is strong in the regime R/ℓ < 1, but small in the regime R/ℓ > 1 (in the limit R/ℓ → 0 it diverges). These states are present in various potentials: regularized Coulomb [10,11] 5 , parabolic [6,12] 6 and finite-range potentials [7,9], see figures 2(a)-(c).…”