Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons.

Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases.

New disordered anyon phase of doped graphene zigzag nanoribbon.

We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigzag edges.

Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences.

An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g.

Topological Gap States of Rectangular Armchair Ribbon.

We consider a rectangular graphene armchair ribbon with an excitation gap. The boundary of this system consists of two short zigzag edges and two long armchair edges. Within such a ribbon, topological gap states exist that are localized along the zigzag edges.

Stability of Anomalous States of a Local Potential in Graphene.

Graphene Landau levels have discrete energies consisting zero energy chiral states and non-zero energy states with mixed chirality. Each Landau level splits into discrete energies when a localized potential is present. A simple scaling analysis suggests that a localized potential can act as a strong perturbation, and that it can be even more singular in graphene than in ordinary two-dimensional systems of massful electrons.

Coulomb Impurity Problem of Graphene in Strong Coupling Regime in Magnetic Fields.

We investigate the Coulomb impurity problem of graphene in strong coupling limit in the presence of magnetic fields. When the strength of the Coulomb potential is sufficiently strong the electron of the lowest energy boundstate of the n = 0 Landau level may fall to the center of the potential. To prevent this spurious effect the Coulomb potential must be regularized.

Impurity cyclotron resonance of anomalous Dirac electrons in graphene.

We have investigated a new feature of impurity cyclotron resonances common to various localized potentials of graphene. A localized potential can interact with a magnetic field in an unexpected way in graphene. It can lead to formation of anomalous boundstates that have a sharp peak with a width R in the probability density inside the potential and a broad peak of size magnetic length ℓ outside the potential.

Optical properties of Dirac electrons in a parabolic well.

A single electron transitor may be fabricated using qunatum dots. A good model for the confinement potential of a quantum dot is a parabolic well. Here we consider such a parabolic dot made of graphene.

Can a repulsive potential in graphene have boundstates in a magnetic field?

We consider Klein tunneling through a repulsive and cylindrical potential with range R and strength V. Recently it was found that, in the strong coupling regime R/l < 1, the repulsive potential can have bound states peaked inside the potential with tails extending over l mean square root of 2(N+1), where N is Landau level (LL) index and f is the magnetic length. The presence of these bound states is a consequence of a subtle interplay between Klein tunneling and quantization effect of magnetic fields.

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

We have investigated the effect of inter-Landau level mixing on confinement/deconfinement in antidot potentials of states with energies less than the potential height of the antidot array. We find that, depending on the ratio between the size of the antidot R and the magnetic length [Formula: see text], probability densities display confinement or deconfinement in antidot potentials (B is the magnetic field). When R/ℓ < 1 inter-Landau level mixing is strong and probability densities with energy less than the potential height are non-chiral and localized inside antidot potentials.

Dirac electrons of a split-gate Hall bar.

In this work we study several unusual properties of Klein tunneling through the abrupt and flat barriers of a split-gate Hall bar system of graphene. We show that Klein tunneling of Dirac electrons can be rather strong in such a system, and that a significant electron density can be present under the barrier. It can be shown that the probability wavefunctions for large angular momenta are identical to the probability wavefunctions of the same angular momenta in the absence of the potential barrier, i.

Room-temperature charge stability modulated by quantum effects in a nanoscale silicon island.

We report on transport measurement performed on a room-temperature-operating ultrasmall Coulomb blockade devices with a silicon island of sub5 nm. The charge stability at 300K exhibits a substantial change in slopes and diagonal size of each successive Coulomb diamond, but remarkably its main feature persists even at low temperature down to 5.3K except for additional Coulomb peak splitting.

Coupling of surface and lowest Landau level states in a rectangular graphene dot.

A rectangular graphene dot with two zigzag edges and two armchair edges have electronic states in the presence of a magnetic field that are localized on the zigzag edges with non zero values of the wavefunction inside the dot. We have investigated the dependence of these wavefunctions on the size of the dot, and explain the physical origin of them in terms of surface and the lowest Landau level (LLL) states of infinitely long nanoribbons. We find that the armchair edges play a crucial role by coupling the surface and LLL states.

Electronic properties of a graphene antidot in magnetic fields.

We report on several unusual properties of a graphene antidot created by a piecewise constant potential in a magnetic field. We find that the total probability of finding the electron in the barrier can be nearly one while it is almost zero outside the barrier. In addition, for each electron state of a graphene antidot there is a dot state with exactly the same wavefunction but with a different energy.

Coulomb blockade and kondo effect in a quantum Hall antidot.

We propose a general capacitive model for an antidot, which has two localized edge states with different spins in the quantum Hall regime. The capacitive coupling of localized excess charges, which are generated around the antidot due to magnetic flux quantization, and their effective spin fluctuation can result in Coulomb blockade, h/(2e) Aharonov-Bohm oscillations, and the Kondo effect. The resultant conductance is in qualitative agreement with recent experimental data.