Related papers: Atomic Collapse in Disordered Graphene Quantum Dot…
Atomic collapse can be observed in graphene because of its large "effective" fine structure constant, which enables this phenomenon to occur for an impurity charge as low as $Z_c\sim 1-2$. Here, we investigate the effect of the sublattice…
Electrons in graphene, behaving as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a novel state of superheavy atoms stripped of…
We address the problem of an unscreened Coulomb charge in graphene, and calculate the local density of states and displaced charge as a function of energy and distance from the impurity. This is done non-perturbatively in two different…
Quantum criticality, a manifestation of emergent scale invariance in electron wavefunctions arises from intricate many-body quantum entanglement. One of the natural venues for the criticality is clean undoped Dirac semimetals, known as a…
We study interacting Dirac quasiparticles in disordered graphene and find that an interplay between the unscreened Coulomb interactions and pseudo-relativistic quasiparticle kinematics can be best revealed in the ballistic regime, whereas…
We study quantum electrodynamics with 2+1 dimensional massless Dirac fermion around a Coulomb impurity. Around a large charge with atomic number Z > 137, the QED vacuum is expected to collapse due to the strong Coulombic force. While the…
The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from the behavior of non-relativistic electrons seen in traditional atomic and impurity systems. Surprisingly, many key theoretical predictions for…
The supercritical instability in a system of two identical charged impurities in gapped graphene described in the continuous limit by the two-dimensional Dirac equation has been studied. The case where the charge of each impurity is…
In this paper, we numerically study the bound electron states induced by long range Coulomb impurity in gapped graphene and the quasi-bound states in supercritical region based on the lattice model. We present a detailed comparison between…
It is well known that there are resonant states with complex energy for the supercritical Coulomb impurity in graphene. We show that opening of a quasiparticle gap decreases the imaginary part of energy, |ImE|, of these states and…
Quantum electrodynamics predicts that heavy atoms ($Z > Z_c \approx 170$) will undergo the process of atomic collapse where electrons sink into the positron continuum and a new family of so-called collapsing states emerges. The relativistic…
The electronic states of an electrostatically confined cylindrical graphene quantum dot and the electric transport through this device are studied theoretically within the continuum Dirac-equation approximation and compared with numerical…
We investigate the excitonic instability in the theory of Dirac fermions in graphene with long-range Coulomb interaction. We analyze the electron-hole vertex relevant for exciton condensation in the ladder approximation, showing that it…
We numerically investigate critically delocalized wavefunctions in models of 2D Dirac fermions, subject to vector potential disorder. These describe the surface states of 3D topological superconductors, and can also be realized through…
The Coulomb impurity problem of graphene, in the absence of a magnetic field, displays discrete scale invariance. Applying a magnetic field introduces a new magnetic length scale $\ell$ and breaks discrete scale invariance. Moreover, a…
In this paper, we perform a systematic study on the electronic, magnetic, and transport properties of the hexagonal graphene quantum dots (GQDs) with armchair edges in the presence of a charged impurity using two different configurations:…
We provide a theoretical model for electronic transitions in a two-dimensional (2D) artificial atom in a graphene monolayer. The artificial atom is due to the presence of a charged adatom (Coulomb impurity) in the layer and interacts with a…
The thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, the Anderson transition is studied for the BCC and FCC lattices. We obtain high precision results for the critical…
We present the first results of numerical simulations of a 2+1 dimensional fermion field theory based on a recent proposal for a model of graphene, consisting of N_f four-component Dirac fermions moving in the plane and interacting via an…
We develop a field-theoretic approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov--Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one…