We determine here the evolution of the bandgap energy with size in graphene quantum dots (GQDs). We find oscillatory behaviour of the bandgap and explain its origin in terms of armchair and zigzag edges. The electronic energy spectra of GQDs are computed using both the tight binding model and ab initio density functional methods. The results of the tight binding model are analyzed by dividing zigzag graphene quantum dots into concentric rings. For each ring, the energy spectra, the wave functions and the bandgap are obtained analytically. The effect of inter-ring tunneling on the energy gap is determined. The growth of zigzag terminated GQD into armchair GQD is shown to be associated with the addition of a one-dimensional Lieb lattice of carbon atoms with a shell of energy levels in the middle of the energy gap of the inner zigzag terminated GQD. This introduces a different structure of the energy levels at the bottom of the conduction and top of the valence band in zigzag and armchair GQD which manifests itself in the oscillation of the energy gap with increasing size. The evolution of the bandgap with the number of carbon atoms is compared with the notion of confined Dirac Fermions and tested against ab initio calculations of Kohn-Sham and TD-DFT energy gaps.
We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band k→·p→ Hamiltonian or by a four-band k→·p→ Bernevig–Hughes–Zhang (BHZ) Hamiltonian. The trivial versus topological properties of the BHZ Hamiltonian are characterized by the different topologies that arise when mapping the in-plane wavevectors through the BHZ Hamiltonian onto a Bloch sphere. In the topologically nontrivial case, edge states are formed in the disc and square geometries of the quantum dot. We account for the effects of compressive strain in topological insulator quantum dots by means of the Bir–Pikus Hamiltonian. Tuning strain allows topological phase transitions between topological and trivial phases, which results in the vanishing of edge states from the energy gap. This may enable the design of a quantum strain sensor based on strain-driven transitions in HgTe topological insulator square quantum dots.
We present a theory of excitons in gated bilayer graphene
(BLG)
quantum dots (QDs). Electrical gating of BLG opens an energy gap,
turning this material into an electrically tunable semiconductor.
Unlike in laterally gated semiconductor QDs, where electrons are attracted
and holes repelled, we show here that lateral structuring of metallic
gates results in a gated lateral QD confining both electrons and holes.
Using an accurate atomistic approach and exact diagonalization tools,
we describe strongly interacting electrons and holes forming an electrically
tunable exciton. We find these excitons to be different from those
found in semiconductor QDs and nanocrystals, with exciton energy tunable
by voltage from the terahertz to far infrared (FIR) range. The conservation
of spin, valley, and orbital angular momentum results in an exciton
fine structure with a band of dark low-energy states, making this
system a promising candidate for storage, detection and emission of
photons in the terahertz range.
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