The electronic structure of vertically stacked self-assembled quantum disks is studied within the effective mass approximation. The energy spectrum is calculated in the adiabatic approximation and using an exact diagonalization technique. The influence of the strain, dot separation, and the magnetic field on the formation of coupled quantum dot levels is discussed.

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS₂, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron–electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe–Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

We present results of optical experiments and theoretical analysis on the high-quality single-layer MoS₂ which reveal the fine structure of charged excitons, i.e., trions. In the emission spectra we resolve and identify two trion peaks, T₁ and T₂, resembling the pair of singlet and triplet trion peaks (T_S and T_T) in tungsten-based materials. However, in polarization-dependent photoluminescence measurements we identify these peaks as intra- and inter-valley singlet trions due to the trion fine structure distinct from that already known in bright and dark 2D materials with large conduction-band splitting induced by the spin-orbit coupling. We show that the trion energy splitting in MoS₂ is a sensitive probe of inter- and intra-valley carrier interaction. With additional support from theory we claim that the existence of these singlet trions combined with an anomalous excitonic g-factor together suggest that monolayer MoS₂ has a dark excitonic ground state, despite having "bright" singleparticle arrangement of spin-polarized conduction bands.

We present a theory of the electronic properties of gated graphene nanoribbon rings with zigzag edges in Möbius and cylindrical configurations. The finite width opens a gap and nontrivial topology of the Möbius ring leads to a single edge with edge states with an induced, effective gauge field, in analogy to topological insulators. The single zigzag edge leads to a shell of degenerate states at the Fermi level and a ferromagnetic (FM) ground state at half-filling, i.e., at charge neutrality, due to electron-electron interactions. For fractional fillings, both the magnetic moment and the energy gap are found to oscillate as a function of the shell filling. In cylindrical rings, the two edges lead to AF ground state at half-filling but FM ground state at fractional fillings. DOI: http://dx.doi.org/10.1103/PhysRevB.87.035435 ©2013 American Physical Society

The radiative recombination of electrons from a quasi-two-dimensional electron gas with holes localized on acceptors is investigated. The emission spectra for a single heterojunction are calculated including screening and the dynamical response of the Fermi sea. The line-shape analysis provides unambiguous identification of the Fermi-edge singularity in the emission spectra of the two-dimensional electron gas.

A theory of electronic properties of a spin-singlet quantum Hall droplet at filling factor $\nu =2\mathrm{}$ in a parabolic quantum dot is developed. The excitation spectrum and the stability of the droplet due to the transfer of electrons into the second Landau level at low magnetic fields and due to spin flip at the edge at higher magnetic fields are determined using Hartree-Fock, exact diagonalization, and spin-density functional methods. We show that above a critical number of electrons $N_c$ the unpolarized $\nu =2\mathrm{}$ quantum Hall droplet ceases to be a ground state in favor of spin-polarized phases. We determine the characteristic pattern in the addition and current-amplitude Coulomb blockade spectra associated with the stable $\nu =2\mathrm{}$ droplet. We show that the spin transition of the droplet at a critical number of electrons is accompanied by the reversal of the current-amplitude modulation at the $\nu =2\mathrm{}$ line, as observed in recent experiments.