Comment to article "A light--hole exciton in a quantum dot" by Y.H.Huo et al, Nature Physics 10, 46 (2014)

The exciton ground state in strained quantum dots similar to those fabricated in article specified in the title is shortly discussed within a relevant model Hamiltonian. Some characteristics of the light--hole exciton ground state reached in a dot under the tensile biaxial strain appear to be sensitive to the strain anisotropy breaking a purity of this state. It refers in particular to a degree of the in--plane polarization of the emission and the fine structure of the ground state.Comment: 6 pages, 2 figure

Edge States of a Periodic Chain with Four-Band Energy Spectrum

Tight-binding model on a finite chain is studied with four-fold alternated hopping parameters $t_{1,2,3,4}$. Imposing the open boundary conditions, the corresponding recursion is solved analytically with special attention paid to the occurrence of edge states. Corresponding results are strongly corroborated by numeric calculations. It is shown that in the system there exist four different edge phases if the number of sites is odd, and eight edges phases if the chain comprises even number of sites. Phases are labelled by $\sigma_1\equiv{\rm sgn}(t_1t_3-t_2t_4)$, $\sigma_2\equiv{\rm sgn}(t_1t_4-t_2t_3)$ and $\sigma_3\equiv{\rm sgn}(t_1t_2-t_3t_4)$. It is shown that these quantities represent gauge invariant topological indices emerging in the corresponding infinite chains.Comment: 12 pages, 15 figures, typos correcte

On the NCCS model of the quantum Hall fluid

Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the $\nu=1$ integer quantum Hall effect (IQHE) state on the fractional quantum Hall effect (FQHE) $\nu=\frac{1}{2p+1}$ FQHE states. Using the hydrodynamical description of the quantum Hall fluid, it is shown that these transformations are generated by vector fields satisfying the Gauss law in the interacting non-commutative Chern-Simons gauge theory, and the corresponding field-theory Lagrangian is reconstructed. It is demonstrated that the geometric transformations induce quantum-mechanical non-unitary similarity transformations, establishing the interplay between integral and fractional QHEs.Comment: 4 pages, no figures, minor corrections, accepted in Eur. Phys. J.

Polarization dynamics in quantum dots: The role of dark excitons

We study an impact of the fine structure of the heavy--hole ground state exciton confined in semiconductor quantum dots on the photoluminescence polarization dynamics solving the relevant system of the rate equations. The presence of the dark excitons is usually ignored and the polarization decay is assumed to be caused by direct transitions within the radiative doublet. We demonstrate that in strongly confined quantum dots the dark excitons, which are energetically well below the bright excitons, have actually a decisive effect on the polarization dynamics due to their persistent nature. The linear polarization shows nonexponential decay controlled by a conversion of the dark into a bright exciton. To get quantitative answers for specific quantum dot structures, all the necessary information can be obtained already from experiments on the luminescence dynamics following nonresonant excitation in these dots.Comment: 12 pages, 3 figure

Shakeup spectrum in a two-dimensional electron gas in a strong magnetic field

The shakeup emission spectrum in a two-dimensional electron gas in a strong magnetic field is calculated analytically. The case of a localized photocreated hole is studied and the calculations are performed with a Nozieres-De Dominicis-like Hamiltonian. The hole potential is assumed to be small compared to the cyclotron energy and is therefore treated as a perturbation. Two competing many-body effects, the shakeup of the electron gas in the optical transition, and the excitonic effect, contribute to the shakeup satellite intensities. It is shown, that the range of the hole potential essentially influences the shakeup spectrum. For a short range interaction the above mentioned competition is more important and results in the shakeup emission quenching when electrons occupy only the lowest Landau level. When more than one Landau level is filled, the intensities of the shakeup satellites change with magnetic field nonmonotonically. If the interaction is long range, the Fermi sea shakeup processes dominate. Then, the satellite intensities smoothly decrease when the magnetic field increases and there is no suppression of the shakeup spectrum when the only lowest Landau level is filled. It is shown also that a strong hole localization is not a necessary condition for the SU spectrum to be observed. If the hole localization length is not small compared to the magnetic length, the SU spectrum still exists. Only the number of contributions to the SU spectrum reduces and the shakeup processes are always dominant.Comment: 23 pages, 4 figure

Topological Solitons in Noncommutative Plane and Quantum Hall Skyrmions

We analyze topological solitons in the noncommutative plane by taking a concrete instance of the quantum Hall system with the SU(N) symmetry, where a soliton is identified with a skyrmion. It is shown that a topological soliton induces an excitation of the electron number density from the ground-state value around it. When a judicious choice of the topological charge density $J_{0}(\mathbf{x})$ is made, it acquires a physical reality as the electron density excitation $\Delta \rho ^{\text{cl}}(\mathbf{x})$ around a topological soliton, $\Delta \rho ^{\text{cl}}(\mathbf{x})=-J_{0}($. Hence a noncommutative soliton carries necessarily the electric charge proportional to its topological charge. A field-theoretical state is constructed for a soliton state irrespectively of the Hamiltonian. In general it involves an infinitely many parameters. They are fixed by minimizing its energy once the Hamiltonian is chosen. We study explicitly the cases where the system is governed by the hard-core interaction and by the noncommutative CP$^{N-1}$ model, where all these parameters are determined analytically and the soliton excitation energy is obtained.Comment: 18 pages (to be published in PRD

On the Meissner effect in the Relativistic Anyon superconductors

The relativistic model with two types of planar fermions interacting with the Chern-Simons and Maxwell fields is applied to the study of anyon superconductor. It is demonstrated, that the Meissner effect can be realized in the case of the simultaneous presence of the fermions with a different magnetic moment interactions. Under the certain conditions there occures an extra plateau at the magnetization curve. In the order under consideration the spectrum of the electromagnetic field excitations contains the long-range interaction and one massive "photon" state.Comment: 21 pages, 4 figures, late

Nambu-Goldstone modes and the Josephson supercurrent in the bilayer quantum Hall system

An interlayer phase coherence develops spontaneously in the bilayer quantum Hall system at the filling factor $\nu =1$. On the other hand, the spin and pseudospin degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor $\nu =2$. There emerges a complex Nambu-Goldstone mode with a linear dispersion in the zero tunneling-interaction limit for both cases. Then its phase field provokes a Josephson supercurrent in each layer, which is dissipationless as in a superconductor. We study what kind of phase coherence the Nambu-Goldstone mode develops in association with the Josephson supercurrent and its effect on the Hall resistance in the bilayer quantum Hall system at $\nu=1,2$, by employing the Grassmannian formalism.Comment: 43 pages, 5 figures. arXiv admin note: text overlap with arXiv:1207.0003, arXiv:1211.038

Exact Symmetries of Electron Interactions in the Lowest Landau Level

Considering the system of interacting electrons in the lowest Landau level we show that the corresponding four-fermion Hamiltonian is invariant with respect to the local area-preserving transformations. Testing a certain class of interaction potentials, we find that this symmetry is universal with respect to a concrete type of potentials.Comment: Revtex4, 8 page

Spin Supercurrent in the Canted Antiferromagnetic Phase

The spin and layer (pseudospin) degrees of freedom are entangled coherently in the canted antiferromagnetic phase of the bilayer quantum Hall system at the filling factor $\nu =2$. There emerges a complex Goldstone mode describing such a combined degree of freedom. In the zero tunneling-interaction limit ($\Delta_{\text{SAS}}\rightarrow 0$), its phase field provokes a supercurrent carrying both spin and charge within each layer. The Hall resistance is predicted to become anomalous precisely as in the $\nu =1$ bilayer system in the counterflow and drag experiments. Furthermore, it is shown that the total current flowing in the bilayer system is a supercurrent carrying solely spins in the counterflow geometry. It is intriguing that all these phenomena occur only in imbalanced bilayer systems.Comment: 5 pages, 1 figur