P. Pietiläinen

Optical Signatures of Spin-Orbit Interaction Effects in a Parabolic Quantum Dot

We demonstrate here that the dipole-allowed optical absorption spectrum of a parabolic quantum dot subjected to an external magnetic field reflects the interelectron interaction effects when the spin-orbit (SO) interaction is also taken into account. We have investigated the energy spectra and the dipole-allowed transition energies for up to four interacting electrons parabolically confined, and have uncovered several novel effects in those spectra that are solely due to the SO interaction.

Energy levels and magneto-optical transitions in parabolic quantum dots with spin-orbit coupling

We report on the electronic properties of few interacting electrons confined in a parabolic quantum dot based on a theoretical approach developed to investigate the influence of Bychkov-Rashba spin-orbit (SO) interaction on such a system. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Here we present accurate results for the energy levels and optical-absorption spectra for parabolic quantum dots containing up to four interacting electrons, in the presence of spin-orbit coupling and under the influence of an externally applied, perpendicular magnetic field. We have described in detail a very accurate numerical scheme to evaluate these quantities. We have evaluated the effects of the SO coupling on the Fock-Darwin spectra for quantum dots made out of three different semiconductor systems, InAs, InSb, and GaAs. The influence of SO coupling on the single-electron spectra manifests itself by primarily lifting the degeneracy at zero magnetic field, rearrangement of some of the energy levels at small magnetic fields, and level repulsions at high fields. These results are explained as due to mixing of different spinor states for increasing strength of the SO coupling. As a consequence, the corresponding absorption spectra reveal anticrossing structures in the two main lines of the spectra. For interacting many-electron systems we observed the appearence of discontinuities, anticrossings, and new modes that appear in conjunction with the two main absorption lines. These additional features arise entirely due to the SO coupling and are a consequence of level crossings and level repulsions in the energy spectra. An intricate interplay between the SO coupling and the Zeeman energies is shown to be responsible for these additional features seen in the energy spectra. Optical absorption spectra for all three types of quantum dots studied here show a common feature: new modes appear, mostly near the upper main branch of the spectra around

Interacting-electron states and the persistent current in a quantum ring

2\phantom{\rule{0.3em}{0ex}}\mathrm{T}

Electron correlations in a quantum dot with Bychkov-Rashba coupling

, that become stronger with increasing SO coupling strength. Among the three types of systems considered here, the optical signature of the SO interaction is found to be the strongest in the absorption spectra of the GaAs quantum dot, but only at very large values of the SO coupling strength, and appears to be the weakest for the InSb quantum dot. Experimental observation of these modes that appear solely due to the presence of the SO coupling would provide a rare glimpse into the role of the SO coupling in nanostructured quantum systems.

Half-Polarized Quantum Hall States

Abstract We study the effect of Coulomb interaction on the magnetic moment (associated with the persistent current) in a quantum ring. The few-electron states in a quantum ring with and without the Coulomb interaction are investigated. For an ideally narrow ring, the interaction merely shifts the spectrum to higher energy and the magnetic moment is almost insensitive to the interaction. Qualitative estimates of a large system where electrons also occupy higher Landau levels indicate that Coulomb interaction mixes some of the states resulting in a sharp increase in magnetization.

Collective Excitations in the Fractionally Quantized Hall Effect and the Magnetoplasmon Mode

We report on a theoretical approach developed to investigate the influence of the Bychkov-Rashba interaction on a few interacting electrons confined in a quantum dot. We note that the spin-orbit coupling profoundly influences the energy spectrum of interacting electrons in a quantum dot. Interelectron interaction causes level crossings in the ground state and a jump in magnetization. As the coupling strength is increased, that jump is shifted to lower magnetic fields. Low-field magnetization will therefore provide a direct probe of the spin-orbit coupling strength in a quantum dot.

The fractional quantum hall effect : properties of an incompressible quantum fluid

We report a theoretical analysis of the half-polarized quantum Hall states observed in a recent experiment. Our numerical results indicate that the ground state energy of the quantum Hall nu = 2 / 3 and nu = 2 / 5 states versus spin polarization has a downward cusp at half the maximal spin polarization. We map the two-component fermion system onto a system of excitons and describe the ground state as a liquid state of excitons with nonzero values of exciton angular momentum.

Electronic compressibility of graphene: The case of vanishing electron correlations and the role of chirality

We have studied the shift of magnetoplasmon dispersion from the cyclotron energy for 1/3 and 1/5 filling of the lowest Landau level (one-spin state). Evaluating exactly the excitation energies (to leading order in the interactions) for finite electron systems in a periodic rectangular geometry, we find that, for the density-wave mode, when at most one electron is elevated to the higher Landau level, the collective excitation has the same dispersion as that for the intra-Landau level case. We have also shown that such a result is quite general and is independent of the size of the system. The energy shift is qualitatively similar to the case where the Landau level is fully occupied.

Donor centers and absorption spectra in quantum dots

1. Introduction.- 2. Ground State.- 2.1 Finite-Size Studies: Rectangular Geometry.- 2.2 Laughlins Theory.- 2.3 Spherical Geometry.- 2.4 Monte Carlo Results.- 2.5 Reversed Spins in the Ground State.- 2.6 Finite Thickness Correction.- 2.7 Liquid-Solid Transition.- 3. Elementary Excitations.- 3.1 Quasiholes and Quasiparticles.- 3.2 Finite-Size Studies: Rectangular Geometry.- 3.3 Spin-Reversed Quasiparticles.- 3.4 Spherical Geometry.- 3.5 Monte Carlo Results.- 3.6 Experimental Investigations of the Energy Gap.- 3.7 The Hierarchy: Higher Order Fractions.- 4. Collective Modes: Intra-Landau Level.- 4.1 Finite-Size Studies: Spherical Geometry.- 4.2 Rectangular Geometry: Translational Symmetry.- 4.3 Spin Waves.- 4.4 Single Mode Approximation: Magnetorotons.- 5. Collective Modes: Inter-Landau Level.- 5.1 Filled Landau Level.- 5.2 Fractional Filling: Single Mode Approximation.- 5.3 Fractional Filling: Finite-Size Studies.- 6. Further Topics.- 6.1 Effect of Impurities.- 6.2 Higher Landau Levels.- 6.3 Even Denominator Filling Fractions.- 6.4 Half-Filled Landau Level in Multiple Layer Systems.- 7. Open Problems and New Directions.- Appendices.- A The Landau Wave Function in the Symmetric Gauge.- B The Hypernetted-Chain Primer.- C Repetition of the Intra-Mode in the Inter-Mode.- References.

Hypernetted Chain Theory of Charged Impurity

A recent surprising finding that electronic compressibility measured experimentally in monolayer graphene can be described solely in terms of the kinetic energy [J. Martin et al., Nat. Phys. 4, 144 (2008)] is explained theoretically as a direct consequence of the linear energy dispersion and the chirality of massless Dirac electrons. For bilayer graphene we show that contributions to the compressibility from the electron correlations are restored. We attribute the difference to the respective momentum dependence of the low-energy-band structures of the two materials.