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The electronic structure of lens-shaped self-assembled quantum dots is studied as a function of the dot size, the confining potential, and the magnetic field. The parabolic confining potential and its corresponding energy spectrum are shown to be an excellent approximation. The magnetoexciton spectrum is calculated and compared with recent experiments. ͓S0163-1829͑96͒02932-3͔

A theory of charged excitons X − in a dilute 2D electron gas in a high magnetic field is presented. In contrast to previous calculations, three bound X − states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a "bright" triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a "dark" triplet. The interaction of bound X − 's with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is found that the short-range character of the e-X − interactions effectively isolates bound X − states from a dilute e-h plasma. This results in the insensitivity of the photoluminescence spectrum to the filling factor ν, and an exponential decrease of the oscillator strength of the dark triplet X − as a function of ν −1 .71. 35.Ji, 71.35.Ee, 73.20.Dx

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We report on detailed temperature dependent (T = 7-295 K) optical spectroscopy studies of WSe, WS, MoSe and MoS monolayers exfoliated onto the same SiO/Si substrate. In the high energy region of absorption type (reflectivity contrast-RC) and emission (photo-luminescence-PL) spectra of all the monolayers resonances related to the neutral and charged excitons (X and T) are detected in the entire measured temperature range. The optical amplitudes of excitons and trions strongly depend on the temperature and two dimensional carrier gas (2DCG) concentration. In the low energy PL spectra of WSe and WS we detect a group of lines (L) which dominates the spectra at low temperatures but rapidly quenches with the increase in the temperature. Interestingly, in the same energy range of the RC spectra recorded for WS, we observe an additional line (L ), which behaves in the same way as the L lines in the PL spectra. The optical amplitude of L and T resonances in the RC spectra strongly increases with the growth of the 2DCG concentration. On the base of these observations we identify the L resonance in the RC spectra as arising from the fine structure of the trion. We also propose that the line interpreted previously in PL spectra of WSe and WS as related to the biexciton emission is a superposition of the biexciton, trion and localized exciton emission. We find that with the temperature increase from 7-295 K the total PL intensity decreases moderately in WSe and WS, strongly in MoS and dramatically in MoSe.

The pseudopotentials describing the interactions of quasiparticles in fractional quantum Hall (FQH) states are studied. Rules for the identification of incompressible quantum fluid ground states are found, based upon the form of the pseudopotentials. States belonging to the Jain sequence ν = n(1 + 2pn) −1 , where n and p are integers, appear to be the only incompressible states in the thermodynamic limit, although other FQH hierarchy states occur for finite size systems. This explains the success of the composite Fermion picture.

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin ν = 1 3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE's form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE's. The series of finite-size incompressible ground states are identified at the QE filling factors νQE = 1 2 , 1 3 , 2 3 , corresponding to the electron fillings ν = 3 8 , 4 11 , 5 13 . The equivalent quasihole (QH) states occur at νQH = 1 4 , 1 5 , 2 7 , corresponding to ν = 3 10 , 4 13 , 5 17 . All these six novel FQH states were recently discovered experimentally. Detailed analysis indicates that QE or QH correlations in these states are different from those of well-known FQH electron states (e.g., Laughlin or Moore-Read states), leaving the origin of their incompressibility uncertain. Halperin's idea of Laughlin states of QP pairs is also explored, but is does not seem adequate.

We report on exact diagonalization studies for fully spin polarized 5/2 fractional quantum Hall effect, incorporating Landau level mixing through the Bishara-Nayak effective interaction. We find that there is an experimentally accessible region in the phase diagram where the Pfaffian model accurately describes not only the ground state but also the neutral and charged excitations. These results are consistent with the observed persistence of the 5/2 Hall effect down to very low magnetic fields; they are also relevant to the experimental attempts to detect nonabelian braid statistics. The proposed route to nonabelian braid statistics in the 5/2 fractional quantum Hall effect (FQHE) [1][2][3], discovered more than two decades ago [4], proceeds through a sequence of remarkable emergences. To minimize the bulk of the repulsive interaction, electrons in the second Landau level (LL) dress themselves with two vortices to transform into composite fermions [5]; composite fermions (CFs) experience a vanishing magnetic field and form a Fermi sea [6]; the CF Fermi sea, however, is unstable due to a weak residual attractive interaction between composite fermions, which causes an equal spin p x ± ip y pairing, thereby opening a gap and producing an FQHE state [1,2,7]; the Abrikosov vortices of the paired CF state support zero mode solutions, namely majorana CFs, which are symmetric combinations of the CF creation and annihilation operators [3]; these obey nonabelian braid statistics [3] and are potential candidates for fault tolerant topological quantum computation [8].While the decisive verification of these ideas will eventually come from laboratory experiments, we have come to expect any successful theoretical postulate in the field of FQHE to pass the test against "computer experiments," that is, exact solutions of the full many body problem for finite systems typically containing up to 16-18 particles. A concrete realization of the above physics is through the Pfaffian (Pf) model of Moore and Read [1], which has been subjected to such tests. The Pf wave function for the ground state has a moderate overlap with the exact Coulomb ground state, which can be improved either by artificially strengthening the short range part of the interaction [9][10][11] or by considering the effect of finite thickness [12]. The sensitivity to such slight modifications in the interaction indicates that the physical 5/2 FQHE state lies close to an instability. An adiabatic connection has been shown in finite system studies between the Coulomb and the Pf ground states [11,13,14]. The situation is less clear for excitations, however. A test of the Pf quasiholes has not found them to be satisfactory approximations of the actual quasiholes of the unperturbed Coulomb interaction [15], and an adiabatic connection between the Pf and the Coulomb quasiparticles and quasiholes has not yet been demonstrated. Given that the nonabelian braid properties of the quasiparticles and quasiholes are of primary interest, it would appear important to ascertain the...