arXiv subjects

Arkadiusz Wojs

Publications and source records attributed to Arkadiusz Wojs.

At least 37 records · Page 2Linked to original sources

arXiv2004

Interaction and dynamical binding of spin waves or excitons in quantum Hall systems

Interaction between spin waves (or excitons) moving in the lowest Landau level is studied using numerical diagonalization. Becuse of complicated statistics obeyed by these composite particles, their effective interaction is completely different from the dipole-dipole interaction predicted in the model of independent (bosonic) waves. In particular, spin waves moving in the same direction attract one another which leads to their dynamical binding. The interaction pseudopotentials V_[up,up](k) and V_[up,down](k) for two spin waves with equal wavevectors k and moving in the same or opposite directions have been calculated and shown to obey power laws V(k) ~ k^alpha at small k. A high value of alpha_[up,up]~4 explains the occurrence of linear bands in the spin excitation spectra of quantum Hall droplets.

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arXiv2004

Fractional Quantum Hall States of Clustered Composite Fermions

The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin nu=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 nu_QE=1/2, 1/3, 2/3, corresponding to the electron fillings nu=3/8, 4/11, 5/13. The equivalent quasihole (QH) states occur at nu_QH=1/4, 1/5, 2/7, corresponding to nu=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.

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arXiv2004

Residual interactions and correlations among Laughlin quasiparticles: Novel hierarchy states

The residual interactions between Laughlin quasiparticles can be obtained from exact numerical diagonalization studies of small systems. The pseudopotentials V_QP(R)$ describing the energy of interaction of QE's (or QH's) as a function of their "relative angular momentum" R cannot support Laughlin correlations at certain QP filling factors (e.g., nu_QE}=1/3 and nu_QH=1/5). Because of this the novel condensed quantum fluid states observed at nu=4/11, 4/13 and other filling fractions cannot possibly be spin polarized Laughlin correlated QP states of the composite Fermion hierarchy. Pairing of the QP's clearly must occur, but the exact nature of the incompressible ground states is not completely clear.

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arXiv2003

Quasi two-dimensional electron-hole systems in a perpendicular magnetic field

The electronic properties of quasi two-dimensional multicomponent systems are investigated in the presence of a perpendicular magnetic field. The effects of the presence of a few valence band holes on the properties of quantum Hall systems are examined by analyzing the results of exact numerical diagonalization of small electron-hole systems confined to the spherical surface. The novel type of elementary excitations, the angular momenta, binding energies, interaction pseudopotentials, and effects on the photoluminescence spectrum are presented.

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arXiv2003

Novel Families of Fractional Quantum Hall States: Pairing of Composite Fermions

Fractional quantum Hall (FQH) states have recently been observed at unexpected values of the filling factor nu. Here we interpret these states as a novel family of FQH states involving pairing correlations rather than Laughlin correlations among the quasiparticles (QP's). The correlations depend upon the behavior of the QP-QP pseudopotential V_QP(L'), the interaction energy of a pair as a function of the pair angular momentum L'. This behavior, known from numerical studies of small systems, is used to demonstrate that pairing correlations give rise to FQH states at the experimentally observed values of nu.

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arXiv2003

Pairing and condensation of Laughlin quasiparticles in fractional quantum Hall systems

From the analysis of their interaction pseudopotentials, it is argued that (at certain filling factors) Laughlin quasiparticles can form pairs. It is further proposed that such pairs could have Laughlin correlations with one another and form condensed states of a new type. The sequence of fractions corresponding to these states includes all new fractions observed recently in experiment (e.g., ν=5/13, 3/8, or 4/11).

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arXiv2003

Composite fermions in quantum Hall systems

The occurrence of incompressible quantum fluid states of a two dimensional system is a result of electron--electron interactions in a highly degenerate fractionally filled Landau level. Novel quasiparticles (QP's) called composite Fermions (CF's) have allowed a simple single particle description of the most prominent incompressible states. Residual interactions among these QP's are investigated. These interactions determine the type of "daughter states" that can occur at the next generation. We demonstrate that at certain values of the QP filling factor nu_QP, Laughlin correlations among the QP's give rise to states of the standard CF hierarchy. At other values of nu_QP pairing of QP's is found leading to a novel hierarchy of incompressible states.

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arXiv2003

Novel excitonic states and photoluminescence in quantum hall systems

The formation and possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite Fermions) that can occur in a 2D electron in the presence of a strong magnetic field. Examples of such bound states are interband neutral and charged excitons, fractionally charged "anyon excitons", spin waves, skyrmions, or "skyrmion excitons". Possible decay processes include radiative recombination, experimentally observed in photoluminescence or spin transitions, important in the context of nuclear spin relaxation.

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arXiv2003

Excitonic complexes in quantum Hall systems

The formation and various possible decay processes of neutral and charged excitonic complexes in electronic integral and fractional quantum Hall systems are discussed. The excitonic complexes are bound states of a small number of the relevant negatively and positively charged quasiparticles (e.g., conduction electrons and valence holes, reversed-spin electrons and spin holes, Laughlin quasielectrons and quasiholes, composite fermions) that occur in an electron system under specific conditions (e.g., electron density, well width, electric and magnetic fields, or hydrostatic pressure). The examples of such bound states are interband neutral and charged excitons, fractionally charged "anyon excitons", spin waves, skyrmions, or "skyrmion excitons". Their possible decay processes include radiative recombination, experimentally observed in photoluminescence or far infrared emission, or spin transitions, important in the context of nuclear spin relaxation.

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arXiv2003

Justification for the composite fermion picture

The mean field (MF) composite Fermion (CF) picture successfully predicts the low-lying bands of states of fractional quantum Hall systems. This success cannot be attributed to the originally proposed cancellation between Coulomb and Chern--Simons interactions beyond the mean field and solely depends on the short range of the repulsive Coulomb pseudopotential in the lowest Landau level (LL). The class of pseudopotentials is defined for which the MFCF picture can be applied. The success or failure of the MFCF picture in various systems (electrons in the lowest and excited LL's, Laughlin quasiparticles) is explained.

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arXiv2003

Pairing of Composite Fermions, Laughlin Correlations, and the Fractional Quantum Hall Hierarchy

A novel hierarchy of fractional quantum Hall (FQH) states in the lowest Landau level (LL) is proposed to explain recently observed FQH fractions such as nu=5/13, 3/8, or 4/11. Based on the analysis of their interaction pseudopotentials, it is argued that the Laughlin quasiparticles (particles/holes in a partially filled composite fermion LL) form pairs. These pairs are proposed to have Laughlin correlations with one another and to form condensed states at a sequence of fractions which includes all new fractions observed in experiment.

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arXiv2002

Nuclear spin relaxation in integral and fractional quantum Hall systems

We report on the numerical study of the relaxation rates of nuclear spins coupled through the hyperfine interaction to a two dimensional electron gas (2DEG) at magnetic fields corresponding to both fractional and integral Landau level (LL) fillings nu. The Hamiltonians of up to 20 interacting electrons are diagonalized exactly in the spherical geometry, neglecting finite layer width, disorder, and LL mixing. The spectral functions tau^-1(E) describing response of the 2DEG to the reversal of an embedded localized spin are calculated. In a (locally) incompressible nu=1 or 1/3 state, the finite Coulomb energy of short spin waves, together with the small nuclear Zeeman energy, prevent nuclear spin relaxation even in the limit of vanishing electron Zeeman energy E_Z. However, we find that the nuclear spins can couple to the internal excitations of mobile finite-size skyrmions that appear in the 2DEG at sufficiently low E_Z and at nu slightly different from 1 or 1/3. The experimentally observed dependence of nuclear spin relaxation rate on E_Z and nu is qualitatively explained in terms of the occurrence of skyrmions and antiskyrmions of various topological charge.

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arXiv2002

Novel excitonic states in quantum Hall systems: Bound states of spin waves and a valence band hole

If the Zeeman energy is small, the lowest energy excitations of a two dimensional electron gas at filling factor nu=1 are spin waves (spin flip excitations). At nu slightly larger (smaller) than unity, reversed spin electrons (spin holes) can form bound states with K spin waves that are known as skyrmions, S_K^- (antiskyrmions, S_K^+). It is suggested in this work that a valence hole can also bind K spin waves to form an excitonic complex X_K^+, analogous to the S_K^+. One spin hole of the S_K^+ is simply replaced by the valence hole. At nu<=1, a small number of S_K^+'s are present before introduction of the valence hole. The (S_K^+)-(X_K^+) repulsion leads to correlations and photoluminescence similar to those of a dilute electron-(charged-exciton) (e-X^-) system at nu<=1/3. At nu>=1, the (S_K^-)-(X_K^+) attraction can potentially lead to different behavior.

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arXiv2001

Spin instabilities and quantum phase transitions in integral and fractional quantum Hall states

The inter-Landau-level spin excitations of quantum Hall states at filling factors nu=2 and 4/3 are investigated by exact numerical diagonalization for the situation in which the cyclotron (hbar*omega_c) and Zeeman (E_Z) splittings are comparable. The relevant quasiparticles and their interactions are studied, including stable spin wave and skyrmion bound states. For nu=2, a spin instability at a finite value of epsilon=hbar*omega_c-E_Z leads to an abrupt paramagnetic to ferromagnetic transition, in agreement with the mean-field approximation. However, for nu=4/3 a new and unexpected quantum phase transition is found which involves a gradual change from paramagnetic to ferromagnetic occupancy of the partially filled Landau level as epsilon is decreased.

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arXiv2001

Skyrmions in integral and fractional quantum Hall systems

Numerical results are presented for the spin excitations of a two-dimensional electron gas confined to a quantum well of width w. Spin waves and charged skyrmion excitations are studied for filling factors nu=1, 3, and 1/3. Phase diagrams for the occurrence of skyrmions of different size as a function of w and the Zeeman energy are calculated. For nu=3, skyrmions occur only if w is larger than about twice the magnetic length. A general necessary condition on the interaction pseudopotential for the occurrence of stable skyrmion states is proposed.

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arXiv2001

Spin excitation spectra of integral and fractional quantum Hall systems

Results are presented of detailed numerical calculations for the spin excitation spectra of a two-dimensional electron gas confined in a quantum well of finite width w, at magnetic fields corresponding to the fractional and integral fillings of the lowest and of excited Landau levels. Spin waves and skyrmions are identified, and their mutual interactions are studied at filling factors nu=1/3, 1, 3, and 5. The smallest skyrmions at nu=1/3 are equivalent to composite fermion charged excitons X_CF^(+/-). Bose condensates of nearly noninteracting spin waves and Laughlin correlations between finite-size skyrmions are found at nu=1 and 1/3 and, for w larger than about two magnetic lengths, also at nu=3 and 5. A general criterion for the occurrence of skyrmions at odd integral fillings and at Laughlin fractional fillings of the lowest Landau level is given in terms of the interaction pseudopotentials. This explains the dependence of skyrmion states on w observed in excited Landau levels.

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arXiv2001

Photoluminescence of the incompressible Laughlin liquid: Excitons, charged excitons, and fractionally charged excitons

The photoluminescence (PL) of a two-dimensional electron gas (2DEG) in a high magnetic field is studied as a function of the filling factor and the separation d between the electron layer and the valence hole. Depending on the magnitude of d relative to the magnetic length lambda, two distinct regimes in the response of the 2DEG to the valence hole occur, with different elementary emission processes contributing to the PL spectrum. At d lambda ("weak coupling" regime), the hole decouples or binds one or two Laughlin quasielectrons to form fractionally charged excitons (FCX's). The binding energies as well as the emission energies and intensities of all X- and FCX states are calculated.

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arXiv2001

Reversed-Spin Quasiparticles in Fractional Quantum Hall Systems and Their Effect on Photoluminescence

The energy, interaction, and optical properties of reversed-spin quasielectrons (QE_R's) in fractional quantum Hall systems are studied. Based on the short range of the QE_R-QE_R repulsion, a partially unpolarized incompressible nu=4/11 state is postulated within Haldane hierarchy scheme. To describe photoluminescence, a reversed-spin fractionally charged exciton hQE_R (QE_R bound to a valence hole h) is predicted. In contrast to its spin-polarized analog, hQE_R is strongly bound and radiative.

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