arXiv subjects

Arkadiusz Wojs

Publications and source records attributed to Arkadiusz Wojs.

At least 55 records · Page 3Linked to original sources

arXiv2001

Electron correlations in a partially filled first excited Landau level

The form of electron correlations in a partially filled degenerate Landau level (LL) is related to the behavior of the anharmonic part of the interaction pseudopotential. Unlike in the lowest LL, the pseudopotential in the first excited LL is harmonic at short range. As a result, the incompressible states in this LL have different correlations, occur at different filling factors nu, and cannot be described by a composite fermion model. The series of Laughlin-correlated states of electron pairs is proposed at nu=2+2/(q_2+2) with integer q_2. It includes Moore-Read nu=5/2 state and the nu=7/3 state. Despite coincidence of the values of nu, the latter state has different correlations than Laughlin state of single electrons at nu=1/3 and, in finite systems, occurs at a different LL degeneracy (flux).

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arXiv2001

Energy, interaction, and photoluminescence of spin-reversed quasielectrons in fractional quantum Hall systems

The energy and photoluminescence spectra of a two-dimensional electron gas in the fractional quantum Hall regime are studied. The single-particle properties of reversed-spin quasielectrons (QE$_{\rm R}$'s) as well as the pseudopotentials of their interaction with one another and with Laughlin quasielectrons (QE's) and quasiholes (QH's) are calculated. Based on the short-range character of the QE$_{\rm R}$--QE$_{\rm R}$ and QE$_{\rm R}$--QE repulsion, the partially unpolarized incompressible states at the filling factors $ν={4\over11}$ and ${5\over13}$ are postulated within Haldane's hierarchy scheme. To describe photoluminescence, the family of bound $h($QE$_{\rm R})_n$ states of a valence hole $h$ and $n$ QE$_{\rm R}$'s are predicted in analogy to the found earlier fractionally charged excitons $h$QE$_n$. The binding energy and optical selection rules for both families are compared. The $h$QE$_{\rm R}$ is found radiative in contrast to the dark $h$QE, and the $h($QE$_{\rm R})_2$ is found non-radiative in contrast to the bright $h$QE$_2$.

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arXiv2001

Mechanical effects in quantum dots in magnetic and electric fields

The mechanical effects in finite two-dimensional electron systems (quantum dots or droplets) in a strong perpendicular magnetic field are studied. It is shown that, due to asymmetry of the cyclotron dynamics, an additional in-plane electric field causes a ground state transition accompanied by a change in the average total angular momentum of the system, unless the lateral confining potential is exactly parabolic. A precise mechanical experiment is proposed in which a macroscopic angular momentum of a dense matrix of quantum dots could be measured and used to detect and estimate anharmonicity of the confinement.

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arXiv2001

Interaction and Particle-Hole Symmetry of Laughlin Quasiparticles

The pseudopotentials describing interaction of Laughlin quasielectrons (QE) and quasiholes (QH) in an infinite fractional quantum Hall system are studied. The QE and QH pseudopotentials are similar which suggests the (approximate) particle--hole symmetry recovered in the thermodynamical limit. The problem of the hypothetical symmetry-breaking QE hard-core repulsion is resolved by the estimate that the ``forbidden'' QE pair state has too high energy and is unstable. Strong oscillations of the QE and QH pseudopotentials persist in an infinite system, and the analogous QE and QH pair states with small relative angular momentum and nearly vanishing interaction energy are predicted.

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arXiv2000

Energy spectra and photoluminescence of fractional quantum Hall systems containing a valence-band hole

The energy spectrum of a two-dimensional electron gas (2DEG) interacting with a valence-band hole is studied in the high magnetic field limit as a function of the filling factor nu and the separation d between the electron and hole layers. For d smaller than the magnetic length lambda, the hole binds one or more electrons to form neutral (X) or charged (X-) excitons. The low-lying states can be understood in terms of Laughlin-like correlations among the constituent charged fermions (electrons and X-). For d comparable to lambda, the electron-hole interaction is not strong enough to bind a full electron, and fractionally charged excitons hQEn (bound states of a hole and one or more Laughlin quasielectrons, QE) are formed. The effect of these excitonic complexes on the photoluminescence spectrum is studied numerically for a wide range of values of nu and d.

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arXiv2000

Transformation of Statistics in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane's spherical geometry, the Fermion angular momentum l_F is replaced by l_B=l_F-(N-1)/2. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular momentum L_12) increases as L_12(L_12+1). Similar bands of low energy states occur in the two spectra if V increases more quickly than this.

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arXiv2000

Electron-Hole Systems in Narrow Quantum Wells: Excitonic Complexes and Photoluminescence

The energy and photoluminescence (PL) spectra of a two-dimensional electron gas (2DEG) interacting with a valence-band hole are studied in the high-magnetic-field limit as a function of the filling factor nu and the separation $d$ between the electron and hole layers. For d smaller than the magnetic length lambda, the hole binds one or more electrons to form neutral (X) or charged (X-) excitons, and PL probes the lifetime and binding energies of these complexes rather than the original correlations of the 2DEG. The low-lying states can be understood in terms of Laughlin-type correlations among the constituent negatively charged Fermions (electrons and X-'s). For d large compared to lambda, the electron--hole interaction is not strong enough to bind a full electron, and fractionally charged excitons (bound states of the hole and one or more Laughlin quasielectrons) hQEn are formed. The PL selection rule associated with rotational invariance (conservation of L) is only weakly violated in the interacting plasma, and the position and oscillator strengths of PL lines can be predicted and compared with numerical calculations.

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arXiv2000

Fractionally charged magneto-excitons

The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime is studied. The response of the 2DEG to an optically injected valence hole depends on the separation d between the electron and hole layers. At d smaller than the magnetic length lambda, the PL spectrum shows recombination of neutral (X) and charged (X-) excitons. At d>lambda, the hole binds one or two Laughlin quasielectrons (QE) of the 2DEG to form fractionally charged excitons (FCX), hQE or hQE2. Different FCX states have different optical properties, and their stability depends critically on the presence of QE's in the 2DEG. This explains discontinuities observed in the PL spectrum at such (Laughlin) filling factors as nu=1/3 or 2/3.

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arXiv2000

Negatively Charged Excitons and Photoluminescence in Asymmetric Quantum Well

We study photoluminescence (PL) of charged excitons ($X^-$) in narrow asymmetric quantum wells in high magnetic fields B. The binding of all $X^-$ states strongly depends on the separation $δ$ of electron and hole layers. The most sensitive is the ``bright'' singlet, whose binding energy decreases quickly with increasing $δ$ even at relatively small B. As a result, the value of B at which the singlet--triplet crossing occurs in the $X^-$ spectrum also depends on $δ$ and decreases from 35 T in a symmetric 10 nm GaAs well to 16 T for $δ=0.5$ nm. Since the critical values of $δ$ at which different $X^-$ states unbind are surprisingly small compared to the well width, the observation of strongly bound $X^-$ states in an experimental PL spectrum implies virtually no layer displacement in the sample. This casts doubt on the interpretation of PL spectra of heterojunctions in terms of $X^-$ recombination.

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arXiv2000

Electron Correlations in Partially Filled Lowest and Excited Landau Levels

The electron correlations near the half-filling of the lowest and excited Landau levels (LL's) are studied using numerical diagonalization. It is shown that in the low lying states electrons avoid pair states with relative angular momenta ${\cal R}$ corresponding to positive anharmonicity of the interaction pseudopotential $V({\cal R})$. In the lowest LL, the super-harmonic behavior of $V({\cal R})$ causes Laughlin correlations (avoiding pairs with ${\cal R}=1$) and the Laughlin-Jain series of incompressible ground states. In the first excited LL, $V({\cal R})$ is harmonic at short range and a different series of incompressible states results. Similar correlations occur in the paired Moore-Read $ν={5\over2}$ state and in the $ν={7\over3}$ and ${8\over3}$ states, all having small total parentage from ${\cal R}=1$ and 3 and large parentage from ${\cal R}=5$. The $ν={7\over3}$ and ${8\over3}$ states are different from Laughlin $ν={1\over3}$ and ${2\over3}$ states and, in finite systems, occur at a different LL degeneracy (flux). The series of Laughlin correlated states of electron pairs at $ν=2+2/(q_2+2)={8\over3}$, ${5\over2}$, ${12\over5}$, and ${7\over3}$ is proposed, although only in the $ν={5\over2}$ state pairing has been confirmed numerically. In the second excited LL, $V({\cal R})$ is sub-harmonic at short range and (near the half-filling) the electrons group into spatially separated larger $ν=1$ droplets to minimize the number of strongly repulsive pair states at ${\cal R}=3$ and 5.

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arXiv2000

The Fermion-Boson Transformation in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum $l_F$ is replaced by $l_B= l_F-{1\over2}(N-1)$. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical if and only if the pseudopotential is ``harmonic'' in form. However, similar low energy bands of states with Laughlin correlations occur in the two spectra if the interaction has short range. The transformation is used to clarify the relation between Boson and Fermion descriptions of the hierarchy of condensed fractional quantum Hall states.

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arXiv2000

Photoluminescence from fractional quantum Hall systems: Role of separation between electron and hole layers

The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime is studied as a function of the separation $d$ between the electron and valence hole layers. The abrupt change in the response of the 2DEG to the optically injected hole at $d$ of the order of the magnetic length $λ$ results in a complete reconstruction of the PL spectrum. At $d<λ$, the hole binds one or two electrons to form neutral ($X$) or charged ($X^-$) excitons, and the PL spectrum probes the lifetimes and binding energies of these states rather than the original correlations of the 2DEG. At $d>2λ$, depending on the filling factor $ν$, the hole either decouples from the 2DEG to form an ``uncorrelated'' state $h$ or binds one or two Laughlin quasielectrons (QE) to form fractionally charged excitons $h$QE or $h$QE$_2$. The strict optical selection rules for bound states are formulated, and the only optically active ones turn out to be $h$, $h$QE* (an excited state of the dark $h$QE), and $h$QE$_2$. The ``anyon exciton'' $h$QE$_3$ suggested in earlier studies is neither stable nor radiative at any value of $d$. The critical dependence of the stability of different states on the presence of QE's in the 2DEG explains the observed anomalies in the PL spectrum at $ν={1\over3}$ and ${2\over3}$.

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arXiv2000

Energy spectra of fractional quantum Hall systems in the presence of a valence hole

The energy spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime interacting with an optically injected valence band hole is studied as a function of the filling factor $ν$ and the separation $d$ between the electron and hole layers. The response of the 2DEG to the hole changes abruptly at $d$ of the order of the magnetic length $λ$. At $d<λ$, the hole binds electrons to form neutral ($X$) or charged ($X^-$) excitons, and the photoluminescence (PL) spectrum probes the lifetimes and binding energies of these states rather than the original correlations of the 2DEG. The ``dressed exciton'' picture (in which the interaction between an exciton and the 2DEG was proposed to merely enhance the exciton mass) is questioned. Instead, the low energy states are explained in terms of Laughlin correlations between the constituent fermions (electrons and $X^-$'s) and the formation of two-component incompressible fluid states in the electron--hole plasma. At $d>2λ$, the hole binds up to two Laughlin quasielectrons (QE) of the 2DEG to form fractionally charged excitons $h$QE$_n$. The previously found ``anyon exciton'' $h$QE$_3$ is shown to be unstable at any value of $d$. The critical dependence of the stability of different $h$QE$_n$ complexes on the presence of QE's in the 2DEG leads to the observed discontinuity of the PL spectrum at $ν={1\over3}$ or ${2\over3}$.

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arXiv2000

Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential

The mean field composite Fermion (CF) picture successfully predicts angular momenta of multiplets forming the lowest energy band in fractional quantum Hall (FQH) systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field, because these interactions have totally different energy scales. Rather, it results from the behavior of the Coulomb pseudopotential V(L) (pair energy as a function of pair angular momentum) in the lowest Landau level (LL). The class of short range repulsive pseudopotentials is defined that lead to short range Laughlin like correlations in many body systems and to which the CF model can be applied. These Laughlin correlations are described quantitatively using the formalism of fractional parentage. The discussion is illustrated with an analysis of the energy spectra obtained in numerical diagonalization of up to eleven electrons in the lowest and excited LL's. The qualitative difference in the behavior of V(L) is shown to sometimes invalidate the mean field CF picture when applied to higher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state in the first excited LL. The analysis of the involved pseudopotentials also explains the success or failure of the CF picture when applied to other systems of charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticles in the FQH hierarchy or charged excitons in an electron-hole plasma.

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arXiv2000

Composite Fermions in Fractional Quantum Hall Systems

The composite Fermion (CF) picture offers a simple intuitive way of understanding many of the surprising properties of a strongly interacting two-dimensional electron fluid in a large magnetic field. The simple way in which the mean field CF picture describes the low lying bands of angular momentum multiplets for any value of the applied magnetic field is illustrated and compared with the results of exact numerical diagonalization of small systems. The justification of the success of the CF approach is discussed in some detail, and a CF hierarchy picture of the incompressible quantum fluid states is introduced. The CF picture is used to understand the energy spectrum and photoluminescence of systems containing both electrons and valence band holes.

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arXiv2000

Energy spectra and photoluminescence of charged magneto-excitons

Charged magneto-excitons X- in a dilute 2D electron gas in narrow and symmetric quantum wells are studied using exact diagonalization techniques. An excited triplet X- state with a binding energy of about 1 meV is found. This state and the singlet are the two optically active states observed in photoluminescence (PL). The interaction of X-'s with electrons is shown to have short range, which effectively isolates bound X- states from a dilute e-h plasma. This results in the insensitivity of PL to the filling factor nu. For the "dark" triplet X- ground state, the oscillator strength decreases exponentially as a function of 1/nu which explains why it is not seen in PL.

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arXiv2000

Charged Excitons in a Dilute 2D Electron Gas in a High Magnetic Field

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 nu, and an exponential decrease of the oscillator strength of the dark triplet X- as a function of 1/nu$.

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arXiv1999

Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes

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 nu=n/(1+2pn), 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.

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