Anyon excitons

Abstract

We propose a model of an anyon exciton consisting of a hole and several anyons, and apply it to the spectroscopy of an incompressible quantum liquid. Fractionalization of the electron charge makes properties of such entities quite different from those of usual magnetoexcitons. The model describes a number of properties established by few-particle simulations, including an abrupt change in emission vs electron-hole asymmetry of the system. The attractive field of a hole may eliminate the hard core constraint for anyons. The effect of exciton-magnetoroton coupling is discussed. PACS numbers: 73.20.Dx, Phenomena in two-dimensional (2D) electron systems related to the fractional quantum Hall effect (FQHE) [1,2] and Wigner crystallization were originally discovered by means of magnetotransport. Later on the formation of an incompressible quantum liquid (IQL) [3], underlying the FQHE, and related phenomena have been investigated by optical experiments, which have become a powerful tool in the field [4]. These findings stimulated theoretical activity on the optical spectroscopy of the FQHE [5][6][7][8]. It has been shown that a hidden symmetry, which is inherent in 2D systems with charge symmetric electron-hole interaction (V ee = Vhh = -Veh), results in exact cancellation of the effect of the electron background on optical spectra. Optical spectra of symmetric systems are trivial, since they coincide with the spectra of free magnetoexcitons, and are insensitive to electron phase transitions. Therefore, the spectroscopy of chargeasymmetric systems acquires a special importance. Gap widths for IQLs determined from cusp strengths [5(a)] in extrinsic optical emission spectra were reported [4(a)] for such systems.It is one of the most remarkable properties of IQLs that their elementary excitations carry fractional charge [3], and are anyons [9,10], i.e., obey fractional statistics [11,12]. The theory [5(c),8] predicts that fractional charges should manifest themselves by dramatic changes in the position and the intensity of the emission band vs the asymmetry parameter. The ratio h/l, where h is a distance between electron and hole confinement planes, and / = (ch/eH) 1 / 2 is the magnetic length, may be chosen as such a parameter. Numerical simulations for few-electron systems are accessible only for small values of h/l < 1. For the opposite limit case of strongly asymmetric systems, h/l > 1, the approach based on the anyon concept seems to be most promising. An exciton, appearing against a background of an electron IQL, is a neutral entity consisting of a valence hole and several anyons, e.g., if the filling factor v = 1/3, the charge of anyons e* = -e/3, their statistical charge a = -1/3 (for comparison, a -0 for boso»ns, and a = 1 for fermions) [9], and the number of anyons N = 3. If h ^> /, the mean separation between anyons in an exciton is about h, which is larger than the anyon size, I. Therefore, anyons are well defined particles, anyon-anyon and anyon-hole interactions follow a Coulomb law in the leading approximati...

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

“…Although hQE is dark, its first excited state, hQE*, is both bound and radiative and can contribute to the PL spectrum. The charge neutral "anyon exciton" hQE 3 suggested by Rashba et al 27 is neither bound nor radiative. Finally, the radiative excitonic state (k = 0 charge neutral e-h pair weakly coupled to the 2DEG) breaks apart at d > 2λ.…”

“…[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] In symmetrically doped quantum wells (QW), where both conduction electrons and valence holes are confined in the same 2D layer, the photoluminescence (PL) spectrum of an electron gas (2DEG) probes the binding energy and optical properties of neutral and charged excitons (bound states of one or two electrons and a hole, X = e-h and X − = 2e-h), rather than the original correlations of the 2DEG itself. The experiments [10][11][12][13][14][15][16][17][18][19][20] and theory [30][31][32][33][34][35][36] agree that the X − can exist in the form of a number of different bound states, whose binding energies depend strongly on the well width w and composition, magnetic field B, etc., but (at least in dilute systems) much less on the electron filling factor ν.…”

The hierarchy of incompressible fractional quantum Hall states

“…The χ The e − X − PDF for different QXs; curve for χ + resembles e − e PDF of Laughlin liquid; shoulders for χ and χ + reflect additional charge quanta pushed onto the hole (Wójs et al, 2006a). discontinuity is different from that due to anyon excitons (Chen and Quinn, 1994b;Parfitt and Portnoi, 2003;Portnoi and Rashba, 1996;Rashba and Portnoi, 1993;Wójs and Quinn, 2000b,c) anticipated in much wider wells (e.g., for w ≥ 40 nm at n = 2 × 10 11 cm −2 ). The two effects can be distinguished by different magnitude (∼ ∆ IQL vs ∆ ± ) and opposite direction of the jump of emission energy when passing through ν = 1/3.…”

Two-dimensional electron-hole systems in a strong magnetic field: Composite fermion picture for multicomponent plasmas

“…9 For N h = 1 these systems serve as simple guides to understanding photoluminescence. [1][2][3][4][5] For larger values of N h it is possible to form a multi-component plasma containing electrons and X − k complexes. 7 We propose a model 10 for determining the incompressible quantum fluid states 11 of such plasmas, and confirm the validity of the model by numerical calculations.…”

“…Recently there has been considerable interest in two dimensional systems containing both electrons and holes in the presence of a strong magnetic field. [1][2][3][4][5][6][7][8] In such systems, neutral (X 0 ) and charged excitons (X − ) and larger exciton complexes (X − k , k neutral X 0 's bound to an electron) can occur. The excitonic ions X − k are long-lived Fermions, 6,7 whose energy spectra contain Landau level structure.…”