Coulomb Correlation and Band Gap Renormalization at High Carrier Densities in Quantum Wires

Abstract

We have studied the luminescence of narrow quantum wires at photoexcitation densities of up to ϳ3 3 10 6 cm 21 . We show that even at these densities, which are well above the expected Mott density of 8 3 10 5 cm 21 , excitonic recombination dominates over other recombination channels in stark contrast with the behavior of quantum wells and bulk structures at equivalent densities. As we observe no significant shift in the peak energy with density, an upper limit to the band gap renormalization can be set. [S0031-9007(97)03044-5] 71.27. + a, 78.47. + p Excitonic effects in a one dimensional (1D) system are expected to be even more significant than they are in two and three dimensional systems [1][2][3]. An enhancement of excitonic correlations [4] and an increased oscillator strength [5] have been observed experimentally. The question that then beckons is, up to what densities will excitons remain stable in quantum wires (QWRs); put otherwise one may wonder at what density the Mott transition occurs in optically excited QWRs. A fascinating aspect of high density studies, the Mott transition has been an active field of research over the past three decades [6], and there remain a number of open questions regarding this transition in three, two, and one dimensions [7]. In QWRs the transition is expected to occur when the insulating excitonic phase transforms into a conducting free electron-hole (e-h) plasma at a carrier density of about 8 3 10 5 cm 21 [3]. This transition has so far not been observed in optical studies, although it would be most interesting to probe it and associated effects such as a possible hysteresis in the Mott density [8].Semiconductor QWRs have also been actively studied, as it is expected that the singularity in the density of states in a quasi-1D system may lower threshold current densities, thus improving the performance of semiconductor lasers [9][10][11]. The common procedure of computing the optical gain using a 1͞ p E density of states is, however, incomplete as a number of effects such as inhomogeneities, Coulomb interactions, and many body effects are neglected. A better understanding of the recombination of a dense e-h plasma in QWRs is thus called for, and the subject has attracted considerable attention of late [4,[12][13][14][15][16].Recent progress in the growth of semiconductor nanostructures has made available wires of good quality which should open the way for rigorous studies that probe the different interactions that occur in quasi-1D systems. It is then unfortunate that the picture that emerges from the published literature on high density phenomena in QWRs is confused and contradictory. A prime example of such ambiguity is the issue of band gap renormalization (BGR). Experimental reports range from evidence for a very large band gap energy shift [12,15], to no shift at all [4,13,14], with some authors observing shifts only due to the carriers in other subbands [16]. The theoretical results are equally ambiguous. Some models predict a very large BGR [17 -19], even large...

Many-Body Renormalization of Semiconductor Quantum Wire Excitons: Absorption, Gain, Binding, and Unbinding

“…We find, consistent with a number of hitherto unexplained experimental observations [1][2][3], that the self-energy and the vertex corrections tend to cancel each other leading to an almost constant (in density) absorption/gain peak all the way to (and considerablely above) the Mott transition which occurs around a density of n c ∼ 3 × 10 5 cm −1 for 70Å wide T-quantum wires.…”

“…a density-dependent shrinkage of the fundamental band gap due to electron and hole self-energy corrections), which should vary strongly as a function of the photoexcited electron-hole density [7][8][9]. This striking lack of any dependence of the observed photoluminescence peak energy on the photoexcitation density has led to the suggestion [1,2] that the observed quantum wire photoluminescence may be arising entirely from an excitonic (as opposed to an electron-hole plasma (EHP)) recombination mechanism, and the effective excitonic energy is, for unknown reasons, a constant (as a function of carrier density) in 1D quantum wires. This, however, introduces a new puzzle because one expects the excitonic level to exhibit a "blue shift" (i.e.…”

“…Recent interest has focused on low dimensional excitons in artificially structured semiconductor quantum well or wire systems where carrier confinement may substantially enhance the excitonic binding energy leading to novel optical phenomena. In this Letter we consider the formation, stability, and optical properties of one dimensional (1D) excitons in semiconductor quantum wires, a problem which has attracted a great deal of recent experimental [1][2][3] and theoretical [4-6] attention. Our motivation has been a number of recent puzzling experimental observations [1,2], which find the photoluminescence emitted from an initially photoexcited semiconductor quantum wire plasma to be peaked essentially at a constant energy independent of the magnitude of the photoexcitation intensity.…”

“…In this Letter we consider the formation, stability, and optical properties of one dimensional (1D) excitons in semiconductor quantum wires, a problem which has attracted a great deal of recent experimental [1][2][3] and theoretical [4-6] attention. Our motivation has been a number of recent puzzling experimental observations [1,2], which find the photoluminescence emitted from an initially photoexcited semiconductor quantum wire plasma to be peaked essentially at a constant energy independent of the magnitude of the photoexcitation intensity. This is surprising because one expects a strongly density-dependent "red shift" in the peak due to the exchange-correlation induced band gap renormalization (BGR) (i.e.…”

Low-temperature photoluminescence spectra of highly excited quantum wires

“…Optical-nonlinear properties have been studied intensely in bulk and low-dimensional semiconductors [1][2][3][4][5][6][7][8][9][10][11][12]. At high densities the low-temperature optical spectra of semiconductors show a peak near the Fermi energy.…”