Dynamics of excitons in a potential trap at ultra-low temperatures: paraexcitons in Cu₂O

Abstract

We present experiments on the luminescence of excitons confined in a potential trap at sub-Kelvin temperatures after nanosecond pulsed laser excitation. Analysis of the experimental results with a rate model shows that the so-called Auger decay of yellow excitons, which in previous studies led to a rapid decay of the excitons at high densities and thus prevented reaching the critical density for Bose-Einstein condensation (BEC), is greatly reduced for paraexcitons. We demonstrate that exciton numbers well above 10 10 can be collected in a potential trap, albeit at temperatures in the 10 K range. During their lifetime of about 500 ns the paraexcitons cool down to the temperature of the He bath. This opens up the possibility to observe a BEC of paraexcitons provided that the bath temperature can be reduced to below 100 mK.(1) with 0 being the average oscillator frequency of the trapping potential and ζ the Riemann zeta function, decreases much faster with temperature, T , than in free space.Due to their unique properties, the excitons of the so-called yellow series in the semiconductor cuprous oxide (Cu 2 O) are still considered one of several promising candidates for excitonic BEC (for reviews see [4][5][6]). This is related to the large binding energy of 150 meV, which shifts the Mott density to 10 19 cm −3 at cryogenic temperatures [7,8]. Made up of doubly degenerate valence and conduction bands, the ground state of this series splits into the triply degenerate orthoexciton and the nondegenerate paraexciton, which is the energetically lowest exciton state, = 12.1 meV below the orthoexciton states. Due to the positive parity of the bands, the orthoexciton is only weakly optically allowed (quadrupole transition with oscillator

Modeling of the thermalization of trapped paraexcitons inCu2Oat ultralow temperatures

“…These excitons consist of a hole in the + 7 valence band and an electron in the + 6 conduction band, and they have a + 2 symmetry. The experimentally determined lifetimes for these excitons are [7] τ = 300 ns and [5] τ = 650 ns and hence remarkably long. The main question we want to address is: Do the excitons reach the crystal lattice temperature of the order of 100 mK within their finite lifetime?…”

“…Cuprous oxide (Cu 2 O) has been in the focus of experimental studies for decades and continues to be of interest today [1][2][3][4][5][6][7]. Due to the long lifetime and the high binding energy, paraexcitons in Cu 2 O are a good candidate for the experimental realization of an excitonic Bose-Einstein condensate (BEC) in a three-dimensional system.…”

Multicomponent exciton gas in cuprous oxide: cooling behaviour and the role of Auger decay

“…To model the Auger-like two-body decay we use a kaveraged Auger rate A as commonly employed to explain experimental data [18,29,30]. The loss of excitons of the i-th species can then be described by the collision term (17) with constant Auger rates A ij .…”

Unexpectedly slow two particle decay of ultra-dense excitons in cuprous oxide

“…The density n is difficult to calibrate [15,19,[21][22][23][32][33][34][35][36][37][38][39] and absolute measurements were therefore not attempted.…”