[Paper Review] Formation of an order in a system of exciton condensed phase islands in quantum wells

V. I. Sugakov|arXiv (Cornell University)|Jul 15, 2004

Semiconductor Quantum Structures and Devices3 citations

TL;DR

This paper proposes that the periodic fragmentation observed in luminescence rings from indirect excitons in double quantum wells arises from the formation of exciton condensed phase islands along the ring, driven by attractive exciton-exciton interactions including dominant Van der Waals forces. Using a kinetic model of exciton diffusion, recombination, and island growth, the study explains the macroscopic periodicity as a result of condensation instability at high exciton densities, with the critical temperature for fragmentation matching experimental values near 2 K.

ABSTRACT

A theory of exciton condensed phase creation in two-dimensional system is presented. The theory is applied to explain the appearance of the periodical fragmentation which was observed last years in luminescence from the ring around laser spot in crystal with double quantum wells.

Motivation & Objective

• To explain the origin of periodic fragmentation in luminescence rings observed in indirect exciton systems in double quantum wells.
• To investigate the role of attractive exciton-exciton interactions, particularly Van der Waals forces, in enabling the formation of exciton condensed phases.
• To model the spatial distribution and dynamics of exciton density and island formation under non-uniform pumping conditions.
• To link theoretical predictions of condensed phase island formation with experimental observations at low temperatures (~2 K).

Proposed method

• Formulated a system of coupled kinetic equations for electron, hole, and exciton densities in two-dimensional quantum wells under Gaussian pumping.
• Incorporated exciton production rate $ G = qWn_e n_h $ and accounted for diffusion, recombination, and lifetimes in the equations.
• Applied a kinetic model for island formation, using a distribution function $ f_n $ to describe the probability of an island having $ n $ excitons.
• Defined probability currents $ j_n $ that include exciton capture, escape, decay, and local pumping over island areas.
• Used a simplified model of the condensed phase, requiring only energy per pair, volume per pair, and surface energy, without full many-body theory.
• Estimated Van der Waals interaction via second-order perturbation theory, showing it dominates over dipole-dipole repulsion at distances < 6 exciton radii.

Experimental results

Research questions

• RQ1 What causes the periodic fragmentation in the luminescence ring of indirect excitons in double quantum wells?
• RQ2 How do attractive exciton-exciton interactions, particularly Van der Waals forces, enable the formation of exciton condensed phases?
• RQ3 Can a kinetic model of island growth explain the macroscopic periodicity of the fragmented ring structure?
• RQ4 Why does the fragmentation disappear at temperatures above ~2 K, and how does this relate to the condensation energy?

Key findings

• The periodic fragmentation in the luminescence ring is attributed to the formation of exciton condensed phase islands along the ring, where exciton density peaks.
• Van der Waals interactions between indirect excitons are attractive and exceed dipole-dipole repulsion at distances below 3–6 exciton radii, enabling condensation.
• The critical temperature for fragmentation disappearance (2.16 K) matches experimental observations (~2 K), supporting the model's validity.
• The binding energy per electron-hole pair in the condensed phase is estimated at 0.8 meV (10 K), consistent with experimental emission line positions.
• The model explains the macroscopic periodicity without requiring full many-body theory, relying only on basic condensed phase parameters like energy and volume per pair.
• The emission line shift of the fragment is minimal (sub-width) compared to free excitons, indicating that spectral line broadening mechanisms must be analyzed in conjunction with phase structure.