Biexciton as a Feshbach resonance and Bose–Einstein condensation of paraexcitons in Cu₂O

Abstract

Paraexcitons, the lowest energy exciton states in Cu 2 O, have been considered a good system for realizing exciton Bose-Einstein condensation (BEC). The fact that their BEC has not been attained so far is attributed to a collision-induced loss, whose nature remains unclear. To understand collisional properties of cold paraexcitons governing their BEC, we perform a theoretical analysis of the s-wave paraexciton-paraexciton scattering at low temperatures. We show the two-channel character of the scattering, where incoming paraexcitons are coupled to a biexciton in a closed channel. Being embedded in the paraexciton scattering continuum, the biexciton is a Feshbach resonance giving rise to a paraexciton loss and a diminution of their background scattering length. In strain-induced traps, the biexciton effects generally increase with stress. Thus the scattering length a of trapped paraexcitons decreases monotonically with stress turning its sign as stress goes beyond a critical value. In the stress range with a<0, the paraexciton loss increases with stress, whereas in that with a>0 the loss is almost stress-independent. Importantly, that in the latter case the loss rate can be reduced to such small values that it has no effects on BEC by lowering temperatures to near one Kelvin and below. Our approximate calculations give the critical value of stress in the range just above one kilobar; thus BEC of strain-confined paraexcitons might be attained under low stress at a subkelvin temperature.

Symmetry-dependent exciton-exciton interaction and intervalley biexciton in monolayer transition metal dichalcogenides

“…Meanwhile, the potential shape remains the same for all ML TMDs with a repulsive wall at small distances and an exponential fall at larger ones. These features are characteristic of the interaction between excitons, 52,60 resembling that between atoms in diatomic molecules. 34 Further, for freestanding ML TMDs, the intravalley interaction strength is somewhat above 2E b a 2…”

“…x relevant to the low-density limit under consideration, one can still treat excitons as bosons interacting via the effective two-body interaction. 48,52 To formulate an exciton Hamiltonian, we start from the fermionic electron-hole Hamiltonian H eh . We adopt here the method of Haug and Schmitt-Rink that consists in a low-density expansion of the electron and hole density and pair operators into products of exciton operators.…”

“…Description of the exchange exciton-exciton interaction is a problematic issue because of its nonlocality. 52 We will draw the interaction's qualitative features from basic symmetry principles and perform an approximate quantitative analysis relying on calculations for limiting cases. As a result of the Pauli exclusion principle, the exchange exciton-exciton interaction is short-range, repulsive between identical excitons and between bright and dark ones.…”

“…Independent of the valley position, U Γ−Γ (r) is closely similar to its counterpart in conventional semiconductors: each of its terms is a product of two two-center integrals met in theory of diatomic molecules. 52,60 The difference is, the carrier-carrier interaction has the form of the Keldysh potential and the consequent exciton wave function is a variational one instead of the hydrogenic function.…”

“…The approach proposed in ref. 52, which consists in expanding the exchange interaction energy density into a series of powers of α, can be applied. However, with α ≈ β ≈ 1/2, one has to retain a large number of the series terms yielding a high order differential equation.…”