Topologically enhanced exciton transport

Abstract

Excitons dominate the optoelectronic response of many materials. Depending on the time scale and host material, excitons can exhibit free diffusion, phonon-limited diffusion, or polaronic diffusion, and exciton transport often limits the efficiency of optoelectronic devices such as solar cells or photodetectors. We demonstrate that topological excitons exhibit enhanced diffusion in all transport regimes. Using quantum geometry, we find that topological excitons are generically larger and more dispersive than their trivial counterparts, promoting their diffusion. We apply this general theory to organic polyacene semiconductors and show that exciton transport increases up to fourfold when topological excitons are present. We also propose that non-uniform electric fields can be used to directly probe the quantum metric of excitons, providing a rare experimental window into a basic geometric feature of quantum states. Our results provide a new strategy to enhance exciton transport in semiconductors and reveal that mathematical ideas of topology and quantum geometry can be important ingredients in the design of next-generation optoelectronic technologies.

Fig. 1. Topologically enhanced exciton transport.

Topologically-enhanced diffusive transport of excitons (blue/red) with inversion symmetry-protected topological ${\mathbb{Z}}_2$invariant P_exc in the presence of phonons (wiggly orange lines). Due to exciton-phonon interactions, the propagating excitons in topological excitonic band can be scattered, dephased, and the diffusive transport of the excitons can be further altered with non-uniform electric fields introducing a controllable forcing. We show that non-trivial excitonic quantum geometry can be manifested in all these transport features.

Fig. 2. Enhanced free exciton diffusion.

Free diffusion of (a) topologically non-trivial (Topo.) and (b) trivial (Triv.) excitons. The diffusivity of topologically non-trivial excitons is bounded from below by the excitonic ${\mathbb{Z}}_2$ invariant. Parameters for n = 5 polypentacene are used, with the DFT predicted combination of intracell (t₁) and intercell (t₂) hoppings employed in (a) while the order is flipped in (b), to directly ascertain the impact of topology. c Exciton diffusion constant as a function of t₁ and t₂ with t₂ > t₁ (t₂ < t₁) representing topological and trivial excitons respectively. Breakdown of the contribution to the exciton diffusion, shown in (c), by (d) exciton band dispersion and (e) exciton geometry (Geo.).

Fig. 3. Non-uniform electric fields.

a Schematic of non-uniform electric field, $\nabla \mathcal{E}\left(R\right)\ne 0$, on a polypentacene crystal. The quantum metric of the topological exciton leads to a larger force due to the electric field (orange) compared to the trivial case. b Electric field induced tuning of the exciton group velocity ${\tilde{v}}_Q$ of the lowest exciton band for different values of t₂ and fixed t₁ = 0.33 eV. Our extracted value of t₂ for polypentacene from DFT is 0.52 eV. The solid coloured lines (purple to red) show the exciton group velocity with an applied electric field while the dashed lines show the corresponding velocity in the absence of an applied electric field. The velocity plots with increasing t₁ are offset by 0.5 eV for clarity.

Fig. 4. Topology-enhanced phonon-mediated transport in polyacene chains.

a–b Exciton-phonon matrix elements resolved in initial Q and final $Q^{\prime }$ excitonic centre-of-mass momentum in Polypentacene. c Phonon-induced exciton dephasing as function of initial momentum Q at 50 K (orange) and 300 K (blue) in polypentacene. The trivial and topological exciton dephasings are shown by the solid and dashed lines, respectively. d Phonon-mediated exciton diffusion for trivial (blue) and topological (pink) excitons in polypentacene (Pent) as a function of temperature (Temp). For comparison, we show the phonon-mediated exciton diffusion for polyheptacene (Hept) for trivial (red) and topological (orange) excitons.

Fig. 5. Transport of topological exciton-polarons.

Exciton-polaron and exciton band dispersion, relative to band gap (E_Gap) for (a) topological and (b) trivial excitons. The lowest (next lowest) polaron energy is shown in blue (orange). A clear polaron shift is observed in both cases. c Schematic of reduced transport of exciton-polarons compared to bare excitons. d Ratio of free exciton to exciton-polaron group velocities in polypentacene at 300K for trivial (Triv.) and topological (Topo.) regimes, shown in green and red, respectively. The blue region indicates mass enhancement and slower exciton-polarons while the pink region indicates mass reduction and faster excitons.