Topologically-enhanced exciton transport

Excitons, Coulomb-bound electron-hole pairs, dominate the optoelectronic response of a multitude of semiconductors Wang et al. (2018); Perea-Causin et al. (2022); Posmyk et al. (2024). Prominent examples include organic Mikhnenko et al. (2015); Valencia et al. (2023) and low-dimensional Chernikov et al. (2014); Yu et al. (2015); Dresselhaus et al. (2007) semiconductors, each a vast and versatile family of compounds which host excitons with large binding energies that can reach hundreds of milielectronvolts Mikhnenko et al. (2015); Giannini et al. (2022). The formation, dynamics, lifetime, and transport of excitons dictate the efficiency of a host of technological applications, from solar cells Wilson et al. (2011); Congreve et al. (2013) and light-emitting diodes Xu et al. (2021); Chowdhury et al. (2025), to biosensors Shanmugaraj and John (2019); Geldert et al. (2017). From a material perspective, the chemical and structural diversity available in the design of organic and low-dimensional semiconductors allows fine-tuning of the electronic and excitonic properties for customized device applications Huang et al. (2018).

Despite their promise, one of the key limitations of organic semiconductors is the low mobility of excitons Giannini et al. (2022); Sneyd et al. (2021); Muth et al. (2024). For example, low exciton mobility has been shown to inhibit the efficiency of organic semiconductor based solar cells Ghorab et al. (2022) since excitons decay before being extracted. As another example, in some organic systems the fission of optically active singlet excitons into pairs of optically inactive triplet excitons could help boost efficiency beyond the Shockley-Queisser limit Congreve et al. (2013), but the diffusion of these triplets is even slower than that of singlets Muth et al. (2024), and again exciton transport is a limiting factor. Other schemes, such as organic co-crystals Gunder et al. (2021); Chen et al. (2023) and organic-inorganic interfaces Bettis Homan et al. (2017); Bowman et al. (2022); Thompson et al. (2023a), again suffer from exciton mobility limitations.

In this work, we propose topology as a new avenue to enhance exciton transport. The topology of electrons is well-established Qi and Zhang (2011); Hasan and Kane (2010); Armitage et al. (2018), leading to remarkable transport properties such as quantum Hall phenomena Chang et al. (2023). A natural question to ask is whether topological ideas can be extended to excitons, which are starting to be explored in two-dimensional van der Waals layered materials Wu et al. (2017); Kwan et al. (2021), organic semiconductors Jankowski et al. (2024), and idealised models Davenport et al. (2024); Zhu et al. (2024). In this context, a recent remarkable result concerns the topologically-induced non-trivial Riemannian geometry of exciton wavefunctions. Specifically, it has been demonstrated that exciton quantum geometry, phrased in terms of the quantum metric Provost and Vallee (1980), provides a lower bound on the centre-of-mass spread $\xi$ of excitons Jankowski et al. (2024):

where $a$ is the lattice parameter of the crystal and $P_{\text{exc}}$ is an excitonic topological invariant protected by crystalline inversion symmetry. The relationship between topology, quantum geometry, and exciton properties is general and can be applied to different topological invariants in different dimensions and in different material platforms Bouhon et al. (2023). For example, in a one-dimensional setting, exemplified by organic polyacenes Cirera et al. (2020); Romanin et al. (2022); Jankowski et al. (2024), the excitonic topology can be characterised through a topological invariant $P_{\text{exc}}\in\mathbb{Z}_{2}$, associated with the first Stiefel-Whitney characteristic class $w_{1}\in\mathbb{Z}_{2}$ that reflects the unorientability of an excitonic band Jankowski et al. (2024); Ahn et al. (2019); Bouhon et al. (2020).

Qualitatively, the bound in Eq. (1) implies that topological excitons are more delocalised, and can be larger, than their trivial counterparts. In this work, we exploit this key insight to demonstrate that topological excitons exhibit enhanced transport compared to their trivial counterparts. We demonstrate enhanced exciton transport in all regimes, ranging from free exciton diffusion at femtosecond timescales to phonon-limited and polaronic diffusion at longer picosecond timescales. We also illustrate these general results in a family of organic polyacene crystals, where we find that topological excitons exhibit a four-fold increase in their transport compared to their trivial counterparts. Overall, our work establishes topology as a new avenue for improving optoelectronic technologies.

To explore the role of topology on exciton transport, we focus on a one-dimensional system that has recently been predicted to host topological excitons Jankowski et al. (2024). In this setting, single-particle electron properties are described by the Su-Schrieffer-Heeger (SSH) model Su et al. (1979, 1980):

with $c^{\dagger}_{B,j}/c_{A,j}$ being the creation/annihilation operators for the electrons at sublattices $A,B$, in unit cell $j$, and alternating hopping parameters $t_{1}$ and $t_{2}$. The topological phase realising topological edge states corresponds to $t_{2}>t_{1}$, and the trivial phase corresponds to $t_{2}<t_{1}$ Su et al. (1979, 1980).

From these single-particle electron and hole states, we then describe the exciton properties using the Wannier equation Thompson et al. (2023b, a); Jankowski et al. (2024), which directly incorporates the electron-hole Coulomb interaction. The solution of the Wannier equation yields exciton bands $E_{\nu Q}$ associated with exciton states $\ket{\psi^{\text{exc}}_{\nu Q}}$, where $\nu$ is the band index and $Q$ is the exciton centre-of-mass momentum. We also introduce $\ket{u^{\text{exc}}_{\nu Q}}$ as the cell-periodic part of the excitonic Bloch state $\ket{\psi^{\text{exc}}_{\nu Q}}=e^{iQR}\ket{u^{\text{exc}}_{\nu Q}}$, where $R=(r_{\mathrm{e}}+r_{\mathrm{h}})/2$ is the centre-of-mass position of the exciton, with electron position $r_{\mathrm{e}}$ and hole position $r_{\mathrm{h}}$. The topology of excitons in one-dimensional centrosymmetric semiconductors can be captured by a $\mathbb{Z}_{2}$ invariant $P_{\text{exc}}$, which can be directly obtained from the excitonic states Jankowski et al. (2024).

A material realisation of this model is provided by polyacene chains composed of $n$-ring acene molecules, where $n=3,5,7$, linked by a carbon-carbon bond on the central carbon atoms. Illustrative examples, polyanthracene ($n=3$) and polypentacence ($n=5$), are shown in Fig. 1. These polyacenes exhibit a topologically trivial exciton phase with $P_{\text{exc}}=0$ for $n=3$, and a topological phase with $P_{\text{exc}}=1$ for $n=5,7$ Jankowski et al. (2024).

We emphasise that the model and materials described above are for illustrative purposes only, and the key findings of this work are generally applicable to the transport of topological excitons in any material and dimension.

Upon photoexcitation, excitons diffuse freely at femtosecond timescales Rosati et al. (2020); Ashoka et al. (2022); Zhang et al. (2022). The exciton diffusion constant is given by (see SM):

where $E_{\nu Q}$ is the exciton energy dispersion for band $\nu$, $\Delta^{\mu\nu}_{Q}=E_{\mu}(Q)-E_{\nu}(Q)$ is the energy difference between the pair of exciton bands $\mu$ and $\nu$, and $g^{\mu\nu}_{xx}(Q)=\braket{\partial_{Q}u^{\text{exc}}_{\mu Q}|u^{\text{exc}}_{\nu Q}}\braket{u^{\text{exc}}_{\nu Q}|\partial_{Q}u^{\text{exc}}_{\mu Q}}$ is the excitonic multiband quantum metric. The exciton diffusivity in Eq. (3) has two contributions: the first term arises from the energy dispersion, and the second term arises from the quantum geometric properties of the associated exciton states.

We next show that the geometric term in the exciton diffusivity of Eq. (3) leads to enhanced transport for topological excitons. Starting with the flat band limit, the contribution from the exciton energy dispersion vanishes, as $\partial^{2}E_{\nu Q}/\partial Q^{2}=0$. Therefore, the exciton diffusion comes entirely from the geometric contribution. The geometric contribution scales according to $\Delta^{\mu\nu}_{Q}g^{\mu\nu}_{xx}(Q)\propto 1/\Delta^{\mu\nu}_{Q}$ (see SM), and in the flat band limit, focusing on the lowest exciton band, we can approximate the geometric contribution to the diffusivity as ${D_{\nu=1}\approx\frac{\Delta}{\hbar}\sum_{\mu\neq\nu=1}\langle g^{\mu\nu}_{xx}(Q)\rangle}$, where $\Delta$ is the smallest $Q$-independent gap from the band. We can then define the Brillouin zone average quantum metric $\langle g^{\nu}_{xx}(Q)\rangle$ associated with exciton band $\nu$ by tracing over the interband contributions according to $\langle g^{\nu}_{xx}(Q)\rangle=\sum_{\mu\neq\nu}\langle g^{\mu\nu}_{xx}(Q)\rangle$, and we obtain that the diffusivity in the flat band limit is:

Using the bound $\xi^{2}\geq\frac{a^{2}P_{\text{exc}}^{2}}{4}$ from Eq. (1), and noting that the exciton centre-of-mass spread is related to the metric according to $\xi^{2}=\langle g^{\nu=1}_{xx}(Q)\rangle$, we identify a lower bound on the geometric contribution to the exciton diffusivity:

Therefore, diffusive exciton transport in the lowest exciton band is directly impacted by the underlying exciton topology: the geometric contribution to the exciton diffusivity exhibits a lower bound for topological excitons ($P_{\mathrm{exc}}=1)$ but no bound for trivial excitons ($P_{\mathrm{exc}}=0$). This is a direct consequence of the lower bound on the exciton centre-of-mass spread, as determined by quantum geometry, which makes topological excitons larger and therefore facilitates diffusion.

Moving to the general dispersive case, both topological and trivial excitons will have equivalent contributions from the band dispersion to the diffusivity. Therefore, we can generally claim that topological excitons in the diffusive regime exhibit enhanced transport compared to their trivial counterparts.

To numerically illustrate the above results, we consider polypentacene as an example of a material hosting topological excitons with $t_{2}>t_{1}$. We construct an initial exciton wavepacket, formed around the photoexcitation spot, and we calculate the subsequent exciton diffusion that leads to the spatial spread depicted in Fig. 2(a). To test the importance of the topology-bound geometric contribution, we also consider the scenario in which the values of the hopping parameters are swapped, so that $t_{2}<t_{1}$ and we are in the trivial regime. The corresponding exciton diffusion is depicted in Fig. 2(b). The two scenarios have the same band dispersion, leading to the same first term in Eq. (3). However, the topological exciton diffuses more rapidly, a consequence of the geometric term in the diffusivity, which is bounded by below for topological excitons. These results explicitly demonstrate that exciton diffusion is enhanced in polypentacene driven by the underlying exciton topology.

More generally, Fig. 2(c) presents the diffusion constant as a function of $t_{2}$ and $t_{1}$ allowing us to demonstrate the wide applicability of our results. For any pair $\{t_{1},t_{2}\}$, if $t_{2}>t_{1}$ (topological excitons) then the diffusion constant is significantly larger than for the equivalent pair with $t_{1}>t_{2}$ (trivial). When $t_{1}$ and $t_{2}$ are significantly different, the resulting diffusivities can differ by several orders of magnitude. The band contribution to the diffusion for topological and trivial excitons is equivalent [Fig. 2(d)], peaking at $t_{1}\sim t_{2}$, where the electron and exciton band structures become most dispersive. In contrast the geometric contribution is distinctly larger for the topological excitons compared to trivial ones [Fig. 2(e)]. Non-zero topological transport in the flat band limit can be seen by comparing the $t_{1}=0$ or $t_{2}=0$ limit in Fig. 2(d,e) for the topological and trivial excitons, respectively.

We next explore driven exciton transport under non-uniform electric fields, which we demonstrate can be used to directly probe the exciton quantum geometry. The exciton group velocity $\langle v_{\nu Q}\rangle$ associated with band $\nu$ is given in one dimension by (see Methods) :

where $\langle v^{0}_{\nu Q}\rangle$ is the free exciton group velocity and $\nabla_{R}\mathcal{E}(R)$ is the applied electric field gradient which couples to the electron-hole distance $\langle r\rangle$. According to Eq. (6), the total exciton group velocity has a contribution from the free exciton group velocity $\langle v^{0}_{\nu Q}\rangle$, and a contribution from the quantum metric derivatives. In one dimension, the latter can be described by the Christoffel symbols $\Gamma^{\mu\nu}_{xxx}(Q)=\frac{1}{2}\partial_{Q}g^{\mu\nu}_{xx}(Q)$. Overall, an exciton moving in a non-uniform electric field experiences a force, leading to either acceleration or deceleration of the exciton, and a modulation of the exciton group velocity.

The geometric contribution to the exciton group velocity in Eq. (6) depends on the energy difference $\Delta^{\mu\nu}_{Q}$ between bands $\mu$ and $\nu$. This dependence can be suppressed by increasing dielectric screening, for example through strongly polar substrates, such that $\Delta^{\mu\nu}_{Q}\approx\Delta$ can be made approximately uniform over the exciton Brillouin zone. In this regime, the non-linear exciton transport in non-uniform electric fields is directly given by the quantum geometric Christoffel symbols.

In Fig. 3(a), we schematically show the impact of an applied non-uniform electric field on exciton transport, where topological excitons experience an enhanced transport. Quantitatively, we perform a numerical simulation of the exciton group velocity for polypentacene, and additional simulations where we vary $t_{2}$ freely, and for simplicity we set the electric field gradient to be constant $\nabla_{R}\mathcal{E}(R)=0.1$ V/nm². Figure 3(b) shows the excitonic group velocity $\langle v_{\nu Q}\rangle$ modulated by a non-uniform electric field (coloured, shaded) at different values of $t_{2}$ for a fixed value $t_{1}$= 0.3 eV. The group velocity $v_{Q}$ in the absence of an external field is shown with the dashed lines. In the trivial regime, $\langle v_{\nu Q}\rangle\approx\langle v^{0}_{\nu Q}\rangle$ due to the vanishing quantum metric $g_{xx}^{\mu\nu}\approx 0$ and vanishing variations thereof, $\Gamma^{\mu\nu}_{xxx}\approx 0$. The topological regime ($t_{2}>t_{1}$) shows a more complex behaviour. At small finite $Q$, the exciton diffusion is slowed down by the electric field with $\langle v_{\nu Q}\rangle\ll\langle v^{0}_{\nu Q}\rangle$ and even shows an opposite sign. At larger $Q$, the force induced by the non-uniform electric field on the topological excitons becomes larger, leading to a huge enhancement of the excitonic group velocity. This effect is most significant for $t_{2}$ reasonably close to $t_{1}$ within the range $t_{2}<0.5$ eV. For larger $t_{2}$, the quantum metric contribution shrinks, owing to the smaller excitons Jankowski et al. (2024) such that the group velocity with and without electric field begin to converge again, see the red curve Fig. 3(b).

Qualitatively, the distinct response of topological and trivial excitons under a non-uniform electric field can again be related to their different centre-of-mass localisations and relative sizes. Trivial excitons have a smaller size, and therefore are less subject to electric field gradients. The quantum metric in the momenta conjugate to the relative electron-hole position $r$, and the centre-of-mass coordinates $R$, precisely reflect the corresponding spreads and localisations of excitons (see Methods).

Following free exciton diffusion at femtosecond timescales, excitons experience phonon-limited diffusion at picosecond timescales Thompson et al. (2022); Cohen et al. (2024). In this regime, the exciton diffusion is given by:

where $v_{\nu Q}$ is the exciton group velocity, $\Gamma_{\nu Q}$ is the exciton-phonon scattering rate, $E_{\nu Q}$ is the exciton band energy, $k_{\mathrm{B}}$ is the Boltzmann constant, $T$ is temperature, and $\mathcal{Z}$ is the partition function. The role that topology and quantum geometry play on phonon-limited exciton diffusion depends on the interplay between the exciton group velocity and exciton-phonon scattering rates featuring in Eq. (7).

Starting with the exciton group velocity, topological excitons exhibit enhanced group velocities (see Methods):

where the second term represents the geometric contribution that enhances the group velocity of topological excitons.

In terms of exciton-phonon scattering rates, the key microscopic quantities are the exciton-phonon scattering matrix elements $\mathcal{D}^{\mu\nu}_{Qq\beta}$ which describe the scattering from an initial exciton $(\nu,Q)$ into a final exciton $(\mu,Q+q)$ mediated by a phonon $(\beta,q)$ of momentum $q$ and energy $\hbar\omega_{\beta q}$. In turn, the exciton-phonon matrix elements can be written in terms of individual electron-phonon scattering matrix elements $g^{mn}_{kq\beta}$ modulated by the exciton envelope function (see Methods). The electron-phonon scattering matrix elements describe the scattering from an initial electron (hole) $(n,k)$ into a final electron (hole) $(m,k+q)$ mediated by a phonon $(\beta,q)$. Topological electrons were previously found to significantly contribute to the electron-phonon coupling underpinned by $g^{mn}_{kq\beta}$ through electronic quantum geometric terms Yu et al. (2024). As a consequence, topological electrons enhance exciton-phonon coupling matrix elements $\mathcal{D}^{\mu\nu}_{Qq\beta}$, and we confirm this numerically as shown in Fig. 4(a-b).

The preceding discussion implies that topological electrons will enhance the resulting exciton-phonon scattering matrix elements, but not all topological electrons lead to topological excitons. Topological excitons can arise from obstructed electrons and holes Jankowski et al. (2024), and in this scenario the topology-enhanced electron-phonon scattering matrix elements will result in topology-enhaned exciton-phonon matrix elements. These in turn will lead to enhanced exciton-phonon scattering rates $\Gamma_{\nu Q}$. However, unobstructed electrons and holes can also give rise to topological excitons due to the electron-hole contribution Jankowski et al. (2024); Davenport et al. (2024). In this second scenario, there is no enhancement of the electron-phonon scattering matrix elements, resulting in topological excitons that exhibit no enhancement in the exciton-phonon scattering rates $\Gamma_{\nu Q}$.

Overall, we end up with two scenarios. In the first scenario, the diffusion of topological excitons is enhanced when the underlying electrons and holes are trivial, driven by the topologically-driven enhancement of the exciton group velocity $v_{\nu Q}$. In the second scenario, corresponding to topological excitons with underlying topological electrons and holes, both the exciton group velocity $v_{\nu Q}$ and the exciton-phonon scattering rates $\Gamma_{\nu Q}$ are enhanced. The diffusivity of Eq.(7) depends on the ratio $v_{\nu Q}/\Gamma_{\nu Q}$, and therefore the diffusion of topological excitons in this scenario may be enhanced or suppressed. In the numerical example below, the enhancement of the group velocity dominates and the topological excitons exhibit enhanced transport.

To illustrate these results numerically, we consider the topological excitons in polyacenes. Polyacenes exhibit topological excitons with underlying topological electrons and holes. This is the only regime we can explore as there are no known material candidates hosting topological excitons with underlying trivial electrons and holes. In Fig. 4(a-b) we show the exciton-phonon scattering matrix elements from an initial state $Q$ to a final state $Q^{\prime}$ for polypentacene ($t_{2}>t_{1}$) and compare it to the trivial counterpart where the values of the hopping parameters are swapped ($t_{2}<t_{1}$). We use dimensionless units, as we are interested in the impact of the topology rather than the absolute values of the matrix elements. We observe different couplings for different momenta, depending on the topology associated with the Zak phases of the electronic and hole states comprising the excitons, with the peak intensities being dictated by the quantum geometry of individual electrons and holes, as well as their momentum-dependent interaction. We find that the $Q/Q^{\prime}$ dependence on the exciton-phonon coupling is the same in both the trivial and topological case, however the magnitude is significantly enhanced in the topological case as expected from the discussion above.

One way to probe the impact of phonon scattering is via the exciton dephasing $\Gamma_{Q}=\sum_{\nu}\Gamma_{\nu Q}$. When $Q=0$, the dephasing corresponds to the non-radiative lifetime of the lowest exciton state. In Fig. 4(c), we present the calculated exciton dephasing as a function of momentum at $50$ K (orange) and $300$ K (blue) for polypentacene (solid lines) and its trivial counterpart (dashed lines). The dephasing depends on the population of phonons, which increases as a function of temperature. As such the dephasing at $300$ K is significantly larger than that at $50$ K. Irrespective of temperature, the dephasing is larger in the topological case, which can be understood by the larger magnitude of the exciton-phonon matrix elements of the topological regime compared to the trivial one. The excitonic dispersions themselves are almost identical, so any density of states effects in the allowed scattering channels Thompson et al. (2022) are approximately equivalent for both trivial and topological exciton dephasing. As a result, the same qualitative features are observed in the dephasing curves for both topological and trivial exictons at high and low temperatures. An initial increase in the dephasing can be observed at small $Q$, characterised by the emission of acoustic phonons scattering back to the $Q=0$ state or at larger temperatures, absorption of phonons. This gives rise to a distinct bump feature Thompson et al. (2022) between $Q=0.1$ nm^-1 and $Q=0.5$ nm^-1. At around $Q=0.8$ nm^-1, the exciton energy difference compared to $Q=0$ nm^-1 corresponds to the optical phonon energy. As a result intraband optical phonon relaxation becomes possible leading to a sharp increase in the dephasing. At larger momentum $Q$ such relaxation remains possible, however, the exciton density of states at higher-momentum states is lower, leading to an overall decrease in the dephasing. At very large $Q>3$ nm^-1, the exciton band flattens (cosine-like) leading to an increase in the excitonic density of states and a corresponding increase in scattering channels. As a result, peak is seen in the 300 K dephasing at $Q=4.7$ nm^-1, but an equivalent peak is not present in the 50 K results as the thermal occupation of optical phonons is very small in the latter case.

We also calculate the phonon-limited exciton diffusion coefficients using Eq. (7) and report the results in Fig. 4(d). In this example, the competition between the geometric contribution to the excitonic group velocity and to the enhanced exciton-phonon coupling leads to an overall enhancement of the diffusion in the topological regime. Taking solely the band contribution to the exciton velocity, the increased exciton-phonon dephasing associated with topological excitons leads to topological excitons diffusing about four times more slowly than trivial excitons at all temperatures, see Fig. S1. However, taking the exciton band geometry into account, leads to an increase in the exciton group velocity at low $Q$ in both the trivial and topological regime. While a fairly modest increase in the case of trivial excitons, the vastly enhanced exciton metric in the topological regime leads to a large increase in the exciton group velocity of the low $Q$ yet highly populated $Q=0$ states. As a result the exciton diffusion is much larger in the topological regime, even despite the enhanced exciton-phonon coupling which increases the scattering term. The temperature dependence in Fig. 4(d) reflects this interpretation, with low temperatures corresponding to an increase in the relative population of low momentum excitons which have a large group velocity enhancement. The reduced exciton-phonon coupling at low temperatures adds to this behaviour and we see a monotonic decrease in the exciton diffusion in both trivial and topological excitons.

When the interaction between excitons and phonons becomes sufficiently large, excitons can become localised by the lattice Markvart and Greef (2004); Hansen et al. (2022), becoming heavier and undergoing slower transport. These exciton-polarons have been studied extensively Baranowski et al. (2024); Knorr et al. (2024); Dai et al. (2024a), and are particularly relevant in organic systems where their formation hinders the already limited energy transfer across organic optoelectronic devices Coehoorn et al. (2017). Hence, understanding the transport of excitons in this strong coupling regime is crucial.

We calculate the exciton band dispersion for polypentacene as renormalised by exciton-polarons at $300$ K by treating the exciton-phonon interaction self-consistently (see Methods). The renormalised exciton-polaron dispersion for polypentacene is shown in Fig. 5(a), with the trivial counterpart shown in Fig. 5(b). In both cases, polaron formation results in an energy shift and in a decrease in the group velocity, but notably the topological exciton-polaron exhibits a larger energy shift and a larger reduction in velocity with a correspondingly increased mass, which we attribute to the topology-driven increase in the exciton-phonon interactions. Figure  5(d) shows the ratio of the free excitonic to the polaronic group velocities. We find the usual low-momentum decrease of the exciton-polaron velocity ($v_{\text{Exc}}/v_{\text{Exc-Pol}}>1$ ) in both the trivial (green) and topological (red) cases, corresponding to a polaron velocity around $70\%$ of that of the free exciton.

Experimentally, the formation of exciton polarons will lead to a red shift of the excitonic resonance energy Hurtado Parra et al. (2022) in the spectrum of absorbed/emitted light on a picosecond timescale. Importantly, the band topology of the exciton-polarons is the same as that of the bare excitons, and we note that at large $Q$ the topological exciton-polaron bands are close in energy but do not cross, analogous to the bare exciton case. Our results show that the band contribution to the polaron velocity is reduced in the topological case, however the same metric contribution to the exciton transport holds, given that the polaron bands do not cross and possess the same underlying metric.

Overall, our results show that the topologically-bounded localisation properties of excitons dramatically affect their transport properties. Compared to their trivial counterparts, topological excitons sustain faster free transport, have lower effective masses, and their transport signatures are more robust to polaronic effects. The enhanced transport of topological excitons is expected to be experimentally trackable in the polyacenes Cirera et al. (2020), where the underlying electronic topology has already been observed. Experimentally, the dynamics of exciton transport can be visualised with time-resolved photoluminescence Sung et al. (2019); Rosati et al. (2020) or with transient absorption Schnedermann et al. (2019).

We show that topological excitons also experience stronger electron-phonon coupling-driven exciton-phonon coupling, compared to their trivial counterparts. This observation respects the expected enhancement of electron-phonon coupling of the constituent electrons and holes that host non-trivial quantum geometry Yu et al. (2024). As discussed earlier, the stronger exciton-phonon coupling experienced by topological excitons results in higher dephasing rates, but we find that these are not sufficient for the topological excitons to violate the original quantum geometric bounds of the free exciton propagation, as compared to the trivial excitons. Similarly, the transport of topological excitons in the polaronic regime is also robust against coupling to the lattice of organic crystals. These findings, accounting for the presence of physical effects present in all semiconducting materials, show that our diagnosis of quantum geometric manifestations on excitons should persist under experimental conditions.

Finally, we stress that the exciton transport properties and the associated exciton quantum geometry and topology can be controlled using an appropriate dielectric environment Jankowski et al. (2024), chemical modifications, and temperature, which modifies the population of the exciton (and phonon) states. Therefore, our findings provide a general quantum mechanical formalism and mathematical insights to theoretically understand the experimentally controllable geometric manifestations due to excitonic topologies, as reflected in the discussed excitonic transport in semiconductor materials.

We have demonstrated that the transport of topological excitons is significantly enhanced compared to that of trivial excitons. This discovery arises from the lower bound that the centre-of-mass excitonic quantum geometry sets on the exciton localisation, making topological excitons larger and therefore more mobile. We have shown that enhanced topological exciton transport holds in sub-picosecond free transport regime and in the picosecond phonon-limited and polaronic transport regimes. Additionally, we have illustrated these discoveries in a family of polyacene organic semiconductors. Our results are general, and we expect that exciton topology can be exploited to enhance the transport properties of a wide variety of semiconductors for applications in optoelectronic devices.