Intertube excitonic coupling in nanotube van der Waals heterostructures

Excitons dominate the optics of atomically-thin transition metal dichalcogenides and 2D van der Waals heterostructures. Interlayer 2D excitons, with an electron and a hole residing in different layers, form rapidly in heterostructures either via direct charge transfer or via Coulomb interactions that exchange energy between layers. Here, we report prominent intertube excitonic effects in quasi-1D van der Waals heterostructures consisting of C/BN/MoS$_2$ core/shell/skin nanotubes. Remarkably, under pulsed infrared excitation of excitons in the semiconducting CNTs we observed a rapid (sub-picosecond) excitonic response in the visible range from the MoS$_2$ skin, which we attribute to intertube biexcitons mediated by dipole-dipole Coulomb interactions in the coherent regime. On longer ($>100$ps) timescales hole transfer from the CNT core to the MoS$_2$ skin further modified the MoS$_2$'s absorption. Our direct demonstration of intertube excitonic interactions and charge transfer in 1D van der Waals heterostructures suggests future applications in infrared and visible optoelectronics using these radial heterojunctions.

that subsequently dissociates across the junction, [10][11][12][13] or by probing the internal transitions of interlayer excitons. 14 In type II heterojunctions an electron-hole pair generated in one material will separate via charge transfer on ultrafast (sub-picosecond) timescales, creating a long-lived interlayer exciton that straddles the interface. Alternatively, Förster-type non-radiative dipole-dipole interactions can mediate rapid energy transfer between layers in vdW heterostructures, also on picosecond timescales. [15][16][17] Later after photoexcitation, once a semiconductor's electrons have cooled by transferring energy to the lattice, 18 heat transfer can further modify the electronic properties of adjacent layers and thereby change its absorption. Disentangling these combined effects of direct charge transfer, Coulomb-mediated energy transfer, and heat transport between layers in vdW heterostructures is thus a significant challenge.
Here, we report an investigation of the intertube excitonic response of a nano-coaxial cable, formed by a 1D van der Waals (vdW) heterostructure (Fig. 1a). The core consisted of bundles of semiconducting and metallic carbon nanotubes (CNTs), wrapped by insulating BN nanotubes, and with a sheath made of semiconducting MoS 2 nanotubes (NTs). [19][20][21] The strong excitonic response of the CNTs and the MoS 2 NTs, combined with the longrange alignment of the different nanotubes within the heterostructure and large sample areas (∼ 1cm 2 ), made this an ideal system to study the fundamentals of intertube electronic and excitonic coupling. We demonstrate that the Coulomb force creates strong intertube excitonic coupling by comparing the femtosecond transient absorption spectra and dynamics after the initial creation of excitons either in the CNTs or in the MoS 2 .
There are two distinct paradigms by which the light-matter interaction in such a 1D vdW heterostructure may be understood (Fig. 1b). Either (i) excitons (solid lines) behave independently of the quasiparticles in the other components of the heterostructure, and the optical properties are an effective medium average of the response of the independent constituents, or (ii) the Coulomb forces between quasiparticles in different layers (dashed lines) create electronic correlations with a unique optical response. Simple physical arguments in favour of this second possibility can be advanced. For instance, electrostatics predicts that a free charge in a CNT will be screened by an opposite charge in the sheath (Fig. 1c), forming an intertube exciton. A dipole field in the CNT, i.e. an excitonic polarisation, will induce a dipole in the MoS 2 NT (Fig. 1d), creating an intertube biexciton. Dynamically, one may predict that intertube biexcitons and intertube excitons form with different rates following the creation of a coherent excitonic polarisation in the CNT using an infrared pump pulse.
An intertube biexciton should form rapidly, as it is mediated via the Coulomb force, while intertube excitons require longer to form as charge transfer between the CNT core and MoS 2 skin must occur. By separating the core and skin with BN nanotubes charge transfer rates can be suppressed (as BN is a good tunnel barrier owing to its wide bandgap), slowing intertube excitonic formation.
Indirect evidence of the importance of intertube interactions comes from the optical absorption, Fig. 1e, obtained for the pristine CNT films, after BN overgrowth, and after MoS 2 nanotube growth. As discussed previously, the C@BN@MoS 2 heteronanotube films have an optical absorbance from the UV to the THz that can be roughly understood as resulting from the combination of the equilibrium absorbance of the constituent nanotubes in isolation. 19 However, in the infrared range, below the band edge of the MoS 2 , the C@BN@MoS 2 heteronanotube film has an enhanced absorbance in comparison to the C@BN and CNT reference films. One explanation of this effect is that Coulomb correlations between the MoS 2 and the CNTs enhances the excitonic absorption of the S 11 , S 22 , M 11 excitons in the CNTs, much in the way that electron-hole pairs boost the absorption strength near the band edge of a direct gap semiconductor. Alternatively, the MoS 2 growth may have modified the effective dielectric function, increasing the amount of reflection loss, or a fraction of the MoS 2 nanotubes may be metallic 22 and hence absorb in the infrared. Photoluminescence (PL) spectroscopy is also sensitive to intertube interactions: for instance the A exciton PL efficiency was found to be enhanced for BN@MoS 2 NTs with respect to that of C@BN@MoS 2 NTs. 23 In order to establish uniquely whether intertube Coulomb interactions modify the ground Energy Optical absorption for pristine CNT films (red), and C@BN (green) and C@BN@MoS 2 (blue) heteronanotubes. f. In the excitonic picture, with a common ground state energy E |00> , the heterostructure has exciton energy levels E |10> for the S 11 excitons in the CNT and E |01> for an exciton in the MoS 2 (e.g. the A exciton). The intertube biexciton has an energy level E |11> , which is lower in energy than E |01> + E |01> by an amount ∆. Pumping into the S 11 state at E |10> (red line) lowers the ground-state population, thereby changing the amount of probe light (blue lines) absorbed. state electronic and the optical properties of 1D vdW heterostructures, we introduce a scheme based on multi-colour pump-probe spectroscopy (Fig. 1f ). A heterostructure with Coulombcoupled states has excitonic energy levels E mn , where m, n = 0 denotes the ground state, |00 >, m = 1 denotes an S 11 exciton in a semiconducting CNT, and n = 1 labels an A or B exciton in the MoS 2 . By pumping at an energy E 1 = E |10> − E |00> in the infrared, a fraction of the system is moved from the ground state |00 > to the |10 > state. If the heterostructure has a common Coulomb-coupled ground state then an optical probe To further elucidate the dynamic response of the C@BN@MoS 2 heteronanotubes, we performed reference experiments with a C@BN NT film without MoS 2 NTs. Figure 2b shows a broadband, weaker response from the higher lying excitonic transitions in the CNTs   Figure 3). At lower IR fluence we found τ = 43 fs, suggesting the intertube excitonic response persisted essentially only within the coherent regime, while at higher IR fluence the intertube excitonic response was longer lived (τ = 166 fs). After the IR drive field has finished, the coherent S 11 polarisation decoheres at a rate set by both exciton momentum scattering and exciton population transfer processes. For example, optically-bright S 11 singlet excitons can relax to lower energy optically-dark triplet excitons. Alternatively, they can transfer their energy via nonradiative near-field coupling to another nearby nanotube with a finite density of states at the same energy, 26 such as a metallic CNT. Regardless of the mechanism by which the coherent S 11 excitonic polarisation is removed, the induced excitonic response of the MoS 2 is lowered when the S 11 polarisation weakens. Decoherence of the excitonic polarisation component in the MoS 2 can also cause the destruction of intertube correlations. Hence the intertube excitonic contribution decays on timescales comparable to, or faster than, the timescale for recovery of the C@BN reference sample's interband response, which was 220 fs and faster (Supplemental Fig. S4). The excitonic response of A and B excitons directly created in the MoS 2 NTs under 3.0 eV excitation recovered more slowly (Fig. 2f).  Figure 4: Time evolution of the pump induced change in OD for the C@BN@MoS 2 heteronanotube film at later pump-probe delay times. a. Following IR excitation at 70 µJcm −2 , the coherent intertube excitonic effects disappear within 1 ps, followed by a slower increase in the response from the MoS 2 , which then does not decay within the 3 ns time window of the experiment. b. Under direct (UV) excitation at 200 µJcm −2 the transient OD recovers monotonically towards equilibrium. c. Slices at constant energy (averaged over 2.02-2.04 eV around the B exciton) reveal the differing dynamics at later times under IR excitation. Simple fits (dashed lines) allow indicative timescales to be extracted: an exponential decay (of the form y(t) = ae −t/τ d , with τ d = 60 ps) for direct excitation of the MoS 2 at 3.0 eV, or an exponential rise (of the form y(t) = a(1 − e −t/τr ), with τ r = 220 ps) for excitation at 0.6 eV.
( Fig. 4c) is consistent with our estimates of hole tunneling times from the CNTs to the MoS 2 : using a model of quantum tunneling through the BN barrier 28 we estimated hole tunneling times of 100 ps-1 ns (Supplemental Fig. S9). While the indirect excitons thus created do not directly absorb, the transfer of quasiparticles from one layer to another modifies the absorption rate in the same way as discussed for the ultrafast intertube response.
In summary, the results presented in this work show that intertube coupling plays a pivotal role in the optical response of quasi-1D van der Waals heterostructures. Infrared excitation of the carbon nanotube cores created a response from the MoS 2 sheath on two different timescales. The initial ultrafast response at early times (around 100 fs) was dominated by intertube excitonic coupling mediated by the Coulomb interaction, while charge transfer via quantum tunneling at later times (around 100 ps) produced indirect intertube excitons.
The results demonstrate that the visible and UV optical properties of one component of a heterostructure (here the MoS 2 NTs) can be manipulated by selective excitation of another constituent (the CNTs). Therefore, efficient intertube coupling and the effective control of light at different wavelengths can be readily achieved in heteronanotubes.