## Abstract

Anisotropic materials with oppositely signed dielectric tensors support hyperbolic polaritons, displaying enhanced electromagnetic localization and directional energy flow. However, the most reported hyperbolic phonon polaritons are difficult to apply for active electro-optical modulations and optoelectronic devices. Here, we report a dynamic topological plasmonic dispersion transition in black phosphorus via photo-induced carrier injection, i.e., transforming the iso-frequency contour from a pristine ellipsoid to a non-equilibrium hyperboloid. Our work also demonstrates the peculiar transient plasmonic properties of the studied layered semiconductor, such as the ultrafast transition, low propagation losses, efficient optical emission from the black phosphorus’s edges, and the characterization of different transient plasmon modes. Our results may be relevant for the development of future optoelectronic applications.

### Similar content being viewed by others

## Introduction

Anisotropy has proven to offer exciting possibilities for understanding light-matter interaction processes in optics. Layered materials with positive dielectric tensors, such as ReS_{2}, MoS_{2}, and SnS^{1,2,3}, are known to preserve anisotropic waveguides. When a material’s dielectric tensor exhibits oppositely signed elements, its iso-frequency contours (IFCs) appear with hyperboloid shapes and allow hyperbolic polaritons. Hyperbolic polaritons have been the subject of many studies in layered materials, such as h-BN, WSe_{2}, ZrSiSe, α-MoO_{3}, α-V_{2}O_{5}, and natural crystals like tin oxide, calcite, β-Ga_{2}O_{3}, and CdWO_{4}^{4,5,6,7,8,9,10,11,12}, which are highly desirable in various applications^{13,14,15,16,17}. Usually, the hyperbolic IFCs in momentum space are closely related to remarkable polaritonic properties, including enhanced electromagnetic field localization and energy flow engineering.

Most hyperbolic phonon polaritons exhibit insusceptibility to electro-optical manipulation. However, layered semiconductors, such as Black phosphorus (BP), may offer an alternative due to the possibility of manipulating the charge carriers. The BP, a typical layered semiconductor with layer-dependent direct bandgap ranging from 1.7 eV in a monolayer to 0.3 eV in bulk^{18}, has garnered extensive research interest due to its anisotropic band structure. These unique features have promoted BP as a promising platform for developing innovative devices, such as high-performance electronics, infrared sensors, and electronic band engineering^{19,20,21,22,23}.

The anisotropy in the BP’s electronic band and optical permittivity could result in significant anisotropic optical conductivity^{24,25,26}, which suggests the BP supports hyperbolic plasmon polaritons^{27,28,29,30}, but its low intrinsic electrical carrier doping level hinders the practical realization of the hyperbolic plasmons^{31,32,33}.

This work activated and manipulated the robust transient hyperbolic plasmons in the BP slabs by inducing the BP’s dielectric tensors with opposite signs by ultrafast laser pulses. Usually, the photo-induced electronic transitions can significantly boost carrier density^{5,34,35}, which offers a practical route for optically tuning plasmons. The photo-pumping process in our work injects ample hot charge carriers into the BP, thereby triggering hyperbolic plasmons that are otherwise absent in the pristine state. These resulting non-equilibrium states then allow the IFCs to topological transition from the pristine ellipsoid to a rare transient hyperboloid, which is distinctive in plasmons^{6,36}. Analysis of the dynamic features of the non-equilibrium states at different pump-probe delays revealed the coexistence of a ~5 ps propagating plasmonic mode and a ~40 ps localized edge plasmonic mode.

## Results

### Realization of transient hyperbolic plasmons

Figure 1a shows the experimental setup of the nanoscopy with ultrafast lasers utilized to study the photo-induced hyperbolic plasmonic response of the BP slabs (see Methods). Since the BP is a biaxial crystal, acquiring its non-equilibrium dielectric tensor is necessary to determine the transient plasmonic dispersion. The dielectric tensor of the bulk BP has a diagonal form \(\left[\varepsilon \right]={diag}[{\varepsilon }_{x},{\varepsilon }_{y},{\varepsilon }_{z}]\) (*x* is armchair, *y* is zigzag); thus, the dielectric elements *ε*_{j} are typically depicted using the Drude expression^{37}:

Where *γ*_{j} is the carrier scattering rate, \({\omega }_{p,j}=\sqrt{\frac{n{e}^{2}}{{m}_{j}^{*}{\varepsilon }_{0}}}\) is the plasmon frequency, *n* is the electron or hole density, \(\omega\) is the angular frequency of probe light, *ε*_{∞,j} is the high-frequency permittivity, *ε*_{0} is the vacuum permittivity, \({m}_{j}^{*}=\frac{{m}_{e,j}^{*}{m}_{h,j}^{*}}{{m}_{e,j}^{*}+{m}_{h,j}^{*}}\) is the reduced effective mass combining the electron (\({m}_{e}^{*}\)) and the hole (\({m}_{h}^{*}\))^{34}. Equation 1 indicates that *ε*_{j} is obtained by subtracting the *ε*_{pl,j} from the *ε*_{∞,j}, which signifies that a positive *ε*_{∞,j} weakens the negative change induced by *ε*_{pl,j} in *ε*_{j}, the dielectric screening effect^{37}.

The ultrafast optical pumping (photon energy *hν* = 0.8 eV) triggers the electronic transition from the valence band to the conduction band, as shown in Fig. 1b. The dispersion of the electronic bands in the zigzag direction is flatter than the armchair direction, resulting in a larger effective mass^{26}. From \({m}_{\left(e,h\right),j}^{*}={\hslash }^{2}{k}_{j}\frac{\partial {k}_{j}}{\partial {E}_{(C,V)}}\)^{38}, we obtain the anisotropic reduced effective mass, where: \({m}_{x}^{*}=0.12{m}_{0}\), \({m}_{y}^{*}=0.32{m}_{0}\), \({m}_{z}^{*}=0.10{m}_{0}\), \({m}_{0}\) is the electron mass. These values can be used to obtain the pump-excited anisotropic plasmonic resonance with the Drude ratio^{39,40}:

Figure 1c shows BP’s nano-Fourier-transform infrared spectroscopy (nano-FTIR), with a pumping fluence of 0.5 mJ/cm^{2} at *hν* = 0.8 eV to inject the photo-induced carriers. We fitted the nano-FTIR spectra using a dipole model incorporating the effective dielectric constant \(\left\langle \varepsilon \right\rangle=\sqrt{\langle {\varepsilon }_{{plane}}\rangle {\varepsilon }_{z}}\) at a pump-probe delay *τ* = 200 fs with a carrier concentration corresponding to 1.3 × 10^{19 }cm^{−3}. The dielectric tensor of BP was extracted through this method, where \(\langle {\varepsilon }_{{plane}}\rangle\) is the averaged in-plane dielectric constant^{41,42}.

Figure 1d presents the real part of dielectric elements by fitting the spectra shown in Fig. 1c. The signs of the real part of dielectric elements in the armchair and zigzag direction are both positive as a result of the intensely screened plasmon frequency \({\omega }_{p,j}^{*}=\frac{{\omega }_{p,j}}{\sqrt{{\varepsilon }_{\infty,j}}}\) (*ε*_{∞,x} = 18 and *ε*_{∞,y} = 14). However, the sign of the real part of the dielectric element in the *z* direction becomes negative due to a much weaker dielectric screening (*ε*_{∞,z} = 9.75)^{43}. Consequently, the non-equilibrium BP exhibits oppositely signed dielectric elements, suggesting considerable optical anisotropy between the in and out-of-plane.

To elucidate the hyperbolic dispersion, the IFCs of the BP slabs is employed (*k*_{j} is the wavevector along *j* direction, *j* = *x, y, z*; *k*_{0} is the wavevector of the free space light)^{44}:

Hyperbolic IFCs at *v/c* = 950 cm^{−1} were realized by substituting these dielectric elements into Eq. (3) with and without pump excitation. The results, presented in Fig. 1e, f, reveal a topological transition of the IFCs from the pristine ellipsoidal shape to a non-equilibrium hyperbolic shape, thus affirming the capability of the BP slabs to activate photonic switching hyperbolic transient plasmons^{24,25}.

We further positioned a 310-nm-thick BP on a round gold disk to experimentally verify the presence of hyperbolic plasmons. Figure 1g shows that the hyperbolic IFCs allow the gold disk’s edge to launch conical-shaped energy rays, producing two bright rings separated by a dark ring above the round gold disk’s edge^{5,6,13,45}. Accordingly, the near-field image in Fig. 1h of the non-equilibrium state BP/gold stacked structure clearly shows a dark ring sandwiched by two bright rings above the gold disk, while the pristine BP/gold does not exhibit any ring pattern, confirming the excitation of the photo-induced out-of-plane hyperbolic transient plasmons in BP (Supplementary Note 8).

### Propagation mechanism of plasmons

The robust and complex near-field interference patterns allow retrieval of the subtle scattering mechanisms of the BP’s transient hyperbolic plasmons. Figure 2a shows the 353-nm-thick BP slab, with the edge parallel to the zigzag direction (Supplementary Note 1). Figure 2b presents the hyperbolic transient plasmonic fringes propagating along the armchair direction of the BP slab. Figure 2c shows the angle of the incidence, *θ*, defined as the angle between the BP edge and the projection of the probe beam, is varied in this experiment. We found that when the polarization direction of the *p*-polarized probe beam is perpendicular to the BP edge (*θ* = 90° and 270°), the BP edges act as efficient antennas to launch transient plasmons.

Figure 2b and d display two sets of fringes with different fringe spacings. The short-period fringes dominate when the probe beam is perpendicular to the BP edge (*θ* = 90° and 270°), while the long-period fringes dominate when the probe beam is parallel to the BP edge (*θ* = 0° and 180°). The period of the long-period fringes is equal to the transient plasmons wavelength *λ*_{p}^{46,47}. Figure 2e shows the amplitude of the Fourier transformation of the fringe curves in Fig. 2d (*θ* = 0° and 90°), which showed the wavevector ratio between the long and short period of fringes is 2, indicating the coexistence of both the tip and edge-launched plasmons.

To describe the *θ* dependence of near-field fringes, we employed the following model, taking into account the tip and edge-launching mechanisms and the geometrical decay^{48}:

The \({A}_{1},{A}_{2}\left|\sin \theta \right|,{A}_{3}\left|\sin \theta \right|\) describe the relative strength of the tip-launching + edge-emission route, the edge-launching + tip-emission route, and the edge-launching + secondary-tip-launching + edge-emission route, respectively, *x* is the tip-edge separation distance, *q*_{p} is the momentum of plasmon, and *φ* is a phase shift of each propagation route.

Equation (4) shows that at *θ* = 0° and 180°, only \({A}_{1}\) exists, leading to the long-period fringes govern; at *θ* = 90° and 270°, the destructive interference between \({A}_{1}\) and \({A}_{2}\left|\sin \theta \right|\) lessens the strength of the long-period fringe, leading to the short-period fringes \({A}_{3}\left|\sin \theta \right|\) domination (Cases for illumination from *θ* = 0° to 328° in Supplementary Note 3). The necessity to include the \({A}_{3}\left|\sin \theta \right|\) term in Eq. (4) implies that the BP edge-launched polaritons could further polarize the metal tip of the nanoscopy and induce a secondary tip-launched polariton, which is uncommon in van der Waals materials, such as the graphene, the h-BN, and the α-MoO_{3}^{46,47,49}. The high efficiency of edge-launched polaritons underscores the role of the BP edge as an efficient optical antenna capable of converting free-space light into polaritons.

Figure 3a depicts the propagation of transient plasmons in a 700-nm-thick BP when the incident probe beam is perpendicular to the zigzag edge. As indicated in Fig. 2 previously, the fringe period in Fig. 3a equals *λ*_{p}/2 or *λ*_{p} for the transient plasmons propagating along the armchair or zigzag direction, respectively. This results from the destructive interference between \({A}_{1}\) and \({A}_{2}\left|\sin 90^\circ \right|\) for transient plasmons propagating along the armchair direction and the vanishing of \({A}_{2}\left|\sin 0^\circ \right|\) and \({A}_{3}\left|\sin 0^\circ \right|\) for transient plasmons propagating along the zigzag direction.

Intriguingly, the fringe period along the armchair direction of the 700-nm-thick BP in Fig. 3a is identical to that of the 353-nm-thick BP in Fig. 2b, which contradicts the volume polaritonic dispersion relation observed in other layered materials, where the polariton’s wavelength increases with the slab’s thickness^{4,6,7}. According to the Beer–Lambert law, the bulky BP’s pump absorption coefficient for *hν* = 0.8 eV photon is *α*_{pump} ~ 0.01 nm^{−1}, implying that most photo-induced carriers exist in a space charge layer with a fixed thickness of about \(\frac{1}{{\alpha }_{{pump}}}\)^{50,51,52}. For most polaritonic materials, there is no need to consider light penetration depth’s influence on polaritonic properties. However, for transient plasmons, it is necessary to consider the impact of the pumping light’s penetration depth because photo-induced carriers only exist where the pumping light can reach inside a material.

The BP slabs of 160–1000 nm thicknesses were used to confirm the space charge layer. Figure 3b, c shows the in-plane anisotropic transient plasmons wavelengths along the armchair direction *λ*_{p, armchair} = 925 nm and zigzag direction *λ*_{p, zigzag} = 976 nm are independent of the BP slab thickness, suggesting that transient plasmons exist solely within the space charge layer. Accordingly, the transient plasmons’ wavelength is determined by the thickness of the space charge layer instead of the entire thickness of BP slabs.

Numerical simulations were conducted to gain further insight into the real part of z component electric field Re*(E*_{z}*)* of the simplified 5-layer model in Fig. 3d. The BP slabs were exposed to ambient conditions in the experiment and suffered degradation^{53}. Nevertheless, the degradation did not deteriorate deeper into the BP due to a dense P_{x}O_{y} layer of about 5-nm-thick on the surface^{54,55,56,57}, which has been considered in the simulation. The thickness of the space charge layer was optimized for 120 nm, equivalent to the reciprocal value of the pumping photons’ absorption coefficient *α*_{pump}. The simulated results in Fig. 3e, f show the independence of thickness of the BP (*d* = 200 nm and 800 nm) on the wavelength of the transient plasmons (at *v/c* = 950 cm^{−1}), which corresponds well with the experimental observation in Fig. 3b, c with *λ*_{p, armchair} = 915 nm and *λ*_{p, zigzag} = 963 nm.

Moreover, the superior carrier mobility of the BP allows long-range transient plasmon propagation^{39}. Figure 3g, h shows the low-loss transient plasmons, with up to 9 bright stripes observed, corresponding to a propagation length of approximately 10 μm. The curves were fitted using Eq. (4), leading to high-quality factors \(Q=\frac{{{{{\mathrm{Re}}}}}[{q}_{p}]}{{Im}[{q}_{p}]}\) with *Q*_{armchair} = 22.18 and *Q*_{zigzag} = 18.59. These *Q* factors are comparable to those found in high-*Q* plasmonic systems such as carbon nanotubes and suspended graphene^{58,59}, which is critical for constructing plasmonic connecting networks. Subsequently, the *Q* factors were used to assess the long propagating decay time \({\tau }_{p}=\frac{Q}{\nu }\) with *τ*_{p, armchair} = 778 fs and *τ*_{p, zigzag} = 652 fs (*v/c* = 950 cm^{−1} is the central frequency of hyperbolic plasmon in the Supplementary Note 5). The values of *τ*_{p, armchair}, and *τ*_{p, zigzag} are consistent with the hot carrier scattering rates along the zigzag and armchair directions^{60}, indicating low propagating loss for the transient plasmons.

### Dynamics of transient plasmons

The BP transient hyperbolic plasmons are modes coupled by the probing photons and the non-equilibrium oscillating charge carriers. The propagation properties of the transient plasmons along the armchair direction are further analyzed, presented in Fig. 4, showing similarity to the results along the zigzag direction in supplementary Note 7. The normalized time-resolved near-field images *s*_{3}*/s*_{3,Si} were captured at different time delays *τ* from −2 ps to 60 ps in Fig. 4a. At *τ* = −2 ps, the absence of fringe is attributed to low initial carrier density. The increment in photo-induced carrier density at *τ* = 0 to 0.2 ps results in clear fringes in the near-field images.

To further understand the dynamics of the transient plasmons, we extracted the relative strengths of the first (*∆S*_{1}) and the second (*∆S*_{2}) bright stripes from Fig. 4b. *∆S*_{1} represents the impact of both the propagating transient plasmons and edge-related effects, while *∆S*_{2} is considered purely related to the propagating transient plasmons. *∆S*_{1} and *∆S*_{2} show a bi-exponential and exponential decay in Fig. 4c, respectively, with a fast time constant of *τ*_{1f} = *τ*_{2f} = 2.2 ps, indicating the rapid reduction of the hot carrier density due to carrier trapping of defect states introduced by surface degradation^{61}. However, a slow relaxation of *∆S*_{1} with a time constant of *τ*_{1s} = 37 ps is also present, showing a residual near-field intensity of *∆S*_{1} = 0.16 at *τ* = 10 ps due to the conductivity change and the carrier accumulation formed as an edge mode^{62,63,64,65}.

The time-resolved near-field images analysis reveals the presence of two transient plasmons: the ~5 ps propagating mode characterized by a series of fringes parallel to the edge and the ~40 ps localized edge mode embedded in the first bright fringe. Figure 4a and the corresponding line cuts in Fig. 4b show that the fringe contrast of the propagating transient plasmons depends on *τ*, as the reduction of carrier density redshifts the frequency region of the propagating mode out of the fixed imaging bandwidth. Despite the decrease in carrier density over time, the spacing of the fringes remains nearly constant, as the broadband probing light covers the whole frequency span of the transient plasmons before their near-field amplitude decreases (Supplementary Note 5, 6)^{34}.

## Discussion

This letter introduced a promising approach to optically manipulate robust transient hyperbolic plasmons in the layered semiconductor black phosphorus using a dedicated ultrafast nanoscopy scheme. Optical pumping allows the BP’s IFCs to topologically transit from the pristine ellipsoid to the non-equilibrium hyperboloid, exhibiting exotic non-equilibrium hyperbolic plasmon properties, such as the optically tunable plasmonic dispersion and the coexistence of different transient plasmonic modes. Therefore, layered semiconductors like black phosphorus may facilitate versatile optoelectronics applications with active dynamic optical control.

## Methods

### Preparation of the black phosphorus

The BP slabs were isolated from their crystal counterpart (Shanghai Onway Technology Co., Ltd) by mechanical exfoliation. By keeping the direction of each exfoliation consistent, the unique rectangular shape of the BP slabs could be realized. Then, the BP slabs were transferred onto the freshly cleaned Si substrates in a glove box (APURIS IGBS1800). Shallow P_{x}O_{y} layers were formed during the exfoliation process for less than half an hour, and the samples were kept in the glove box except for the measurement.

### Ultrafast nanoscopy setup

The ultrafast nanoscopy contains three Erbium-doped fiber amplifiers connected to the same oscillator with a 76-fs pulse duration and 80 MHz repetition frequency (TOPTICA Photonics AG). Amplifiers 1 and 2 emitted near-infrared (NIR) pulses with a wavelength of 1500–1600 nm and a power of 400 mW, and amplifier 3 emitted super-continuum pulses (980–2200 nm) using a nonlinear fiber. The pump branch was emitted from amplifier 1, and the probe branch was produced by difference frequency generation processes between amplifiers 2 and 3. By tuning the pitch angle of the nonlinear crystal (GaSe-1000H1, EKSMA OPTICS) to meet the phase-matching condition, The mid-infrared (MIR) broadband probe pulses (*v/c* = 850–1200 cm^{−1}) were obtained. The pump and probe pulses were spatially overlapped on the metalized Pt/Ir tip (ARROW-NCPt, Nanoworld) through a parabolic mirror of a commercial scattering-type scanning near-field optical microscopy (attocube systems AG). Samples were settled on a customized rotation platform to change the probe incident angles.

### Numerical simulations

The numerical simulation of the propagating of hyperbolic plasmon was calculated by the finite-element numerical simulation software (COMSOL). The boundary mode analysis and frequency domain module of COMSOL was used to simulate the near-field waveguide mode and propagation rays of volume hyperbolic plasmon, respectively.

## Data availability

Relevant data supporting the key findings of this study are available within the article and the Supplementary Information file. All raw data generated during the current study are available from the corresponding authors upon request.

## References

Mooshammer, F. et al. In-plane anisotropy in biaxial ReS2 crystals probed by nano-optical imaging of waveguide modes.

*ACS Photonics***9**, 443–451 (2022).Luan, Y. et al. Imaging anisotropic waveguide exciton polaritons in tin sulfide.

*Nano Lett.***22**, 1497–1503 (2022).Hu, D. et al. Tunable modal birefringence in a low-loss Van Der Waals waveguide.

*Adv. Mater.***31**, 1807788 (2019).Dai, S. et al. Tunable phonon polaritons in atomically thin van der waals crystals of boron nitride.

*Science***343**, 1125–1129 (2014).Sternbach, A. J. et al. Programmable hyperbolic polaritons in van der Waals semiconductors.

*Science***371**, 617 (2021).Shao, Y. et al. Infrared plasmons propagate through a hyperbolic nodal metal.

*Sci. Adv.***8**, eadd6169 (2022).Ma, W. et al. In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal.

*Nature***562**, 557–562 (2018).Taboada-Gutiérrez, J. et al. Broad spectral tuning of ultra-low-loss polaritons in a van der Waals crystal by intercalation.

*Nat. Mater.***19**, 964–968 (2020).Feres, F. H. et al. Sub-diffractional cavity modes of terahertz hyperbolic phonon polaritons in tin oxide.

*Nat. Commun.***12**, 1995 (2021).Ma, W. et al. Ghost hyperbolic surface polaritons in bulk anisotropic crystals.

*Nature***596**, 362–366 (2021).Passler, N. C. et al. Hyperbolic shear polaritons in low-symmetry crystals.

*Nature***602**, 595–600 (2022).Hu, G. et al. Real-space nanoimaging of hyperbolic shear polaritons in a monoclinic crystal.

*Nat. Nanotechnol.***18**, 64–70 (2022).Dai, S. et al. Subdiffractional focusing and guiding of polaritonic rays in a natural hyperbolic material.

*Nat. Commun.***6**, 6963 (2015).Bylinkin, A. et al. Real-space observation of vibrational strong coupling between propagating phonon polaritons and organic molecules.

*Nat. Photonics***15**, 197–202 (2021).Zheng, Z. et al. Phonon polaritons in twisted double-layers of hyperbolic van der Waals Crystals.

*Nano Lett.***20**, 5301–5308 (2020).Duan, J. et al. Enabling propagation of anisotropic polaritons along forbidden directions via a topological transition.

*Sci. Adv.***7**, eabf2690 (2021).Hu, H. et al. Doping-driven topological polaritons in graphene/α-MoO3 heterostructures.

*Nat. Nanotechnol.***17**, 940–946 (2022).Qiao, J., Kong, X., Hu, Z.-X., Yang, F. & Ji, W. High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus.

*Nat. Commun.***5**, 4475 (2014).Wang, X. et al. Highly anisotropic and robust excitons in monolayer black phosphorus.

*Nat. Nanotechnol.***10**, 517–521 (2015).Xia, F., Wang, H. & Jia, Y. Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics.

*Nat. Commun.***5**, 4458 (2014).Tran, V., Soklaski, R., Liang, Y. & Yang, L. Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus.

*Phys. Rev. B***89**, 235319 (2014).Chaudhary, K. et al. Engineering phonon polaritons in van der Waals heterostructures to enhance in-plane optical anisotropy.

*Sci. Adv.***5**, eaau7171 (2019).Zhou, S. et al. Pseudospin-selective Floquet band engineering in black phosphorus.

*Nature***614**, 75–80 (2023).Ghosh, B. et al. Anisotropic plasmons, excitons, and electron energy loss spectroscopy of phosphorene.

*Phys. Rev. B***96**, 035422 (2017).Low, T. et al. Plasmons and screening in monolayer and multilayer black phosphorus.

*Phys. Rev. Lett.***113**, 106802 (2014).Liao, B. et al. Spatial-temporal imaging of anisotropic photocarrier dynamics in black phosphorus.

*Nano Lett.***17**, 3675–3680 (2017).Low, T. et al. Polaritons in layered two-dimensional materials.

*Nat. Mater.***16**, 182–194 (2017).Wang, F. et al. Prediction of hyperbolic exciton-polaritons in monolayer black phosphorus.

*Nat. Commun.***12**, 5628 (2021).van Veen, E. et al. Tuning two-dimensional hyperbolic plasmons in black phosphorus.

*Phys. Rev. Appl.***12**, 014011 (2019).Nemilentsau, A., Low, T. & Hanson, G. Anisotropic 2D materials for tunable hyperbolic plasmonics.

*Phys. Rev. Lett.***116**, 066804 (2016).Pogna, E. A. A. et al. Unveiling the detection dynamics of semiconductor nanowire photodetectors by terahertz near-field nanoscopy.

*Light: Sci. Appl.***9**, 189 (2020).Wunnicke, O. Gate capacitance of back-gated nanowire field-effect transistors.

*Appl. Phys. Lett.***89**, 083102 (2006).Arcangeli, A. et al. Gate-tunable spatial modulation of localized plasmon resonances.

*Nano Lett.***16**, 5688–5693 (2016).Huber, M. A. et al. Femtosecond photo-switching of interface polaritons in black phosphorus heterostructures.

*Nat. Nanotechnol.***12**, 207–211 (2017).Ni, G. X. et al. Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene.

*Nat. Photonics***10**, 244–247 (2016).Wang, C. et al. Van der Waals thin films of WTe2 for natural hyperbolic plasmonic surfaces.

*Nat. Commun.***11**, 1158 (2020).Frenzel, A. J. et al. Anisotropic electrodynamics of type-II Weyl semimetal candidate WTe

_{2}.*Phys. Rev. B***95**, 245140 (2017).Zawadzki, W. Electron transport phenomena in small-gap semiconductors.

*Adv. Phys.***23**, 435–522 (1974).Li, L. et al. Black phosphorus field-effect transistors.

*Nat. Nanotechnol.***9**, 372–377 (2014).Cai, Y., Zhang, G. & Zhang, Y.-W. Layer-dependent band alignment and work function of few-layer phosphorene.

*Sci. Rep.***4**, 6677 (2014).Kehr, S. C. et al. Anisotropy contrast in phonon-enhanced apertureless near-field microscopy using a free-electron laser.

*Phys. Rev. Lett.***100**, 256403 (2008).Chui, S. T. et al. Effect of sample anisotropy on scanning near-field optical microscope images.

*J. Appl. Phys.***129**, 083105 (2021).Valagiannopoulos, C. A., Mattheakis, M., Shirodkar, S. N. & Kaxiras, E. Manipulating polarized light with a planar slab of black phosphorus.

*J. Phys. Commun.***1**, 045003 (2017).Álvarez-Pérez, G., Voronin, K. V., Volkov, V. S., Alonso-González, P. & Nikitin, A. Y. Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals.

*Phys. Rev. B***100**, 235408 (2019).Li, P. et al. Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing.

*Nat. Commun.***6**, 7507 (2015).Wang, L. et al. Manipulating phonon polaritons in low loss 11B enriched hexagonal boron nitride with polarization control.

*Nanoscale***12**, 8188–8193 (2020).Cheng, G. et al. Nano-imaging of an edge-excited plasmon mode in graphene.

*Nanoscale***10**, 16314–16320 (2018).Woessner, A. et al. Highly confined low-loss plasmons in graphene–boron nitride heterostructures.

*Nat. Mater.***14**, 421–425 (2015).Zhao, Y. et al. Ultralow-loss phonon polaritons in the isotope-enriched α-MoO3.

*Nano Lett.***22**, 10208–10215 (2022).Penillard, A. et al. Infrared optical anisotropic properties and photocarriers lifetime in 2D black phosphorus by angle-resolved absorption and reflectometry.

*J. Appl. Phys.***125**, 243107 (2019).Li, D. et al. Polarization and thickness dependent absorption properties of black phosphorus: new saturable absorber for ultrafast pulse generation.

*Sci. Rep.***5**, 15899 (2015).Eisele, M. et al. Ultrafast multi-terahertz nano-spectroscopy with sub-cycle temporal resolution.

*Nat. Photonics***8**, 841–845 (2014).van Druenen, M. et al. Evaluating the surface chemistry of black phosphorus during ambient degradation.

*Langmuir***35**, 2172–2178 (2019).Chi, L., Lee, M.-H., Chu, T.-Y. & Tao, Y. Excitonic effect in black phosphorus oxides.

*2D Mater.***9**, 015007 (2021).Grasseschi, D. et al. Oxygen impact on the electronic and vibrational properties of black phosphorus probed by synchrotron infrared nanospectroscopy.

*2D Mater.***4**, 035028 (2017).Tian, H. et al. Anisotropic black phosphorus synaptic device for neuromorphic applications.

*Adv. Mater.***28**, 4991–4997 (2016).Edmonds, M. T. et al. Creating a stable oxide at the surface of black phosphorus.

*ACS Appl. Mater. Interfaces***7**, 14557–14562 (2015).Shi, Z. et al. Observation of a Luttinger-liquid plasmon in metallic single-walled carbon nanotubes.

*Nat. Photonics***9**, 515–519 (2015).Hu, H. et al. Active control of micrometer plasmon propagation in suspended graphene.

*Nat. Commun.***13**, 1465 (2022).Iyer, V., Ye, P. & Xu, X. Mid-infrared ultrafast carrier dynamics in thin film black phosphorus.

*2D Mater.***4**, 021032 (2017).Beard, M. C., Turner, G. M. & Schmuttenmaer, C. A. Transient photoconductivity in GaAs as measured by time-resolved terahertz spectroscopy.

*Phys. Rev. B***62**, 15764–15777 (2000).Fei, Z. et al. Edge and surface plasmons in graphene nanoribbons.

*Nano Lett.***15**, 8271–8276 (2015).Nikitin, A. Y. et al. Real-space mapping of tailored sheet and edge plasmons in graphene nanoresonators.

*Nat. Photonics***10**, 239–243 (2016).Nikitin, A. Y., Guinea, F., García-Vidal, F. J. & Martín-Moreno, L. Edge and waveguide terahertz surface plasmon modes in graphene microribbons.

*Phys. Rev. B***84**, 161407 (2011).Abate, Y. et al. Nanoscopy reveals surface-metallic black phosphorus.

*Light: Sci. Appl.***5**, e16162–e16162 (2016).

## Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant Nos. 2022YFA1203500, J.C.), the National Natural Science Foundation of China (Grant Nos. 12204125, M.X.; 51971070, Q.L.; 10974037, Q.L.), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDB 30000000, J.C.; XDB 36000000, Q.D.; XDA 09020300, Q.L.), Eu-FP7 Project (No. 247644, Q.L.). J.C. acknowledges the support from CAS Youth Interdisciplinary Team.

## Author information

### Authors and Affiliations

### Contributions

R.F., Y.Q., and M.X. contributed equally to this work. M.X. and J.C. conceived the study. M.X. and R.F. performed the optical nanoscopy and Raman measurements. Y.Q., S.C., Q.L., and Q.D. fabricated the samples and performed the TEM measurements. Y.Z. fabricated the gold disk. M.X., R.F., X.L., Y.Z., R.C., B.L., and H.W. performed the theoretic analysis and numerical simulations. J.C. supervised the work. M.X., R.F., and J.C. wrote the manuscript. All authors discussed the results and commented on the paper.

### Corresponding authors

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

*Nature Communications* thanks Yinming Shao and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.

## Additional information

**Publisher’s note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

## Rights and permissions

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

## About this article

### Cite this article

Fu, R., Qu, Y., Xue, M. *et al.* Manipulating hyperbolic transient plasmons in a layered semiconductor.
*Nat Commun* **15**, 709 (2024). https://doi.org/10.1038/s41467-024-44971-3

Received:

Accepted:

Published:

DOI: https://doi.org/10.1038/s41467-024-44971-3

## Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.