Tunable infrared Plasmons in low dimensional semiconductors

Internship supervisors Dr Jean-Marie Poumirol (jean-marie.poumirol@cemes.fr) and Dr Caroline Bonafos CEMES-CNRS, Groupe NeO

Location CEMES-CNRS, 29 rue Jeanne Marvig, 31055 Toulouse cedex 4, France This research master's degree research project could be followed by a PhD. YES X NO □ Abstract/work package/short bibliography/illustration Surface Plasmons are electromagnetic waves coupled with the collective oscillations of the free charge carriers. They are localized at the interface between two medias of opposite permittivity. Excited by light these modes form a hybrid quasi-particle with photons called polaritons. Plasmon-polaritons are strongly localized and confine the electromagnetic field to a volume smaller than the diffraction limit [1]. The resulting local electric field induces an unprecedented enhancement of the optical processes. Polaritonic modes are the perfect tool to confine, control and manipulate light at the nanometric scale. From a more fundamental point of view, the subwavelength confinement and resulting enhancement of the electromagnetic field, provides a platform to study light-matter interaction in nanoscopic systems. Noble metals, principally gold and silver, have for a long time been the reference materials in this field. Recently, it’s been realized that the band properties of some semiconductor deeply affect the collective excitations of coulomb interacting electrons, allowing an unprecedented dynamic control over their plasmonic resonances [2]. The goal of the scientific project in which this internship take place is to study the formation and the optoelectronic properties of the new plasmon polariton modes that appear in two types of semi-conductors: Transition metal dichalcogenide (TMD) [3,6] and hyper doped silicon nanostructures [5]. The master internship is focused first on studying the infrared optical properties of: (i) silicon based metasurfaces, to determine the impact of electron-phonon coupling on the plasmonic lifetime and energy; (ii) BN encapsulated WSe2 and MoSe2 heterostructures, to measure the dielectric function at low energy. In a second time the experimental set-up will be upgraded and coupled to a tunable NIR-visible laser source that will be used to optically pump carriers into the system. Helicity of the laser light will be used to selectively dope one valley over the other and generate non-reciprocal plasmon propagation [5]. This work will be very useful for other works in progress, in particular to help quantifying the impact of valley selective doping on the plasmon polariton propagation.

Fig. 1: (a) Illustration of tunable plasmonic resonance observed in hyper doped silicon metasurfaces. One can see that depending on the structure doping level (controlled by phosphorus implantation) the maximum of absorption of the system can be tuned all over the Infrared regime. [4] (b) Propagating of surface plasmon polariton wavefront: (a) In isotropic systems like graphene, plasmons are propagating in all directions uniformly; (b) In TMD chiral plasmon will propagate along certain directions preferentially. [3] This internship, is supported by the ANR program (French Research National Agency), and a PhD will start in October 2022 following the work done during the internship. The metasurfaces are performed in the framework of several collaborations with LAAS and LPCNO.

NATUREMATERIALS DOI: 10.1038/NMAT4792 FOCUS | REVIEW ARTICLE

Box 2 | 2D plasmonic materials and optical conductivity.

Isotropic plasmon(graphene)

Hyperbolic plasmon(anisotropic materials)

Chiral plasmon(gapped Dirac materials)

Plasmon-polaritons (PPs) can be launched with a nano-antenna,such as a gold disc, as illustrated. The propagating PPs wavefrontcan then be spatially mapped with the SNOM47. Graphene PPshave a circular wavefront, since its optical conductivity tensor isisotropic, that is, σxx =σyy ≡σ0, with σ0= iD/π(ω+ i/τ ), whereD= e2µ/!2 is known as the Drude weight, µ is the chemicalpotential in graphene and τ is the electron’s lifetime. Anisotropic2D materials (for example, black phosphorus8,56) imply σxx ̸=σyy , and could potentially host hyperbolic PPs. In hyperbolicmedia, the permittivities along the Cartesian axes are opposite insigns (that is, Im[σxx ·σyy]<0), which can fundamentally changehow light interacts with matter. The mechanism relies on theinterplay between anisotropic intraband and interband motions9,which can render capacitive and inductive optical responsesalong the two axes. In SNOM experiments, these effects couldbe observed as PPs rays launched with an optical antenna, asillustrated above. Gapped Dirac materials (for example, transitionmetal dichalcogenides54,55) are a unique class of materials wherethe two electronic valleys at the Fermi energy exhibit circular

dichroism. The electronic wavefunctions in the two valleys ‘twist’differently (that is, Berry phase), hence imparting a sense ofchirality, and result in a different response to circular polarizedlight54,55. Pumping with circularly polarized light effectively leadsto population imbalance in the two valleys, which are relatedto each other by time-reversal symmetry. This results in a finitetransverse conductivity (that is, σxy ̸= 0) and the appearance ofnon-reciprocal chiral edge modes6,7 as illustrated. It should bepossible to detect these effects with ultrafast pump–probe SNOMwith a small radius of curvature tip of ∼10 nm.

σ =[

σxx σxyσyx σyy

]:

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

Graphene :σxx =σyy ,σxy =σxy =0Anisotropic :σxx ̸=σyy , Im[σxx ·σyy]>0,σxy =σxy =0Hyperbolic :σxx ̸=σyy , Im[σxx ·σyy]<0,σxy =σxy =0Gapped Dirac :σxx =σyy ,σxy =−σxy ̸=0

reflected and incident PPs (see Fig. 1b) from which the complexq can be extracted. In such experiments, spacing between fringesis the PP half-wavelength, that is, π/Re[q], while the fringes decayexponentially as exp(−Im[q]x).

To directly compare and quantify the behaviour of variouspolaritonic materials, a series of figures of merit have beenestablished. Commonly used figures of merit for PPs are:γ ≡ Im[q]/Re[q], where γ −1/2π gives the number of cyclesthe PP can propagate before its amplitude decays by 1/e, and thelight confinement factor β , which is obtained by normalizing Re[q]to the free-space wavevector. Experiments with hBN-encapsulatedgraphene have achieved β ∼150 and γ −1>25 (ref. 45), see Fig. 1c.Hence, the current state of the art in graphene PP has alreadysurpassed the performance of SPPs along air/silver interfaces(γ −1 ≈10 across the visible spectral range, where β >10 (ref. 36)).In these graphene-based devices, the inverse damping γ −1 wasfound to be dominated by phonons in graphene and hBN46,

rather than those of extrinsic ionized impurities as in earlierexperiments on SiO2 substrates4,5 where γ −1 ∼ 5. Steps have alsobeen undertaken to develop resonant optical gold rod antennas and2D spatial conductivity patterns for direct launching and control ofpropagating PPs47 as illustrated in Fig. 1d,e respectively.

Plasmon-polaritons beyond grapheneGraphene has paved the way for the discovery and exploration ofother atomic 2D materials with new physical properties48, amongthemnew types of PP. For example, Bernal-stacked bilayer graphenehas recently received attention as a new plasmonic material,both theoretically49 and experimentally50,51. It allows for efficientswitching of the plasmonic Drude weight with the applicationof a vertical electric field50, due to the opening of an electronicbandgap52. It also accommodates a mid-infrared-active opticalphonon mode53, which can hybridize with the PPs to feature noveleffects such as electromagnetically induced transparency and slow

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185

(a) (b)NATUREMATERIALS DOI: 10.1038/NMAT4792 FOCUS | REVIEW ARTICLE

Box 2 | 2D plasmonic materials and optical conductivity.

Isotropic plasmon(graphene)

Hyperbolic plasmon(anisotropic materials)

Chiral plasmon(gapped Dirac materials)

Plasmon-polaritons (PPs) can be launched with a nano-antenna,such as a gold disc, as illustrated. The propagating PPs wavefrontcan then be spatially mapped with the SNOM47. Graphene PPshave a circular wavefront, since its optical conductivity tensor isisotropic, that is, σxx =σyy ≡σ0, with σ0= iD/π(ω+ i/τ ), whereD= e2µ/!2 is known as the Drude weight, µ is the chemicalpotential in graphene and τ is the electron’s lifetime. Anisotropic2D materials (for example, black phosphorus8,56) imply σxx ̸=σyy , and could potentially host hyperbolic PPs. In hyperbolicmedia, the permittivities along the Cartesian axes are opposite insigns (that is, Im[σxx ·σyy]<0), which can fundamentally changehow light interacts with matter. The mechanism relies on theinterplay between anisotropic intraband and interband motions9,which can render capacitive and inductive optical responsesalong the two axes. In SNOM experiments, these effects couldbe observed as PPs rays launched with an optical antenna, asillustrated above. Gapped Dirac materials (for example, transitionmetal dichalcogenides54,55) are a unique class of materials wherethe two electronic valleys at the Fermi energy exhibit circular

dichroism. The electronic wavefunctions in the two valleys ‘twist’differently (that is, Berry phase), hence imparting a sense ofchirality, and result in a different response to circular polarizedlight54,55. Pumping with circularly polarized light effectively leadsto population imbalance in the two valleys, which are relatedto each other by time-reversal symmetry. This results in a finitetransverse conductivity (that is, σxy ̸= 0) and the appearance ofnon-reciprocal chiral edge modes6,7 as illustrated. It should bepossible to detect these effects with ultrafast pump–probe SNOMwith a small radius of curvature tip of ∼10 nm.

σ =[

σxx σxyσyx σyy

]:

⎧⎪⎪⎪⎨

⎪⎪⎪⎩

Graphene :σxx =σyy ,σxy =σxy =0Anisotropic :σxx ̸=σyy , Im[σxx ·σyy]>0,σxy =σxy =0Hyperbolic :σxx ̸=σyy , Im[σxx ·σyy]<0,σxy =σxy =0Gapped Dirac :σxx =σyy ,σxy =−σxy ̸=0

reflected and incident PPs (see Fig. 1b) from which the complexq can be extracted. In such experiments, spacing between fringesis the PP half-wavelength, that is, π/Re[q], while the fringes decayexponentially as exp(−Im[q]x).

To directly compare and quantify the behaviour of variouspolaritonic materials, a series of figures of merit have beenestablished. Commonly used figures of merit for PPs are:γ ≡ Im[q]/Re[q], where γ −1/2π gives the number of cyclesthe PP can propagate before its amplitude decays by 1/e, and thelight confinement factor β , which is obtained by normalizing Re[q]to the free-space wavevector. Experiments with hBN-encapsulatedgraphene have achieved β ∼150 and γ −1>25 (ref. 45), see Fig. 1c.Hence, the current state of the art in graphene PP has alreadysurpassed the performance of SPPs along air/silver interfaces(γ −1 ≈10 across the visible spectral range, where β >10 (ref. 36)).In these graphene-based devices, the inverse damping γ −1 wasfound to be dominated by phonons in graphene and hBN46,

rather than those of extrinsic ionized impurities as in earlierexperiments on SiO2 substrates4,5 where γ −1 ∼ 5. Steps have alsobeen undertaken to develop resonant optical gold rod antennas and2D spatial conductivity patterns for direct launching and control ofpropagating PPs47 as illustrated in Fig. 1d,e respectively.

Plasmon-polaritons beyond grapheneGraphene has paved the way for the discovery and exploration ofother atomic 2D materials with new physical properties48, amongthemnew types of PP. For example, Bernal-stacked bilayer graphenehas recently received attention as a new plasmonic material,both theoretically49 and experimentally50,51. It allows for efficientswitching of the plasmonic Drude weight with the applicationof a vertical electric field50, due to the opening of an electronicbandgap52. It also accommodates a mid-infrared-active opticalphonon mode53, which can hybridize with the PPs to feature noveleffects such as electromagnetically induced transparency and slow

NATUREMATERIALS | VOL 16 | FEBRUARY 2017 | www.nature.com/naturematerials

© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

185

References: 1. Maier, S. A. Plasmonics : Fundamentals and applications; Springer Science and Business Media (2007). 2. Optical far-infrared properties of a graphene monolayer and multilayer, Falkovsky, L. & Pershoguba, Phys. Rev. B 76, 153410 (2007). 3. Polaritons in layered two-dimensional materials, T. Low et al, Nature Materials 16, 182–194 (2017)) 4. Chiral plasmons without magnetic field, Song, J. C et. al. Proc Natl Acad Sci USA 113, 4658–4663 (2016). Recent publications of the NeO team on the topic: 5. Hyper-Doped Silicon Nanoantennas and Metasurfaces for Tunable Infrared Plasmonics, J.-M. Poumirol, C. Bonafos et al, ACS Photonics, 8, 5, 1393–139 (2021) 6. Unveiling the optical emission channels of monolayer semiconductors coupled to silicon nanoantennas, J.-M. Poumirol, V. Paillard et al, ACS Photonics 7, 3106 (2020)

Keywords, areas of expertise (max 30 words)

Nano-optics, silicon antennas, Fourier transform infrared spectroscopy, plasmonics, non-reciprocal optics, 2D materials.

Required skills for the internship (max 30 keywords)

Very good background in general physics (optics, electromagnetism, solid state physics, quantum physics) e.g. B.S. in physics, strong interest in optical experiments.