Fermi polaron-polaritons in MoSe 2 Meinrad Sidler, Patrick Back, Ovidiu Cotlet, Ajit Srivastava, Thomas Fink, Martin Kroner, Eugene Demler, Atac Imamoglu
Quantum impurity problem • Nonperturbative interaction between a single quantum object/impurity and a degenerate Bose or Fermi system • Infinite mass impurity - Fermi-edge singularity - Kondo physics • Mobile impurity - polaron physics: modification of mass - transport
Polarons in condensed-matter and ultracold atoms Lattice polarons: electrons dressed with phonons Polarons in a BEC: a new strong coupling regime Fermi-polarons: metastable repulsive polarons Zwierlein (2009), Köhl (2012), Grimm (2012)
Polaritons in 2D materials: A new Bose-Fermi mixture for polaron physics Outline 1) Properties of transition metal dichalcogenide (TMD) monolayers 2) Cavity-polaritons in MoSe2 monolayer embedded in a fiber-microcavity
Transition Metal Dichalcogenides: A new class of truly 2d semiconductors Formula: MX 2 M = Transition Metal X = Chalcogen Se Mo Electrical property Material Se Semiconducting MoS 2 MoSe 2 WS 2 WSe 2 MoTe 2 WTe 2 Layered Semimetallic TiS 2 TiSe 2 materials effective Metallic, CDW, NbSe 2 NbS 2 NbTe 2 monolayer Superconducting TaS 2 TaSe 2 TaTe 2
Crystal structure • Monolayer has a honeycomb lattice Se,S W, Mo
Crystal structure • Monolayer has a honeycomb lattice Se,S W, Mo • Valley semiconductor: physics at ±K K Г -K
Crystal structure • Monolayer has a honeycomb lattice Se,S W, Mo • Valley semiconductor: physics at ±K • Broken inversion symmetry K band gap Г -K
Band Structure at K-points (Valleys) • 2 valley/pseudospin flavors • Spin-valley-locking • Berry curvature -K K • Conduction-band spin-orbit sign is different ~ 4-40 meV for MoSe 2 and WSe 2 ~1.7 - 2 eV > 100 meV ȁ ۧ ȁ ۧ ↑ ↓ ȁ ۧ ȁ ۧ ↓ ↑
Optical addressing of valleys in MoSe 2 ±K valleys respond to ± σ polarized light → valley addressability like spin protection of spin coherence due to spin- valley locking? ȁ ۧ -K ȁ ۧ ↓ ↑ K ȁ ۧ ȁ ۧ ↑ ↓ 𝜏 − 𝜏 + ȁ ۧ ȁ ۧ ↑ ↓ ȁ ۧ ȁ ۧ ↓ ↑ Mak et. al., Nat. Nanotech. 7 , 494 (2012).
Optical addressing of valleys in MoSe 2 ±K valleys respond to ± σ polarized light → valley addressability like spin protection of spin coherence due to spin- valley locking? ȁ ۧ -K ȁ ۧ ↓ ↑ K ȁ ۧ ȁ ۧ ↑ ↓ 𝜏 − 𝜏 + 𝜏 − 𝜏 + ȁ ۧ ȁ ۧ ↑ ↓ ȁ ۧ ȁ ۧ ↓ ↑ Mak et. al., Nat. Nanotech. 7 , 494 (2012).
Optical addressing of valleys in MoSe 2 ±K valleys respond to ± σ polarized light → valley addressability like spin protection of spin coherence due to spin- valley locking? ȁ ۧ -K ȁ ۧ ↓ ↑ K ȁ ۧ ȁ ۧ ↑ ↓ Valley mixing requires - spin flip and short-range impurities - Electron-hole exchange 𝜏 − 𝜏 + 𝜏 − 𝜏 + ȁ ۧ ȁ ۧ ↑ ↓ ȁ ۧ ȁ ۧ ↓ ↑ Mak et. al., Nat. Nanotech. 7 , 494 (2012).
Photoluminescence (PL) of TMD monolayers • Excitation of high-energy free electron- hole pairs • Strong Coulomb interaction due to lack of screening (truly 2D) 2 eV
Photoluminescence (PL) of TMD monolayers • Excitation of high-energy free electron- hole pairs • Strong Coulomb interaction due to lack of screening (truly 2D) 0.5 eV • Excitons form with huge binding energy of 500 meV (GaAs: ~ 10 meV) 2 eV
Photoluminescence (PL) of TMD monolayers • Excitation of high-energy free electron- hole pairs • Strong Coulomb interaction due to lack of screening (truly 2D) 0.5 eV 30 meV • Excitons form with huge binding energy of 500 meV (GaAs: ~ 10 meV) 2 eV • PL is dominated by decay from exciton and trion
Photoluminescence (PL) of a monolayer MoSe 2 • PL dominated by exciton and trion peaks • Most flakes are electron doped hence the trion peak T = 4 ° K trion • Smallest linewidth: Δ𝐹 = 3 meV exciton • Radiative lifetime: Γ 𝑠𝑏𝑒 ≥ 1 meV • small exciton Bohr radius strong light-matter coupling wavelength (nm)
Intrinsic quantum well (QW) in a microcavity q z Upper Emission energy (eV) polariton Photon Exciton q k // ~ 5meV k // = w /c sin( q ) Lower polariton 0 𝑙 𝑞ℎ k in-plane ( μ m -1 ) 10 • Polaritons have an effective mass ~ 10 −4 𝑛 𝑓𝑦𝑑 ; in-plane momentum is a good quantum number • Polaritons interact (weakly) due to their exciton component
Semi-integrated fiber cavity (J. Reichel) • Allows for coupling a wide range of emitters to a cavity with µm size beam radius: • GaAs QW/2DEG, MoSe 2 • Tunable vacuum field strength and long cavity lifetime allowing for high-precision spectroscopy • Fiber mirror with a radius of curvature ~10 µm, allows for a beam waist < 1µm + Finesse > 100,000
Strong Coupling of MoSe 2 to a microcavity • Dimple shot into a fiber forms top mirror of DBR coated 0d cavity • Piezo to tune cavity length
Sample design • Graphene serves as a top gate • Tunable electron density
Sample design • All flakes are exfoliated and stacked using pick-up transfer technique
perturbative coupling • measure unperturbed MoSe 2 spectrum at a long cavity length (~10 µm) • transmission spectrum of one cavity mode tuned across the MoSe 2 absorption spectrum
perturbative coupling • At every cavity length, we fit a lorentzian to the transmission spectrum
perturbative coupling • At every cavity length, we fit a lorentzian to the transmission spectrum • Plotting the cavity linewdth against its center wavelength reveals the MoSe 2 absorption spectrum
perturbative coupling • At every cavity length, we fit a lorentzian to the transmission spectrum • Plotting the cavity linewdth against its center wavelength reveals the MoSe 2 absorption spectrum • Two distinct resonances
perturbative coupling • strong electron density dependence • Increasing electron density shifts both resonances to higher energies • Rapid broadening of the higher energy peak
perturbative coupling trion exciton The direct optical creation of a bound molecular trion state is strongly suppressed due to vanishing oscillator strength - Initial state: delocalized electron on the Fermi surface - Final state: electron localized around exciton
Optical resonances in absorption • exciton energy lowered by electron-hole pair excitations from the degenerate Fermi sea: attractive polaron • Concurrently, the system develops a metastable repulsive-polaron state
Trio ion-Exciton Spectrum modelle led as a Fermi i Pola laron • To model the system we assume the following Hamiltonian: cavity photon energy exciton energy Fermi sea of electron energy electron – exciton interaction • Interacting many-body system
Trio ion-Exciton Spectrum modelle led as a Fermi i Pola laron Polaron Chevy-Ansatz (prior work: Suris) exciton Exciton + Fermi-sea electron-hole pair Quasi-particle weight: 𝜚 0 ≠ 0 ensures that polaron has finite oscillator strength
Trio ion-Exciton Spectrum modelle led as a Fermi i Pola laron Polaron Chevy-Ansatz Describes trion for 𝑟 = 𝑙 𝐺 (delocalized hole)
Calculated spectrum • Using a truncated basis (Chevy ansatz) we get: attractive polaron repulsive polaron molecule (trion)
Fermi energy dependence of the spectrum Experiment Theory repulsive polaron attractive polaron Blue shift of attractive polaron is due to phase space filling. In WSe 2 a red shift is expected
Trion vs. attractive polaron • Assume a strongly bound exciton at r = 0 Attractive Trion Polaron 1/ 𝑙 𝐺 r r 𝑏 𝑈𝑠𝑗𝑝𝑜 Net charge: -e Net charge: 0
Polarons • How do we know we see the attractive polaron and not the trion? • Overlap between initial and final state is very small for trion • Coupling to light is small
Photo luminescence • PL expected from trion • PL and absorption data are in good agreement for low electron densities • With increasing Fermi energy we observe a splitting between absorption and PL peak • As well as a decrease of PL intensity (expected when Fermi energy > trion binding)
Strong Light-Matter Coupling in TMDs Strong Coulomb interaction Large normal-mode splitting 2D, massive Dirac limit, (GaAs ~ 5 meV) • Possibility of room temperature polariton condensation • Ω R comparable to trion binding (E T ) and accessable Fermi energies (E F ) 37
Strong coupling to cavity • No electron doping: exciton polaritons with a splitting of 16 meV • avoided crossing centered at the exciton resonance
Strong coupling to cavity • E F < E T , Ω R : both repulsive to the attractive polaron
Strong coupling to cavity The observation of strong coupling between cavity and lower energy resonance proves that the latter is an attractive polaron
Signatures of polaron formation for an ultra-light polariton impurity? • To model the system we assume the following Hamiltonian: cavity photon energy exciton energy photon - exciton interaction Fermi sea of electron energy electron – exciton interaction
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