Quantum impurity problem Nonperturbative interaction between a - - PowerPoint PPT Presentation

Meinrad Sidler, Patrick Back, Ovidiu Cotlet, Ajit Srivastava, Thomas Fink, Martin Kroner, Eugene Demler, Atac Imamoglu

Fermi polaron-polaritons in MoSe2

Quantum impurity problem

• Nonperturbative interaction between a single quantum
• bject/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: MX2 M = Transition Metal X = Chalcogen Layered materials

Electrical property Material Semiconducting MoS2 MoSe2 WS2 WSe2 MoTe2 WTe2 Semimetallic TiS2 TiSe2 Metallic, CDW, Superconducting NbSe2 NbS2 NbTe2 TaS2 TaSe2 TaTe2

Se Se Mo effective

monolayer

• Monolayer has a honeycomb lattice

Crystal structure

Se,S W, Mo

• Monolayer has a honeycomb lattice
• Valley semiconductor: physics at ±K

Crystal structure

Se,S W, Mo K Г

• K

• Monolayer has a honeycomb lattice
• Valley semiconductor: physics at ±K
• Broken inversion symmetry

 band gap

Crystal structure

Se,S W, Mo K Г

• K

• 2 valley/pseudospin flavors
• Spin-valley-locking
• Berry curvature
• Conduction-band

spin-orbit sign is different for MoSe2 and WSe2

Band Structure at K-points (Valleys)

~ 4-40 meV > 100 meV ~1.7 - 2 eV

K

• K

ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓

Optical addressing of valleys in MoSe2

K

• K

ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓

Mak et. al., Nat. Nanotech. 7, 494 (2012).

𝜏−

±K valleys respond to ±σ polarized light → valley addressability like spin protection of spin coherence due to spin- valley locking?

𝜏+

Optical addressing of valleys in MoSe2

K

• K

ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓

Mak et. al., Nat. Nanotech. 7, 494 (2012).

𝜏−

±K valleys respond to ±σ polarized light → valley addressability like spin protection of spin coherence due to spin- valley locking?

𝜏− 𝜏+ 𝜏+

Optical addressing of valleys in MoSe2

K

• K

ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓ ȁ ۧ ↑ ȁ ۧ ↓

Mak et. al., Nat. Nanotech. 7, 494 (2012).

𝜏−

±K valleys respond to ±σ polarized light → valley addressability like spin protection of spin coherence due to spin- valley locking? Valley mixing requires

• spin flip and short-range impurities
• Electron-hole exchange

𝜏− 𝜏+ 𝜏+

• Excitation of high-energy free electron-

hole pairs

• Strong Coulomb interaction due to lack
• f screening (truly 2D)

Photoluminescence (PL) of TMD monolayers

2 eV

• Excitation of high-energy free electron-

hole pairs

• Strong Coulomb interaction due to lack
• f screening (truly 2D)
• Excitons form with huge binding

energy of 500 meV (GaAs: ~ 10 meV)

Photoluminescence (PL) of TMD monolayers

0.5 eV 2 eV

• Excitation of high-energy free electron-

hole pairs

• Strong Coulomb interaction due to lack
• f screening (truly 2D)
• Excitons form with huge binding

energy of 500 meV (GaAs: ~ 10 meV)

• PL is dominated by decay from exciton

and trion

Photoluminescence (PL) of TMD monolayers

0.5 eV 2 eV 30 meV

• PL dominated by exciton and trion peaks
• Most flakes are electron doped

hence the trion peak

• Smallest linewidth:

Δ𝐹= 3 meV

• Radiative lifetime:

Γ𝑠𝑏𝑒 ≥ 1 meV

• small exciton Bohr radius 

strong light-matter coupling

Photoluminescence (PL) of a monolayer MoSe2

exciton trion wavelength (nm) T = 4° K

Intrinsic quantum well (QW) in a microcavity

Upper polariton Lower polariton ~ 5meV Exciton Photon

kin-plane (μm-1) Emission energy (eV) 𝑙𝑞ℎ 10

• Polaritons have an effective mass ~10−4𝑛𝑓𝑦𝑑; in-plane momentum is a

good quantum number

• Polaritons interact (weakly) due to their exciton component

z q q k// k// = w/c sin(q)

• Allows for coupling a wide range of

emitters to a cavity with µm size beam radius:

• GaAs QW/2DEG, MoSe2
• 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

Semi-integrated fiber cavity (J. Reichel)

• Dimple shot into a fiber forms top

mirror of DBR coated 0d cavity

• Piezo to tune cavity length

Strong Coupling of MoSe2 to a microcavity

• Graphene serves as a top gate
• Tunable electron density

Sample design

• All flakes are exfoliated and stacked

using pick-up transfer technique

Sample design

• measure unperturbed MoSe2

spectrum at a long cavity length (~10 µm)

• transmission spectrum of one

cavity mode tuned across the MoSe2 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 MoSe2 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 MoSe2 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

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

perturbative coupling exciton trion

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

cavity photon energy exciton energy Fermi sea of electron energy electron – exciton interaction

• To model the system we assume the following Hamiltonian:
• Interacting many-body system

Trio ion-Exciton Spectrum modelle led as a Fermi i Pola laron

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: 𝜚0 ≠ 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 = 𝑙𝐺 (delocalized hole)

• Using a truncated basis (Chevy ansatz) we get:

molecule (trion) repulsive polaron attractive polaron

Calculated spectrum

Experiment

Fermi energy dependence of the spectrum

Theory

repulsive polaron attractive polaron

Blue shift of attractive polaron is due to phase space filling. In WSe2 a red shift is expected

• Assume a strongly bound exciton at r = 0

Trion vs. attractive polaron

r r Trion

Attractive Polaron

𝑏𝑈𝑠𝑗𝑝𝑜 1/𝑙𝐺

Net charge: -e Net charge: 0

• 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

Polarons

• 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)

Photo luminescence

Strong Coulomb interaction Large normal-mode splitting

37

Strong Light-Matter Coupling in TMDs

(GaAs ~ 5 meV)

2D, massive Dirac limit,

• Possibility of room temperature polariton condensation
• ΩR comparable to trion binding (ET) and accessable Fermi energies (EF)

• No electron doping:

exciton polaritons with a splitting of 16 meV

• avoided crossing centered at the

exciton resonance

Strong coupling to cavity

• EF < ET, ΩR:

both repulsive to the attractive polaron

Strong coupling to cavity

Strong coupling to cavity

The observation of strong coupling between cavity and lower energy resonance proves that the latter is an attractive polaron

cavity photon energy exciton energy photon - exciton interaction Fermi sea of electron energy electron – exciton interaction

• To model the system we assume the following Hamiltonian:

Signatures of polaron formation for an ultra-light polariton impurity?

• strong coupling transmission

spectrum at resonance

• oscillator strength transfers from

repulsive to attractive polaron

• At high electron densities, the

attractive polaron splitting decreases again due to the spectral width of the polaron resonance

Strong coupling to cavity

New features/open problems:

• Competition between polaron and polariton formation: quantum

impurity with an ultralow mass

• Possibility to investigate Bose-polarons: electron dressed with

polaritons or a K valley polariton dressed with Bogoluibov excitations from a (–K) valley polariton condensate

• Interaction between two attractive-polaron-polaritons: polariton

blockade

• Signatures of interacting electron-polariton system in transport

Patrick Back, Ovidiu Cotlet, Ajit Srivastava, Thomas Fink, Martin Kroner, Eugene Demler, Atac Imamoglu

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