Polarons - univie.ac.at

PolaronsAn introduction toBasic concepts

andRecent findings

Ulrike DieboldMichael SchmidMartin SetvinIgor Sokolović

Cesare FranchiniGeorg KresseThomas HahnMichele Reticcioli

Quasi-particle:Electronic carrier + altered phonons

[Emin (2013)]

Polaron

Delocalized electron Polaron

Charge carriers –-> polaron formation

[Setvin, PRL (2014)]

Path-integral formalism [Feynman (1955)]

Self trapping [Landau (1933)]

Continuum approximation [Pekar (1946)]:

- effective mass

- coupling constant

The weak coupling limit (α<1)[Frölich (1954)]

A polaron story

The strong coupling limit[Holstein (1959)]

The weak coupling limit (α<1)[Frölich (1954)]:

- Second quantization, perturbation theory

- Cloud thickness:

- Effective mass:

A polaron story

The strong coupling limit[Holstein (1959)]:

- Electron hopping:

[Devreese (2010)]

Solvable in the adiabatic and non-adiabatic limits:renormalized hopping integral t

The weak coupling limit (α<1)[Frölich (1954)]:

Polaron features

The strong coupling limit[Holstein (1959)]:

Large polaron(or continuum polaron)

Small polaron(or lattice polaron)

Long-range electron-phonon interaction

Radius >> lattice parameter

Shallow state (~10 meV)

Coherent motion(scattered occasionally by phonons)

Mobility >> 1 cm2/V/secHeavy massWeakly scattered by phonons

Falling mobility with increasing Temperature

Short-range electron-phonon interaction

Radius ~ lattice parameter

Mid-gap state (~1 ev)

Incoherent motion(assisted by phonons)

Mobility << 1 cm2/V/sec

Arising mobility with increasing Temperature

Observation techniques

Charge carriers introduced by:- irradiation- lattice defects (dopants, vacancies, ...)

Polarons probed by- Scanning Tunneling Microscopy and Spectroscopy (STM and STS)- Angle-resolved photoemission spectroscopy (ARPES)- Electron Paramagnetic Resonance (EPR)- Infra-red (IR) spectroscopy- Time-resolved Kerr spectroscopy- Current measurements

Computationally:- DFT (DFT+U, HSE, Molecular Dynamics)- Diagrammatic Quantum Monte Carlo

Where?Oxides, Perovskites, Organic materials, DNA, ...

Polarons in bulk TiO2


Devreese, Bull. Soc. Belge Phys. (1963)Nagels, Denayer, Devreese, Sol. St. Commun. (1963)

First observation of polarons[according to Stoneham (2007)]

Hole small polaronsin UO

2-x

Measured quantity:current

Charge carrier origin:O vacancies

[Crevecoeur, Wit, J. Phys. Chem. Solids (1970)]

Hole small polaronsin Li-doped MnO

Measured quantity:current

Charge carrier origin:Li dopants

Small polaron hopping via Molecular Dynamics

[Kowalski, PRL (2010)][Reticcioli, hopefully 2018]


[Reticcioli, PRX (2017)]

Measurement technique:STM/STS


Electron Small polarons in r-TiO2

~70% Experimental STM


Measurement technique:STM/STS

Charge carrier origin:Nb dopants

Electron Large polaronlike states in a-TiO2

[Miyata, Science Advances (2017)]

Measurement technique:Time-resolved opticalKerr effect (TR-OKE)

Charge carrier origin:irradiation

Hole polaron: HSE results for CsPbBr3

CH3NH

3PbBr

3 and CsPbBr

3

TR-OKE on CH3NH

3PbBr

3

Large polarons on PbBr sublattice

>Egap

The cell is too small for electron polarons that are more delocalized because of the different states in the CB and VB

τ1,2

= 0.3, 3.4 ps (phonon+photoinjection)

[Verdi, Nature Com. (2017)]

[Moser, PRL (2013)]

Measurement techniqueARPES


a-TiO2

increasing doping

CB

satellites

CB

satellites

CB only

Electron Large polarons

Measurament technique:EPR

Charge carrier origin:defects

[Yang, PRB (2013)]

[Lenjer, PRB (2002)]

[Possenriede, Ferroelectricts (1994)]

BaTiO3

r-TiO2

Measurament technique:EPR

Charge carrier origin:Irradiation

[Yusupov, PRB (2011)]Nb doped (1.2%) KTaO

3

Attempt of interpretation:Signal I: also in pure KTO => trapped chargeSignal II: only in doped KTO => associated to Nb-O electron and hole states

[Sezen, Sc. Reports (2015)]

Measurement technique:IR-adsorbtion spectroscopy

Charge carrier origin:UV-irradiation

orH adatoms

Small polarons in r-TiO2

[Freytag, Sc. Reports (2016)]

Measurement technique:Mid-IR spectroscopy

Charge carrier origin:irradiation

Δ νOH=−3 cm−1O Hole small polarons => Δ El. Pot. =>

near stoichiometric lithium niobate LiNbO3

[Cao, Sc. Reports (2017)]

Measurement technique:IR spectroscopy


NO adsorbed on r-TiO2

No el. polaron: 1870

With el. polaron: 1751

νNO

Small polarons

“Brave” assumptions:- no CO at V

O’s

- ΔνNO

not affected by VO’s

(cm-1)

AFM STM (filled states)

CO at Ti5c rows, with CO at VO in between

CO at VO

Bright: CO at Ti5c with S0 polaron.Darker: CO at Ti5c with no polaron.

(a)

(b)

(c)

CO adsorption on r-TiO2

[Reticcioli, hopefully soon]

Measurement technique:STM


Small polarons

S0-NNN to VO

S0-NNN to VO

Filled state STM

CO on VO

S1 polaron

r-TiO2

Polarons affected by defects but not confined.

SrTiO3 [Hao, PRB (2015)]


r-TiO2

Polarons affected by defects but not confined.

r-TiO2

Repulsion between polarons.

TiO2stoichiometric

(110) Rutile surface

sputteringannealing

TiO

S1

S0

O

S0

Reduced Surface

VO

Oxygen Vacancy

AFM

O2c

rows

O2c

(1x2) Structural Reconstruction

High T

Critical VO= 16.7% ML

AFM

STM, empty states

Exp. Critical VO

DFT Phase Diagram

No agreementwith experiment

- High Vo concentration

- Ti2O

3 not stable

Exp. Critical VO

ST

M, m

id-g

ap s

tate

s

[001]

[001]

3x1 periodicityfor V

O=16.7%

Related topics:

- Magnetic polarons & Colossal Magnetoresistance

- Bipolarons and High Temperature Superconductivity

- Polarons and quantum dots

- Polaronic transport in DNA

[Emin (2013)]

PolaronsAn introduction toBasic concepts

andRecent findings

Ulrike DieboldMichael SchmidMartin SetvinIgor Sokolović

Cesare FranchiniGeorg KresseThomas HahnMichele Reticcioli

Polarons - univie.ac.at

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