Photodoped charge transfer insulators Denis Gole CCQ, Flatiron - PowerPoint PPT Presentation

Photodoped charge transfer insulators Denis Golež CCQ, Flatiron Institute Taming Non-Equilibrium Systems: from Quantum Fluctuation to Decoherence, July 2019 1/ 59

Mott insulators ◮ Failure of band theory ◮ Strong electron-electron interaction ◮ Hubbard model and Mott gap ◮ Metal-insulator transition c † � � H = − t i ,σ c j ,σ + U n i ↓ n i ↑ < i , j >σ i 2/ 59

Charge transfer insulators ◮ Multi band physics 3/ 59

Charge transfer insulators ◮ Multi band physics ◮ Zaanen-Sawatzky-Allen diagram CTI ∆<0 Mott F. Gebhard, The Mott Metal-Insulator Transition 4/ 59

Charge transfer insulators ◮ Multi band physics ◮ Zaanen-Sawatzky-Allen diagram F. Gebhard, The Mott Metal-Insulator Transition 5/ 59

Pump-probe on Mott insulators ◮ Use strong laser pulses to photo-excite charge carriers ◮ Delayed probe pulse (optics, photo-emission, RIXS, . . . ) 6/ 59

Photo-excitation of Mott insulators - II ◮ Use strong laser pulses to photo-excite charge carriers ◮ Mobile doublons and holons 7/ 59

Relaxation ◮ Holon and doublon number conserved ◮ Role of bosonic modes ( spins, phonons, plasmons ) ◮ Kinetic processes Semsarna, et.al. PRB 82,224302(2010) Eckstein, et.al. PRB 035122 (2011) Lenarčič, et.al. PRL 111,016401 (2013) 8/ 59

Thermalization ◮ Holon doublon recombination ◮ Exponentially suppressed - energy conservation ◮ Time scale separation between cooling and thermalization Semsarna, et.al. PRB 82,224302(2010) Eckstein, et.al. PRB 035122 (2011) Lenarčič, et.al. , PRL 111,016401 (2013) 9/ 59

Goals ◮ Is multiband picture essential ? ◮ Properties of trapped states ◮ Role of collective modes: charge and spin screening 10/ 59

Table of contents 11/ 59

DMFT [ c † � � H = − t j c i + h . c . ] + U n i ↓ n i ↑ < i , j > i ◮ Hybridization function ∆( t , t ′ ) ◮ Local self-energy 1.0 0.5 ) ∆ ( ω 0.0 − 0.5 − 1.0 0 5 10 15 20 ω 12/ 59

� ✄ DMFT [ c † � � H = − t j c i + h . c . ] + U n i ↓ n i ↑ < i , j > i ◮ Hybridization function ∆( t , t ′ ) ◮ Local self-energy 1.0 0.5 ) 0.0 ( ✂ 0.5 ✂ 1.0 0 5 10 15 20 ✁ 13/ 59

DMFT and screening [ c † � � � H = − t j c i + h . c . ] + U n i ↓ n i ↑ + V n i n j < i , j > i < i , j > ◮ Hybridization function ∆( t , t ′ ) ◮ Effective interaction W ( t , t ′ ) ◮ Local self-energy and polarization 1.0 0.5 ) ∆ ( ω 0.0 − 0.5 V − 1.0 0 5 10 15 20 0.15 t 0.10 0.05 0.00 ( ) ω W -0.05 -0.10 -0.15 -0.20 0 5 10 15 20 25 30 14/ 59

DMFT and screening [ c † � � � H = − t j c i + h . c . ] + U n i ↓ n i ↑ + V n i n j < i , j > i < i , j > ◮ Hybridization function ∆( t , t ′ ) ◮ Effective interaction W ( t , t ′ ) ◮ Local self-energy and polarization - EDMFT 1.0 0.5 ) ∆ ( ω 0.0 − 0.5 − 1.0 0 5 10 15 20 0.15 0.10 1 0.05 0.00 ( ) ω -0.05 W -0.10 --0.15 -0.20 -0.25 0 5 10 15 20 25 30 15/ 59

Non-local fluctuations q k k Σ k = Σ EDMFT + Σ GW − Σ GW Σ GW (t,t ′ ) = k k − q t ′ t k loc Π k = Π EDMFT + Π GW k − q − Π GW k loc Π k (t,t ′ ) = t t ′ q 1. Effect of non-local fluctuations using GW+EDMFT References: ◮ Eq. implementation (Sun et.al. PRB 66,085120 (2002)) ◮ Full implementation (Ayral et.al. PRL 109, 226401 (2012) ) ◮ Non-equilibrium implementation (DG et.al. PRL 118,246402(2017)) ◮ Ab-initio for SrVO 3 (Boehnke et.al. PRB 94,201106(2016)) 16/ 59

Phase diagram ◮ Role of multiband and screening ◮ Half-filled and high-temperatures J. Orenstein et.al. Science 228, 468(2000) 17/ 59

Emery model H = H e + H kin + H int n p � n d � H e = ǫ d i + ( ǫ d + ∆ pd ) i , i i ,δ t αβ ij c † � � H kin = i ασ c j βσ , ij σ ( α,β ) ∈ ( d , p x , p y ) U αβ i n β � � ij n α H int = j , ij ( α,β ) ∈ ( d , p x , p y ) La 2 CuO 4 : U dd = 5 . 0 eV, U dp = 2 . 0 eV, t dp = 0 . 5 eV, t dd = − 0 . 1 eV, t pp = 0 . 15 eV, ∆ pd = − 3 . 5 eV 18/ 59

Multiscale description ◮ Downfolding for Emery model ◮ d-orbital within DMFT and p-orbitals with computational cheaper approaches (HF,GW) 19/ 59

Equilibrium spectrum ◮ Antibonding band - Zhang-Rice singlet ◮ Bonding band ◮ Upper Hubbard band 1.0 d-GW p-GW 0.8 d-HF p-HF 0.6 ) A ( 0.4 0.2 0.0 5 0 5 20/ 59

Photo-excitation ◮ Transfer from p to d electrons ◮ Photo-induced double occupancy ◮ Number of holes on d orbital h d = ∆ d occ − 2∆ n p 0.025 0.10 d occ 0.000 n 0.05 0.025 = 6.0 0 20 40 60 20 40 60 t [fs] t [fs] 21/ 59

PES ◮ Dynamical screening without importance Eq 0.6 0.6 , t ) HF 0.4 0.4 A ( 0.2 0.2 0.0 0.0 5 0 5 0.6 0.6 [eV] , t ) 0.4 0.4 GW A ( 0.2 0.2 0.0 0.0 5 0 5 [eV] 22/ 59

t-PES ◮ Hartree shift due to electron-hole attraction ∆Σ H dd = ( U dd − 2 U dp )∆ n d t=36 fs 0.6 Eq , t ) 0.4 A ( 0.2 0.0 5 0 5 [eV] 23/ 59

t-PES: dynamical screening t=36 fs 0.6 0.6 Eq , t ) HF 0.4 0.4 A ( 0.2 0.2 0.0 0.0 5 0 5 0.6 0.6 [eV] , t ) 0.4 0.4 GW A ( 0.2 0.2 0.0 0.0 5 0 5 [eV] 24/ 59

Single band Mott insulator ◮ Minor reduction and broadening of the Hubbard gap ◮ Dynamical screening enhanced in multiband case Eq DG et.al. PRB 92,195123(2015) 25/ 59

Optical conductivity ◮ Red shift ◮ Enhancement by dynamical screening 0.00 Eq 0.02 0.03 , t p ) 40 fs , t p ) 0.00 0.02 ( ( 0.02 0.01 0.00 0.0 2.5 5.0 0.0 2.5 5.0 [eV] [eV] 26/ 59

Optical conductivity - experiment ◮ Pump probe on La 2 CuO 4 -transient reflectivity ◮ Above gap (3.5 eV) excitation 1 0.95 eV 3.1 eV 0 =0.05±0.05 ps –1 1.5 2.0 2.5 Energy (eV) Novelli et.al. Nat. Comm. 6112(2014) 27/ 59

Optical conductivity ◮ Red shift ◮ Enhancement by dynamical screening ◮ Larger renormalization in experiment ◮ Effect of AFM Dyn Sta 28/ 59

Screening Charge susceptibility Im [ χ ( t , ω )] 1. Photo-induced screening channel 2. Strong scattering with plasmons → broadening of spectrum 29/ 59

Message I ◮ Strong band gap renormalization in charge-transfer insulators ◮ Importance of non-local fluctuations (dynamical screening) ◮ Effect of incoherent dynamics on experimental probes ◮ Similar results by hybrid time-dependent DFT: N. Tancogne-Dejean, et.al. PRL 121, 097402 (2018) N. Tancogne-Dejean, et.al. arXiv:1906.11316 30/ 59

NiO 31/ 59

Lattice structure ◮ Inter-penetrating antiferromagnetic planes ◮ AFM is dominant 32/ 59

Electronic structure ◮ Two electrons in two e g -orbitals ◮ Excitations: magnons, Hund and CT excitations 33/ 59

Electronic structure ◮ LDA + DMFT description J. Kunes, et.al. PRB 75, 165115 (2017) 34/ 59

2PPE - experiment ◮ Charge transfer excitation ◮ Surface states 4 3 C 2 S 1 0 V -1 O 2p -2 4 8 12 16 20 35/ 59

2PPE - experiment ◮ Charge transfer excitation ◮ Surface states 4 3 C 2 S 1 0 V -1 O 2p -2 4 8 12 16 20 36/ 59

Pump-probe ◮ Pump h ν P =4.2 eV ◮ Ultra-fast relaxation ◮ Oscillating photo-induced in-gap state 37/ 59

In-gap state ◮ Long-lived coherent dynamics of in-gap state ◮ Strongly damped at Neél temperature 38/ 59

In-gap state ◮ Long-lived coherent dynamics of in-gap state ◮ Strongly damped at Neél temperature 39/ 59

Modeling ◮ String states 40/ 59

Modeling ◮ Ground state: High-spin AFM ◮ Photo-induced triplon and hole ◮ String states 41/ 59

Multiband model ◮ Neglect excitonic effects ◮ Mapping to two-band t-J problem (Zhang-Rice construction) ◮ Atomic, kinetic and AFM contribution H = ˆ H loc + H kin + H ex (1) 42/ 59

Multiband model Local excitations T ◮ Kanamori interaction for d orbitals triplon states (d 9 L -1 ) ◮ J H =1 eV J 3H S0 ♭ in-gap state (d* 8 L) ◮ Hubbard and Hund physics J 2H ◮ Ground state: high-spin state S0 J H ◮ Solve within DMFT S1 0 ground state (d 8 L) ( U ′ − J H δ σσ ′ ) n i ασ n i βσ ′ ˆ � � � � H loc = U n i ,α ↑ n i α ↓ − µ ˜ n i ασ + i ,α i ασ i ,α<β σ,σ ′ � c † c † c † c † � � + γ J H ˜ i α ↑ ˜ i α ↓ ˜ c i β ↓ ˜ c i β ↑ + ˜ i α ↑ ˜ i β ↓ ˜ c i α ↓ ˜ c i β ↑ i ,α<β (2) c † c † � � H kin = − t 0 (˜ ia σ ˜ c ja σ + ˜ ja σ ˜ c ia σ ) (3) a σ � i , j � 43/ 59

Multiband model Local excitations T triplon states (d 9 L -1 ) J 3H S0 ♭ ◮ Superexchange interaction J ex J 2H in-gap state (d* 8 L) ◮ Mean-field approximation S0 J H J ex S1 ♭ S1 0 ground state (d 8 L) � � H ex = J ex S ia · S ja + S ib · S jb → J ex S ia · � S ja � + � S ib � · S jb � ij � � ij � (4) 44/ 59

PES - theory 1.0 5 0.8 4 0.6 ω[eV] ◮ Photo-induced in-gap state 0.4 3 ◮ Hund excitation 0.2 2 0.0 1 t= 60 fs Eq 10 -4 10 -2 0 50 A(ω,t) t [fs] 45/ 59

PES - theory ◮ Photo-induced in-gap state 1.0 5 ◮ Hund excitation 0.8 4 0.6 ω[eV] 0.4 3 PES PES 0.2 2 0.0 1 t= 60 fs Eq PES 10 -4 10 -2 0 50 A(ω,t) t [fs] H. Strand, et.al. PRB 96, 165104 (2017) 46/ 59