Manipulation of band gap upon photoexcitationof an excitonic insulator

Denis Golež, Martin Eckstein, Philipp WernerSelene Mor, Claude Monney, Julia Stahler

26. October 2016

Table of Contents

Introduction

Semimetal - gap closureModelDynamics of gap closure

Semiconductor - gap enhancement

SemiconductorI Exciton is a bound pair of electron and hole due to Coulomb

interactionI Excitonic insulator: spontaneous symmetry breaking due to

Coulomb interaction predicted by Mott in the early 60’s

I Semiconductor and semimetal limitI Experimental candidates: semiconducting(Ta2NiSe5) and

semimetal(1T − TiSe2)

EB

Denis Golež Manipulation of excitonic insulator

SemiconductorI Exciton is a bound pair of electron and hole due to Coulomb

interactionI Excitonic insulator: spontaneous symmetry breaking due to

Coulomb interaction predicted by Mott in the early 60’sI Semiconductor and semimetal limitI Experimental candidates: semiconducting(Ta2NiSe5) and

semimetal(1T − TiSe2)

EB

Denis Golež Manipulation of excitonic insulator

Semi-metalTwo band spin-less fermions with longer range interaction

H =∑

kα(εkα + ∆α)c†k,αck,α + 12

∑i ,j

∑αα′ V αα′

|i−j|niαnj,α′

Hdip =∑

k A(t)c†k,1ck,0 + H.c.

Symmetry breaking: spatial symmetry and charge conservationwithin the bands 〈c†k+Q,1ck,2〉 6= 0Time dependent Hartree-Fock and GW approximation

Denis Golež Manipulation of excitonic insulator

t-ARPES

Time dependent PES

I(ω, tp) = i∫

dtdt ′S(t)S(t ′)eiω(t−t′)G<k (tp + t, tp + t ′)

S(t) is probe pulse envelope.I Photo excitation with strong pulseI Partial photoinduced population in the upper bandI Strong excitation close the gap, weak only partially

−π/2 −π/4 0 −π/4 π/2

−4

−2

0

2

4

Eq

−π/2 −π/4 0 −π/4 π/2

−4

−2

0

2

4

t = 2.1

−π/2 −π/4 0 −π/4 π/2

−4

−2

0

2

4

t = 7.0

−π/2 −π/4 0 −π/4 π/2

−4

−2

0

2

4

t = 20.

Denis Golež Manipulation of excitonic insulator

Dynamics of order parameter

Order parameter 〈c†k+Q,1ck,2〉I Reduction of the order parameterI Different long time limit for weak(strong) excitationsI For strong excitation two time dynamics

0 5 10 15t

0.0

0.1

0.2

0.3

0.4

0.5

|ρ12|

(c)

A0 = 0.5A0 = 1A0 = 1.5A0 = 1.9

5

t

3

4 φ

4 6 8 10 12 14 16 18 20t

10−3

10−2

10−1

|ρ12|

(a)

A0 = 1.3A0 = 1.4A0 = 1.5A0 = 1.6

Denis Golež Manipulation of excitonic insulator

Dynamical phase transitionI Prethermalization scenario: system is in the long lived trapped

stateI Critical slowing down at nonthermal critical pointI Long time dynamics and thermal critical point: temperature

vs dopingI Connection with PES

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8A0

0.0

0.2

0.4

0.6

0.8

1.0

1/τ Ac

τAMτdeτIτth

0.03 0.08 0.17 0.2 0.26δn

Denis Golež Manipulation of excitonic insulator

Gap closureTransfer of kinetic energy to condensate

I Gap prevents fast recombinationI Intraband relaxation due to el.-el. scatteringI Impact ionization

Screening scenarioI Screening decrease the effective interaction

5 10 15 20 25 30t

−0.05

0.00

0.05

0.10

δn

(a)

A0 = 0.5A0 = 0.7A0 = 0.9A0 = 1

−1 0 1ω

0246

A<

(ω)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7∆E

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

∆n

(b)

Denis Golež Manipulation of excitonic insulator

ScreeningFrequency dependent interaction

Wq(ω) = εq(ω)−1Vq

I How to construct low energy model ?I Which energy scale is responsible for gap dynamics

"Phenomenological" approach

Veff = ∆/|ρ12|

0 1 2 3 4 5ω

−10

−8

−6

−4

−2

0

2

Tr[Re[W

(ω)]−Vloc]

(a)-2.8-1.40.01.42.84.25.67.08.49.8

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9∆

0.15

0.20

0.25

0.30

0.35

0.40

|ρ12|

A0 = 0.5A0 = 0.7A0 = 0.9A0 = 1A0 = 1.1A0 = 1.25A0 = 1.5Eq −HFEq

Denis Golež Manipulation of excitonic insulator

Semiconductor - gap enhancementt-ARPES on Ta2NiSe5:

I Gap increase as one lowers temperature - possible excitonicinsulator

I After photo-excitation momentum dependent renormalizationof gap size

I Weak excitation vs strong excitations

Denis Golež Manipulation of excitonic insulator

Proposed mechanismHartree-Fock with nonthermal distribution function

I Fast intra-band relaxation of electronsI Bottleneck due to presence of the gapI Hartree shift leads to more resonating states at k = 0

0.0k

p/4- p/40.0k

p/4- p/4

-0. 01

-0. 02

-0. 03

0.00

0.10

0. 02

0. 03

EE-

F

1 0f

( )d( )b

2

1 1

ground statenon-thermalthermalizedDBGR+

Hartree

Denis Golež Manipulation of excitonic insulator

Conclusions

Semimetal limit and gap closureSemiconductor limit and gap manipulation

I Gap closure for semimetal: DG et.al., Phys. Rev. B 94,035121 (2016)

I Selene Mor et.al., Band-gap enhancement in semiconductorlimit: arXiv:1608.05586

Denis Golež Manipulation of excitonic insulator