manipulation of band gap upon photoexcitation of an excitonic …€¦ · manipulation of band gap...

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