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
