Harshani Wijewardane

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Time-dependent Kohn-Sham theory with memory

• Harshani Wijewardane
• Carsten Ullrich
• University of Missouri-Columbia

Work supported by Research Corporation and
Petroleum Research Fund
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Time-dependent density-functional theory (TDDFT)

• variety of applications using ALDA
• - excitation energies (linear response)
• - strongly driven systems (TDKS)
• challenges/open issues
• - more complex excitations (multiple,
  charge-transfer)
• - single-molecule transport
• - optical response/excitons in insulators

• ideal testing ground for TDDFT and TD-CDFT
• intersubband dynamics in quantum wells

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Single particle states
Collective excitation Intersubband plasmon
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Nonlinear intersubband dynamics

• Generation of higher harmonics
• J.N.Heyman et al., PRL 72, 2183 (1994)
• Coherent control over photocurrents
• E.Dupont et al., PRL 74, 3596 (1995)
• Intensity-dependent absorption
• K.Craig et al., PRL 76, 2382 (1996)
• Coherent control of optical bistability
• H.O.Wijewardane and C.A.Ullrich, APL 84, 3984
  (2004)

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Time dependent Kohn-Sham (TDKS) equation
TDDFT needs approximation for XC
Adiabatic Local Density Approximation (ALDA)
Can we find Vxc(r,t ) as a functional of n(r,t
), where tltt ? (has memory, yet local)
Violates Harmonic potential theorem !
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Application of TD-CDFT in linear regime/frequency
domain

• polarizabilities of molecular chains van
  Faassen et al., PRL 88, 186401(2002)
• optical response of bulk insulators de Boeij et
  al., J. Chem. Phys. 115, 1995 (2001)
• linewidths of ISB plasmons C. A. Ullrich and
  G. Vignale, PRL 87, 037402 (2001)
• molecular transport Na Sai et al.,
  cond-mat/0411098

Now TD-CDFT in nonlinear regime/time domain
H. O. Wijewardane and C. A. Ullrich,
cond-mat/0411157
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In the presence of external scalar and vector
potential, the TDKS equation is
xc vector potential
xc viscoelastic stress in the electron liquid
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For a quantum well, xc vector potential can be
transformed into scalar potential
and
Qian-Vignale (QV) (2002)
Memory kernel
Gross-Kohn (GK) (1985)
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Analytical model density
(2)
(1)
(3)
(4)
Animation http//www.missouri.edu/ullrichc/resea
rch.html
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(No Transcript)
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GaAs/AlGaAs 40nm quantum well
sudden switching
e
e 0
initially
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Dissipation of excitation energy
Power spectrum
?13 - 2?12

?12
?13 2?12
Ts lowest ISB relaxation time Tf fast decay
of hot electrons
weak excitation
strong excitation
sideband modulation ( ?13 - 2?12 )
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• TDDFT memory enters through viscosity of
  electron liquid
• Retardation causes decoherence and energy
  relaxation
• Relaxation dynamics changes with stronger
  excitation
• Powerful tool to describe nonlinear electron
  dynamics in the presence
• of dissipation

H. O. Wijewardane and C. A. Ullrich,
cond-mat/0411157
http//www.missouri.edu/ullrichc/res
earch.html