![Page 1: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/1.jpg)
QuasiparticlesQuasiparticles, dynamics,, dynamics, andand coupled coupled nanowiresnanowires
Theory division and Center for Integrated Nanotechnologies,Los Alamos National Laboratory
[email protected] Trugman
![Page 2: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/2.jpg)
electron-phonon interaction
![Page 3: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/3.jpg)
electron-phonon interaction
![Page 4: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/4.jpg)
electron-phonon interaction
![Page 5: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/5.jpg)
Lev Landau
L. D. Landau, Phys. Z. Sowjetunion 3, 644 (1933)
![Page 6: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/6.jpg)
Lev Landau
L. D. Landau, Phys. Z. Sowjetunion 3, 644 (1933)
![Page 7: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/7.jpg)
Holstein Hamiltonian
† † † †
0
,
( . .) ( )
el ph el ph
i j i i i i i i
i j i i
H H H H
t c c h c a a c c a a! "
#
< >
= + +
= # + + # +$ $ $xi
![Page 8: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/8.jpg)
The two-site version of this problem maps exactly onto a spin-1/2 particle coupled tobosons.
![Page 9: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/9.jpg)
The two-site version of this problem maps exactly onto a spin-1/2 particle coupled tobosons.
(but we will consider mainly the infinitelattice version in this talk)
![Page 10: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/10.jpg)
It is common to make an approximation at thisstage, such as the semiclassical approximation(classical phonons, quantum electrons), or Born-Oppenheimer, surface hopping, ….Problematic.
![Page 11: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/11.jpg)
It is common to make an approximation at thisstage, such as the semiclassical approximation(classical phonons, quantum electrons), or Born-Oppenheimer, surface hopping, ….Problematic.
Numerically calculate quantum statics and dynamics in large variational many-body Hilbert space, including fully quantum phonons. Numerically exact.
![Page 12: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/12.jpg)
state space
0
![Page 13: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/13.jpg)
state space
0
-λ
-t -t
![Page 14: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/14.jpg)
state space
0
-λ√2
-λ-t
![Page 15: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/15.jpg)
state space(infinite lattice)
0
![Page 16: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/16.jpg)
ground state energy
-2.46968472393287071561
S. Cuichi et.al. Phys. Rev. B56, 4494 (1997)
-2.4DMFT (dynamical mean-field)
Li-Chung Ku et al., Phys. Rev.B. 65, 174306 (2002), …
VED
W. Wellein et al., Phys. Rev.B 56, 4513 (1997)
-2.4696847Finite-Cluster ED
E. Jeckelman et al., Phys. Rev.B 57, 6376 (1998)
-2.46968DMRG
A. H. Romero et al., J Chem.Phys. 109, 6540 (1998)
-2.4693GL variational method
V. Cataudella et al., Phys.Rev. B 62, 1496 (2000)
-2.467Cataudella et al.
P. E. Kornilovitch, Phys. Rev.Lett. 81, 5382 (1998)
-2.47QMC (Monte-Carlo)
H. B. Shore et al, Phys. Rev. B7, 4537 (1973)
-2.464Shore et al.
Y. Toyozawa, Prog. Theor.Phys. 26, 29 (1961)
-2.456Toyozawa
01t! "= = =
![Page 17: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/17.jpg)
Dynamics of quasiparticle formation in electron-phonon coupled systems.
• How are phonons excited and how do they evolve intothe correlated phonon cloud of the polaronquasiparticle?
• How much time does it take to form a polaron from abare (delocalized) electron?
• What is the effect of dimension on the dynamics ofpolaron formation?
di Hdt
!!=
![Page 18: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/18.jpg)
Quantum Dynamics
• Movie I (lambda=0.4)
• Movie II (lambda=0.8)
Polaron EnergyDispersion
![Page 19: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/19.jpg)
state space(infinite lattice)
0
![Page 20: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/20.jpg)
![Page 21: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/21.jpg)
LCMO: Comparison of all-optical (LCMO: Comparison of all-optical (ΔA / A) and THz (and THz (Δσ) data datareveals dynamic spectral weight transfer: below reveals dynamic spectral weight transfer: below TTcc
Δσ , ΔA
/ A
•All optical and THz data reveal identicaldynamics (dynamic spectral weight transfer).
Induced Far-IR conductivity decrease.
Increased absorption at 1.5 eV.
A. J. Taylor et al.
![Page 22: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/22.jpg)
A. Sugita et al., PRL 86, 2185 (2001)
Optical pump-probe on MX chain,PtI, quasi-1D, excitons
This work
![Page 23: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/23.jpg)
N.-H Ge et al, Science 279, 202 (1998) A.D. Miller et al, Science 297, 1163 (2002)
Two-photon photoemission,alkanes on Ag, Harris et al.
![Page 24: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/24.jpg)
2†( , ) 0 ( )
n k n
n
A k c E! " != # $%
Spectral Function
![Page 25: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/25.jpg)
Quasiparticle excited states(strong coupling)
Spectral function
Quantum beat
( )† †
0 0 0 0c c a a! = +
On-site lattice distortion
![Page 26: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/26.jpg)
Coupled quantum wires From 1d to 3d
![Page 27: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/27.jpg)
Previous work, classical approximation, infinite mass phonons, 1d qualitatively different than 3d (Emin).
![Page 28: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/28.jpg)
Previous work, classical approximation, infinite mass phonons, 1d qualitatively different than 3d (Emin).
What happens when you continuously connecttwo limits that cannot be connected?
![Page 29: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/29.jpg)
Quasiparticleeffective mass as afunction of el-phcoupling (fullyquantum)
![Page 30: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/30.jpg)
Polaron radius as a function of el-ph coupling.
![Page 31: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/31.jpg)
Increasing the el-ph coupling causes the mass toincrease in both the parallel and perpendiculardirections.
By the same amount?
![Page 32: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/32.jpg)
Additional mass enhancement in theperpendicular direction compared to the paralleldirection.
![Page 33: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/33.jpg)
![Page 34: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/34.jpg)
![Page 35: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/35.jpg)
collaborators
Li-Chung KuJanez BoncaHolger FehskeAndreas Alvermann
Richard AverittRohit PrasankumarAntoinette TaylorSue Dexheimer
![Page 36: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/36.jpg)
SummarySummary
1. The properties of quasiparticles are of general interest(condensed matter, high energy). This approach isapplicable to other kinds of quasiparticles, such as thespin polaron (htc) and the exciton dressed by phonons.
2. Calculated the fully quantum ground state, excited states,and dynamics far from equilibrium of quasiparticleformation in real time and real space in a large many-body Hilbert space.
3. Calculated the properties of coupled quantum wires, 1dto 3d crossover.
![Page 37: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/37.jpg)
References:References:
unpublished; and
Alvermann, Fehske, ST, PRB 78, 165106 (2008).
Ku, ST, PRB 75, 014307 (2007).
Demsar, Averitt, Ahn, Graf, ST, Kabanov, Sarrao, Taylor, PRL 91, 027401 (2003).
Ku, ST, Bonca, PRB 65, 174306 (2002).
![Page 38: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/38.jpg)
![Page 39: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/39.jpg)
![Page 40: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/40.jpg)
state spaceelectron and phonons in electric field
![Page 41: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/41.jpg)
hole in an antiferromagnet (htc)
![Page 42: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/42.jpg)
![Page 43: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/43.jpg)
![Page 44: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/44.jpg)
BO / classical phonons
electron wavepacketR
![Page 45: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/45.jpg)
quantum phonons, exact
electron wavepacketR
![Page 46: Quasiparticles, dynamics, and coupled nanowires](https://reader031.vdocuments.mx/reader031/viewer/2022012505/6180b1847861063459252332/html5/thumbnails/46.jpg)
Semiclassical gives wrong answer: says electron nevertraps to form a polaron if initial wavepacket is wide.
Why?
semiclassical: 1/N of an electron on each site.quantum mechanics: full electron on one of the N sites.
BO / semiclassical:what are the phonons doing?exact QM: what are the phonons doing if the electron is on site 1?what are the phonons doing if the electron is on site 2?…