Introduction Model and Motivation Results Conclusions Umklapp Scattering In Doped Two-Leg Ladders Neil Robinson Rudolf Peierls Centre for Theoretical Physics, University of Oxford Quantum Correlations Students Workshop, 2nd July 2012 N. Robinson University of Oxford Umklapp Scattering In Doped Two-Leg Ladders
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Umklapp Scattering In Doped Two-Leg Ladders · 2012. 7. 4. · Umklapp Scattering 1D Hubbard model at half- lling Model and Motivation Extended-Hubbard model on the two-leg ladder
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Introduction Model and Motivation Results Conclusions
Umklapp Scattering In Doped Two-Leg Ladders
Neil Robinson
Rudolf Peierls Centre for Theoretical Physics, University of Oxford
Quantum Correlations Students Workshop, 2nd July 2012
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
Collaborators
Fabian Essler Eric Jeckelmann Alexei Tsvelik
University of Oxford ITP Hannover Brookhaven National Laboratory
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
Outline
IntroductionUmklapp Scattering1D Hubbard model at half-filling
Model and MotivationExtended-Hubbard model on the two-leg ladderExperimental motivations
ResultsTheoretical approachPhysical pictureEffective low-energy theory
ConclusionsConclusion
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
Umklapp Scattering: A Brief Refresher
DefinitionElectron-electron scattering with total initial and final momentumdiffering by a reciprocal lattice vector G
K1 + K2 = K3 + K4 + G
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
Umklapp Processes in 1D SystemsI Two electrons close to Fermi point scatter
K1 + K2 = K3 + K4 + G ↔ 4kF = G = 2π→ only at half-filling can transfer momentum to lattice
EF-kF kF
Dp = 4 kF
-Π 0 Π
0
k
EHkL
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
1D Hubbard Model at Half-FillingSimplest model of interacting fermions
One electron per site = half-filling = Umklapp activation
Energy gap for single-particle excitations. Low-energy: spin chain
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
Theoretical Model: Extended-Hubbard Model
H = −t∑`,σ
2∑j=1
a†j ,`+1,σaj ,`,σ + a†j ,`,σaj ,`+1,σ
− t⊥∑`,σ
a†1,`,σa2,`,σ + a†2,`,σa1,`,σ + U∑j ,`
nj ,`,↑nj ,`,↓
+ V⊥∑`
n1,`n2,` + V‖∑j ,`
nj ,`nj ,`+1 +∑j ,`
Wj cos(K`)nj ,`,
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions
Motivation
I X-ray scattering on “telephone number” compoundsSr14−xCaxCu24O41
I CDW order observed without lattice distortionI Origin: interladder long-range Coulomb interaction?I Treat in mean field → periodic electrostatic potential
I Stripe ordering in x = 1/8 doped La2−xSrxCuO4
I Carbon nanotubes with surface adsorbed noble gasesI Periodic structure on nanotube surfaceI External periodic electrostatic potential
N. Robinson University of Oxford
Umklapp Scattering In Doped Two-Leg Ladders
Introduction Model and Motivation Results Conclusions