Post on 13-Apr-2018
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Crystallization of fractional
quasiparticles in a quasi-helical dot
Fabio Cavaliere
(Dipartimento di Fisica - Università di Genova)
Filippo Maria Gambetta (DIFI - Genova)
Simone Barbarino (SNS - Pisa)Maura Sassetti (DIFI - Genova)
Università di Genova Dipartimento di Fisica CNR-SPIN
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Standard quantum wire
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Standard quantum wire
Right-moversLeft-movers
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Spin-orbit quantum wire
[e.g. InAs, Y. Sidor et al
., Phys. Rev. B 75
, 125120 (2007); S. Csonka et al
., Nano Lett
. 8
, 3932 (2008)]
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Spin-orbit quantum wire
[e.g. InAs, Y. Sidor et al
., Phys. Rev. B 75
, 125120 (2007); S. Csonka et al
., Nano Lett
. 8
, 3932 (2008)]
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Quasi-helical quantum wire
Right-moversLeft-movers
P. Streda et al
., Phys. Rev. Lett. 90
, 256601 (2003);
T. Meng et al
., PRB 88
, 035437 (2013);F.M.Gambetta et al
., PRB 91, 235421 (2015)
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Electron interactions
T. Meng et al ., PRB 88, 035437 (2013)
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Electron interactions
T. Meng et al ., PRB 88, 035437 (2013)
1. The main gap is enhanced
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Electron interactions
C. L. Kane et al., PRL 88, 036401 (2002); J. C. Y. Teo et al ., PRB 89, 085101 (2014); Y. Oreg et al ., PRB 89, 115402 (2014)
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Electron interactions
A t special fillings, d r e s sed Zeeman inter actions ar e r esonant
C. L. Kane et al., PRL 88, 036401 (2002); J. C. Y. Teo et al ., PRB 89, 085101 (2014); Y. Oreg et al ., PRB 89, 115402 (2014)
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Electron interactions II
C. L. Kane et al., PRL 88, 036401 (2002); J. C. Y. Teo et al ., PRB 89, 085101 (2014); Y. Oreg et al ., PRB 89, 115402 (2014)
2. For strong enough electron interactions new gaps open,
and fractional QP excitations appear
Filling factor w.r.t
the main gap!
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Ground-state signatures?
Fractional QP excitations induce peculiar effects on
non-equilibrium properties (current, shot noise,…)
Y. Oreg et al ., PRB 89, 115402 (2014) ; T. Meng et al ., PRB 89, 045111 (2014);
D. Rainis et al., PRL 112, 196803 (2013); E. Cornfeld et al., PRB 91, 115427 (2014)
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Ground-state signatures?
Fractional QP excitations induce peculiar effects on
non-equilibrium properties (current, shot noise,…)
Y. Oreg et al ., PRB 89, 115402 (2014) ; T. Meng et al ., PRB 89, 045111 (2014);
D. Rainis et al., PRL 112, 196803 (2013); E. Cornfeld et al., PRB 91, 115427 (2014)
Can such fractional quasiparticles be detected in
equilibrium, ground-state properties?
F. Cavaliere et al ., submitted (2015)
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Ground-state signatures?
Fractional QP excitations induce peculiar effects on
non-equilibrium properties (current, shot noise,…)
Y. Oreg et al ., PRB 89, 115402 (2014) ; T. Meng et al ., PRB 89, 045111 (2014);
D. Rainis et al., PRL 112, 196803 (2013); E. Cornfeld et al., PRB 91, 115427 (2014)
Can such fractional quasiparticles be detected in
equilibrium, ground-state properties?
F. Cavaliere et al ., submitted (2015)
Study the particle density of a quasi-helical quantum dot!
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Normal 1D quantum dots
Weak interactions: Friedel oscillations
(a quick reminder!)
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Normal 1D quantum dots
Strong interactions: Wigner molecule!
(a quick reminder!)
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Quasi-helical quantum dot
open boundaries
(a Luttinger liquid model)
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Quasi-helical quantum dot
open boundaries
(a Luttinger liquid model)
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Quasi-helical quantum dot
open boundaries
(a Luttinger liquid model)
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Quasi-helical quantum dot
The fields obey the Hamiltonian
Q
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Quasi-helical quantum dot
The fields obey the Hamiltonian
Kinetic energy and forward interactions
Q i h li l d
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Quasi-helical quantum dot
The fields obey the Hamiltonian
Kinetic energy and forward interactions
Q i h li l d
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Quasi-helical quantum dot
The fields obey the Hamiltonian
Kinetic energy and forward interactions
Dressed Zeeman interaction at
Q i h li l d
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Quasi-helical quantum dot
The fields obey the Hamiltonian
Kinetic energy and forward interactions
Dressed Zeeman interaction at
Si G d d l
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Sine-Gordon model
One can decompose
Si G d d l
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Sine-Gordon model
One can decompose
Si G d d l
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Sine-Gordon model
for strong interactions
The massive field pins
El t d it
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Electron density
Ground-state ( T=0, N electrons) average (large mass!)
El t d it
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Electron density
Ground-state ( T=0, N electrons) average (large mass!)
El t d it
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Electron density
Ground-state ( T=0, N electrons) average (large mass!)
El t d it
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Electron density
Ground-state ( T=0, N electrons) average (large mass!)
Density oscillates with peaks!
F ti l i ti l
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Fractional quasiparticles
F. Cavaliere et al ., arXiv:1509.03965 (2015)
F ti l i ti l
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Fractional quasiparticles
F. Cavaliere et al ., arXiv:1509.03965 (2015)
F ti l i ti l
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Fractional quasiparticles
F. Cavaliere et al ., arXiv:1509.03965 (2015)
Fractional q asiparticles
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Fractional quasiparticles
F. Cavaliere et al ., arXiv:1509.03965 (2015)
Wigner molecule of fr actional quasipar ticles?
Conclusions
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Conclusions
A Wigner crystal of fractional quasiparticles in the GS
F. Cavaliere et al ., arXiv:1509.03965 (2015)
Conclusions
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Conclusions
A Wigner crystal of fractional quasiparticles in the GS
What is the spin pattern of such crystal?
Finite mass corrections?
F Cavaliere et al arXiv:1509 03965 (2015)