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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)