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Separation of neutral and charge modes in one dimensional chiral edge channels

Separation of neutral and charge modes in one dimensional chiral edge channels. vincent.freulon@ens.fr. 1. 2. 3. 4. 3. 2. 4. 1. 2. 1. 4. 3. Electronic Hong-Ou-Mandel dip. fermions. bosons. f =2.1 GHz. Single electron emitter. Dip not going to zero .

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Separation of neutral and charge modes in one dimensional chiral edge channels

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  1. Separation of neutral and charge modes in one dimensional chiral edge channels vincent.freulon@ens.fr

  2. 1 2 3 4 3 2 4 1 2 1 4 3 Electronic Hong-Ou-Mandel dip fermions bosons f=2.1 GHz Single electron emitter Dip not going to zero. Decoherenceeffect ! E. Bocquillon et al., Science 339no. 6123 pp. 1054-1057 GDR méso Aussois 2013 – vincent.freulon@ens.fr

  3. An electronic Mach-Zehnderinterferometer Gaz 2D • Noisy inner • edgechannel • reduction of V visibility : 62% VG Y. Ji et al., Nature 422, 415 (2003) P. Roulleau et al., Phys. Rev. Lett.100, 126802 (2008) P. Roulleau et al., Phys. Rev. Lett.101, 186803 (2008) P.-A. Huynh et al., Phys. Rev. Lett. 108, 256802 (2012) VG(mV) GDR méso Aussois 2013 – vincent.freulon@ens.fr

  4. Energy relaxation betweenchannelsatυ=2 H. Le Sueur et al., PRL 105, 056803 (2010). • Outeredgechanneldriven • out of equilibrium. • non-equilibrium double dip • relaxes over ~3µm. • broaderdipthanequilibrium. • Inneredgechanneldriven • out of equilibrium. • dipbroadens as L isincreased. • outeredgechannelheats up. Energy exchanges betweencopropagatingchannels. GDR méso Aussois 2013 – vincent.freulon@ens.fr

  5. Separation in charge and neutral modes Capacitive couplingbetweenchannels decoupled propagation in ch. 1 & 2 2 new eigenmodes : - slow neutralmode - fastcharge mode m/s I.P. Levkivskyi et al., PRB 78, 045322 (2008) P. Degiovanni et al., PRB 80, 241307(R) (2009) D.L. Kovrizhin et al., PRB 81, 155318 (2010) Neder et al., PRL 96 016804 (2006) In nanowires: O.M. Auslaender et al., Science 308 5718 (2005) H. Steinberg et al., Nat. Phys. 4 3 (2007) GDR méso Aussois 2013 – vincent.freulon@ens.fr

  6. Edge magneto-plasmons In frequencydomain: edgemagneto-plasmons(EMP) • In the "frequency domain": charge oscillations • Sine wave induced in outer edge channel GDR méso Aussois 2013 – vincent.freulon@ens.fr

  7. Edge magneto-plasmons In frequencydomain: edgemagneto-plasmons(EMP) • In the "frequency domain": charge oscillations • Sine wave induced in outer edge channel • Phase shift between both modes: GDR méso Aussois 2013 – vincent.freulon@ens.fr

  8. Edge magneto-plasmons In frequencydomain: edgemagneto-plasmons(EMP) • In the "frequency domain": charge oscillations • Sine wave induced in outer edge channel • Phase shift between both modes: • GHz m/s GDR méso Aussois 2013 – vincent.freulon@ens.fr

  9. Experimentalrealisation Scattering of EMP over propagation lengthbetween source and QPC Sine excitation. No tunneling (capacitive coupling). 1 2 GDR méso Aussois 2013 – vincent.freulon@ens.fr

  10. Experimentalrealisation ) QPC partially open QPC completelyclosed GDR méso Aussois 2013 – vincent.freulon@ens.fr

  11. Experimentalresults • Points spiraling in the complex plane (damping). • Charge oscillations. E. Bocquillonet al., Nature Comm. 4, 1839 (2013). GDR méso Aussois 2013 – vincent.freulon@ens.fr

  12. Dispersion relation of the neutral mode E. Bocquillonet al., Nature Comm. 4, 1839 (2013). Dispersion relation • 2 non-dispersive regimes. • non-zero imaginary part • reveals damping. Long range Short range GDR méso Aussois 2013 – vincent.freulon@ens.fr

  13. Short-range model Local (zero-range) density-density interactions ⇔ distributed capacitance between channels • No characteristic length • ⇔ 1 timescale • ⇔ constant velocity Short-range model Low-frequencyregime: wellreproduced Oscillations: 1 timescale ⇒ not enough I.P. Levkivskyi et al., PRB 78, 045322 (2008) P. Degiovanniet al., PRB 80, 241307(R) (2009) D.L. Kovrizhin et al., PRB 81, 155318 (2010) Also in non-chiral Lüttinger liquids:I. Safi et al., PRB 52, R17040 (1995) GDR méso Aussois 2013 – vincent.freulon@ens.fr

  14. Long-range model Long-range charge-charge interactions ⇔ capacitance between channels • Range ≃ propagation length • ⇔ 2 time-scales • ⇔ 2 different velocities Long-range model Low-frequencyregime: wellreproduced Oscillations: 2 timescales ⇒ sufficient Dissipation: well reproduced, origin unknown ? • Dissipation: • compatible with RC circuit description GDR méso Aussois 2013 – vincent.freulon@ens.fr

  15. Conclusion • In IQHR: • Capacitive couplingbetweenchannels (Coulomb interactions), • Range of the coupling: propagation length, • Two propagation regimes: • then m/s • then m/s • Both non dispersive. • Perspectives: • Understand the effect of couplingprobedusing EMP (collective modes) in term of twoparticleinterferences (HOM). GDR méso Aussois 2013 – vincent.freulon@ens.fr

  16. B. Plaçais J.-M. Berroir G. Fève A. Marguerite V. Freulon People involved Mesoscopic Physics group, LPA ENS, pièce L175 former members : E. Bocquillon, J. Gabelli, A. Mahé, F. D. Parmentier, Theory, ENS Lyon P. Degiovanni C. Grenier D. Ferraro E. Thibierge Samples Fab, LPN Marcoussis A. Cavanna Y. Jin GDR méso Aussois 2013 – vincent.freulon@ens.fr

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