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Interaction effects in a transport through a point contact

Interaction effects in a transport through a point contact. Collaborators A. Khaetskii (Univ. Basel) Y. Hirayama (NTT) Contents Quantum Point Contact (QPC) Conductance Anomaly Brief review of proposed Theories Scattering by spin fluctuation Open questions and Outlook.

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Interaction effects in a transport through a point contact

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  1. Interaction effects in a transport through a point contact • Collaborators • A. Khaetskii (Univ. Basel) • Y. Hirayama (NTT) • Contents • Quantum Point Contact(QPC) • Conductance Anomaly • Brief review of proposed Theories • Scattering by spin fluctuation • Open questions and Outlook Yasuhiro Tokura (NTT Basic Research Labs.) ISSP Int. Summer School

  2. Two terminal conductance of quasi-1D system Landauer’s formula Non-interacting, zero temperature Quantum Point Contact (QPC) Ballistic and adiabatic limit B.J.van Wees, et al, Phys. Rev. B 43 (’91) 12431. Conductance quantization (Zero field) ISSP Int. Summer School

  3. Field, Temperature, and Bias dependence In-plane field B// dependence: Finite temperature: gmBB// Bias dependence: We restrict only to linear transport ISSP Int. Summer School

  4. Conductance anomaly • Mesoscopic mystery: Anomalous conductance plateau near 0.7 X 2e2/h • In-plane field drives the anomaly smoothly to 0.5 Spin related phenomena ? • The structure is enhanced with temperatures • Not a simple quantum interference effect • Ground state property seems not responsible ISSP Int. Summer School K.J.Thomas, et al, Phys. Rev. Lett. 77 (’96) 135.

  5. Temperature dependence • Quantum interference simply disappears for higher temperature The structure persists after raster scan – imperfection is negligible • Activation behavior Collective excitation on the contact? A. Kristensen, et al, Physica B 249-251 (’98) 180. ISSP Int. Summer School

  6. Spontaneous spin polarization? • Interaction is more important for lower density (rs=Eee/EF ~1/nl) • Absence of polarized ground state in 1D • Lieb-Mattice theory • Conduction band pinning Explains experiments amazingly well Homogeneous 1D model is not relevant! C.-K. Wang and K.-F. Berggren, Phys. Rev. B54 (’96) 14257. E.Lieb and D. Mattis, Phys. Rev. 125 (’62) 163. H. Bruus, et al, Physica E 10 (’01) 97. ISSP Int. Summer School

  7. Inhomogeneous system T. Rejec, et al, Phys. Rev. B 67 (’03) 75311. • Singlet-triplet origin • Naturally formed bulge • Effective attractive potential • Ground state calculation by mean field theory • Hartree-Fock (HF) • Local spin density functional theory(LSDF) Spontaneous local charge/spin formation? Y. Meir, et al, Phys. Rev. Lett. 89 (’02) 196802. O.P.Sushkov, Phys. Rev. B 67 (’03) 195318. ISSP Int. Summer School

  8. Kondo effect ? • Kondo-like characteristics in dI/dV • Effective Anderson model How robust is spin ½ state? • Other models • Phonon scattering • Wigner crystal S.M.Cronenwet, et al, Phys. Rev. Lett. 88 (’02) 226805. G.Seeling and K. A. Matveev, Phys. Rev. Lett. 90 (’03) 176804. B.Spivak and F. Zhou, Phys. Rev. B61 (’00) 16730. Y. Meir, et al, Phys. Rev. Lett. 89 (’02) 196802. ISSP Int. Summer School

  9. Effective Hamiltonian Adiabatic approximation 1D+reservoirs model A.Shimizu and T.Miyadera,Physica B249-251 (’98) 518. A.Kawabata, J. Phys.Soc.Jpn. 67 (’98) 2430. ISSP Int. Summer School

  10. x’ V1D(x,x’) L/2 Interaction -L/2 L/2 x l: thickness of 2DEG • Effective 1D model • Hartree-Fock approximation -L/2 ISSP Int. Summer School

  11. Scattering with Friedel oscillations Correction to transmission amplitude K.A.Matveev,D.Yue,and L.I.Glazman, Phys. Rev. Lett. 71 (’93) 3351. Friedel oscillation at absolute zero The HF contribution in the reservoirs: For sufficiently short-range potential, there is region of dG(T)/dT<0, but… ISSP Int. Summer School

  12. Beyond Hartree-Fock approximation In real 2D system, G. Zala, et al., Phys. Rev. B64 (’01) 214204. The HF contribution on the contact: Only linear correction:in the context of “metal-insulator transition” in 2D may show resonance at zero T. Assuming featureless HF potential, we search for collective mode effective for electron scattering. ISSP Int. Summer School

  13. Collective mode - paramagnon • Homogeneous system with short range interaction, I: RPA:random phase approximation Stoner mean-field condition is determined at q,w~0 Paramagnon excitation for I0<1, q,w~0 ISSP Int. Summer School

  14. Localized paramagnon Characteristic frequency: To couple spin and charge, we need finite scattering: Y.Tokura and A. Khaetskii, Physica E12 (’02) 711. ISSP Int. Summer School

  15. Conductance by Kubo formula • Neglect interaction in reservoirs • (large density, 2D) • -Kubo formula is safely used. D.L.Maslov and M. Stone, Phys. Rev. B52 (’95) R5539. A.Kawabata, J.Phys. Soc.Jpn. 65 (’96) 30. A. Shimizu, ibid, 65 (’96) 1162. ISSP Int. Summer School

  16. Lowest RPA correction dTa vanishes at absolute zero. Both corrections vanishes when |t|2=0 or 1. Y.Tokura, Proc. ICPS-26 (’03) Ed. A. R. Long and J. H.Davis. ISSP Int. Summer School

  17. Numerical results • Model static potential U1(x)=U0cosh-2(2x/L) • Using susceptibility function near |t|2=1 Energy and length in unit of U0 and kv=(2mU0)1/2/h ISSP Int. Summer School

  18. Equivalent semiclassical model Y. Levinson and P. Wolfle, Phys. Rev. Lett. 83 (99) 1399. Time-dependent scattering theory Almost equivalent to Kubo formula result with replacement: ISSP Int. Summer School

  19. Adiabatic limit If low frequency fluctuation is dominant, O. Entin-Wohlman, et al., Phys. Rev. B65 (’02) 195411. Therefore, temperature-dependent (classical) correction is proportional to the second derivative of T(m). ISSP Int. Summer School

  20. Why 0.7 ? • “Free” conductance • Correction increase with temperature –classical correction • Zero-temperature mass correction G enhancement Total: ISSP Int. Summer School

  21. Outlook Localized ½ spin is essential ? • Bias dependence – relevance to Kondo-like behavior ? • Magnetic field dependence –suppress spin fluctuations • Shot noise characteristics – suppression near 0.7 structure ? R. C. Liu, et al., Nature 391 (’98) 263. ISSP Int. Summer School

  22. Summary • The conductance anomaly found in a quantum point contact is critically reviewed. • Electron interaction and spin effect are essential to understand the phenomena. • Using an effective inhomogeneous one-dimensional model, conductance is derived in Kubo formula within random phase approximation. • Scattering by paramagnon fluctuation can explain the anomaly and its temperature dependence. ISSP Int. Summer School

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