2003/8/18ISSP Int. Summer School Interaction effects in a transport through a point contact Collaborators A. Khaetskii (Univ. Basel) Y. Hirayama (NTT) Contents 1. Quantum Point Contact (QPC) 2. Conductance Anomaly 3. Brief review of proposed Theories 4. Scattering by spin fluctuation 5. Open questions and Outlook Yasuhiro Tokura (NTT Basic Research Labs.)

2003/8/18ISSP Int. Summer School 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) Conductance quantization (Zero field)

2003/8/18ISSP Int. Summer School Field, Temperature, and Bias dependence In-plane field B // dependence: Finite temperature: Bias dependence: We restrict only to linear transport g  B B //

2003/8/18ISSP Int. Summer School Conductance anomaly Mesoscopic mystery: Anomalous conductance plateau near 0.7 X 2e 2 /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 K.J.Thomas, et al, Phys. Rev. Lett. 77 (’96) 135.

2003/8/18ISSP Int. Summer School 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 (’98) 180.

2003/8/18ISSP Int. Summer School Interaction is more important for lower density (r s =E ee /E F ~1/n l ) Absence of polarized ground state in 1D Lieb-Mattice theory Conduction band pinning Explains experiments amazingly well Homogeneous 1D model is not relevant! Spontaneous spin polarization? H. Bruus, et al, Physica E 10 (’01) 97. E.Lieb and D. Mattis, Phys. Rev. 125 (’62) 163. C.-K. Wang and K.-F. Berggren, Phys. Rev. B54 (’96)

2003/8/18ISSP Int. Summer School Inhomogeneous system T. Rejec, et al, Phys. Rev. B 67 (’03) Y. Meir, et al, Phys. Rev. Lett. 89 (’02) O.P.Sushkov, Phys. Rev. B 67 (’03) 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?

2003/8/18ISSP Int. Summer School 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) Y. Meir, et al, Phys. Rev. Lett. 89 (’02) G.Seeling and K. A. Matveev, Phys. Rev. Lett. 90 (’03) B.Spivak and F. Zhou, Phys. Rev. B61 (’00)

2003/8/18ISSP Int. Summer School Effective Hamiltonian Adiabatic approximation 1D+reservoirs model A.Shimizu and T.Miyadera,Physica B (’98) 518. A.Kawabata, J. Phys.Soc.Jpn. 67 (’98) 2430.

2003/8/18ISSP Int. Summer School Interaction  : thickness of 2DEG Effective 1D model Hartree-Fock approximation x x’ L/2 -L/2 V 1D (x,x’)

2003/8/18ISSP Int. Summer School Scattering with Friedel oscillations Correction to transmission amplitude K.A.Matveev,D.Yue,and L.I.Glazman, Phys. Rev. Lett. 71 (’93) Friedel oscillation at absolute zero For sufficiently short-range potential, there is region of dG(T)/dT<0, but … The HF contribution in the reservoirs:

2003/8/18ISSP Int. Summer School Beyond Hartree-Fock approximation In real 2D system, G. Zala, et al., Phys. Rev. B64 (’01) Only linear correction:in the context of “ metal-insulator transition ” in 2D The HF contribution on the contact: may show resonance at zero T. Assuming featureless HF potential, we search for collective mode effective for electron scattering.

2003/8/18ISSP Int. Summer School Collective mode - paramagnon Homogeneous system with short range interaction, I: Stoner mean-field condition is determined at q,  ~0 Paramagnon excitation for I 0 <1, q,  ~0 RPA:random phase approximation

2003/8/18ISSP Int. Summer School Localized paramagnon Y.Tokura and A. Khaetskii, Physica E12 (’02) 711. Characteristic frequency: To couple spin and charge, we need finite scattering:

2003/8/18ISSP Int. Summer School Conductance by Kubo formula 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) Neglect interaction in reservoirs (large density, 2D) -Kubo formula is safely used.

2003/8/18ISSP Int. Summer School Lowest RPA correction  T a 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.

2003/8/18ISSP Int. Summer School Numerical results Model static potential U 1 (x)=U 0 cosh -2 (2x/L) Using susceptibility function near |t| 2 =1 Energy and length in unit of U 0 and k v =(2mU 0 ) 1/2 /h

2003/8/18ISSP Int. Summer School Equivalent semiclassical model Y. Levinson and P. Wolfle, Phys. Rev. Lett. 83 (99) Time-dependent scattering theory Almost equivalent to Kubo formula result with replacement:

2003/8/18ISSP Int. Summer School Adiabatic limit O. Entin-Wohlman, et al., Phys. Rev. B65 (’02) If low frequency fluctuation is dominant, Therefore, temperature-dependent (classical) correction is proportional to the second derivative of T(  ).

2003/8/18ISSP Int. Summer School Why 0.7 ? “ Free ” conductance Correction increase with temperature – classical correction Zero-temperature mass correction G enhancement Total:

2003/8/18ISSP Int. Summer School Outlook 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. Localized ½ spin is essential ?

2003/8/18ISSP Int. Summer School 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.