Interaction effects in a transport through a point contact

1
Interaction effects in a transport through a
point contact
Yasuhiro Tokura (NTT Basic Research Labs.)

• 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

2
Two terminal conductance of quasi-1D system
Landauers 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)
3
Field, Temperature, and Bias dependence
In-plane field B// dependence
Finite temperature
gmBB//
Bias dependence We restrict only to linear
transport
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

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.
6
Spontaneous spin polarization?

• Interaction is more important for lower density
  (rsEee/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.
7
Inhomogeneous system

• 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?

T. Rejec, et al, Phys. Rev. B 67 (03) 75311.
Y. Meir, et al, Phys. Rev. Lett. 89 (02) 196802.
O.P.Sushkov, Phys. Rev. B 67 (03) 195318.
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
[phone].
B.Spivak and F. Zhou, Phys. Rev. B61 (00) 16730.
Y. Meir, et al, Phys. Rev. Lett. 89 (02) 196802.
9
Effective Hamiltonian

• Adiabatic approximation

1Dreservoirs model
A.Shimizu and T.Miyadera,Physica B249-251 (98)
518. A.Kawabata, J. Phys.Soc.Jpn. 67 (98) 2430.
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Interaction
x
V1D(x,x)
L/2
L/2
-L/2
x
-L/2

• l thickness of 2DEG
• Effective 1D model
• Hartree-Fock approximation

11
Scattering with Friedel oscillations
K.A.Matveev,D.Yue,and L.I.Glazman, Phys. Rev.
Lett. 71 (93) 3351.
Friedel oscillation at absolute zero

• Correction to transmission amplitude

The HF contribution in the reservoirs
For sufficiently short-range potential, there is
region of dG(T)/dTlt0, but
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 correctionin 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.
13
Collective mode - paramagnon

• Homogeneous system with short range interaction,
  I

RPArandom phase approximation

• Stoner mean-field condition is determined at q,w0

• Paramagnon excitation for I0lt1, q,w0

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

16
Lowest RPA correction

• dTa vanishes at absolute zero.
• Both corrections vanishes when t20 or 1.

Y.Tokura, Proc. ICPS-26 (03) Ed. A. R. Long and
J. H.Davis.
17
Numerical results

• Model static potential U1(x)U0cosh-2(2x/L)
• Using susceptibility function near t21

Energy and length in unit of U0 and kv(2mU0)1/2/h
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
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).
20
Why 0.7 ?

• Free conductance
• Correction increase with temperature classical
  correction
• Zero-temperature mass correction
• G enhancement

Total
21
Outlook

• Bias dependence relevance to Kondo-like
  behavior ?
• Magnetic field dependence suppress spin
  fluctuations
• Shot noise characteristics suppression near 0.7
  structure ?

Localized ½ spin is essential ?
R. C. Liu, et al., Nature 391 (98) 263.
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.