Spin-orbit coupling and electron-phonon scattering - Fachbereich ...

2.3 Electron transport in one-dimensional systems with Rashba effect 39
PSfrag replacements
k SO ,κ,E 0
k SO ′ ,κ′ ,E 0
′
x = a
x
I
II
Figure 2.9: Stepwise constant external fields which change at a single interface.
We mention that neither the eigenenergy nor the wavenumber depend on the
sign of the magnetic field. Solely the representation of the spinor in the basis of σ z
changes. For a sign change of the magnetic field (κ → −κ), from (2.41) follows
ξ k,+ (−κ) = −ξ k,− (κ) = ξ ∗ k,− (κ), (2.44)
ξ k,− (−κ) = −ξ k,+ (κ) = ξ ∗ k,+ (κ). (2.45)
Transport in the presence of a magnetic modulation
We now address the question how the transport properties of the 1D-QWR is affected
by a modulation of the external parameters (B, α, E 0 ). Experimentally
this could be done by e.g. magnetic superlattices [91,92] which modulate periodically
the strength of the magnetic field. We will concentrate on system parameters
corresponding to such an experimental situation with weak magnetic modulation
and SO coupling compared to Fermi energy. Generalisation to other parameter
regimes is straightforward. Although results will be presented only for magnetic
modulation, the formulation of the transmission problem will be outlined for arbitrary
changes of external parameters. In a ballistic 1D system which is connected
to leads the conductance is related to the transmission properties of the system via
the Landauer formular [93, 94].
∑
∣ ∣
G = G 0
t nσ→n ′ σ 2 ′ ,
nn ′ ,σσ ′
G0 = e2
h , (2.46)
where t nσ→n ′ σ ′ is the probability amplitude for transmission from state (nσ) in
the source lead to state (n ′ σ ′ ) in the drain lead. In the following, we will restrict
ourselves to calculating these transmission amplitudes.
We start with considering the transport through a single interface (located at
x = a) between regions with different parameters k SO , κ, E 0 , see Fig. 2.9. The
transmission properties of the interface can be calculated analogously to textbook