The 0.7 anomaly in quantum point contacts

This thesis aims at shedding light on the microscopic origin of a
phenomenon in the field of semiconductor nanostructures, which
occurs in transport through a short and narrow quasi
one-dimensional constriction, the quantum point contact (QPC).
Unlike the stepwise increase of linear conductance of a QPC as
function of its width in units of the quantum GQ, which is well
understood and was predicted already in the 1950s, an additional
shoulder-like step at 0.7xG_Q raises questions since its discovery
in 1996 : the 0.7 anomaly. Subsequent experimental investigations
revealed a plethora of accompanying features of this fascinating
structure. Most famously these include a strong reduction of
conductance in the sub-open regime of a QPC as function of external
parameters such as magnetic field, temperature or bias voltage.
While it is agreed upon that the 0,7 anomaly arises from
electron-electron interactions, the high number of theoretical
attempts at an explanation indicates that the detailed microscopic
origin of the peculiar shoulder is still subject to controversal
discussions. In particular no theory seems to describe the whole
variety of signatures of the 0.7 anomaly sufficiently. Here, we
present a microscopic model that qualifies to meet this
requirement. We model the effective barrier of the lowest transport
mode of a QPC by a one-dimensional parabolic potential with
short-ranged Coulomb interactions. By systematic analysis of
experimental data we show that a parabolic barrier approximates the
actual barrier shape of the QPC adequately well. In order to
understand the physics of a QPC in detail, we put emphasis on the
noninteracting properties of our model; we find a pronounced
maximum in the local density of states in the vicinity of the
barrier center at energies just above the potential. Importantly,
this "van Hove ridge", which can be associated with slow electrons
above the barrier coincides with the chemical potential if the QPC
is tuned to be sub-open. Here, it causes an enhancement of
backscattering at finite interactions and a subsequent anomalous
reduction of conductance. In case of a magnetic field the
underlying mechanism for this reduction is an interaction-enhanced
local depopulation of the disfavoured spin species' subband; at
finite excitation energies the reduction is a consequence of an
interaction-enhanced inelastic backstattering probability. Hence,
the interplay of van Hove ridge and electron-electron interactions
provides a natural explanation for the appearance of the 0.7
anomaly and its various features. We calculate properties of our
interacting one-dimensional QPC model using two methods: A
specially developed approximation scheme within the functional
renormalization group (fRG) provides reliable results for the
magnetic field dependence of the 0.7 anomaly at zero temperature.
At finite temperature and finite bias voltage we rely on second
order perturbation theory in the interaction (SOPT). Since SOPT's
validity is restricted to weaker interaction strength, where
calculations clearly show the right trend but not yet the full
manifestation of the 0.7 anomaly, we are currently setting up an
extension of our fRG approach within the Keldysh formalism, which
will allow us to also explore finite excitation energies.