In Leipzig, I am primarily working on topological superconductivity. In particular I have worked on semiconductor nanowires with strong spin-orbit coupling in proximity to an s-wave superconductor. In a strong magnetic field these systems are thought to host the so-called Majorana fermions. We studied the case where the proximitised wire forms a quantum dot in the Coulomb blockade regime and calculated the transmission of electrons through such a setup, in both the trivial and topological regimes. We found that these can be distinguished by the presence or absence of so-called phase lapses, where the transmission phase abruptly changes by pi.
In Frankfurt I was mainly working on the functional renormalization group and its application
to strongly correlated systems. Within this context I have recently worked on a model for
the Ising-nematic quantum critical point in two-dimensional metals. At such a critical point
the fluctuations decohere the Landau quasiparticles and break the Fermi liquid behaviour.
Moreover, the existence of gapless excitations means that the standard Hertz-Millis approach
fails and finite anomalous dimensions occur beyond RPA. The functional renormalization
group provides a non-perturbative way of calculating these. Apart from this I have also worked on
spin-orbit coupled bosons where we showed that such systems can exhibit spontaneous ferromagnetism
for attractive interactions. More recently I have worked on non-analyticities in 2D Fermi liquids. Here we showed
that various quasi-particle properties become non-analytic in a weak
external magnetic field. Most recently we have re-examined the X-ray
problem and shown how to recover the leading order parquet results within
a simple truncation of the functional renormalization group flow equations.
During my undergraduate studies I worked, under the supervision of Professor David
Khmelnitskii, on disorder physics. Specifically, in my final year research project, I considered
the band tail problem in four and five dimensions. The band tail, which originated from
studies of highly doped semiconductors, is an exponential tail in the density of states at very
low energies. In less than four dimensions it is readily accessible using replica methods but
in higher dimensions this becomes more dificult. As an alternative method of regularization
I instead used Efetov's supersymmetry and was able to calculate the tail.
Summary of research topics
Application of the functional renormalization group to strongly correlated systems
Non-Fermi liquid metals
Corrections within Fermi liquid theory
Multi-channel bosonisation within the functional renormalization group
Spin-orbit coupled bosons
Casper Drukier, Heinrich-Gregor Zirnstein, Bernd Rosenow, Ady Stern, and Yuval Oreg ArXiv:1806.01399
Evolution of the transmission phase through a Coulomb-blockaded Majorana wire