43 research outputs found
Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
We present a general methodology towards the systematic characterization of
crystalline topological insulating phases with time reversal symmetry (TRS).~In
particular, taking the two-dimensional spinful hexagonal lattice as a proof of
principle we study windings of Wilson loop spectra over cuts in the Brillouin
zone that are dictated by the underlying lattice symmetries.~Our approach finds
a prominent use in elucidating and quantifying the recently proposed
``topological quantum chemistry" (TQC) concept.~Namely, we prove that the split
of an elementary band representation (EBR) by a band gap must lead to a
topological phase.~For this we first show that in addition to the Fu-Kane-Mele
classification, there is -symmetry protected
classification of two-band subspaces that is obstructed by the
other crystalline symmetries, i.e.~forbidding the trivial phase. This accounts
for all nontrivial Wilson loop windings of split EBRs \textit{that are
independent of the parameterization of the flow of Wilson loops}.~Then, we show
that while Wilson loop winding of split EBRs can unwind when embedded in
higher-dimensional band space, two-band subspaces that remain separated by a
band gap from the other bands conserve their Wilson loop winding, hence
revealing that split EBRs are at least "stably trivial", i.e. necessarily
non-trivial in the non-stable (few-band) limit but possibly trivial in the
stable (many-band) limit.~This clarifies the nature of \textit{fragile}
topology that has appeared very recently.~We then argue that in the many-band
limit the stable Wilson loop winding is only determined by the Fu-Kane-Mele
invariant implying that further stable topological phases must
belong to the class of higher-order topological insulators.Comment: 27 pages, 13 figures, v2: minor corrections, new references included,
v3: metastable topology of split EBRs emphasized, v4: prepared for
publicatio
Influence of the domain walls on the Josephson effect in SrRuO
A detailed theoretical interpretation of the Josephson interference
experiment between SrRuO and Pb reported by Kidwingira \textit{et al}
is given. Assuming chiral p-wave pairing symmetry a Ginzburg-Landau theory is
derived in order to investigate the structure of domain walls between chiral
domains. It turns out that anisotropy effects of the Fermi surface and the
orientation of the domain walls are essential for their internal structure.
Introducing a simple model for a Josephson junction the effect of domain walls
intersecting the interface between SrRuO and Pb is discussed. It is
shown that characteristic deviations of the Fraunhofer interference pattern for
the critical Josephson current as a function of the magnetic field occurs in
qualitative agreement with the experimental finding. Moreover the model is able
also to account for peculiar hysteresis effects observed in the experiment.Comment: 16 pages, 18 figure