Alexey A. Soluyanov
Publications & Preprints
Institute for Theoretical Physics
Wolfgang-Paulistr. 27, HIT G31.4
Telephone: +41 44 6338153
Email: soluyanov -- itp.phys.ethz.ch
- Topological phases in condensed matter physics
Topological insulators and superconductors. Topological phases of interacting systems. Topological quantum computing.
- Band theory of solids
Applications of band theory, first principles calculations. Wannier functions and related techniques.
- Numerical methods for condensed matter
Development of new techniques and methods for solid state physics applications.
Smooth gauge for topological insulators
We developed a technique for constructing smooth Bloch functions
for Z2 quantum spin Hall insulators. As the
initial step the occupied subspace of the system is decomposed
into a direct sum of two topologically non-trivial
subspaces with well defined Chern numbers - Chern bands.
This decomposition is different from the ones suggested
elsewhere and remains robust independently of underlying symmetries and features of
a particular model.
Starting with thus obtained Chern bands, we construct a
non-trivial unitary transformation that rotates the
occupied subspace into a direct sum of topologically
Computing topological invariants without inversion symmetry
We considered the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal invariant insulators. In 2D we used a gauge
corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the Brillouin zone two-torus, it
respects the time-reversal symmetry of the system and allows for a definition of the Z2 invariant in terms of time-reversal polarization. In 3D we applied the 2D approach to
time-reversal invariant planes. The method was illustrated with first-principles calculations on GeTe and on HgTe under  and  strain.
Wannier representation of topological insulators
The problem of constructing Wannier functions for Z2 topological insulators in two dimensions was considered. It was well known that there is a topological obstruction to
the construction of Wannier functions for Chern insulators, but it had been unclear whether this is also true for the Z2 case. We considered the Kane-Mele tight-binding model,
which exhibits both normal (Z2-even) and topological (Z2-odd) phases as a function of the model parameters. In the Z2-even phase, the usual projection-based scheme can be
used to build the Wannier representation. In the Z2-odd phase, we did find a topological obstruction, but only if one insists on choosing a gauge that respects the time-reversal
symmetry, corresponding to Wannier functions that come in time-reversal pairs. If instead we are willing to violate this gauge condition, a Wannier representation becomes
possible. We presented an explicit construction of Wannier functions for the Z2-odd phase of the Kane-Mele model via a modified projection scheme followed by maximal
localization, and confirmed that these Wannier functions correctly represent the electric polarization and other electronic properties of the insulator.