NCTS 1-day workshop on Wannier-functions based Hamiltonians
Wannier functions are functions localized in real space in order to describe the electronic structure of materials. Wannierization codes have become available in most ab initio DFT packages and the Wannier functions can be constructed explicitly. They have become an established tool in the post-processing of ab initio electronics structure calculations. The ab initio DFT band structures can be represented in tight-binding formalism by Wannier functions. Such material-specific tight-binding Hamiltonians are flexible and can be downfolded, allowing including interaction that beyond DFT such as theoretical models for strongly correlated system and superconductivity.
It is worth noting that Wannier functions have been used to obtain the Berry-phase in the microscopic modern theory of polarization and recent applications in topological insulators include the direct evaluation of the Z2 invariants, thus demonstrating their usefulness in practical situations.
This NCTS 1-day workshop consists of one talk in the morning and hand-on tutorials in the afternoon.
The title and abstract for the morning talk
Edge Mass-Kink and Fractional Corner Charge in Higher-Order Topological Insulators
Higher-order topological insulators are d-dimensional topological insulators with the absence of (d-1)-dimensional gapless states, of which the bulk-boundary correspondence is manifested as (d-2)-dimensional in-gap states instead. There are various mechanisms that generate such topological phases, still, a unified theory is lacking. A recent theory shows that the 0-dimensional in-gap states emerge at corners where two edges have phase difference between their mass of edge Dirac cones, which explains the origin of the in-gap states in higher-order topological insulators. Yet, the analyses retain in the pen-and-paper level or need the energy spectrum of a nano-disk/nano-ribbons with considerable size, which are both impractical to apply on real materials. I will briefly introduce the concept of mass-kink and demonstrate how to use it to predict the numbers and the distributions of the in-gap states. Then, I will present my recent works on using material specific tight-binding hamiltonians and real-space renormalization group through Green’s function to calculate the phases of mass for edge Dirac cones, which is not only computational cheap but also gives accurate values for fractional corner charges.