Mechanism of high temperature superconductivity
Midgap states & their topological origin
- Generalized Method of Image ---
It is known for many years that what is measured in the tunneling
experiments is the density of state. In the simplest case, the density
of state is the bulk density of state, which is simply the imaginary
part of bulk Green's function. However, it is also known that this is
not correct as the tunneling measurement is a local probe. Then one
needs to replace the density of state by the local density of state.
The conventional approach is to calculate the local density of
state by brutal force. In this work, we are able to write the local
density of state in terms of bulk Green's functions. This is
achieved via the usage of generalized method of image.
- Supersymmetry ---
Recent advances in nanotechnology have made
bottom-up assembly of single nanowires feasible in
laboratories. While conventional studies of the 1D wire
focuses on its bulk properties, in practice, assembled nanowires can
only have finite lengths and must terminate at some sites.
However, sometimes, the termination of nanowires introduces
edge modes. Our recent work shows that there exists a
beautiful supersymmetric structure in the energy spectra
and the wavefunctions of these modes.
Remarkably, as a consequence of the symmetry, the wavefunctions
of all midgap states reveals a universal form. Furthermore, the
supersymmetry provides a way of unifying impurity states (bonds)
and the midgap states.