Workshop on Topological Phases

Date: 28-29 May 2013
Location: 4270 BPS Bldg.

Saad Zaheer, a graduate student from University of Pennsylvania who is working with Eugene Mele (a regular collaborator with Charles Kane), will come to East Lansing from May 28th to May 29th.

On May 28th, he will give a workshop on topological phases building the entire theory using the SSH model as an example and will also introduce us to topological superconductors. This workshop will take almost four hours (with a short break) and will be in room 4270 of the BPS Building from 12:15 to 4:00 pm.

On May 29th, we will have a seminar, where he will present his current research. This will take place in room 1400 of the BPS Building, from 11:00 am to 12:30 pm.

Updated 2nd-day plan:  On May 29th, there will be a continuation of the workshop (see below) in room 1400 of the BPS Building from 11:30 am to 1:00 pm, followed in the same room by the seminar on “Dirac Semimetals in Three Dimensions” from 1:00 to 2:00 pm.

Due to quite a few requests we agreed on a new timeframe for the second day's workshop and seminar.

We will still meet in room 1400, but will continue the workshop from 11:30am to 1:00pm, the focus will be on topological superconductors and the rise of Majorana fermions.

The seminar will start at 1:00pm.


BPS building in room 1400 from 11:30am to 1:00pm.

There has recently been a considerable amount of interest in topological phases of band insulators. In the first half of this workshop, I will introduce the notion of topology in band insulators by analyzing the Su Schrieffer Heeger (SSH) model and deriving a topological invariant analogous to topological numbers familiar from the theory of compact manifolds. The SSH model has all the essential features of a topological insulator specifically including restrictions whenever a symmetry is present. This will naturally lead to extensions of the SSH model into higher dimensions such as quantum Hall insulators, and two and three dimensional topological insulators. In the second half, I will introduce the concept of a topological superconductor by ‘adding’ the particle-hole symmetry of superconductors to band insulators. Finally I will review some of the exotic boundary states associated with topological superconductors such as chiral majorana fermions.

Seminar Title: Dirac Semimetals in Three Dimensions

In this talk, I will show that the pseudo relativistic physics of graphene can be extended to three dimensional crystal systems. Following the rapid advancement of research into topologically insulating phases of matter, there has been interest in so called topologically stable Weyl semimetals. Weyl semimetals are lower symmetry descendants of a Dirac semimetal which is described by a four band Hamiltonian linear in momentum in all directions. In addition to mediating the phase transition between a topological and a normal insulator in crystals with inversion symmetry, Dirac points are guaranteed to exist as irreducible representations of certain crystallographic spacegroups. I will provide a group theoretic criteria that can be used to classify all the high symmetry points in the 230 spacegroups under time reversal symmetry that can host Dirac points. This provides a platform upon which to launch an extensive search of real materials that may occur as Dirac semimetals. Density functional theory calculations indicate that β-cristobalite BiO2 is indeed such a material, exhibiting three Dirac points at the Fermi level.