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November 14, 2012   >>
Wednesday, November 14
11/14 - Seminar (theoretical, informal): Raffaele Resta, University of Trieste, Italy
<p>Raffaele Resta - <a href="" target="_blank">speaker's webpage</a><br />Department of Physics<br />University of Trieste, Italy</p>
<p><strong>Topological Order in Electronic Wavefunctions</strong></p>
<p>Topology is defined as a branch of mathematics that describes properties which remain unchanged under continuous deformations; such properties are labelled by integer numbers, named topological invariants. If a measurable physical property of a macroscopic system is an integer (in appropriate units), then it can be measured in principle with infinite precision.</p>
<p>To this day, the most spectacular manifestation of topology in nonrelativistic quantum mechanics is the quantum Hall effect; the "integerness" of the relevant invariant is experimentally verified to 10<sup>−9</sup>. The last five years witnessed a booming interest in topological insulators (TIs), defined as materials whose ground state shows topological order in absence of an applied magnetic field.</p>
<p>So far, topological order has been invariably addressed in <strong>k</strong> space, where different values of the invariant characterize ground-state wavefunctions which are differently "knotted", and cannot be transformed into each other by a continuous deformation. But topological order must also be observable in the bulk of the material, even for inhomogeneous samples, and independently of the boundary conditions. We have shown that a "topological marker" -- sampling the Chern number locally in <strong>r</strong> space -- can indeed be defined. Simulations on finite samples, performed within open boundary conditions, prove the effectiveness of our marker for several cases: crystalline, disordered, and inhomogeneous (heterojunctions) [1].</p>
<p>[1] R. Bianco and R. Resta, <em>Mapping topological order in coordinate space</em>, Phys. Rev. B <strong>84</strong>, 241106(R) (2011).</p>
Frick Chemistry Laboratory, A57  ·  4:00 p.m. 5:30 p.m.