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 Karl Franzens University Graz

Graz University of Technology 

Topological Superconductivity: A New Quantum State of Matter
Prof. Dr. Werner Hanke
Lehrstuhl für Theoretische Physik 1, Julius-Maximilians-Univeristät Würzburg
17:15 - 18:15 Tuesday 17 June 2014 TUG P2

The search for topological states of matter has generated an enormous activity in
condensed‐matter physics, both experimentally and theoretically.
In quantum systems, atoms and their electrons can form many different states of matter, such as crystalline solids, magnets, and superconductors. Those different states can be classified by the symmetries they spontaneously break - translational, rotational and gauge symmetries, respectively, for the examples above. Before 1980, all states of matter in condensed‐matter systems could be classified by the principle of broken symmetry. The quantum Hall state provided then the first example of a quantum state that has no spontaneously broken symmetry. Its behavior depends only on its topology and not on its specific geometry; it was topologically distinct from all previously known states of matter.
Recently, new classes of topological states have emerged, called quantum spin Hall states or topological insulators as well as their superconducting cousins. A topological superconductor (SC) is a new state of quantum matter, which possesses a full pairing gap in the bulk but gapless surface states. A chiral superconductor with broken time‐reversal symmetry (TRS) may be considered the superconducting analogue of the quantum Hall phase, whereas a topological superconductor conserving TRS is closely related to the quantum spin Hall phase. Recently, chiral SCs have enjoyed significant attention, exhibiting a variety of exotic phenomena based on their non‐trivial topology: they can host Majorana vortex bound states and gapless chiral edge modes, that carry quantized thermal or spin currents. The Majorana edge states are elusive fermionic particles equivalent to their own antiparticles, which have potential applications in fault‐tolerant topological quantum computation.
In this colloquium, we review some pertinent aspects of topological superconductivity, in particular, where we are at in the theory providing a reliable criterion for this new quantum state of matter. Sr2RuO4 and doped graphene are considered as hallmark candidates.