Sommerfeld Theory Colloquium (ASC)

Majorana fermions are spatially localized superpositions of electron and hole excitations in the middle of a superconducting energy gap. These unusual particles have been predicted to occur at the interface between a magnetic and superconducting electrode, in contact with a topological insulator (such as a Bi crystal or a HgTe quantum well). A single qubit can be encoded nonlocally in a pair of spatially separated Majorana fermions. Such Majorana qubits are in demand as building blocks of a topological quantum computer, but direct experimental tests of the nonlocality remain elusive.

We propose a method to probe the nonlocality by means of crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other bound state. The resulting splitting of a Cooper pair by the Majorana qubit produces a pair of excitations that are maximally entangled in the momentum (rather than the spin) degree of freedom, and might be used as "flying qubits" in quantum information processing.

To illuminate how electroweak symmetry breaking shapes the physical world, we investigate what the world would be like in the absence of electroweak symmetry breaking at the usual scale, whether by the conventional Higgs mechanism or by any of its alternatives, including dynamical symmetry breaking and higher-dimensional formulations. Many interesting charac- teristics of the models stem from the fact that the effective strength of the weak interactions is much closer to that of the residual strong interactions than in the real world. The Higgs- free models not only provide informative contrasts to the real world, but also lead us to consider intriguing issues in the application of field theory to the real world.