CPM Seminar

Engineering non-Abelian topological phases and Majorana fermions in solid state systems

Jason Alicea

University of California, Irvine

Exchange statistics, which characterizes how wavefunctions evolve under particle interchange, is one of the most fundamental properties of nature and ultimately underlies most condensed matter phenomena. Interchanging bosons and fermions, for instance, leaves the wavefunction either unchanged or with an extra overall minus sign. The story becomes much richer in a class of superconducting states supporting exotic particles known as “Majorana fermions”. Interchanging Majorana particles produces not only a phase, but moves the system from one quantum state to another. Apart from revealing something very fundamental about nature, Majorana fermions also hold promise for implementing decoherence-free quantum computation. In this talk I will discuss how one can engineer such phases in the laboratory using heterostructures built from well-understood materials such as semiconductors and superconductors. I will also describe how 1D systems can be used to meaningfully exchange Majorana fermions, in spite of that fact that exchange statistics is usually viewed as ill-defined in 1D.