Majorana zero modes in condensed matter: From topological quantum computing milestones to Majorana-dimer models

Condensed matter realizations of Majorana zero modes constitute potential building blocks of a topological quantum computer and thus have recently been the subject of intense theoretical and experimental investigation.  In the first part of this talk, I will introduce a new scheme for preparation, manipulation, and readout of these zero modes in semiconducting wires coated with mesoscopic superconducting islands.  This approach synthesizes recent materials growth breakthroughs with tools long successfully deployed in quantum-dot research, notably gate-tunable island couplings, charge-sensing readout, and charge pumping.  Guided by these capabilities, we map out numerous milestones that progressively bridge the gap between Majorana zero-mode detection and long-term quantum computing applications.  These include (1) detecting non-Abelian anyon ‘fusion rules’ in two complementary schemes, one based on charge sensing, the other using a novel Majorana-mediated charge pump, (2) validation of a prototype topological qubit, (3) braiding to demonstrate non-Abelian statistics, and (4) observing the elusive topological phase transition accompanying the onset of Majorana modes.  With the exception of braiding, these proposed experiments require only a single wire with as few as two islands, a setup already available in the laboratory.  In the second part of the talk, I will introduce a new class of 2D microscopic models---termed ‘Majorana-dimer models’---which generalize well-known quantum dimer models by dressing the bosonic dimers with pairs of Majorana modes.  These models host a novel interacting topological phase of matter which has the same bulk anyonic content as the chiral Ising theory, albeit with a fully gapped edge.  These seemingly contradictory statements can be reconciled by noting that our phase is inherently fermionic:  it can be understood as the product of an Ising phase with a topological p-ip superconductor.  Potential physical realizations of this exotic state via a lattice of strongly interacting Majorana modes will be discussed.