Towards Synthetic Nonabelions in Graphene Heterostructures
Abstract
The goal of this proposal is to use graphene heterostructures as a platform for engineering nonabelian defect states, including Majorana and parafermion bound states. In the last decade, the possibility of using ground state topological degeneracy as a basis for quantum computation has gone from being a distant dream to an ambitious but reasonable possibility. Recent advances owe much to a shift in focus to a ÔsyntheticÕ approach. Rather than seek nonabelian anyons as elementary excitations in ÔnaturalÕ electronic systems, the disparate ingredients required are assembled through proximity effects. For example, Majorana bound states (MBSs)Ñthe simplest nonabelian defect stateÑcan be engineered by inducing superconductivity in an effectively spinless, one dimensional fermionic wire. As the experimental hunt for MBSs intensifies, the question arises as to whether richer parafermion and Fibonacci anyon ground states can be realized using the same synthetic approach. Theory answers this in the affirmative: although no-go theorems forbid parafermions in strictly 1D systems, coupled fractional quantum Hall (QH) edge modes can provide the necessary ingredients to engineer effectively 1D systems hosting defect states with richer quantum statistics. Graphene heterostructures are an ideal system to pursue synthetic nonabelions, providing viable routes to realizing all of the requirements for engineering, detecting, and manipulating Majorana and parafermion bound states (MBSs and PBSs) at current levels of technology. Two major experimental challenges prevent the immediate realization of MBS and PBSs in graphene heterostructures: lack of a complete phase diagram of integer- and fractional-quantum Hall states in bilayer (BL) and double layer (DL) systems most promising for engineering nonabelian defects, and insufficient understanding of the physics of QH interfaces, the tailoring of which forms the basis for all synthetic parafermion proposals. Our approach is to Classify the electronic phases of graphene double layers using a novel thermodynamic technique (year 1-2); Control superconducting proximity effects (year 1), interlayer tunneling (year 1-2), and symmetry breaking in helical edge state (year 1), using MBS detection as a benchmark (year 2); Combine these results to enable parafermion detection in graphene bilayers and double layers (year 3). Parafermion bound states are an important milestone towards fully protected topological quantum computation. PBSs allow two out of the necessary three elementary gate operations in a quantum bit to be fully protected from decoherenceÑMBSs, in contrast, only protect one. Furthermore, we expect that the increased experimental control over ground states and interfaces in graphene heterostructures will also contribute to more concrete proposals to realize Fibonacci anyons, the minimally dense anyon required for universal fault tolerant quantum computation where arbitrary unitary transformations of a qbit can be effected, immune from all local sources of decoherence.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 16, 2018
- Source ID
- W911NF1610482
Entities
People
- Andrea Young
Organizations
- Army Contracting Command
- United States Army
- University of California, Santa Barbara