EAGER: BRAIDING: Lattice engineered nonabelian defects in fractional Chern insulators

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

Nontechnical Abstract: in the last decade, the possibility of utilizing unusual quantum statistics of emergent states of matter as a basis for quantum computation has gone from being a distant dream to an ambitious but reasonable possibility. Recent advances are based on assembly of required ingredients through proximity effects. In this approach, two materials with complementary properties are placed in close proximity to each other, for example allowing superconductivity to be introduced into materials which have complementary properties. Most prominently, Majorana bound states, the simplest states that can support certain forms of quantum computation, can be engineered by inducing superconductivity in a one-dimensional wire. As the experimental hunt for Majorana bound states intensifies, the question arises as to whether even richer ground states can be realized using the same synthetic approach. This proposal describes a route towards realizing such states in a newly discovered class of topologically ordered metamaterials known as fractional Chern insulators. Remarkably, these class of metamaterials allow the requisite disparate properties to be engineered with single-site resolution in an artificial lattice, opening completely new design principles for quantum devices. Technical Abstract: 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 `synthetic' approach. Rather than seeking nonabelian anyons as elementary excitations in 'natural' electronic systems, the disparate ingredients required are assembled through proximity effects. For example, Majorana bound state - the simplest nonabelian defect state - can be engineered by inducing superconductivity in an effectively spinless, one dimensional fermionic wire. As the experimental hunt for Majorana bound states intensifies, the question arises as to whether richer parafermion and Fibonacci anyon ground states can be realized using the same synthetic approach. This proposal describes a route towards realizing nonabelian defects in the recently discovered fractional Chern insulators in graphene heterostructures, including parafermion bound states. Fractional Chern insulators are generalizations of fractional quantum Hall states to lattice systems. Like conventional fractional quantum Hall states, the low-lying charged excitations of gapped fractional Chern insulators have anyonic statistics; however, the lattice degree of freedom endows them with new experimental tunability. Under the current proposal, we will classify fractional Chern insulator ground states in lithographically defined superlattices and use them to Engineer lattice defects and sublattice selective contacts for measurement-only braiding of nonabelian defect states. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.