A Home for Anyon?
NEWS & VIEWS
Fractional exchange statistics A home for anyon?
Exotic quasiparticles known as ‘anyons’ have intriguing fundamental and practical properties. A proposal for a solid-state structure in which anyons might ‘live’ provides fresh ideas for getting a practical handle on them.
Kirill Shtengel Frank Wilczek, who coined the term vortex through a semiconducting layer in is in the Department of Physics, University of ‘anyons’, proposed4 a physical picture to the integer quantum Hall state locally expels California, Riverside, California 92521, USA. explain how their unusual exchange statistics half of the electron charge by pushing it e-mail: [email protected] may come about: imagine a situation in towards the boundary. Several assumptions which an electric charge q and a magnetic are implicit here. For example, the precision rom a physicist’s point of view, having flux tubeΦ — such as the magnetic flux of charge quantization is not enforced by any two spatial dimensions is special: a created by a solenoid — are bound together intrinsic energy scales associated with strong F pair of particles trading places behave to form a ‘dyon’ (a hypothetical particle correlations — unlike in fractional quantum very differently in two dimensions than with both electric and magnetic charges). If Hall systems — but rather by the strength they do in three. In three dimensions, any one such particle is moved around another, of coupling between the two subsystems. two sets of paths taken by two identical the phase acquired by the wavefunction is Excitations carrying half a fundamental particles in the process of exchanging their 2qΦ (twice the Aharonov–Bohm phase; in flux are not eigenstates in the integer positions can be continuously morphed natural units). Wilczek argued that if either quantum Hall regime; a superconducting into one another. But in two dimensions, the charge of this dyon is a fraction of the layer must ‘force’ them in. Also, the notion particles can wind around each other in two electron charge e, or its magnetic flux is a of any exchange statistics has a meaning distinct ways, clockwise or anticlockwise. A fraction of the fundamental flux quantum only for quantum particles. Therefore, the profound consequence of this observation 2π/e (or both), then the resulting phase resulting dyonic objects should be truly for quantum mechanics is that in two may differ from a multiple of 2π, signalling quantum before they can be called anyons. dimensions, exchanging identical particles anyonic statistics. Although electrons in the 2DEG considered twice is not equivalent to leaving them alone. The most important feature captured by Weeks et al.3 are indeed quantum objects The particles’ wavefunction after swapping by Wilczek’s toy model is that anyonic with long dephasing lengths and times, the places twice may differ from the original statistics are inextricably connected with superconducting vortices are not necessarily one; particles with such unusual exchange the phenomenon of fractionalization (that so. These issues must be overcome statistics are known as anyons. By contrast, is, excitations in the system carry fractions experimentally before the proposal can be in three dimensions, exchanging particles of fundamental quantum numbers of its put to test. twice cannot change their wavefunction, constituent particles). Fractional quantum Whether or not such a test proves leaving us with only two possibilities: bosons, Hall states — where the transverse electrical successful, their idea may have an interesting whose wavefunction remains the same even conductivity is quantized in non-integer offshoot: it could pave the way for after a single exchange, and fermions, whose multiples of e2/h — are the prime example of manipulating quasiparticles in the fractional exchange only changes the sign of their such behaviour, and other condensed-matter quantum Hall state with filling fraction wavefunction. The theoretical possibility systems (for instance, frustrated magnets 5/2, which is the leading candidate for a of particles taking ‘any phase’ on being and rotating Bose–Einstein condensates) system with non-abelian anyons2,5 — anyons interchanged is currently attracting interest, have also been considered theoretically. The that would be of particular value with a not least due to the realization that anyonic proposal by Weeks et al.3 recalls Wilczek’s view to fault-tolerant topological quantum statistics of quasiparticles (especially of toy model4 in that it provides a physical computing. Unlike the integer quantum Hall the ‘non-abelian’ kind, in which exchanges implementation for creating a dyon binding state, the 5/2 fractional quantum Hall state result in unitary rotations of state vectors in fractionalized electric charge to fractionalized should support excitations with flux 1/2 and a degenerate Hilbert space) could be used to magnetic flux. What makes their system charge 1/4. Using superconducting vortices manipulate quantum information in a way different from those considered previously to bind such excitations could provide a that might lead to the building of a fault- is that fractionalization is achieved not as ‘handle’ with which to manipulate anyons tolerant ‘topological’ quantum computer1 a result of strong correlations between the in this system. An ability to control anyons (for a review, see ref. 2). A number of constituent particles, but rather through is a prerequisite for building, eventually, a practical systems that could support anyons a combination of two weakly interacting topological quantum computer, so any new have been discussed, but Conan Weeks and systems with different properties — a vortex ideas as well as experimental developments colleagues3 (page 796 of this issue) propose lattice in the superconducting layer, and in this direction are welcome. a candidate — based on a superconducting electrons in the doped semiconducting layer. 3 References film grown on top of a semiconductor The key to this construction is the 1. Kitaev, A. Yu. Ann. Phys. 303, 2–30 (2003). that hosts a two-dimensional electron fact that a superconducting flux quantum 2. Das Sarma, S., Freedman, M., Nayak, C., Simon, S. H. & gas (2DEG) — whose properties set it apart is half of the fundamental flux quantum Stern, A. Preprint at