Ady Stern

Proposed experiments to probe the non-Abelian nu = 5/2 quantum hall state.

We propose several experiments to test the non-Abelian nature of quasiparticles in the fractional quantum Hall state at nu = 5/2. In a simplified version of the experiment suggested by [S. Das Sarma, M. Freedman, and C. Nayak, Phys. Rev. Lett. 94, 166802 (2005).], interference is turned on and off when the number of localized quasiparticles between the interfering paths varies between even and odd. We find analogous effects in the thermodynamic properties of closed systems.

Observation of a quarter of an electron charge at the |[ngr]| = 5/2 quantum Hall state

The fractional quantum Hall effect, where plateaus in the Hall resistance at values of 2 / h e ν coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows along the edges carried by charged excitations (quasi particles) whose charge is a fraction of the electron charge. While earlier research concentrated on odd denominator fractional values of ν, the observation of the even denominator ν=5/2 state sparked a vast interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics is “non-abelian”. In other words, interchanging of two quasi particles may modify the state of the system to an orthogonal one, and does not just add a phase as in for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data of shot noise generated by partitioning edge currents in the ν=5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other potentially possible values, such as e/2 and e. While not proving the ‘non-abelian’ nature of the ν=5/2 state, this observation is the first step toward a full understanding of these new fractional charges.The fractional quantum Hall effect, where plateaus in the Hall resistance at values of h/νe2 coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. (Here h is Planck’s constant, ν the filling factor and e the electron charge.) Current flows along the sample edges and is carried by charged excitations (quasiparticles) whose charge is a fraction of the electron charge. Although earlier research concentrated on odd denominator fractional values of ν, the observation of the even denominator ν = 5/2 state sparked much interest. This state is conjectured to be characterized by quasiparticles of charge e/4, whose statistics are ‘non-abelian’—in other words, interchanging two quasiparticles may modify the state of the system into a different one, rather than just adding a phase as is the case for fermions or bosons. As such, these quasiparticles may be useful for the construction of a topological quantum computer. Here we report data on shot noise generated by partitioning edge currents in the ν = 5/2 state, consistent with the charge of the quasiparticle being e/4, and inconsistent with other possible values, such as e/2 and e. Although this finding does not prove the non-abelian nature of the ν = 5/2 state, it is the first step towards a full understanding of these new fractional charges.

Anyons and the quantum Hall effect-A pedagogical review

Abstract The dichotomy between fermions and bosons is at the root of many physical phenomena, from metallic conduction of electricity to super-fluidity, and from the periodic table to coherent propagation of light. The dichotomy originates from the symmetry of the quantum mechanical wave function to the interchange of two identical particles. In systems that are confined to two spatial dimensions particles that are neither fermions nor bosons, coined “anyons”, may exist. The fractional quantum Hall effect offers an experimental system where this possibility is realized. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Furthermore, we devote a large part of the paper to non-abelian anyons, motivating their existence from the point of view of trial wave functions, giving a simple exposition of their relation to conformal field theories, and reviewing several proposals for their direct observation.

Fractional Topological Insulators

We analyze generalizations of two-dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with fractional charge and statistics in addition to protected edge modes. In the case of s(z) conserving toy models, we show that a system is a fractional topological insulator if and only if sigma(sH)/e* is odd, where sigma(sH) is the spin-Hall conductance in units of e/2pi, and e* is the elementary charge in units of e.

Fractionalizing Majorana fermions: non-Abelian Statistics on the Edges of Abelian Quantum Hall States

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of

Universal topological quantum computation from a superconductor-abelian quantum hall heterostructure

\nu= 1/m

Theory of interlayer tunneling in bilayer quantum Hall ferromagnets.

, while electrons of the opposite spin occupy a similar state with

Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires

\nu = -1/m

Inducing Time-Reversal-Invariant Topological Superconductivity and Fermion Parity Pumping in Quantum Wires

. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-abelian anyon of quantum dimension

Quantum Limitations on Superluminal Propagation

\sqrt{2m}