We show that the resistance of the ν = 5/2 quantum Hall state, confined to an interferometer, oscillates with the magnetic field consistent with an Ising-type non-Abelian state. In three quantum Hall ...interferometers of different sizes, resistance oscillations at ν = 7/3 and integer filling factors have the magnetic field period expected if the number of quasiparticles contained within the interferometer changes so as to keep the area and the total charge within the interferometer constant. Under these conditions, an Abelian state such as the (3, 3, 1) state would show oscillations with the same period as at an integer quantum Hall state. However, in an Ising-type non-Abelian state there would be a rapid oscillation associated with the "even-odd effect" and a slower one associated with the accumulated Abelian phase due to both the Aharonov-Bohm effect and the Abelian part of the quasiparticle braiding statistics. Our measurements at ν = 5/2 are consistent with the latter.
The quantum Hall states at filling factorsν=5/2and7/2are expected to have Abelian charge-e/2quasiparticles and non-Abelian charge-e/4quasiparticles. The non-Abelian statistics of the latter is ...predicted to display a striking interferometric signature, the even-odd effect. By measuring resistance oscillations as a function of the magnetic field in Fabry-Pérot interferometers using new high-purity heterostructures, we for the first time report experimental evidence for the non-Abelian nature of excitations atν=7/2. At bothν=5/2and7/2, we also examine, for the first time, the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles. The phase of observede/4oscillations is reproducible and stable over long times (hours) near both filling factors, indicating stability of the fermion parity. At both fractions, when phase fluctuations are observed, they are predominantlyπphase flips, consistent with either fermion parity change or change in the number of the enclosede/4quasiparticles. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature ofe/4quasiparticles; the observed lifetime of their combined fermion parity further strengthens the case for their utility for topological quantum computation.
The presence of Majorana zero-energy modes at vortex cores in a topological superconductor implies that each vortex carries an extra entropy s0, given by (kB 2)ln 2, that is independent of ...temperature. By utilizing this special property of Majorana modes, the edges of a topological superconductor can be cooled (or heated) by the motion of the vortices across the edges. As vortices flow in the transverse direction with respect to an external imposed supercurrent, due to the Lorentz force, a thermoelectric effect analogous to the Ettingshausen effect is expected to occur between opposing edges. We propose an experiment to observe this thermoelectric effect, which could directly probe the intrinsic entropy of Majorana zero-energy modes.
We study strongly correlated electrons on a kagome lattice at 1/6 (and 5/6) filling. They are described by an extended Hubbard Hamiltonian. We are concerned with the limit |t|<<V<<U with a hopping ...amplitude t, nearest-neighbor repulsion V, and on-site repulsion U. We derive an effective Hamiltonian and show, with the help of the Perron-Frobenius theorem, that the system is ferromagnetic at low temperatures. The robustness of ferromagnetism is discussed and extensions to other lattices are indicated.
In this Letter we propose an interferometric experiment to detect non-Abelian quasiparticle statistics--one of the hallmark characteristics of the Moore-Read state expected to describe the observed ...fractional quantum Hall effect plateau at nu = 5/2. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma et al. are also addressed.
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by ...particle-like excitations exhibiting exotic braiding statistics.
P and
T invariance are maintained by a ‘doubling’ of the low-energy degrees of freedom which occurs naturally without doubling the underlying microscopic degrees of freedom. The simplest examples have been the subject of considerable interest as proposed mechanisms for high-
T
c
superconductivity. One is the ‘doubled’ version of the chiral spin liquid. The chiral spin liquid gives rise to anyon superconductivity at finite doping and the corresponding field theory is
U(1) Chern–Simons theory at coupling constant
m=2. The ‘doubled’ theory is two copies of this theory, one with
m=2 the other with
m=−2. The second example corresponds to
Z
2 gauge theory, which describes a scenario for spin-charge separation. Our main concern, with an eye towards applications to quantum computation, are richer models which support non-Abelian statistics. All of these models, richer or poorer, lie in a tightly organized discrete family indexed by the Baraha numbers, 2cos(π/(
k+2)), for positive integer
k. The physical inference is that a material manifesting the
Z
2 gauge theory or a doubled chiral spin liquid might be easily altered to one capable of universal quantum computation. These phases of matter have a field-theoretic description in terms of gauge theories which, in their infrared limits, are topological field theories. We motivate these gauge theories using a parton model or slave-fermion construction and show how they can be solved exactly. The structure of the resulting Hilbert spaces can be understood in purely combinatorial terms. The highly constrained nature of this combinatorial construction, phrased in the language of the topology of curves on surfaces, lays the groundwork for a strategy for constructing microscopic lattice models which give rise to these phases.
We propose an extended Hubbard model on a 2D kagome lattice with an additional ring exchange term. The particles can be either bosons or spinless fermions. We analyze the model at the special filling ...fraction 1/6, where it is closely related to the quantum dimer model. We show how to arrive at an exactly soluble point whose ground state is the "d-isotopy" transition point into a stable phase with a certain type of non-Abelian topological order. Near the "special" values, d=2cos(pi/(k+2), this topological phase has anyonic excitations closely related to SU(2) Chern-Simons theory at level k.
In this Letter, we (1) construct a one-parameter family of lattice models of interacting spins; (2) obtain their exact ground states; (3) derive a statistical-mechanical analogy which relates their ...ground states to O(n) loop gases; (4) show that the models are critical for d</=sqrt2, where d parametrizes the models; (5) note that, for the special values d=2cos(pi/(k+2), they are related to doubled level-k SU(2) Chern-Simons theory; (6) conjecture that they are in the universality class of a nonrelativistic SU(2) gauge theory; and (7) show that its one-loop beta function vanishes for all values of the coupling constant, implying that it is also on a critical line.
We consider the Ashkin–Teller model with negative four-spin coupling but still in the region where the ground state is ferromagnetic. We establish the standard Lebowitz inequality as well as the ...extension that is necessary to prove a divergent susceptibility.
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