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# Antiferromagnetic Resonance and Terahertz Continuum in $$\alpha \text{−}{\mathrm{RuCl}}_{3}$$

Physical Review Letters

American Physical Society (APS)

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### Most cited references49

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### Two-Dimensional Gas of Massless Dirac Fermions in Graphene

(2005)
Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.
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### Fault-tolerant quantum computation by anyons

(1997)
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in pairs and observing the result of fusion. Such computation is fault-tolerant by its physical nature.
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### Anyons in an exactly solved model and beyond

(2005)
A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static $$\mathbb{Z}_{2}$$ gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number $$\nu$$. The Abelian and non-Abelian phases of the original model correspond to $$\nu=0$$ and $$\nu=\pm 1$$, respectively. The anyonic properties of excitation depend on $$\nu\bmod 16$$, whereas $$\nu$$ itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
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### Author and article information

###### Journal
PRLTAO
Physical Review Letters
Phys. Rev. Lett.
American Physical Society (APS)
0031-9007
1079-7114
November 2017
November 28 2017
: 119
: 22
###### Article
10.1103/PhysRevLett.119.227201