The elementary excitations of a fractional quantum Hall liquid are quasiparticles or quasiholes that are neither bosons nor fermions, but are so-called anyons. Here, taking notable fractional quantum Hall (FQH) states as typical examples, we systematically investigate a promising protocol -- the Dehn twist deformation on the torus geometry, to probe the … Moreover, if quasiparticle excitations can be isolated and thenmanipulated,theprospectofanewform of topologically protected quantum compu-tation also exists. Many researchers now find themselves working away from their institutions and, thus, may have trouble accessing the Physical Review journals. know about the fractional quantum Hall effect. In the fractional quantum Hall effect ~FQHE! Disorder is a ubiquitous ingredient that may affect, even drive such phase transitions. A topological quantum computer, an extremely attractive idea for computation protected from mistakes caused by quantum state decoherence, can be realized using non-Abelian anyons [6]. Princeton Univ/Institute for Advanced Study, July 2015 . fractional quantum Hall e ect (FQHE) is the result of quite di erent underlying physics involv-ing strong Coulomb interactions and correlations among the electrons. The numerical data is found to match very well the anyonic prediction. Fractional Quantum Hall Effect The Laughlin Liquid Many-body states Without magnetic field only continous spectrum Bound states Discrete spectrum → Bound states exist Figure: vm vs. m in units of e2/ ǫ0ℓ Girvin Séminaire Poincaré 2 (2004) 53 14/20. These exotic statistics, generally allowed in 2 " 1 dimensions [1], are dimensional ele ctron gases (2DEG) in inequ iva len t Laughlin fractional quantum Hall (F QH) states, as a function of voltage and temp erature. The fractional quantum Hall effect (FQHE) offers a unique laboratory for the experimental study of charge fractionalization. Composite fermions arise in a two-dimensional system subject to a large magnetic field, most famously those systems that exhibit the fractional quantum Hall effect. Competing Fractional Quantum Hall and Electron Solid Phases in Graphene ... eld, and construct a phase diagram of the electron liquid-solid transition. The frequently used "Hall bar" geometry is depicted in Fig. The plasmons herald rotational-symmetry-breaking (nematic) phases in the second Landau level and … We conclude that in the thermodynamic limit, these are likely to be incompressible fractional quantum Hall liquids, albeit with strong short-range crystalline correlations. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced. In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. And tunneling of the Luttinger liquid between edges is shown to enable a direct measurement of the fractional charge of the quasiparticle. We investigate the disorder-driven phase transition from a fractional quantum Hall state to an Anderson insulator using quantum entanglement methods. to fractional quantum Hall states with even denominators. Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids Liu, Zhao; Bhatt, R. N. Abstract. Bitte scrollen Sie nach unten und klicken Sie, um jeden von ihnen zu sehen. https://doi.org/10.1103/PhysRevLett.125.136801, Physical Review Physics Education Research, Log in with individual APS Journal Account », Log in with a username/password provided by your institution », Get access through a U.S. public or high school library ». Projective construction of nonAbelian quantum Hall liquids. Use of the American Physical Society websites and journals implies that In contrast, for fractional quantum Hall state, vanishes at low with an activation gap associated with neutral collective modes rather than charged quasiparticles. %PDF-1.4 The frequently used "Hall bar" geometry is depicted in Fig. The elementary excitations of a fractional quantum Hall liquid are quasiparticles or quasiholes that are neither bosons nor fermions, but are so-called anyons. A brief summary of the Luttinger liquid is given. In addition to carry-ing a fraction of the electron charge, these excitations are generally expected to have exotic exchange statistics which are neither bosonic nor fermionic. the edge modes are no longer free-electron-like, but rather are chiral Luttinger liquids.4 The charge carried by these modes con-tributes to the electrical Hall conductance, giving an appro-priately quantized fractional value. Electrons in semiconductors usually behave like a gas--as independent particles. This suggests a natural explanation for the experimentally observed behavior and a rich phase diagram that admits, in the low-disorder limit, a multitude of crystal-FQHE liquid transitions as the filling factor is reduced. These quasiparticles are quite unlike normal particles in two ways. and fractional quantum Hall (FQH) liquids, and topo-logical insulators and superconductors. (4) for Na=20 majority particles. 1. (a) We plot the radial density ρbm,q(|w|) of an impurity, which is excited to the mth level (m=0, 1, 4), and which is immersed in a FQH liquid at ν=1/q (for q=3 and q=5). Physics B (1994) Nayak & Wilzcek (1996) SU (2) 2 Charge e/5 quasiparticles Fibonacci anyons Read-Rezayi “parafermion” state Read & Rezayi, PRB (1999) Slingerland & Bais (2001) SU (2) 3. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. See Off-Campus Access to Physical Review for further instructions. Published in: Phys.Rev.B 60 (1999) 8827; e-Print: cond-mat/9811111 [cond-mat] DOI: 10.1103/PhysRevB.60.8827 ; View in: ADS Abstract Service; pdf cite. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime: intra–Landau-level plasmons measured by resonant inelastic light scattering. the user has read and agrees to our Terms and In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. First, their charge can be less than the electron charge e. %�쏢 DOI:https://doi.org/10.1103/PhysRevLett.125.136801, Tobias Graß1, Bruno Juliá-Díaz2,3, Niccolò Baldelli1, Utso Bhattacharya1, and Maciej Lewenstein1,4. Fractional quantum Hall liquids J.S. The numerical results are obtained from Monte Carlo sampling in the wave function Eq. The predictions of the macroscopic theory are compared with numerical results for finite systems. Xiao-Gang Wen . Real-space imaging of fractional quantum Hall liquids. Fractional quantum Hall (FQH) liquids are interesting two-dimensional electron sys-tems that possess quasiparticle excitations with fractional charges, obeying quantum statistics di erent from those of bosons and fermions. The first fractional quantum Hall state of this type, 5/2, was found in experiments on magnetotransport in high-mobility two-dimensional … Sign up to receive regular email alerts from Physical Review Letters. 3) Basic notions: ground state degeneracy, quasiparticles, fusion, statistics . The fractional quantum Hall effect is also understood as an integer quantum Hall effect, although not of electrons but of charge-flux composites known as composite fermions. 1999 2004 2009 2014 2019 0 2 4 6 8 10. 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