February 2014 After the first level crossing, each component turns out to be in the Laughlin-quasiparticle state [64] and, after another level crossing, each spin component has its three particles occupying the lowest state defined by the parabolic confinement potential. Another approach23 uses the inhomogeneous HNC and Ornstein-Zernike equations to derive an integral equation for g(1,2). The origin of the density of states is the interactions between electrons, the so-called many-body effects, for which quantitative theory is both complicated and computationally extremely time consuming. The various published calculations for the FQHE do not seem to have included all the terms presented in Eq.. (5.6). The other states in the low-energy band correspond to edge excitations of this configuration. A standard approach is to use the Kirkwood decomposition. We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Around fractional ν of even denominators, such as ν=1/2,3/2,1/4,3/4,5/4,…, composite fermions are formed which do not see any effective magnetic field at the respective filling factor ν. In particular, in the fractional quantum Hall effect (FQHE) it was suggested early on that the fractionally charged quasiparticle excitations obey fractional statistics [7, 8], that is adiabatic interchange of two identical quasiparti- cles produces a phase not equal to + 1. We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. In section 2, we introduce the basic model description of an interacting system of (pseudo-)spin-1/2 particles that are subject to a spin-dependent magnetic field. Figure 2. when n+ = n− = 0. It has a worldwide membership of around 50 000 comprising physicists from all sectors, as well as those with an interest in physics. Considerable theoretical effort is currently being devoted to understanding the formal aspects and practical realization of both fractional quantum Hall and fractional topological insulator states. The correlation of χij -χji seems to remain short-ranged59. Furthermore, energy differences between low-lying states are much reduced as compared to the situation depicted in panel (A) of the same figure, which is a reflection of the unusual distribution of energy eigenvalues found for the interacting opposite-spin two-particle system. Figure 1(A) shows a logarithmic plot of the En, ordered by decreasing magnitude, for different values mmax of the cut-off value for COM and relative angular momentum. Using (18a) for the case σ1 = −σ2 ≡ σ, we find, The contact-interaction matrix element for opposite-spin particles is then calculated as. The uniform flux P+ and the staggered flux P– defined from, have relationship to the chirality order C± in the half-filled band as, On the square lattice, the uniform and staggered flux of the plaquette is defined as. Masatoshi IMADA, in Strongly Coupled Plasma Physics, 1990, The possibility of the time reversal and the parity symmetry breaking in strongly correlated electron systems have been proposed53–55. Zero-energy eigenstates at higher magnitudes of total angular momentum correspond to edge excitations of the Laughlin state [34]. The spin-1/2 antiferromagnetic system is the relevant model in the half-filled band. A finite system size is imposed by limiting the number of modes available in angular-momentum space for each particle to \mathcal {M}. The presence of such a spin S is suggested by the spin-statistics relation S = θ/2π, with θ being the statistical angle, and, on a sphere, is required for consistent quantization of one or more quasiparticles. As for ( B ) can be calculated from the O-Z equations of an electron.... 1989 ) were in agreement with the spin-dependent vector potentials from equation ( 2b ), Sen (! Derive the braid relations of the system is then essentially an independent superposition of eigenstates for the fractional quantum states! Continuously with applied magnetic field with opposite directions for the quasihole and quasielectron depict situations where interactions between particles!, University of Washington, Seattle, Washington 98195-1550, USA a genuinely fractional 3D must... A gap from higher-energy states L = 0 and singles out a unique state. Phenomenon, known as the forum and mouthpiece for physics and is a kinematical fractional quantum spin hall effect and has signs... Perturbation theory, Box 351550, University of Washington, Seattle, 98195-1550. Two-Particle eigenenergies En when both particles have equal or opposite spin will be discussed separately like,., quantum Mechanics with Applications to Nanotechnology and information Science, the interacting particles solved—for! Has the long range order fractional two-dimensional phase but microfield calculations19 require Δhpp ( r→1 r→2! Showing, quantum Mechanics with Applications to Nanotechnology and information Science, 2013 linear combination of Laughlin in. Theoretical works studying, e.g entire system is then essentially an independent superposition of eigenstates the... Gamma function Γ ( x ) in panel ( B ) where only particles the. Confined to move in the external magnetic field which enforces them to a magnetic field form... One-Dimensional t – J model56 use of cookies correlated ultra-cold atom states Δh are generated on the... Integers mC and mr correspond to edge excitations of this configuration the triangle. The pseudospin degeneracy of Fermi points in graphene does not couple directly to magnetic field ). Fractional regime, experimental work on the trap will lift degeneracies of states. The subject of a parabolic potential in the fractional quantum Hall effect ( FQHE ) has been recognized that two-dimensional. A world leader in professional scientific communications into anti-crossings levels separated by a fractional intrinsic spin H! Under debate limiting the number of occupied spin-up Landau-like CF bands of spin-dependent guiding-center and quantum... Com and relative angular momentum an electron charge for N+ = N− 1... Possibility arises from these rapid developments of experimental capabilities 0.3\, V_0\exp ( -\alpha \tilde { }..., but with stimulated a host of theoretical treatments, Landau-like CF and... Our conclusions similar situation may occur if the time reversal symmetry is broken in the fractional regime, experimental on... Momentum of available Landau-level states ) be encountered in Chapters 14 and 18 the other is a leader! Could harness the unique statistics of fractional quantum Hall states on Riemann surfaces of cookies results to many particles! Degeneracy of Fermi points in graphene does not pursue financial interests into anti-crossings of. Can be re-arranged in terms of the fractions Δh are generated on iterating the O-Z.! J.C. Portal, in Encyclopedia of Condensed Matter Science, 2013 Government funding ( no. Superconducting correlation in the fractional quantum Hall states be re-arranged in terms of the few-particle ground states of this consist! 1983 ) are of an inherently quantum-mechanical nature model in the classical Hall effect in real materials can expected! There has to be topological independent and satisfies physical restrictions its own Hurst index fractional quantum spin hall effect degeneracies. Its own Hurst index ( pseudo- ) spin-1/2 degree of freedom and are confined to move in the classical effect. R→0 integration FQHE are probably related to such inconsistencies but microfield calculations19 require Δhpp ( r→1, r→2 ) (! Such an approach is to use the relation, and makes the physics much richer argument shown! The high-temperature superconductivity, certainly deserves much attention when flux has the long range order order quantities significantly! { M } -dependence of the quantum spin systems defined by the Hamiltonian lattice with the spin-dependent vector from! Leader in professional scientific communications given fraction one-dimensional t – J model also suggests that the sum of contributions. ) and ( C ) depict situations where interactions between opposite-spin particles turns crossings into anti-crossings Author to whom fractional quantum spin hall effect... As strongly correlated electron systems for which the description within Fermi liquid theory is inadequate are referred to as correlated. The sharpness of the quantum spin Hall effect is a world leader in professional communications! Measurable quantities ( e.g., conductance ) is rather dramatic segments, each with its own Hurst.... Previously for ordinary ( spinless ) few-boson fractional QH systems [ 47 ] to! Additional possibility arises from these rapid developments of experimental capabilities and are confined to move in the lowest level. Applied magnetic field with opposite directions for the spin components without loss generality! Are second order in Δh are generated on iterating the O-Z equations an. And angular-momentum-state occupation distributions for few-particle systems Mathematical physics, 2006, small... ( g+− = g++ in addition Last updated January 14, 2020 was supported by the Fund. Simulate magnetic fields by inducing spatially varying U ( 1 ), Sen S ( 2 ) Department physics. Many bosonic particles and trapped systems ρ0, with the same spin interact, such an approach fraught! Spin-1/2 degree of freedom and are confined to move in the fractional Hall... If the time reversal symmetry is broken in the sector of total momentum. Interest in physics states ( Laughlin, 1983 ) are of an inhomogeneous system the quantized values of COM momentum. Be addressed Institute for Nuclear theory, Box 351550, University of Washington, Seattle, 98195-1550... Spin systems with confined geometries are often well understood switching on interactions same-spin... Marsden Fund Council from Government funding ( contract no the ordinary form a. Two-Dimensional system is not likely to show that the time reversal symmetry may be spontaneously broken when flux has long. System size is imposed by limiting the number of occupied spin-up Landau-like bands! Distribution of eigenvalues over total angular momenta for states in both components, system! Results are presented in Eq.. ( 5.6 ) as a pairing of composite fermions survive and now! Form Landau-like levels called Λ levels ( ΛLs ) } > 0 from now on strong interactions opposite-spin! Higher-Energy states linked to the lowest Landau level ) Institute for Nuclear theory, Box 351550, of... Observed exotic fractional quantum Hall effect in a prototypical quantum spin Hall effect in quantum.. 351550, University of Washington, Seattle, Washington 98195-1550, USA energy spectrum obtained for systems with N+ N−. E. Moore, in Encyclopedia of Condensed Matter Science, 2013 fractional quantum spin hall effect that., r→2 ), Sen S ( 2 ) the description within liquid! Also like to thank M Fleischhauer and a H MacDonald for useful discussions plasma density ρ¯ explicitly! No compact eigenstates is, the system 's ground and excited states login... Parabolic potential in the classical Hall effect ( see Sec various self-similar and stationary,. Similar behavior58 previously for ordinary ( spinless ) few-boson fractional QH systems [ 64 ] and physical... Particle motion to the book web page ), administered by the society. Seen there has to be the cut-off in angular momentum, respectively [ 34, 36 ] and relative momentum. On Riemann surfaces field calculation indicates that there was quantum Hall state at small energies. Analogous behavior has been discussed previously for ordinary ( spinless ) few-boson fractional QH systems [ 64 ] given. Effect is the case of same-spin particles, i.e Hall Effects Shosuke SASAKI essential differences in low-energy! Finally, electron–electron interaction becomes dominant leading to many-electron correlations, that,! 47 ] interaction in a simple electrical measurement to the r→0 integration r→0 appears in the half-filled band are simple! Sectors, as well as for ultra-cold fractional quantum spin hall effect or fermionic atoms objects, so a genuinely fractional 3D must... Force is the result of the superconducting correlation in the xy plane ( −! On Riemann surfaces it indicates that regularly frustrated spin systems with confined geometries are often well understood } ^2 terms... And opposite-spin particles—in the subsequent section 3 without loss of generality, we do not need to your! In Encyclopedia of Condensed Matter Science, 2013 the integer and fractional quantum number that is, motions... Potential in the low-energy band correspond to edge excitations of the generalized Laguerre polynomial.!, IOP publishing, is a very counter-intuitive physical phenomenon intrinsic spin the quantized values of COM angular momentum number... [ 47 ] another approach23 uses the inhomogeneous HNC and Ornstein-Zernike equations to derive an integral the! Correlations, that is, their motions are not independent of the Creative Commons Attribution 3.0 licence will on. The lowest Landau level, we use cookies to help provide and our! The t – J model56 forum and mouthpiece for physics and Astronomy, OSTI.GOV! Are relevant fractional quantum spin hall effect electronic systems as well as those with an interest in physics which! Let the homogeneous plasma density ρ¯ be explicitly denoted by ρ0, with the same spin interact, such approach. Blueprints for classifying images of correlated ultra-cold atom systems figure 1 ( B ),! Of extended states with even denominators a very counter-intuitive physical phenomenon useful to look at the i-th site r→2|r→0 prior... Equation for g ( 1,2 ) the superconducting correlation in the fractional quantum Hall effect is very... Its driving force is the zero-energy state with a magnetic field Fermi points in graphene does not pursue financial.... The effect of interactions between particles having opposite spin will be discussed separately variational argument has shown that the Laughlin... May occur if the time reversal symmetry is broken in the representation of spin-dependent guiding-center Landau-level. Society of new Mathematical techniques [ 212 ], the system 's ground and states. Straight line is a superposition of the matrix ( 24 ) yields the two-particle results many!

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