Fractional Quantum-Hall Liquid Spontaneously Generated by Strongly Correlated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:math>Electrons

Venderbos, Jörn W. F.; Kourtis, Stefanos; Brink, Jeroen van den; Daghofer, Maria

doi:10.1103/physrevlett.108.126405

Cited by 83 publications

(108 citation statements)

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“…Interacting topological insulator [5][6][7] physics, which FCI is a time-reversal-symmetry-broken representative, is one of the major topics of the current research in the field of strongly correlated systems. FCIs have been reported in many models both for fermionic systems [2][3][4]8] and bosonic cold atom models [9][10][11][12]. Still there is no complete understanding why some model crystal systems are more convenient than others for particular FCI states.…”

Section: Introductionmentioning

confidence: 99%

Geometrical description of fractional Chern insulators based on static structure factor calculations

2013

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We study the static structure factor of the fractional Chern insulator Laughlin-like state and provide analytical forms for this quantity in the long-distance limit. In the course of this we identify averaged over Brillouin zone Fubini Study metric as the relevant metric in the long-distance limit. We discuss under which conditions the static structure factor will assume the usual behavior of Laughlin-like fractional quantum Hall system i.e. the scenario of Girvin, MacDonald, and Platzman [Phys. Rev. B 33, 2481Rev. B 33, (1986]. We study the influence of the departure of the averaged over Brillouin zone Fubini Study metric from its fractional quantum Hall value which appears in the longdistance analysis as an effective change of the filling factor. According to our exact diagonalization results on the Haldane model and analytical considerations we find persistence of fractional Chern insulator state even in this region of the parameter space.

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Section: Introductionmentioning

confidence: 99%

Geometrical description of fractional Chern insulators based on static structure factor calculations

2013

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“…The basic idea of the TFB models is the following: (a) use a 2D lattice-based tight-binding topological-band model to mimic the nontrivial topology of a LL characterized by a nonzero Chern number [23], as first proposed by Haldane [24], and (b) find a parameter region to realize a narrow bandwidth with a smooth Berry curvature to quench the kinetic energy. These new theoretical flatband FQHE discoveries not only improve our understanding about the nature of the FQHE, but also provide us new ways to realize the FQHE in solid state materials [25][26][27][28][29] and ultracold atomic systems [14,30].…”

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confidence: 98%

Topological flat band models with arbitrary Chern numbers

et al. 2012

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We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C = 1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a twoband model on a triangular lattice with a Chern number C = 3 and an N -band square lattice model with C = N for an arbitrary integer N . In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate inter-particle interactions, these models are likely to lead to the formation of novel Abelian and Non-Abelian fractional Chern insulators. As a simple example, we test the C = 2 model with hardcore bosons at 1/3 filling and an intriguing fractional quantum Hall (FQH) state is observed. Introduction -The experimental fractional quantum Hall effect (FQHE) arises from the highly degenerate Landau levels of continuum 2D electron systems, and is described by variational wave functions, first proposed by Laughlin for the primary FQHE states [1] and later generalized by Jain for composite fermion states [2], which are analytic functions of the 2D spatial coordinates. Many important properties of the FQHE, e.g., the hierarchy structures and fractionalized excitations [3,4], can be understood within this framework. It even leads to the predictions of intriguing non-Abelian FQH states at certain filling fractions [5][6][7][8]. Moreover, based on a classification of the pattern of zeros of symmetric (analytic) polynomials, a systematic way to classify FQH states [9,10] has been proposed. Thus, our current theoretical knowledge of FQHE is based on the analytic structure the 2D Landau level (LL) Hilbert space.

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“…First, the QAH state on the checkerboard lattice is actually a prominent candidates for hosting a fractional quantum-Halllike state without a magnetic field, because the topologically nontrivial band can be made almost flat by tuning hoppings and flux [21,40,41]. It turns out that even if the flux and effective hoppings t 1 and t 2 that emerge in the "umbrella" configuration do not lead to very flat bands, additional longerrange hopping −2t 3 (cos 2k x + cos 2k y ) can give a ratio of band gap vs. band width of ≈ 5 for δ = 0.3, considerably less than ratios achievable by tuning all parameters [21] or in t 2g -orbital systems [42,43], but comparable to e g [42] systems or a square-lattice model [44]. Second, it was recently demonstrated that vortex defects of the localized magnetic order underlying a QAH state can carry fractional charge and spin quantum numbers in the electronic sector [45].…”

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confidence: 99%

Switchable Quantum Anomalous Hall State in a Strongly Frustrated Lattice Magnet

et al. 2012

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We establish that the interplay of itinerant fermions with localized magnetic moments on a checkerboard lattice leads to magnetic flux-phases. For weak itineracy the flux-phase is coplanar and the electronic dispersion takes the shape of graphene-like Dirac fermions. Stronger itineracy drives the formation of a non-coplanar, chiral flux-phase, in which the Dirac fermions acquire a topological mass that is proportional to a ferromagnetic spin polarization. Consequently the system self-organizes into a ferromagnetic Quantum Anomalous Hall state in which the direction of its dissipationless edge-currents can be switched by an applied magnetic field. PACS numbers: 71.27.+a , Introduction.-The study of topologically non-trivial states of matter is one of the hottest topics in present day condensed matter physics. An understanding of topological states requires a theoretical paradigm that goes far beyond the concept of global symmetry breaking that has originally been laid out by Landau. It is remarkable that the theoretical predictions on the existence of various topologically ordered states have rather swiftly led to the discovery of an entirely new class of materials, the topological insulators [1][2][3][4]. Recent pioneering experiments have confirmed the key signatures of nontrivial topology in certain materials, e.g. spin-momentumlocked undoubled Dirac fermions [5][6][7] and the Quantum Spin Hall (QSH) effect [8]. These topological insulators are timereversal (TR) invariant generalizations of the first, much older, topological state of matter, the famous Integer Quantum Hall states [9,10] that are induced by a magnetic field, which obviously breaks TR symmetry.In a seminal work in 1988, Haldane established that a magnetic field is not required to induce states with the same topology as IQH states [11]. It was shown that adding complex hopping to a graphene-like Hamiltonian for electrons on a honeycomb lattice opens up topologically nontrivial gaps at the Dirac points, which yields a topologically ordered, insulating state, referred to as a Quantum Anomalous Hall (QAH) state. An important feature of QAH states are edge channels, in which current can run only in one direction; in contrast to QSH states, on a single edge the opposite spin channel carrying the opposite current is absent [12]. QAH states would thus allow very robust, dissipationless charge transport along edge channels, as backscattering would be completely suppressed. However, while signatures of QAH behavior have been reported in some compounds [13][14][15], the QAH state is the only one among these topologically insulating states that remains to be unambiguously identified in experiment.The experimental difficulty is mirrored by the frailty of theoretical mass-generating mechanisms for a graphene-like kinetic energy with a linear dispersion at the Fermi level. TRsymmetry breaking via (magnetic) order requires rather specific and strong longer-range Coulomb interactions [16], because the Dirac cones' vanishing density of states at the Fermi level r...

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Fractional Quantum-Hall Liquid Spontaneously Generated by Strongly Correlatedt2gElectrons

Cited by 83 publications

References 49 publications

Geometrical description of fractional Chern insulators based on static structure factor calculations

Geometrical description of fractional Chern insulators based on static structure factor calculations

Topological flat band models with arbitrary Chern numbers

Switchable Quantum Anomalous Hall State in a Strongly Frustrated Lattice Magnet

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