Fractional Quantum Hall States at Zero Magnetic Field

Neupert, Titus; Santos, Luiz; Chamon, Claudio; Mudry, Christopher

doi:10.1103/physrevlett.106.236804

Cited by 906 publications

(1,029 citation statements)

References 23 publications

Supporting

Mentioning

979

Contrasting

Order By: Relevance

“…More interesting physics occurs when the nearly flat 'Chern' band is partially filled (see Figs 2e and 4). In this case, as pointed out recently, fractional quantum Hall (FQH) states are likely to be realized [39][40][41][42][43][44] . To elaborate this possibility, we perform exact diagonalization calculation after projecting on-site repulsion and NN repulsion into the 1/3 filled highest Chern band (that is, at e g 3.5 + 1/6 ).…”

Section: Resultsmentioning

confidence: 78%

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

et al. 2011

View full text Add to dashboard Cite

Topological insulators are characterized by a non-trivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we predict, based on tight-binding modelling and first-principles calculations, that bilayers of perovskite-type transition-metal oxides grown along the [111] crystallographic axis are potential candidates for two-dimensional topological insulators. The topological band structure of these materials can be fine-tuned by changing dopant ions, substrates and external gate voltages. We predict that LaAuo 3 bilayers have a topologically non-trivial energy gap of about 0.15 eV, which is sufficiently large to realize the quantum spin Hall effect at room temperature. Intriguing phenomena, such as fractional quantum Hall effect, associated with the nearly flat topologically non-trivial bands found in e g systems are also discussed.

show abstract

Section: Resultsmentioning

confidence: 78%

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

et al. 2011

View full text Add to dashboard Cite

show abstract

“…The proposed topological FB is just like a counterpart of the LL, characterized by a Chern number equal to 1 [12]. It has been further shown by numerical simulations that such FBs support QH-like states, exhibiting not only the integer QH effects, but also the fractional QH (FQH) effects [20][21][22]. More importantly, considering the energy scales in lattices, the FQH effects -such as fractionalization and entanglement -can be realized in a much higher temperature in the FB than in the LL [18], charting a revolutionary route towards quantum computation [23].…”

Section: Introduction and Scopementioning

confidence: 81%

Exotic electronic states in the world of flat bands: From theory to material

Liu¹,

Liu²,

Wu³

2014

Chinese Phys. B

208

157

View full text Add to dashboard Cite

It has long been noticed that special lattices contain single-electron flat bands (FB) without any dispersion. Since the kinetic energy of electrons is quenched in the FB, this highly degenerate energy level becomes an ideal platform to achieve strongly correlated electronic states, such as magnetism, superconductivity and Wigner crystal. Recently, the FB has attracted increasing interests, because of the possibility to go beyond the conventional symmetry-breaking phases, towards topologically ordered phases, such as lattice versions of fractional quantum Hall states. This article reviews different aspects of FBs in a nutshell. Starting from the standard band theory, we aim to bridge the frontier of FBs with the textbook solid-state physics. Then, based on concrete examples, we show the common origin of FBs in terms of destructive interference, and discuss various many-body phases associated with such a singular band structure. In the end, we demonstrate real FBs in quantum frustrated materials and organometallic frameworks.

show abstract

“…They are characterized by different PSGs in the bulk. These states can all serve as candidate states for the FCI state found in numerical simulations 12,13,15 . Which state is realized in the simulated model 12,13,15 would be determined by energetics.…”

Section: Introductionmentioning

confidence: 99%

“…However, it takes more than two decades for people to show that similar statement is true even for FQHE. Recently results from a series of model studies [10][11][12][13][14][15][16][17][18] , including convincing evidences from exact diagonalizations [12][13][14][15][16][17] , indicate that fractional quantum hall states exist in the ground states of interacting lattice models, in the absence of an external magnetic field. It is found that the ground state is likely to respect the full lattice symmetry.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry-protected fractional Chern insulators and fractional topological insulators

Lü

Ran

2012

Phys. Rev. B

View full text Add to dashboard Cite

In this paper we construct fully symmetric wavefunctions for the spin-polarized fractional Chern insulators (FCI) and time-reversal-invariant fractional topological insulators (FTI) in two dimensions using the parton approach. We show that the lattice symmetry gives rise to many different FCI and FTI phases even with the same filling fraction ν (and the same quantized Hall conductance σxy in FCI case). They have different symmetry-protected topological orders, which are characterized by different projective symmetry groups. We mainly focus on FCI phases which are realized in a partially filled band with Chern number one. The low-energy gauge groups of a generic σxy = 1/m · e 2 /h FCI wavefunctions can be either SU (m) or the discrete group Zm, and in the latter case the associated low-energy physics are described by Chern-Simons-Higgs theories. We use our construction to compute the ground state degeneracy. Examples of FCI/FTI wavefunctions on honeycomb lattice and checkerboard lattice are explicitly given. Possible non-Abelian FCI phases which may be realized in a partially filled band with Chern number two are discussed. Generic FTI wavefunctions in the absence of spin conservation are also presented whose low-energy gauge groups can be either SU (m) × SU (m) or Zm × Zm. The constructed wavefunctions also set up the framework for future variational Monte Carlo simulations.

show abstract

Fractional Quantum Hall States at Zero Magnetic Field

Cited by 906 publications

References 23 publications

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures

Exotic electronic states in the world of flat bands: From theory to material

Symmetry-protected fractional Chern insulators and fractional topological insulators

Contact Info

Product

Resources

About