Topological Mott Insulators

Raghu, S.; Qi, Xiao-Liang; Honerkamp, Carsten; Zhang, Shou-Cheng

doi:10.1103/physrevlett.100.156401

Cited by 660 publications

(878 citation statements)

References 28 publications

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“…It has been found [84,85] that sufficiently large values of V /t stabilize charge-density-wave phases over semimetallic or Mott insulating phases. Numerical RG calculations [86] have qualitatively confirmed these results but also discovered that second-neighbor repulsions favor topological states with spontaneously broken time-reversal symmetry (i.e. quantum spin Hall phases) over charge-or spin-density waves.…”

Section: Hubbard Correlations and Split Bandsmentioning

confidence: 67%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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Artificial honeycomb lattices offer a tunable platform to study massless Dirac quasiparticles and their topological and correlated phases. Here we review recent progress in the design and fabrication of such synthetic structures focusing on nanopatterning of two-dimensional electron gases in semiconductors, molecule-by-molecule assembly by scanning probe methods, and optical trapping of ultracold atoms in crystals of light. We also discuss photonic crystals with Dirac cone dispersion and topologically protected edge states. We emphasize how the interplay between single-particle band structure engineering and cooperative effects leads to spectacular manifestations in tunneling and optical spectroscopies.

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Section: Hubbard Correlations and Split Bandsmentioning

confidence: 67%

Artificial honeycomb lattices for electrons, atoms and photons

et al. 2013

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“…[4,5,6,7,8,9,10,11,12,13,14,15,17,16]). There, the predominant ordering tendencies are in the particle-hole channel, and usually superconductivity is not among the leading candidates.…”

Section: Undoped and Weakly Doped Graphenementioning

confidence: 99%

“…A large number of exotic states of matter has been proposed theoretically, see e.g. [4,5,6,7,8,9,10,11,12,13,14,15,16,17], but most have not been experimentally observed as of yet. One exception is multi-layer graphene systems where there are now experimental reports of an energy gap opening at low temperatures, which has been ascribed to interactions effects [18,19,20,21,22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Chirald-wave superconductivity in doped graphene

Black‐Schaffer

Honerkamp

2014

J. Phys.: Condens. Matter

172

176

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Abstract. A highly unconventional superconducting state with a spin-singlet d x 2 −y 2 ± id xy -wave, or chiral d-wave, symmetry has recently been proposed to emerge from electron-electron interactions in doped graphene. Especially graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverges, has been argued to likely be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

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“…In the recent literature on interaction driven topological insulators 2,3 , the elusiveness of the QAH state has been ascribed to fluctuations, which typically disfavor the QAH state with respect to a Quantum Spin Hall (QSH) state, which is degenerate with the QAH state on a mean field level. Here we point out that the fluctuations which govern the competition of different gapped phases proposed in bilayer graphene (BLG) [4][5][6] are dominated by the modes not present in the models 2,3 , leaving open the door to formation of a QAH state at zero field in BLG. Also, we will propose a mechanism for inducing the QAH state using external fields.…”

Section: Introductionmentioning

confidence: 99%

Quantum anomalous Hall state in bilayer graphene

2010

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We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean field level. We classify the states in terms of a hidden SU(4) symmetry, and distinguish symmetry protected degeneracies from accidental degeneracies. One of the states, which spontaneously breaks discrete time reversal symmetry but no continuous symmetry, is identified as a Quantum Anomalous Hall (QAH) state, which exhibits quantum Hall effect at zero magnetic field. We investigate the lifting of the accidental degeneracies by thermal and zero point fluctuations, taking account of the modes softened under a renormalisation group procedure (RG). Working in a 'saddle point plus quadratic fluctuations' approximation, we identify two types of RG-soft modes which have competing effects. Zero point fluctuations, dominated by 'transverse' modes which are unique to BLG, favor the QAH state. Thermal fluctuations, dominated by 'longitudinal' modes, favor a SU(4) symmetry breaking multiplet of states. We discuss the phenomenology and experimental signatures of the QAH state in BLG, and also propose a way to induce the QAH state using weak external magnetic fields.

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Topological Mott Insulators

Cited by 660 publications

References 28 publications

Artificial honeycomb lattices for electrons, atoms and photons

Artificial honeycomb lattices for electrons, atoms and photons

Chirald-wave superconductivity in doped graphene

Quantum anomalous Hall state in bilayer graphene

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