Massless Dirac fermions in a square optical lattice

Hou, Jing-Min; Yang, Wen-Xing; Liu, Xiong-Jun

doi:10.1103/physreva.79.043621

Cited by 63 publications

(79 citation statements)

References 54 publications

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“…A relatively simple alternative is offered by the use of gauge potentials: it is indeed possible to show that a square lattice with a constant magnetic field having a π-flux (half of the elementary flux) on each plaquette has an single-particle energy spectrum displaying Dirac points [53]. This observation has been translated in proposals to realize massless (2 + 1) Dirac fermions using external gauge proposals, including ultracold fermions on a square lattice coupled with properly chosen Rabi fields [54], interacting bosons in a 2D lattice produced by a bichromatic light-shift potential with an additional effective magnetic field [55] and bosons with internal energy levels in a tripod configuration [56].…”

Section: Introductionmentioning

confidence: 99%

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Mazzucchi

Lepori

Trombettoni

2013

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, t z ) these Dirac points are unaltered: it is then possible to study the 3D-2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and at half filling there is a quantum phase transition occurring at a critical (negative) interaction U c presenting a linear critical exponent for the gap as a function of |U − U c |. We show that in three dimensions this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of t z .

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Section: Introductionmentioning

confidence: 99%

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Mazzucchi

Lepori

Trombettoni

2013

J. Phys. B: At. Mol. Opt. Phys.

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“…(1), we conclude that robust Dirac-like features in the magnetic miniband spectrum have a systematic appearance. To mention, a Diraclike band has been found in the Hofstadter spectrum of a tight-binding model on a square lattice with flux φ = 1 2 φ 0 per unit cell [15,16]. We also analyzed different realizations of hexagonal moiré superlattices described by Eq.…”

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confidence: 99%

Dirac edges of fractal magnetic minibands in graphene with hexagonal moiré superlattices

et al. 2014

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We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields B p/q = p q φ0/S providing rational magnetic flux through a unit cell of the moiré superlattice created by a hexagonal substrate for electrons in graphene. The Diractype features in the minibands at B = B p/q determine a hierarchy of gaps in the surrounding fractal spectrum, and show that these minibands have topological insulator properties. Using the additional q-fold degeneracy of magnetic minibands at B p/q , we trace the hierarchy of the gaps to their manifestation in the form of incompressible states upon variation of the carrier density and magnetic field.PACS numbers: 73.22.Pr, 73.21.Cd, The fractal spectrum of electron waves in crystals subjected to a strong magnetic field [1, 2] is a fundamental result in the quantum theory of solids [3]. In particular, the bandstructure of electrons on a two-dimensional (2D) lattice is fractured into multiple bands which occur at the values B p q = p q φ 0 /S of the field providing a rational fraction of magnetic flux quantum φ 0 = h/e per unit cell area S [1, 3]. Its image [4], obtained for a square lattice hopping model, known as the Hofstadter butterfly, has stimulated numerous attempts to observe the fractal spectrum of electrons via quantum transport measurements. Since the sparsity of the spectrum increases for larger values of the denominator q in p q (hence smaller gaps), the observation of fractal magnetic bands in real crystals would require unsustainably strong magnetic fields. Hence, early efforts were focused on 2D electrons in periodically patterned GaAs/AlGaAS heterostructures [5], where the superimposed superlattice period was made large enough to obtain low denominator fractions within the experimentally available steady magnetic field range. The more recent observation of moiré superlattices, both for twisted bilayer graphene [6] and graphene residing on substrates with hexagonal facets [7], has shown an alternative way to create a long-range periodic potential for electrons: by making lattice-aligned graphene heterostructures using a hexagonal crystal with an almost commensurate period. For this, hexagonal boron nitride (hBN, with the lattice constant of l hBN = 2.50Å vs l = 2.46Å in graphene) provides a perfect match. Several observations of moiré superlattice effects in graphene-hBN heterostructures have already been reported [8][9][10].In this article, we study magnetic minibands caused by a moiré superlattice in graphene. When the surface layer of the substrate is inversion symmetric, the zeromagnetic-field spectra displays clear secondary Dirac points at the first miniband edge [11][12][13]. We find that generations of massive Dirac electrons systematically reappear at the edges of magnetic minibands at2 ), unit cell area S = √ 3 2 a 2 ) and effective perturbations for electrons in graphene on an hexagonal substrate [θ = 0, and V + = 0.063vb,q , and the surrounding fractal spectrum groups around q-fold degenerate Landau le...

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“…Notably, the 2D atomic Dirac fermions and the related topological phase transition [18][19][20][21][22][23] have been experimentally observed by several groups [24][25][26]. The system can be characterized by the winding number defined by [27] …”

Section: Modelmentioning

confidence: 99%

Dynamics of Weyl quasiparticles in an optical lattice

Wang

Zhang

et al. 2016

Phys. Rev. A

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We investigate the dynamics of the Weyl quasiparticles emerged in an optical lattice where the topological Weyl semimental and trivial band insulator phases can be adjusted with the on-site energy. The evolution of the density distribution is demonstrated to have an anomalous velocity in Weyl semimental but a steady Zitterbewegung effect in the band insulator. Our analysis demonstrates that the chirality of the system can be directly determined from the positions of the atomic center-of-mass. Furthermore, the amplitude and the period of the relativistic Zitterbewegung oscillations are shown to be observable with the time-of-flight experiments.

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Massless Dirac fermions in a square optical lattice

Cited by 63 publications

References 54 publications

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Dirac edges of fractal magnetic minibands in graphene with hexagonal moiré superlattices

Dynamics of Weyl quasiparticles in an optical lattice

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