New Magnetic Field Dependence of Landau Levels in a Graphenelike Structure

Dietl, Petra; Piéchon, Frédéric; Montambaux, Gilles

doi:10.1103/physrevlett.100.236405

Cited by 249 publications

(308 citation statements)

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“…Within a tight-binding description, an anisotropy in the nearest-neighbor hopping parameters makes the Dirac points move away from the high-symmetry K and K points and, under appropriate conditions, merge at time-reversal invariant points in the first Brillouin zone [4][5][6]. Most saliently, this merging of Dirac points is associated with a topological phase transition between a semimetallic phase and a gapped band-insulating phase.…”

Section: Introductionmentioning

confidence: 99%

Merging and alignment of Dirac points in a shaken honeycomb optical lattice

et al. 2012

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Inspired by the recent creation of the honeycomb optical lattice and the realization of the Mott insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, a Floquet theory may be applied to derive a time-independent Hamiltonian. In this effective description, the hopping parameters are renormalized by a Bessel function, which depends on the shaking direction, amplitude and frequency. Consequently, the hopping parameters can vanish and even change sign, in an anisotropic manner, thus yielding different band structures. Here, we study the merging and the alignment of Dirac points and dimensional crossovers from the two dimensional system to one dimensional chains and zero dimensional dimers. We also consider next-nearest-neighbor hopping, which breaks the particle-hole symmetry and leads to a metallic phase when it becomes dominant over the nearest-neighbor hopping. Furthermore, we include weak repulsive on-site interactions and find the density profiles for different values of the hopping parameters and interactions, both in a homogeneous system and in the presence of a trapping potential. Our results may be experimentally observed by using momentum-resolved Raman spectroscopy.

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Section: Introductionmentioning

confidence: 99%

Merging and alignment of Dirac points in a shaken honeycomb optical lattice

et al. 2012

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“…To obtain the algebraic expression of the Hall conductances, we study effects of anisotropy of the hopping parameters on the honeycomb lattice [10,12,13,14]. For the square lattice, as suggested by Aubry-André duality [15], it is known that none of gaps closes when we change the ratio of the hopping parameters, t x /t y , and this facilitates the calculation of its…”

Section: Introductionmentioning

confidence: 99%

Hall conductance, topological quantum phase transition, and the Diophantine equation on the honeycomb lattice

2008

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We consider a tight-binding model with the nearest neighbour hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote t a , can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice. For weak and strong t a regions, respectively, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak t a region shows the unconventional quantization of the Hall conductance, σ xy = −(e 2 /h)(2n + 1), (n = 0, ±1, ±2, · · · ), near the half-filling, while the strong t a region shows only the conventional one, σ xy = −(e 2 /h)n, (n = 0, 1, 2, · · · ). From topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate t a region are concluded. We also study numerically the quantum phase structure in detail, and find that even when t a = 1, namely in graphene case, the system is in the weak t a phase except when the Fermi energy is located near the van Hove singularity or the lower and upper edges of the spectrum.

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“…Explicit examples are tightbinding models on checkerboard and kagome lattices, respectively [9,13]. Topological quadratic Fermi points also appear in physical systems such as bilayer graphene [14][15][16][17][18][19], photonic crystals [20], oxide heterostructures [21], and surface state of topological insulators [22].…”

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Spontaneous Quantum Hall Effect via a Thermally Induced Quadratic Fermi Point

Chern

Batista

2012

Phys. Rev. Lett.

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Gapless electronic systems containing topologically nontrivial Fermi points are sources of various topological insulators. Whereas most of these special band-crossing points are built in the electronic structure of the non-interacting lattice models, we show that a quadratic Fermi point characterized by a non-zero winding number emerges with a collinear triple-Q spin-density-wave state that arises from a perfectly nested but topologically trivial Fermi surface. We obtain a universal low-energy Hamiltonian for the quadratic Fermi point and show that such collinear orderings are unstable against the onset of scalar spin chirality that opens a gap and induces a spontaneous quantum Hall insulator as the temperature tends to zero.

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New Magnetic Field Dependence of Landau Levels in a Graphenelike Structure

Cited by 249 publications

References 20 publications

Merging and alignment of Dirac points in a shaken honeycomb optical lattice

Merging and alignment of Dirac points in a shaken honeycomb optical lattice

Hall conductance, topological quantum phase transition, and the Diophantine equation on the honeycomb lattice

Spontaneous Quantum Hall Effect via a Thermally Induced Quadratic Fermi Point

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