Existence of bulk chiral fermions and crystal symmetry

Mañes, Juan L.

doi:10.1103/physrevb.85.155118

Cited by 191 publications

(209 citation statements)

References 42 publications

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“…To reveal the fascinating physical properties of the linear Dirac SM and the triple Dirac SM at the critical point would be another interesting topic for future studies. (16) and (19). (a) For a topological Dirac semimetal with C 4 symmetry, which has n 2D ¼ 1 on the k z ¼ 0 plane.…”

Section: Discussionmentioning

confidence: 99%

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Classification of stable three-dimensional Dirac semimetals with nontrivial topology

2014

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A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant.

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Section: Discussionmentioning

confidence: 99%

“…The stability of the 3D DP in these materials stems from the fact that the system has additional crystalline symmetries other than the time-reversal symmetry (TRS) and inversion symmetry (IS) [15][16][17][18][19][20] . For instance, Young et al 15,16 have proposed that particular space groups allow 3D DPs as symmetry protected degeneracies.…”

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confidence: 99%

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

2014

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“…The key property of the honeycomb lattice, namely to have Dirac points, is also exhibited by the π-flux square lattice [10][11][12], a tight-binding model with only nearestneighbor hoppings on a square lattice in a perpendicular magnetic field having flux π. The structure of Dirac points is unaltered when passing from a two-dimensional square to a three-dimensional cube with π-flux for each plaquette [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

et al. 2013

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We analyze a tight-binding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic non-Abelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken time-reversal symmetry and its role in driving non-trivial topological phase transitions. By varying the spin-orbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.

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“…Graphene is not an immediate candidate for 3D generalizations: stacking up graphene sheets, because of the coupling along the z-direction, Dirac cones are destroyed [50]. The problem of the existence of Dirac points in 3D lattices has been studied [51,52] by analyzing the required symmetries required: from the point of view of ultracold atoms, a set-up with a low number of hopping connections (possibly, only hoppings between nearest neighbours) is required for practical reason. 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].…”

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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Existence of bulk chiral fermions and crystal symmetry

Cited by 191 publications

References 42 publications

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

Classification of stable three-dimensional Dirac semimetals with nontrivial topology

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

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

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