Topological phases for fermionic cold atoms on the Lieb lattice

Goldman, Nathan; Urban, Daniel F.; Bercioux, Dario

doi:10.1103/physreva.83.063601

Cited by 227 publications

(209 citation statements)

References 90 publications

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“…Indeed, one can check that, while the E = 0 component is longitudinally polarized, the other two are transverse, just like the propagating components of a photon. Pseudospin-one Dirac points have been reported in some two [29][30][31] and three-dimensional 32 systems.…”

Section: A Tight-binding Examplementioning

confidence: 99%

Existence of bulk chiral fermions and crystal symmetry

2012

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We consider the existence of bulk chiral fermions around points of symmetry in the Brillouin zone of nonmagnetic 3D crystals with negligible spin-orbit interactions. We use group theory to show that this is possible, but only for a reduced number of space groups and points of symmetry that we tabulate. Moreover, we show that for a handful of space groups the existence of bulk chiral fermions is not only possible but unavoidable, irrespective of the concrete crystal structure. Thus our tables can be used to look for bulk chiral fermions in a specific class of systems, namely that of nonmagnetic 3D crystals with sufficiently weak spin-orbit coupling. We also discuss the effects of spin-orbit interactions and possible extensions of our approach to Weyl semimetals, crystals with magnetic order, and systems with Dirac points with pseudospin 1 and 3/2. A simple tight-binding model is used to illustrate some of the issues.

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Section: A Tight-binding Examplementioning

confidence: 99%

Existence of bulk chiral fermions and crystal symmetry

2012

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“…In this case, the prototypical example for studying the properties of integer pseudospin intersections has been the square-like "Lieb lattice" shown in Fig. 1(c), originally proposed for cold atoms [43,[45][46][47] and recently realized as a photonic lattice [48][49][50][51][52].…”

Section: Designmentioning

confidence: 99%

Conical intersections for light and matter waves

Leykam

Desyatnikov

2016

Advances in Physics: X

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We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective Dirac equation, with electron spin replaced by a "fermionic" half-integer pseudospin. However, in many systems such as metamaterials, modal symmetries result in the formation of higher order conical intersections with integer or "bosonic" pseudospin. The ability to engineer lattices with these qualitatively different singular dispersion relations opens up many applications, including superior slab lasers, generation of orbital angular momentum, zeroindex metamaterials, and quantum simulation of exotic phases of relativistic matter.

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“…In particular, successful creations of twodimensional (2D) optical lattices with singular DOSs, the Kagome [6] and Lieb (line-centered-square) [7] lattices, have activated theoretical studies on phenomena related to the FBS [8][9][10][11][12][13][14][15][16][17][18][19]. In general, in these 2D lattices, the Mermin-Wagner theorem states that no phase transitions occur at finite temperatures [20].…”

Section: Introductionmentioning

confidence: 99%

Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities

Noda

Yamashita

2015

Phys. Rev. A

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We describe the enhanced magnetic transition temperatures Tc of two-component fermions in three-dimensional layered Lieb lattices, which are created in cold atom experiments. We determine the phase diagram at half-filling using the dynamical mean-field theory. The dominant mechanism of enhanced Tc gradually changes from the (delta-functional) flat-band to the (logarithmic) Van Hove singularity as the interlayer hopping increases. We elucidate that the interaction induces an effective flat-band singularity from a dispersive flat (or narrow) band. We offer a general analytical framework for investigating the singularity effects, where a singularity is treated as one parameter in the density of states. This framework provides a unified description of the singularity-induced phase transitions, such as magnetism and superconductivity, where the weight of the singularity characterizes physical quantities. This treatment of the flat-band provides the transition temperature and magnetization as a universal form (i.e., including the Lambert function). We also elucidate a specific feature of the magnetic crossover in magnetization at finite temperatures.

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Topological phases for fermionic cold atoms on the Lieb lattice

Cited by 227 publications

References 90 publications

Existence of bulk chiral fermions and crystal symmetry

Existence of bulk chiral fermions and crystal symmetry

Conical intersections for light and matter waves

Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities

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