Single Dirac cone with a flat band touching on line-centered-square optical lattices

Abstract

Using ultracold atoms trapped in an optical lattice, we form a line-centered-square lattice in the condensedmatter physics, where a crossover from massive to massless Dirac fermion behavior can be easily achieved by tuning the laser intensities. The present Dirac fermions satisfy a three-component quantum equation for pseudospin-1 fermions, resulting in a single Dirac cone in the energy spectrum, a flat band touching at the Dirac point, and a vanishing Berry's phase. Interestingly, the massless Dirac fermions here may exhibit an all-angle Klein tunneling; i.e., the barrier is completely transparent for all incident angles.

Conical intersections for light and matter waves

“…Namely, wave propagation is governed by an integer pseudospin variant of the Dirac equation, which displays unique effects such as resonant all-angle Klein tunnelling through potential barriers [43,44]. In this case, the prototypical example for studying the properties of integer pseudospin intersections has been the square-like "Lieb lattice" shown in Fig.…”

“…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].…”

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

“…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].…”

Generating and moving Dirac points in a two-dimensional deformed honeycomb lattice arrayed by coupled semiconductor quantum dots

“…[8][9][10] Many physical phenomena, from high conductivity of graphene to the conducting edge states in topological insulators, are attributed to the linear energy bands in the vicinity of the Dirac cones. [11][12][13][14][15] As indicted in various studies, the properties of Dirac cone is exquisitely sensitive to the lattice structure. For instance, strain-induced deformation, external potential and undulation of lattice could inevitably lead to variations of Dirac fermions behaviors.…”