Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Abstract

Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material determines the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a critical limit, the two Dirac points merge and annihilate each other-a situation that has recently attracted considerable theoretical interest but that is extremely challenging to observe in solids. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials in which the topology of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.

Topological states in a ladder-like optical lattice containing ultracold atoms in higher orbital bands

“…We now consider a single species of fermions occupying these orbitals, with the low-lying s orbital of leg B completely filled. Alternatively fermions can be directly loaded into the p x orbital of leg B, leaving the low-lying s empty, by techniques developed in recent experiments 4,6,10 . With these techniques, long-lived meta-stable states of atoms in high orbitals with life time on the order of several hundred milliseconds are demonstrated achievable 6 .…”

“…In the context of ultracold quantum gases, optical lattices engineered with interfering laser beams can realize specific configurations of potentials of single or multiple periods not found in nature. For instance, doublewell superlattices 1,2 have matured into a powerful tool for manipulating orbital degrees of freedom [3][4][5][6][7][8][9][10] . Controls of atoms in the s and p orbitals of the checkerboard 6 and hexagonal 8 optical lattices have also been demonstrated, and correlation between these orbitals tends to give exotic quantum states 6,8,[11][12][13] .…”

Artificial honeycomb lattices for electrons, atoms and photons

“…The authors of Ref. [22] have carried out pioneering work on cold ( 40 K) Fermi gases in honeycomb optical lattices. They have created, moved, and merged Dirac points in a tunable honeycomb lattice.…”

“…The laser configuration is based on three retro-reflected beams, which by control of the detuning δ, create a checkerboard, a triangular, a honeycomb lattice, or a lattice of weakly coupled 1D chains. These fermionic optical lattice techniques [22] were recently contrasted [67] with complementary methods for assembling electron lattices in molecular graphene [19].…”

“…Current methods of design and synthesis include i) nanopatterning of ultra-high-mobility 2D electron gases (EGs) [13][14][15][16][17][18], ii) molecule-by-molecule assembly on metal surfaces by scanning probe methods [19], iii) trapping ultracold fermionic and bosonic atoms in honeycomb optical lattices [20][21][22], and iv) confining photons in honeycomb photonic crystals [23][24][25][26]. Figure 1 summarizes these four different approaches and the relevant tunable parameters.…”