We propose an experimental setup for the observation of quasi-relativistic massless Fermions. It is based on a T3 optical lattice, realized by three pairs of counter-propagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the T3 Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudo-spin S = 1. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.In the past decade, ultra cold atoms have emerged as a fascinating new area linking quantum optics with solid state physics [1]. Essentially, these are the only quantum many-body systems for which the particle interaction is both rather precisely known and controllable. In particular, cold atoms confined in optical lattices (OLs) [2] often present systems with crystalline structure in various spatial dimensions d = 1, 2, 3 described by textbook models from solid state physics with tunable parameters. This implements Feynman's pioneering idea of quantum simulations using one physical system to investigate another one [3]. A celebrated example [4] is the optical realization of the Mott transition, a well-known phenomenon in solid state physics, describing the transition from a metal to an insulator with increasing interaction strength. Furthermore, the possibility to realize an effective magnetic field by rotation of cold atoms in OLs [5] has opened up prospects of studying other fundamental phenomena in a controlled manner such as the fractional quantum Hall effect in d = 2 [6].The recent preparation of single layers of graphene [7] has attracted considerable attention, since this solid state system displays quasi-relativistic motion of electrons on a two-dimensional honeycomb lattice (HCL). However, e.g. due to disorder or impurities, many properties of real graphene cannot fully be accounted for by the idealized Dirac-Weyl Hamiltonian. In this Letter we present a detailed study of the T 3 lattice [8] and show that cold fermionic atoms in such an OL indeed behave as quasi-relativistic massless Dirac-Weyl Fermions. Yet, the T 3 lattice replaces the pseudo-spin S = 1/2 of Dirac-Weyl particles in the HCL by the larger value S = 1. As one of its crucial features, the T 3 lattice exhibits nodes with unequal connectivity. The corresponding class of twodimensional lattices, specifically bipartite lattices, has * Electronic address: dario.bercioux@frias.uni-freiburg.de been studied extensively in the past, with a particular focus on topological localization [8,9], frustration in a magnetic field [10,11], and effects of spin-orbit coupling [12]. The T 3 lattice, illustrated in Fig. 1a, has a unit cell with three different lattice sites, one six-fold coordinated site H, called hub, and two three-fold coordinated sites A and B, called rims. All nearest-neighbor pairs are formed by a rim and a hub. The energy spectrum [...

We investigate the properties of the Lieb lattice, i.e a face-centered square lattice, subjected to external gauge fields. We show that an Abelian gauge field leads to a peculiar quantum Hall effect, which is a consequence of the single Dirac cone and the flat band characterizing the energy spectrum. Then we explore the effects of an intrinsic spin-orbit term -a non-Abelian gauge fieldand demonstrate the occurrence of the quantum spin Hall effect in this model. Besides, we obtain the relativistic Hamiltonian describing the Lieb lattice at low energy and derive the Landau levels in the presence of external Abelian and non-Abelian gauge fields. Finally, we describe concrete schemes for realizing these gauge fields with cold fermionic atoms trapped in an optical Lieb lattice. In particular, we provide a very efficient method to reproduce the intrinsic (Kane-Mele) spin-orbit term with assisted-tunneling schemes. Consequently, our model could be implemented in order to produce a variety of topological states with cold-atoms.

We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by a Dirac-like Hamiltonian associated with a pseudospin one. The enlarged pseudospin S = 1 (instead of S = 1/2 as for graphene) leads to an enhanced "super" Klein tunneling through rectangular electrostatic barriers. Our results are confirmed via numerical investigation of the tight-binding model of the lattice. For a uniform magnetic field, we discuss the Landau levels and we investigate the transparency of a rectangular magnetic barrier. We show that the latter can mainly be described by semiclassical orbits bending the particle trajectories, qualitatively similar as it is the case for graphene. This makes it possible to confine particles with magnetic barriers of sufficient width

Quantum simulators are an essential tool for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices led the field so far, but electronic quantum simulators are proving to be equally relevant. Simulating topological states of matter is one of the holy grails in the field. Here, we experimentally realize a higher-order electronic topological insulator (HOTI). Specifically, we create a dimerized Kagome lattice by manipulating carbon-monoxide (CO) molecules on a Cu(111) surface using a scanning tunneling microscope (STM). We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, while it is absent in the trivial one. Contrarily to conventional topological insulators (TIs), the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our