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 [...

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover governed only by the density parameter r s . For r s . r c , the data are consistent with a Wigner molecule description, while, for r s , r c , Fermi liquid behavior is recovered. The crossover value r c ഠ 4 is surprisingly small. [S0031-9007 (99)08929-2] PACS numbers: 73.20.Dx, 71.10.Ay, 71.10.CaQuantum dots can be considered as solid-state artificial atoms with tunable properties. Confining a small number of electrons N in a two-dimensional electron gas in semiconductor heterostructures, a number of interesting effects arising from the interplay between confinement and the Coulomb interaction between the electrons can be observed [1,2]. Since the confinement potential is usually quite shallow, the long-ranged Coulomb interaction among the electrons plays a prominent role, and in contrast to conventional atoms effective single-particle approximations quickly become unreliable. In the low-density (stronginteraction) limit, r s !`, classical considerations suggest a Wigner crystal-like phase with electrons spatially arranged in shells [3]. With quantum fluctuations, such a phase is best described as a Wigner molecule. In contrast, for high densities (weak interactions), r s ! 0, a Fermi liquidlike description is expected to be valid, where it is more appropriate to think of the behavior as resulting from the single-particle orbitals being filled. The noninteracting limit [4] is then typically used as a starting point for the theoretical description of quantum dots.To date, no reliable information exists for the crossover between these two limits. This is mainly due to a complete lack of sufficiently accurate methods that are able to cover the full range of r s , especially when no magnetic field is present. Exact diagonalization techniques are limited to very small particle numbers and small r s ; otherwise, a large error due to the truncation of the Hilbert space arises [5]. Hartree-Fock calculations become increasingly unreliable for large r s and are known to incorrectly favor spin-polarized states [6]. Similarly, density functional calculations [7] introduce uncontrolled approximations in the absence of exact reference data. In principle, the quantum Monte Carlo (QMC) method is the best candidate for producing reliable data for quantum dots. Unfortunately, the notorious fermion sign problem makes direct QMC simulations almost impossible [8]. To avoid the sign problem, the fixed-node approximation and a related variational approach have been employed in Ref. [9], but the results are no longer exact.In this Letter, we adopt a radically different approach to fermion QMC simulations, based on the recently developed multilevel blocking (MLB) algorithm [10,11]. The MLB algorithm is ab...

The transport properties of a quantum dot that is weakly coupled to leads are investigated by using the exact quantum states of a finite number of interacting electrons. It is shown that in addition to the Coulomb blockade, spin selection rules strongly influence the low temperature transport, and lead to experimentally observable effects. Transition probabilities between states that correspond to successive electron numbers vanish if the total spins differ by | ∆S |> 1/2. In non-linear transport, this can lead to negative differential conductances. The linear conductance peaks are suppressed if transitions between successive ground states are forbidden.

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

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We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.PACS numbers: 75.70.Ak

The one-and two-particle densities of up to four interacting electrons with spin, confined within a quasi one-dimensional "quantum dot" are calculated by numerical diagonalization. The transition from a dense homogeneous charge distribution to a dilute localized Wigner-type electron arrangement is investigated. The influence of the long range part of the Coulomb interaction is studied. When the interaction is exponentially cut off the "crystallized" Wigner molecule is destroyed in favor of an inhomogeneous charge distribution similar to a charge density wave .

The spectral properties of up to four interacting electrons confined within a quasi one-dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is investigated as a function of the electron number and of the system length. The limitations of a description in terms of a capacitance are demonstrated. The energetically lowest lying excitations are physically explained as vibrational and tunneling modes. The limits of a dilute, Wigner-type arrangement of the electrons, and a dense, more homogeneous charge distribution are discussed.