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

We have designed a planar microbattery that allows in situ electrical transport measurement during electrochemical charge and discharge in micron-sized individual crystallites of 2D-layered nanosheets, as well as optical studies (transmittance, Raman spectroscopy), which can give information about the electronic structure of the active material. To demonstrate the utility of our microbattery platform, we study the lithiation of MoS 2 crystallites. We observe that the electrical conductivity of the 2D MoS 2 crystallites is highly dependent on thickness and the rate of lithiation in the fi rst cycle. We use in situ TEM to confi rm that upon rapid fi rst-cycle lithiation the formation of a Mo conductive network imbedded in the Li 2 S matrix leads to an enhanced electrical conductivity compared to the pristine MoS 2 . We applied the results in Li-MoS 2 coin cells with composite electrodes, demonstrating that batteries with fast lithiation on the fi rst cycle showed signifi cantly higher specifi c capacity than batteries lithiated slowly. The microbattery platform can be generally applied to other energy storage materials and a wide range of characterization techniques, and is thus a powerful tool to uncover the properties of nanoscale materials undergoing electrochemical modifi cation. As in the example demonstrated here, we expect this platform will lead to new insights into the operation of battery materials at the nanoscale, leading to new strategies in improving the cell performance.A schematic crystal structure of 2H-MoS 2 is illustrated in Figure 1 a, with the lattice parameters a = 3.16 Å and c = 12.29 Å. Our microbattery platform developed for the in situ measurement of the optical transmittance and electrical transport of 2D nanomaterials is illustrated in Figure 1 b. A MoS 2 crystal and lithium metal are deposited on top of the Cu transport electrodes and current collector, respectively. The MoS 2 fl ake can be charged/discharged by connecting transport electrodes and current collector to an electrochemical workstation. Coupling the microbattery with a transmission optical microscope/probe station, we can then carry out in situ optical transmittance and electrical transport measurements on the same MoS 2 crystal. Optical images of uniform-thickness mechanically exfoliated MoS 2 crystals are shown in Figure 1 c,d, with dimensions as large as 100 µm × 100 µm. We used atomic force microscopy (AFM) to determine the morphology and thickness of exfoliated MoS 2 , in Figure 1 e,f. A photograph of the complete microbattery device is shown in Figure 1 g. The region of the transport electrodes is expanded in Figure 1 h, showing a large uniform area of MoS 2 crystal spanning the electrodes.To understand the intrinsic resistance change during lithiation, an in situ electrical transport measurement was carried out using our microbattery setup. Figure 2 a shows the simultaneously measured resistance and electrochemical potential at a small constant lithiation current at 0.5 µA for a single MoS 2 crystal of thickness 35 n...

We analyze the effect of electron-phonon coupling on the full counting statistics of a molecular junction beyond the lowest order perturbation theory. Our approach allows to take into account analytically the feedback between the non-equilibrium phonon and electronic distributions in the quantum regime. We show that for junctions with high transmission and relatively weak electron-phonon coupling this feedback gives rise to increasingly higher nonlinearities in the voltage dependence of the cumulants of the transmitted charges distribution. PACS numbers: 73.63.Rt, 72.70.+m Single molecule junctions and atomic chains suspended between metallic electrodes constitute a fascinating playground to explore the interplay between electronic and vibronic degrees of freedom, see e.g. Refs. [1][2][3][4][5]. The interest is now not only restricted to the understanding of the mean current-voltage characteristics but has been extended to noise properties 6 and, more generally, to the full counting statistics (FCS) of the transmitted charges. 7,8 An intense theoretical activity has been focussed on the analysis of the simplest model consisting in a resonant level coupled to a single phonon mode in the quantum coherent regime. 7-11 So far, however, several aspects of this problem remain to be clarified. A serious limitation of existing transport theories is that they do not take into account the influence of the non-equilibrium phonon fluctuations in the statistics of the transmitted electrons, namely the feedback of the phonon dynamics on the current-noise properties. 12 This limitation is associated with the breakdown of perturbation theory beyond the lowest order in electron-phonon (e-ph) coupling as reported in Refs. [13]. These works, which demonstrate the necessity of including non-perturbative effects in the analysis, are, however, limited to equilibrium properties of bulk materials or to individual molecules in the sequential tunneling regime.In this work we demonstrate, by a partial resummation of the perturbative expansion, the great impact of the feedback of the phonon dynamics on the quantum transport properties through nanoscale junctions with high transmission and relatively weak e-ph coupling. The actual signatures of phonon fluctuations result from the interplay of several energy scales, i.e. the tunneling rate Γ of electrons, the e-ph coupling λ, the phonon frequency ω 0 and the relaxation rate ∝ η of the local phonon mode due to the coupling with bulk phonons. Depending on the specific sample considered and the efficiency of the relaxation mechanism for the phonon population, one might obtain a regime characterized by a thermal phonon population when η ≫ λ 2 ω 0 /Γ 2 (equilibrated phonons) or a regime where a strong non-equilibrium population is generated when η ≪ λ 2 ω 0 /Γ 2 (unequilibrated phonons). We analyze the crossover between the two regimes and demonstrate that in the regime of unequilibrated phonons the electronic current-noise shows a strong nonlinear behavior as a function of the applied voltage ...