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arXiv:1511.09388 · 2D Materials

Breaking inversion symmetry in a state-dependent honeycomb lattice: artificial graphene with tunable band gap

M Weinberg, Christina Staarmann, C. Ölschläger, Juliette Simonet, K. Sengstock

Published Apr 21, 2016• 23 citations
arXivHTMLPDF

Abstract

Abstract Here, we present the application of a novel method for controlling the geometry of a state-dependent honeycomb lattice: the energy offset between the two sublattices of the honeycomb structure can be adjusted by rotating the atomic quantization axis. This enables us to continuously tune between a homogeneous graphene-like honeycomb lattice and a triangular lattice and to open an energy gap at the characteristic Dirac points. We probe the symmetry of the lattice with microwave spectroscopy techniques and investigate the behavior of atoms excited to the second energy band. We find a striking influence of the energy gap at the Dirac cones onto the lifetimes of bosonic atoms in the excited band.

DOI
10.1088/2053-1583/3/2/024005

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Abstract Here, we present the application of a novel method for controlling the geometry of a state-dependent honeycomb lattice: the energy offset between the two sublattices of the honeycomb structure can be adjusted by rotating the atomic quantization axis. This enables us to continuously tune between a homogeneous graphene-like honeycomb lattice and a triangular lattice and to open an energy gap at the characteristic Dirac points. We probe the symmetry of the lattice with microwave spectroscopy techniques and investigate the behavior of atoms excited to the second energy band. We find a striking influence of the energy gap at the Dirac cones onto the lifetimes of bosonic atoms in the excited band.
Dirac points lie at the heart of many fascinating 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 particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in an optical lattice, a method which so far has only been applied to explore simple lattice structures. In my talk I will report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice [1]. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking the inversion symmetry of the lattice. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other. 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 where the topology of the band structure plays a crucial role, but also provide the possibility to explore many-body phases resulting from the interplay of complex lattice geometries with interactions.
The band spectrum of bosonic atoms in two-dimensional honeycomb optical lattices with the graphene-type structure has been studied. The dispersion laws in the bands and the one-particle spectral densities are calculated for the normal phase in the random phase approximation. The temperature-dependent gapless spectrum with Dirac points located at the Brillouin zone boundary is obtained for the lattice with energetically equivalent sites, with the corresponding chemical potential lying outside the allowed energy band. Different on-site energies in the sublattices are shown to induce the appearance of a gap in the spectrum, so that the chemical potential can be located between the subbands, which gives rise to a substantial reconstruction of the band spectrum. The frequency dependences of the one-particle spectral density for both sublattices are determined as functions of the chemical potential level, the spectral gap magnitude, and the temperature.
We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphenelike honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various geometries accessible with this lattice setup and present a scheme to control the energy offset with external magnetic fields. The competition of the on-site interaction with the offset energy leads to Mott phases characterized by population imbalances between the sublattices. For the definition of an optimal Hubbard model, we demonstrate a scheme that allows for the efficient computation of Wannier functions. Using a cluster mean-field method, we compute the phase diagrams and provide a universal representation for arbitrary energy offsets. We find good agreement with the experimental data for the superfluid to Mott insulator transition.
We present a new model to realize artificial 2D lattices with cold atoms investigating the atomic artificial graphene: a 2D confined matter wave is scattered by atoms of a second species trapped around the nodes of a honeycomb optical lattice. The system allows an exact determination of the Green function, hence of the transport properties. The inter-species interaction can be tuned via the interplay between scattering length and confinements. Band structure and density of states of a periodic lattice are derived for different values of the interaction strength. Emergence and features of Dirac cones are pointed out, together with the appearance of multiple gaps and a non-dispersive and isolated flat band. Robustness against finite-size and vacancies effects is numerically investigated.
Ultracold gases in optical lattices have proved to be a flexible tool to simulate many different phenomena of solid state physics [1, 2]. Recently, optical lattices with complex geometries have been realized [3, 4, 5, 6, 7], paving the way to simulating more realistic systems. The honeycomb structure has recently become accessible in an optical lattice composed of mutually perpendicular laser beams. This lattice structure exhibits topological features in its band structure – the Dirac points. At these points, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In optical lattices, Bloch oscillations [8] resolved both in time and in quasi-momentum space can be directly observed. We make use of such Bloch-Zener oscillations to probe the vanishing energy gap at the Dirac points as well as their position in the band structure. In small band gap regions, we observe Landau-Zener tunneling [7, 9] to the second band and the regions of maximum transfer can be identified with the position of the Dirac points.
We study the entanglement asymmetry for the space-inversion symmetry of free fermions on a two-dimensional honeycomb lattice with an on-site energy imbalance between the two sublattices. We show that the entanglement asymmetry of a local subsystem exhibits nonanalytic dependence on the energy imbalance, due to the presence of Dirac points in the Brillouin zone. We also study the quench dynamics from the ground state into the inversion-symmetric point at which the energy imbalance vanishes. Under certain conditions on the subsystem geometry, the entanglement asymmetry relaxes to a finite value after the quench, revealing that the inversion-symmetry breaking in the initial ground state can persist even under the symmetric dynamics. We attribute the absence of symmetry restoration to the presence of a flat energy dispersion (flat band) in a specific direction.