We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of l = 1 Orbital Angular Momentum (OAM) states of an optical lattice with a diamond chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net π flux through the plaquettes and give rise to a topologically non-trivial band structure and protected edge states. In addition, we demonstrate that quantum interferences between the different tunneling processes involved in the dynamics may lead to Aharanov-Bohm caging in the system. All these analytical results are confirmed by exact diagonalization numerical calculations. arXiv:1807.07533v1 [physics.atom-ph]

We show that a clean multiband superconductor may display one or several phase transitions with increasing temperature from or to frustrated configurations of the relative phases of the superconducting order parameters. These transitions may occur when more than two bands are involved in the formation of the superconducting phase and when the number of repulsive interband interactions is odd. These transitions are signalled by slope changes in the temperature dependence of the superconducting gaps. PACS numbers: 74.25.Dw,74.25.Bt The possibility of multiple bands contributing to the formation of a superconducting phase has been considered in the case of transition metals [1-3], superconducting copper oxides [4] and magnesium diboride [5][6][7]. More recently, sign-reversed two-band superconductivity has been proposed for the iron-based layered pnictides [8,9]. In the two-band case, the relative phase of the superconducting gap functions associated to each band is determined by the sign of the interband interaction, being zero (π) for attractive (repulsive) interband coupling. However, if more than two electronic bands have to be considered in the study of the superconducting phase, the relative phases are not uniquely defined by the signs of the interband interactions and in particular, frustration may occur if the number of repulsive interband interactions is odd.There is a close analogy between such frustrated multiband superconductors and the well studied problem of frustrated Josephson junction arrays since the interband pairing may be regarded as an interband Josephson tunnelling [10]. For example, it is known that a squared Josephson junction array with a π magnetic flux per plaquette is frustrated with a degenerate ground state. The effect of the π magnetic flux is the change of the sign of the Josephson coupling from positive to negative, i. e., a π-junction [11]. Such π-junctions are also present without magnetic flux as a consequence of d-wave pairing symmetry. In the case of a frustrated (odd number) loop of π-junctions, a spontaneous current will be present.Studies of frustrated Josephson junction arrays assume usually symmetric junctions. The case of multiband superconductivity is more closely analogous to the case of an array of asymmetric Josephson junctions [12]. When temperature is increased, strong modifications of the ratios of the interband Josephson tunnelling rates may occur due to the relative changes of the superconducting gaps which are known to happen in multiband superconductors [3]. We show in this manuscript that this may lead to one or two phase transitions with increasing temperature from or to frustrated configurations of the relative phases of the superconducting order parameters (which correspond to degenerate ground states which are chirally different). In very recent works, the ground state of a three-band superconductor with repulsive interband interactions has been studied using a phenomenological Ginzburg -Landau approach [13] and a simplified BCS gap equation system wher...

We show that bosonic atoms loaded into orbital angular momentum l = 1 states of a lattice in a diamond-chain geometry provides a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states, and the relative phases arising naturally in the tunnelling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realised and observed in ongoing experiments.

We address the effect of nearest-neighbor (NN) interactions on the topological properties of the Su-Schrieffer-Heeger (SSH) chain, with alternating hopping amplitudes t1 and t2. Both numerically and analytically, we show that the presence of interactions induces phase transitions between topologically different regimes. In the particular case of one-hole excitations in a half-filled SSH chain, the V /t2 vs. t1/t2 phase diagram has topological phases at diagonal regions of the phase plane. The interaction acts in this case as a passivation potential. For general filling of the SSH chain, different eigensubspaces of the SSH Hamiltonian may be classified as topologically trivial and non-trivial. The two-hole case is studied in detail in the large interaction limit, and we show that a mapping can be constructed of the two-hole SSH eigensubspaces into one-particle states of a non-interacting one-dimensional (1D) tight-binding model, with interfaces between regions with different hopping constants and local potentials. The presence of edge states of topological origin in the equivalent chain can be readily identified, as well as their correspondence to the original two-hole states. Of these states only some, identified by us, are protected and, therefore, truly topological. Furthermore, we found that the presence of the NN interaction generates a state where two holes occupy two consecutive edge states. Such many-body states should also occur for arbitrary filling leading to the possibility of a macroscopic hole gathering at the surface (at consecutive edge states).

We study two-particle states in a Su-Schrieffer-Heeger (SSH) chain with periodic boundary conditions and nearest-neighbor (NN) interactions. The system is mapped into a problem of a single particle in a two-dimensional (2D) SSH lattice with potential walls along specific edges. The 2D SSH model has a trivial Chern number but a non-trivial Zak's phase, the one-dimensional (1D) topological invariant, along specific directions of the lattice, which allow for the presence of topological edge states. Using center-of-mass and relative coordinates, we calculate the energy spectrum of these two-body states for strong interactions and find that, aside from the expected appearance of doublon bands, two extra in-gap bands are present. These are identified as bands of topological states localized at the edges of the internal coordinate, the relative distance between the two particles. As such, the topological states reported here are intrinsically many-body in what concerns their real space manifestation, having no counterpart in single-particle states derived from effective models. Finally, we compare the effect of Hubbard interactions with that of NN interactions to show how the presence of the topological bound states is specific to the latter case.