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A generalization of the graphene honeycomb model to the case where each site in the honeycomb lattice contains a $n-$fold degenerate set of eigenstates of the $C_3$ symmetry has been recently proposed to describe several systems, including triangulene crystals and photonic lattices. These generalized honeycomb models are defined by $(n_a,n_b)$, the number $C_3$ eigenstates in the $a$ and $b$ sites of the unit cell, resulting in $n_a+n_b$ bands. Thus, the $(1,1)$ case gives the coventional honeycomb model that describes the two low-energy bands in graphene. Generalizations, such as $(2,1)$, $(2,2)$ and $(3,3)$ display several non-trivial features, such as coexisting graphene-like Dirac cones with flat-bands, both at zero and finite-energy, as well as robust degeneracy points where a flat-band and a parabolic band meet at the $\Gamma$-point. Here, we explore the edge states of this class of crystals, using as reference triangulene crystals, and we find several types of edge states absent in the conventional $(1,1)$ honeycomb case, associated to the non-trivial features of the two-dimensional (2D) bands of the high-fold case. First, we find dispersive edge states associated to the finite-energy flat-bands, that occur both at the armchair and zigzag termination. Second, in the case of non-centrosymmetric triangulene crystals that lead to a $S=1$ Dirac band, we have a bonding-antibonding pair of dispersive edge states, localized in the same edge so that their energy splitting is reduced as their localization increases, opposite to the conventional behavior of pairs of states localized in opposite edges. Third, for the $(3,3)$ case, that hosts a gap separating a pair of flat conduction and valence bands, we find non-dispersive edge states with $E=0$ in all edge terminations., Comment: 15 pages, 7 figures

This paper aims at introducing a methodology to compute stable coupled state-space models for dynamic substructuring applications by introducing two novel approaches targeted to accomplish this task: a) a procedure to impose Newtons's second law without relying on the use of undamped RCMs (residual compensation modes) and b) a novel approach to impose stability on unstable coupled state-space models. The enforcement of stability is performed by dividing the unstable model into two different models, one composed by the stable poles (stable model) and the other composed by the unstable ones (unstable model). Then, the poles of the unstable state-space model are forced to be stable, leading to the computation of a stabilized state-space model. Afterwards, to make sure that the Frequency Response Functions (FRFs) of the stabilized model well match the FRFs of the unstable model, the Least-Squares Frequency Domain (LSFD) method is exploited to update the modal parameters of the stabilized model composed by the pairs of complex conjugate poles. The validity of the proposed methodologies is presented and discussed by exploiting experimental data. Indeed, by exploiting the FRFs of a real system, accurate state-space models respecting Newton's second law are computed. Then, decoupling and coupling operations are performed with the identified state-space models, no matter the models resultant from the decoupling/coupling operations are unstable. Stability is then imposed on the computed unstable coupled model by following the approach proposed in this paper. The methodology proved to work well on these data. Moreover, the paper also shows that the coupled state-space models obtained using this methodology are suitable to be exploited in time-domain analyses and simulations.

Square-root topology describes models whose topological properties can be revealed upon squaring the Hamiltonian, which produces their respective parent topological insulators. This concept has recently been generalized to $2^n$-root topology, characterizing models where $n$ squaring operations must be applied to the Hamiltonian in order to arrive at the topological source of the model. In this paper, we analyze the Hofstadter regime of quasi-one-dimensional (quasi-1D) and two-dimensional (2D) $2^n$-root models, the latter of which has the square lattice (SL) (known for the Hofstadter Butterfly) as the source model. We show that upon increasing the root-degree of the model, there appear multiple magnetic flux insensitive flat bands, and analytically determine corresponding eigenstates. These can be recast as compact localized states (CLSs) occupying a finite region of the lattice. For a finite flux, these CLSs correspond to different harmonics contained within the same Aharonov-Bohm (AB) cage. Furthermore, as the root-degree increases, a kaleidoscope of butterflies is seen to appear in the Hofstadter diagram, with each butterfly constituting a topologically equivalent replica of the original one of the SL. As such, the index $n$, which uniquely identifies the root-degree of the model, can be seen as an additional fractal dimension of the $2^n$-root model present in its Hofstadter diagram. We discuss how these dynamics could be realized in experiments with ultracold atoms, and measured by Bragg spectroscopy or through observing dynamics of initially localized atoms in a quantum gas microscope., Comment: 19 pages, 14 figures

Molecular hydrogen was pressurized in a diamond anvil cell at temperatures between 5 and 83 K. At a sufficiently high pressure, estimated to be between 477 to 491 GPa, hydrogen became metallic, determined by its reflectance in the near infrared and fit to a Drude free-electron model. We then studied the predicted metastability of metallic hydrogen. At a temperature of 5 K the load on the metallic hydrogen was stepwise reduced until the pressure was zero. While turning the load or pressure down, the sample evidently transformed to the molecular phase and escaped; the sample hole closed. We estimate this pressure to be 113 to 84 GPa. Metallic hydrogen was not observed to be metastable at zero pressure., Comment: 8 pages, 4 figures plus SI

Hermitian bipartite models are characterized by the presence of chiral symmetry and by Lieb's theorem, which derives the number of zero-energy flat bands of the model from the imbalance of sites between its two sublattices. Here, we introduce a class of non-Hermitian models with an arbitrary number of sublattices connected in a unidirectional and cyclical way and show that the number of zero-energy flat bands of these models can be found from a generalized version of Lieb's theorem, in what regards its application to noninteracting tight-binding models, involving the imbalance between each sublattice and the sublattice of lowest dimension. Furthermore, these models are also shown to obey a generalized chiral symmetry, of the type found in the context of certain clock or parafermionic systems. The main results are illustrated with a simple toy model, and possible realizations in different platforms of the models introduced here are discussed., Comment: 13 pages, 7 figures

In this paper, we show that the introduction of long-range hoppings in 1D topological insulator models implies that different possibilities of site indexing must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended SSH chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of "influence" of different chiral symmetries. Furthermore, edge states become a linear combination of edge-like states with different localization lengths and reflect the gradual transition between these different chiral symmetries., Comment: 12 pages, 6 figures

Recently, we have introduced in [A. M. Marques et al., Phys. Rev. B 103, 235425 (2021)] the concept of $2^n$-root topology and applied it to one-dimensional systems. These models require $n$ squaring operations to their Hamiltonians, intercalated with different constant energy downshifts at each level, in order to arrive at a decoupled block corresponding to a known topological insulator (TI) that acts as the source of the topological features of the starting $2^n$-root TI ($\sqrt[2^n]{\text{TI}}$). In the process, $n$ non-topological residual models with degenerate spectra and in-gap impurity states appear, which dilute the topologically protected component of the starting edge states. Here, we generalize this method to several two-dimensional models, by finding the 4-root version of lattices hosting weak and higher-order boundary modes (both topological and non-topological) of a Chern insulator and of a topological semimetal. We further show that a starting model with a non-Hermitian region in parameter space and a complex energy spectrum can nevertheless display a purely real spectrum for all its successive squared versions, allowing for an exact mapping between certain non-Hermitian models and their Hermitian lower root-degree counterparts. A comment is made on the possible realization of these models in artificial lattices., Comment: 21 pages, 14 figures

Square-root topology is a recently emerged subfield describing a class of insulators and superconductors whose topological nature is only revealed upon squaring their Hamiltonians, i.e., the finite energy edge states of the starting square-root model inherit their topological features from the zero-energy edge states of a known topological insulator/superconductor present in the squared model. Focusing on one-dimensional models, we show how this concept can be generalized to $2^n$-root topological insulators and superconductors, with $n$ any positive integer, whose rules of construction are systematized here. Borrowing from graph theory, we introduce the concept of arborescence of $2^n$-root topological insulators/superconductors which connects the Hamiltonian of the starting model for any $n$, through a series of squaring operations followed by constant energy shifts, to the Hamiltonian of the known topological insulator/superconductor, identified as the source of its topological features. Our work paves the way for an extension of $2^n$-root topology to higher-dimensional systems., Comment: 19 pages, 15 figures

We address a particular set of extended Su-Schrieffer-Heeger models with $2n$ sites in the unit cell [SSH($2n$)], that we designate by Sine-Cosine models [SC$(n)$], with hopping terms defined as a sequence of $n$ sine-cosine pairs of the form $\{\sin(\theta_j),\cos(\theta_j)\}$, $j=1, \cdots,n$. These models, when squared, generate a block-diagonal matrix representation with one of the blocks corresponding to a chain with uniform local potentials. We further focus our study on the subset of SC$(2^{n-1})$ chains that, when squared an arbitrary number of times (up to $n$), always generate a block which is again a Sine-Cosine model, if an energy shift is applied and if the energy unit is renormalized. We show that these $n$-times squarable models [SSC$(n)$] and their band structure are uniquely determined by the sequence of energy unit renormalizations and by the energy shifts associated to each step of the squaring process. Chiral symmetry is present in all Sine-Cosine chains and edge states levels at the respective central gaps are protected by it. Zero-energy edge states in a SSC$(j)$ chain (with $j

To understand the most-recent experiment on room-temperature superconductivity in carbonaceous sulfur hydride (CSH) systems under high pressure, we have performed extensive stoichiometry and structure searches of ternary CSH compounds using generic evolutionary algorithms. Judged from the formation enthalpy of different CSH compounds, our studies conclude that certain levels of carbon doping (~5%-6%) in sulfur hydride (H$_3$S) in its R3m and phases gives rise to the most-stable structure (second to the H$_3$S itself) among the various CSH systems found. The replacement of a small amount of sulfur atoms by carbon in compounds like C$_1$S$_{15}$H$_{48}$ and C$_1$S$_{17}$H$_{54}$ results in a stronger electron-phonon coupling and a higher averaged phonon frequency that increases with pressure, thereby leading to room-temperature superconductivity at ~270 GPa. The calculated superconducting transition temperature T$_c$ of C$_1$S$_{15}$H$_{48}$ and C$_1$S$_{17}$H$_{54}$ as a function of pressure shows reasonably good agreement with experimental measurements. Before transition to superconducting states at ~80 GPa, the CSH system is predicted to have a stoichiometry of C$_2$S$_2$H$_{10}$ with a stable structure of P1 symmetry, which is supported by the direct comparison of its Raman spectrum with experiment., Comment: 23 pages with 8 figures (with Supplementary Material)

In flat-band systems, destructive interference leads to the localization of non-interacting particles and forbids their motion through the lattice. However, in the presence of interactions the overlap between neighbouring single-particle localized eigenstates may enable the propagation of bound pairs of particles. In this work, we show how these interaction-induced hoppings can be tuned to obtain a variety of two-body topological states. In particular, we consider two interacting bosons loaded into the orbital angular momentum $l=1$ states of a diamond-chain lattice, wherein an effective $\pi$ flux may yield a completely flat single-particle energy landscape. In the weakly-interacting limit, we derive effective single-particle models for the two-boson quasiparticles which provide an intuitive picture of how the topological states arise. By means of exact diagonalization calculations, we benchmark these states and we show that they are also present for strong interactions and away from the strict flat-band limit. Furthermore, we identify a set of doubly localized two-boson flat-band states that give rise to a special instance of Aharonov-Bohm cages for arbitrary interactions.

Adding interactions to many-body Hamiltonians of geometrically frustrated lattices often leads to diminished subspaces of localized states. In this paper, we show how to construct interacting many-body Hamiltonians, starting from the non-interacting tight-binding Hamiltonians, that preserve or even expand these subspaces. The methods presented involve modifications in the one-body network representation of the many-body Hamiltonians which generate new interacting terms in these Hamiltonians. The subspace of many-particle localized states can be preserved in the interacting Hamiltonian, by projecting the interacting terms onto the subspace of many-body extended states or by constructing the interacting Hamiltonian applying origami rules to the network. Expanded subspaces of localized states are found if interacting terms that mix subspaces with different number of particles are introduced. Furthermore, we present numerical methods for the determination of many-body localized states that allows one to address larger clusters and larger number of particles than those accessible by full diagonalization of the interacting Hamiltonian. These methods rely on the generalization of the concept of compact localized state in the network. Finally, we suggest a method to determine localized states that use a considerable fraction of the network.

In this paper, we discuss the characteristic features of one-dimensional topological insulators with inversion symmetry but noncentered inversion axis in the unit cell, for any choice of the unit cell. In these systems, the global inversion operation generates a k-dependent inversion operator within the unit cell and this implies a nonquantized Zak's phase both for the trivial and nontrivial topological phases. By relating the Zak's phase with the eigenvalues of modified parity operators at the inversion invariant momenta, a corrected quantized form of the Zak's phase is derived. We show that finite energy topological edge states of this family of chains are symmetry protected not by usual chiral symmetry but by a hidden sublattice chiral-like symmetry. A simple justification is presented for shifts in the polarization quantization relation for any choice of endings of these chains., Comment: 7 pages, 2 figures

A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both for integer and non-integer number of unit cells. The solutions are ultimately found to be dependent on the behavior of phase factors whose compact formulas, provided here, make this method simple to implement computationally. The derivation employs the properties of the Hamiltonians of these models, all of which can be written as Hermitian block-tridiagonal Toeplitz matrices. The concept of energy spectrum is generalized to incorporate both bulk and edge bands, where the latter are a function of a complex momentum. The method is then extended to solve the case where one of these chains is coupled at one end to an arbitrary cluster/impurity. Future developments based on these results are discussed., Comment: 18 pages, 10 figures, 2 tables

We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the tunneling amplitudes that allow to describe the system in terms of two decoupled lattice models. Each of these models displays one-dimensional edge states and zero-dimensional corner states that are correlated with the topological properties of the bulk. We show that the topologically non-trivial regime can be explored in a wide range of experimentally feasible values of the parameters of the physical system. Furthermore, we propose an alternative way to characterize the second-order topological corner states based on the computation of the Zak's phases of the bands of first-order edge states.

Chemical abundances for 15 elements (C, N, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, Fe, and Ni) are presented for 83 stellar members of the 4 Gyr old solar-metallicity open cluster M67. The sample contains stars spanning a wide range of evolutionary phases, from G dwarfs to red clump stars. The abundances were derived from near-IR ($\lambda$1.5 -- 1.7$\mu$m) high-resolution spectra ($R$ = 22,500) from the SDSS-IV/APOGEE survey. A 1-D LTE abundance analysis was carried out using the APOGEE synthetic spectral libraries, via chi-square minimization of the synthetic and observed spectra with the qASPCAP code. We found significant abundance differences ($\sim$0.05 -- 0.30 dex) between the M67 member stars as a function of the stellar mass (or position on the HR diagram), where the abundance patterns exhibit a general depletion (in [X/H]) in stars at the main-sequence turnoff. The amount of the depletion is different for different elements. We find that atomic diffusion models provide, in general, good agreement with the abundance trends for most chemical species, supporting recent studies indicating that measurable atomic diffusion operates in M67 stars., Comment: Accepted to ApJ

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 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 $\pi$ 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.

We study two-particle states in a Su-Shrieffer-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., Comment: 12 pages, 8 figures, 1 table

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since July 2014. This paper describes the second data release from this phase, and the fourteenth from SDSS overall (making this, Data Release Fourteen or DR14). This release makes public data taken by SDSS-IV in its first two years of operation (July 2014-2016). Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS); the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data driven machine learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS website (www.sdss.org) has been updated for this release, and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020, and will be followed by SDSS-V., Comment: SDSS-IV collaboration alphabetical author data release paper. DR14 happened on 31st July 2017. 19 pages, 5 figures. Accepted by ApJS on 28th Nov 2017 (this is the "post-print" and "post-proofs" version; minor corrections only from v1, and most of errors found in proofs corrected)

We show how the presence of inversion symmetry in a one-dimensional (1D) lattice model is not a sufficient condition for a quantized Zak's phase. This is only the case when the inversion axis is at the center of the unit cell. When the inversion axis is not at the center, the modified inversion operator within the unit cell gains a k-dependence in some of its matrix elements which adds a correction term to the usual Zak's phase expression1, making it in general deviate from its quantized value. A general expression that recovers a quantized Zak's phase in a lattice model with a unit cell of arbitrary size and arbitrarily positioned inversion axis is provided in this paper, which relates the quantized value with the eigenvalues of a modified parity operator at the inversion invariant momenta., Comment: 4 pages, 2 figures, 2 tables

Open Clusters have long been used to study the chemo-dynamical evolution of the Galactic disk. This requires an homogeneously analysed sample covering a wide range of ages and distances. In this aper we present the OCCASO second data release. This comprises a sample of high-resolution ($R>65,000$) and high signal-to-noise spectra of 115 Red Clump stars in 18 Open Clusters. We derive atmospheric parameters ($T_{\mathrm{eff}}$, $\log g$, $\xi$), and [Fe/H] abundances using two analysis techniques: equivalent widths and spectral synthesis. A detailed comparison and a critical review of the results of the two methods are made. Both methods are carefully tested between them, with the \emph{Gaia} FGK Benchmark stars, and with an extensive sample of literature values. We perform a membership study using radial velocities and the resulting abundances. Finally, we compare our results with a chemo-dynamical model of the Milky Way thin disk concluding that the oldest Open Clusters are consistent with the models only when dynamical effects are taken into account., Comment: 19 pages, 11 figures MNRAS accepted for publication

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratio in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially-resolved spectroscopy for thousands of nearby galaxies (median redshift of z = 0.03). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between redshifts z = 0.6 and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGN and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5-meter Sloan Foundation Telescope at Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5-meter du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in July 2016., Comment: Published in Astronomical Journal

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 topological edge states in the equivalent chain can be readily identifed, as well as their correspondence to the original two-hole states. 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)., Comment: 7 pages, 4 figures

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) began observations in July 2014. It pursues three core programs: APOGEE-2, MaNGA, and eBOSS. In addition, eBOSS contains two major subprograms: TDSS and SPIDERS. This paper describes the first data release from SDSS-IV, Data Release 13 (DR13), which contains new data, reanalysis of existing data sets and, like all SDSS data releases, is inclusive of previously released data. DR13 makes publicly available 1390 spatially resolved integral field unit observations of nearby galaxies from MaNGA, the first data released from this survey. It includes new observations from eBOSS, completing SEQUELS. In addition to targeting galaxies and quasars, SEQUELS also targeted variability-selected objects from TDSS and X-ray selected objects from SPIDERS. DR13 includes new reductions of the SDSS-III BOSS data, improving the spectrophotometric calibration and redshift classification. DR13 releases new reductions of the APOGEE-1 data from SDSS-III, with abundances of elements not previously included and improved stellar parameters for dwarf stars and cooler stars. For the SDSS imaging data, DR13 provides new, more robust and precise photometric calibrations. Several value-added catalogs are being released in tandem with DR13, in particular target catalogs relevant for eBOSS, TDSS, and SPIDERS, and an updated red-clump catalog for APOGEE. This paper describes the location and format of the data now publicly available, as well as providing references to the important technical papers that describe the targeting, observing, and data reduction. The SDSS website, http://www.sdss.org, provides links to the data, tutorials and examples of data access, and extensive documentation of the reduction and analysis procedures. DR13 is the first of a scheduled set that will contain new data and analyses from the planned ~6-year operations of SDSS-IV., Comment: Full information on DR13 available at http://www.sdss.org. Comments welcome to spokesperson@sdss.org. To be published in ApJS

We present a numerical study of quasi-1D frustrated Josephson junction ladders with diagonal couplings and open boundary conditions, in the large capacitance limit. We derive a correspondence between the energy of this Josephson junction ladder and the expectation value of the Hamiltonian of an analogous tight-binding model, and show how the overall superconducting state of the chain is equivalent to the minimum energy state of the tight-binding model in the subspace of one-particle states with uniform density. To satisfy the constraint of uniform density, the superconducting state of the ladder is written as a linear combination of the allowed k-states of the tight-binding model with open boundaries. Above a critical value of the parameter t (ratio between the intra-rung and inter-rung Josephson couplings), the ladder spontaneously develop currents at the edges which spread to the bulk as t is increased until complete coverage is reached. Above a certain value of t, which varies with ladder size (t = 1 for an infinite-sized ladder), the edge currents are destroyed. The value t = 1 corresponds, in the tight-binding model, to the opening of a gap between two bands. We argue that the disappearance of the edge currents with this gap opening is not coincidental, and that this points to a topological origin for these edge current states., Comment: 11 pages, 6 figures

We study the slow time evolution of localized states of the open-boundary Lieb lattice when a magnetic flux is applied perpendicularly to the lattice and increased linearly in time. In this system, Dirac cones periodically disappear, reappear and touch the flat band as the flux increases. We show that the slow time evolution of a localized state in this system is analogous to that of a zero-energy state in a three-level system whose energy levels intersect periodically and that this evolution can be mapped into a classical precession motion with a precession axis that rotates as times evolves. Beginning with a localized state of the Lieb lattice, as the magnetic flux is increased linearly and slowly, the evolving state precesses around a state with a small itinerant component and the amplitude of its localized component oscillates around a constant value (below but close to 1), except at multiples of the flux quantum where it may vary sharply. This behavior reflects the existence of an electric field (generated by the time-dependent magnetic field) which breaks the C4 symmetry of the constant flux Hamiltonian., Comment: 7 pages, 2 figures