Topological Graphene plasmons in a plasmonic realization of the Su-Schrieffer-Heeger Model

Graphene hybrids, made of thin insulators, graphene, and metals can support propagating acoustic plasmons (AGPs). The metal screening modifies the dispersion relation of usual graphene plasmons leading to slowly propagating plasmons, with record confinement of electromagnetic radiation. Here, we show that a graphene monolayer, covered by a thin dielectric material and an array of metallic nanorods, can be used as a robust platform to emulate the Su-Schrieffer-Heeger model. We calculate the Zak's phase of the different plasmonic bands to characterize their topology. The system shows bulk-edge correspondence: strongly localized interface states are generated in the domain walls separating arrays in different topological phases. We find signatures of the nontrivial phase which can directly be probed by far-field mid-IR radiation, hence allowing a direct experimental confirmation of graphene topological plasmons. The robust field enhancement, highly localized nature of the interface states, and their gate-tuned frequencies expand the capabilities of AGP-based devices.T.G.R. acknowledges funding from Fundacao para a Ciência e a Tecnologia and Instituto de Telecomunicacoes. grant number UID/50008/2020.in the framework of the project Sym-Break and Mario G. Silveirinha for useful discussions. Y.V.B., N.M.R.P. and F.H.L.K. acknowledge support from the European Commission through the project "Graphene-Driven Revolutions in ICT and Beyond" (ref. no. 881603, CORE 3). Y.V.B. and N.M.R.P. acknowledge COMPETE 2020, PORTUGAL 2020, FEDER, and the Portuguese Foundation for Science and Technology (FCT) through project POCI-010145-FEDER-028114. F.H.L.K. acknowledges financial support from the Government of Catalonia through the SGR grant, the Spanish Ministry of Economy and Competitiveness, through the "Severo Ochoa" Programme for Centres of Excellence in RD (SEV-2015-0522), Fundacio Cellex Barcelona, Generalitat de Catalunya through the CERCA program, the Mineco grants Ramon y Cajal (RYC-201212281), Plan Nacional (FIS2013-47161-P and FIS2014-59639JIN), and the Agency for Management of University and Research Grants (AGAUR) 2017 SGR 1656. This work was supported by the ERC TOPONANOP under grant agreement n 726001 and the MINECO Plan Nacional Grant 2DNANOTOP under reference no FIS2016-81044-P

KITE : high-performance accurate modelling of electronic structure and response functions of large molecules, disordered crystals and heterostructures

We present KITE, a general purpose open-source tight-binding software for accurate real-space simulations of electronic structure and quantum transport properties of large-scale molecular and condensed systems with tens of billions of atomic orbitals (N ∼ 10^10). KITE’s core is written in C++, with a versatile Python-based interface, and is fully optimized for shared memory multi-node CPU architectures, thus scalable, efficient and fast. At the core of KITE is a seamless spectral expansion of lattice Green’s functions, which enables large-scale calculations of generic target functions with uniform convergence and fine control over energy resolution. Several functionalities are demonstrated, ranging from simulations of local density of states and photo-emission spectroscopy of disordered materials to large-scale computations of optical conductivity tensors and real-space wave-packet propagation in the presence of magneto-static fields and spin–orbit coupling. On-the-fly calculations of real-space Green’s functions are carried out with an efficient domain decomposition technique, allowing KITE to achieve nearly ideal linear scaling in its multi-threading performance. Crystalline defects and disorder, including vacancies, adsorbates and charged impurity centres, can be easily set up with KITE’s intuitive interface, paving the way to user-friendly large-scale quantum simulations of equilibrium and non-equilibrium properties of molecules, disordered crystals and heterostructures subject to a variety of perturbations and external conditions

Topological photonic Tamm states and the Su-Schrieffer-Heeger model

In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional (1D) photonic crystal and a metal. We show that when the system is topologically nontrivial there is a single Tamm state in each of the band gaps, whereas if it is topologically trivial the band gaps host no Tamm states. We connect the disappearance of the Tamm states with a topological transition from a topologically nontrivial system to a topologically trivial one. This topological transition is driven by the modification of the dielectric functions in the unit cell. Our interpretation is further supported by an exact mapping between the solutions of Maxwell's equations and the existence of a tight-binding representation of those solutions. We show that the tight-binding representation of the 1D photonic crystal, based on Maxwell's equations, corresponds to a Su-Schrieffer-Heeger-type model (SSH model) for each set of pairs of bands. By expanding this representation near the band edge we show that the system can be described by a Dirac-like Hamiltonian. It allows one to characterize the topology associated with the solution of Maxwell's equations via the winding number. In addition, for the infinite system, we provide an analytical expression for the photonic bands from which the band gaps can be computed.N.M.R.P., M.I.V., and Y.V.B. acknowledge support from the European Commission through the project GrapheneDriven Revolutions in ICT and Beyond (Ref. No. 785219) and the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Financing UID/FIS/04650/2019. N.M.R.P., T.G.R., and Y.V.B. acknowledge COMPETE2020, PORTUGAL2020, FEDER, and the Portuguese Foundation for Science and Technology (FCT) through Project No. POCI-01-0145-FEDER-028114. The authors acknowledge Andre Chaves for suggesting the starting point of the analytical approach to the photonic bands. N.M.R.P. acknowledges stimulating discussions with Joaquin Fernandez-Rossier on the topic of the paper. J.C.G.H. acknowledges the hospitality of the physics department of SDU, Denmark, where this work was completed. The authors are thankful to Asger Mortensen and Mario Silveirinha for their careful and critical reading of the manuscript

Magnetic effects in sulfur-decorated graphene

The interaction between two different materials can present novel phenomena that are quite different from the physical properties observed when each material stands alone. Strong electronic correlations, such as magnetism and superconductivity, can be produced as the result of enhanced Coulomb interactions between electrons. Two-dimensional materials are powerful candidates to search for the novel phenomena because of the easiness of arranging them and modifying their properties accordingly. In this work, we report magnetic effects of graphene, a prototypical non-magnetic two-dimensional semi-metal, in the proximity with sulfur, a diamagnetic insulator. In contrast to the well-defined metallic behaviour of clean graphene, an energy gap develops at the Fermi energy for the graphene/sulfur compound with decreasing temperature. This is accompanied by a steep increase of the resistance, a sign change of the slope in the magneto-resistance between high and low fields, and magnetic hysteresis. A possible origin of the observed electronic and magnetic responses is discussed in terms of the onset of low-temperature magnetic ordering. These results provide intriguing insights on the search for novel quantum phases in graphene-based compounds.Comment: 6 pages and 5 figure

Entanglement in the One-dimensional Kondo Necklace Model

We discuss the thermal and magnetic entanglement in the one-dimensional Kondo necklace model. Firstly, we show how the entanglement naturally present at zero temperature is distributed among pairs of spins according to the strength of the two couplings of the chain, namely, the Kondo exchange interaction and the hopping energy. The effect of the temperature and the presence of an external magnetic field is then investigated, being discussed the adjustment of these variables in order to control the entanglement available in the system. In particular, it is indicated the existence of a critical magnetic field above which the entanglement undergoes a sharp variation, leading the ground state to a completely unentangled phase.Comment: 8 pages, 13 EPS figures. v2: four references adde

Arene oxidation with malonoyl peroxides

Malonoyl peroxide 7, prepared in a single step from the commercially available diacid, is an effective reagent for the oxidation of aromatics. Reaction of an arene with peroxide 7 at room temperature leads to the corresponding protected phenol which can be unmasked by aminolysis. An ionic mechanism consistent with the experimental findings and supported by isotopic labeling, Hammett analysis, EPR investigations and reactivity profile studies is proposed

Entanglement entropy in aperiodic singlet phases

We study the average entanglement entropy of blocks of contiguous spins in aperiodic XXZ chains which possess an aperiodic singlet phase at least in a certain limit of the coupling ratios. In this phase, where the ground state constructed by a real space renormalization group method, consists (asymptotically) of independent singlet pairs, the average entanglement entropy is found to be a piecewise linear function of the block size. The enveloping curve of this function is growing logarithmically with the block size, with an effective central charge in front of the logarithm which is characteristic for the underlying aperiodic sequence. The aperiodic sequence producing the largest effective central charge is identified, and the latter is found to exceed the central charge of the corresponding homogeneous model. For marginal aperiodic modulations, numerical investigations performed for the XX model show a logarithmic dependence, as well, with an effective central charge varying continuously with the coupling ratio.Comment: 18 pages, 9 figure

Quantum Impurity Entanglement

Entanglement in J_1-J_2, S=1/2 quantum spin chains with an impurity is studied using analytic methods as well as large scale numerical density matrix renormalization group methods. The entanglement is investigated in terms of the von Neumann entropy, S=-Tr rho_A log rho_A, for a sub-system A of size r of the chain. The impurity contribution to the uniform part of the entanglement entropy, S_{imp}, is defined and analyzed in detail in both the gapless, J_2 <= J_2^c, as well as the dimerized phase, J_2>J_2^c, of the model. This quantum impurity model is in the universality class of the single channel Kondo model and it is shown that in a quite universal way the presence of the impurity in the gapless phase, J_2 <= J_2^c, gives rise to a large length scale, xi_K, associated with the screening of the impurity, the size of the Kondo screening cloud. The universality of Kondo physics then implies scaling of the form S_{imp}(r/xi_K,r/R) for a system of size R. Numerical results are presented clearly demonstrating this scaling. At the critical point, J_2^c, an analytic Fermi liquid picture is developed and analytic results are obtained both at T=0 and T>0. In the dimerized phase an appealing picure of the entanglement is developed in terms of a thin soliton (TS) ansatz and the notions of impurity valence bonds (IVB) and single particle entanglement (SPE) are introduced. The TS-ansatz permits a variational calculation of the complete entanglement in the dimerized phase that appears to be exact in the thermodynamic limit at the Majumdar-Ghosh point, J_2=J_1/2, and surprisingly precise even close to the critical point J_2^c. In appendices the relation between the finite temperature entanglement entropy, S(T), and the thermal entropy, S_{th}(T), is discussed and and calculated at the MG-point using the TS-ansatz.Comment: 62 pages, 27 figures, JSTAT macro

X-boson cumulant approach to the periodic Anderson model

The Periodic Anderson Model (PAM) can be studied in the infinite U limit by employing the Hubbard X operators to project out the unwanted states. We have already studied this problem employing the cumulant expansion with the hybridization as perturbation, but the probability conservation of the local states (completeness) is not usually satisfied when partial expansions like the Chain Approximation (CHA) are employed. Here we treat the problem by a technique inspired in the mean field approximation of Coleman's slave-bosons method, and we obtain a description that avoids the unwanted phase transition that appears in the mean-field slave-boson method both when the chemical potential is greater than the localized level Ef at low temperatures (T) and for all parameters at intermediate T.Comment: Submited to Physical Review B 14 pages, 17 eps figures inserted in the tex

Evidence for Quark-Hadron Duality in the Proton Spin Asymmetry A1A_1

Spin-dependent lepton-nucleon scattering data have been used to investigate the validity of the concept of quark-hadron duality for the spin asymmetry $A_1$. Longitudinally polarised positrons were scattered off a longitudinally polarised hydrogen target for values of $Q^2$ between 1.2 and 12 GeV$^2$ and values of $W^2$ between 1 and 4 GeV$^2$. The average double-spin asymmetry in the nucleon resonance region is found to agree with that measured in deep-inelastic scattering at the same values of the Bjorken scaling variable $x$. This finding implies that the description of $A_1$ in terms of quark degrees of freedom is valid also in the nucleon resonance region for values of $Q^2$ above 1.6 GeV$^2$.Comment: 5 pages, 1 eps figure, table added, new references added, in print in Phys. Rev. Let