Unusual properties of midband states in systems with off-diagonal disorder

Triangle Counting Rule: An Approach to Forecast the Magnetic Properties of Benzenoid Polycyclic Hydrocarbons

Open-shell benzenoid polycyclic hydrocarbons (BPHs) are promising materials for future quantum applications. However, the search for and realization of open-shell BPHs with desired properties is a challenging task due to the gigantic chemical space of BPHs, requiring new strategies for both theoretical understanding and experimental advancement. In this work, by building a structure database of BPHs through graphical enumeration, performing data-driven analysis, and combining tight-binding and mean-field Hubbard calculations, we discovered that the number of the internal vertices of the BPH graphs is closely correlated to their open-shell characters. We further established a simple rule, the triangle counting rule, to predict the magnetic ground states of BPHs. These findings not only provide a database of open-shell BPHs, but also extend the well-known Lieb's theorem and Ovchinnikov's rule and provide a straightforward method for designing open-shell carbon nanostructures. These insights may aid in the exploration of emerging quantum phases and the development of magnetic carbon materials for technology applications.

Linker Redox Mediated Control of Morphology and Properties in Semiconducting Iron-Semiquinoid Coordination Polymers

The emergence of conductive 2D and less commonly 3D coordination polymers (CPs) and metal-organic frameworks (MOFs) promises novel applications in many fields. However, the synthetic parameters for these electronically complex materials are not thoroughly understood. Here we report a new 3D semiconducting CP Fe₅ (C₆ O₆ )₃ , which is a fusion of 2D Fe-semiquinoid materials and 3D cubic Fe_x (C₆ O₆ )_y materials, by using a different initial redox-state of the C₆ O₆ linker. The material displays high electrical conductivity (0.02 S cm^-1 ), broad electronic transitions, promising thermoelectric behavior (S² σ=7.0×10^-9  W m^-1  K^-2 ), and strong antiferromagnetic interactions at room temperature. This material illustrates how controlling the oxidation states of redox-active components in conducting CPs/MOFs can be a "pre-synthetic" strategy to carefully tune material topologies and properties in contrast to more commonly encountered post-synthetic modifications.

Robust non-integer conductance in disordered 2D Dirac semimetals

We study the conductanceGof 2D Dirac semimetal nanowires at the presence of disorder. For an even nanowire lengthLdetermined by the number of unit cells, we find non-integer values forGthat are independent ofLand persist with weak disorder, indicated by the vanishing fluctuations ofG. The effect is created by a combination of the scattering effects at the contacts (interface) between the leads and the nanowire, an energy gap present in the nanowire for evenLand the topological properties of the 2D Dirac semimetals. Unlike conventional materials the reducedGdue to the scattering at the interface, is stabilized at non-integer values inside the nanowire, leading to a topological phase for weak disorder. For strong disorder the system leaves the topological phase and the fluctuations ofGare increased as the system undergoes a transition/crossover toward the Anderson localized (insulating) phase, via a non-standard disordered phase. We study the scaling and the statistics ofGat these phases. In addition we have found that the effect of robust non-integerGdisappears for oddL, which results in integerG, determined by the number of open channels in the nanowire, due to resonant scattering.

Physics in nonfixed spatial dimensions via random networks

We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio to uncover various phenomena, such as unconventional properties of the energy spectrum and persistent localized states (PLS) at various energies, corresponding to quantum phases with zero-dimensional (0D) and one-dimensional (1D) order. For small ratio of edges over vertices in the network R we find properties resembling graphene(honeycomb) lattices, like a similar DOS containing a linear dispersion relation at the band center at energy E=0. In addition, we find PLS at various energies including E=-1,0,1, and others, for example, related to the golden ratio. At E=0 the PLS lie at vertices that are not directly connected with an edge, due to partial bipartite symmetries of the random networks (0D order). At E=-1,1 the PLS lie mostly at pairs of vertices (bonds), while the rest of the PLS at other energies, like the ones related to the golden ratio, lie at lines of vertices of fixed length (1D order), at the spatial boundary of the network, resembling the edge states in confined graphene systems with zigzag edges. As the ratio R is increased the DOS of the network approaches the Wigner semicircle, corresponding to random symmetric matrices(Hamiltonians) and the PLS are reduced and gradually disappear as the connectivity in the network increases. Finally, we calculate the spatial dimension D of the network and its fluctuations. We obtain both integer and noninteger D and a logarithmic dependence on R. In addition, we examine the relation of D and its fluctuations to the electronic properties derived. Our results imply that universal physics can manifest in physical systems irrespectively of their spatial dimension. Relations to emergent spacetime in quantum and emergent gravity approaches are also discussed.

Localization of Dirac Fermions in Finite-Temperature Gauge Theory

It is by now well established that Dirac fermions coupled to non-Abelian gauge theories can undergo an Anderson-type localization transition. This transition affects eigenmodes in the lowest part of the Dirac spectrum, the ones most relevant to the low-energy physics of these models. Here we review several aspects of this phenomenon, mostly using the tools of lattice gauge theory. In particular, we discuss how the transition is related to the finite-temperature transitions leading to the deconfinement of fermions, as well as to the restoration of chiral symmetry that is spontaneously broken at low temperature. Other topics we touch upon are the universality of the transition, and its connection to topological excitations (instantons) of the gauge field and the associated fermionic zero modes. While the main focus is on Quantum Chromodynamics, we also discuss how the localization transition appears in other related models with different fermionic contents (including the quenched approximation), gauge groups, and in different space-time dimensions. Finally, we offer some speculations about the physical relevance of the localization transition in these models.

Exchange Rules for Diradical π-Conjugated Hydrocarbons

A variety of planar π-conjugated hydrocarbons such as heptauthrene, Clar's goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The resulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund's rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open- or closed-shell nature. This is accomplished using a combination of analytical arguments and configuration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb's theorem and Ovchinnikov's rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states.

Parity-Induced Thermalization Gap in Disordered Ring Lattices

The gaps separating two different states widely exist in various physical systems: from the electrons in periodic lattices to the analogs in photonic, phononic, plasmonic systems, and even quasicrystals. Recently, a thermalization gap, an inaccessible range of photon statistics, was proposed for light in disordered structures [Nat. Phys. 11, 930 (2015)NPAHAX1745-247310.1038/nphys3482], which is intrinsically induced by the disorder-immune chiral symmetry and can be reflected by the photon statistics. The lattice topology was further identified as a decisive role in determining the photon statistics when the chiral symmetry is satisfied. Being very distinct from one-dimensional lattices, the photon statistics in ring lattices are dictated by its parity, i.e., odd or even sited. Here, we for the first time experimentally observe a parity-induced thermalization gap in strongly disordered ring photonic structures. In a limited scale, though the light tends to be localized, we are still able to find clear evidence of the parity-dependent disorder-immune chiral symmetry and the resulting thermalization gap by measuring photon statistics, while strong disorder-induced Anderson localization overwhelms such a phenomenon in larger-scale structures. Our results shed new light on the relation among symmetry, disorder, and localization, and may inspire new resources and artificial devices for information processing and quantum control on a photonic chip.

Sticking of atomic hydrogen on graphene

Recent years have witnessed an ever growing interest in the interactions between hydrogen atoms and a graphene sheet. Largely motivated by the possibility of modulating the electric, optical and magnetic properties of graphene, a huge number of studies have appeared recently that added to and enlarged earlier investigations on graphite and other carbon materials. In this review we give a glimpse of the many facets of this adsorption process, as they emerged from these studies. The focus is on those issues that have been addressed in detail, under carefully controlled conditions, with an emphasis on the interplay between the adatom structures, their formation dynamics and the electric, magnetic and chemical properties of the carbon sheet.

Topological Subspace-Induced Bound State in the Continuum

We propose and experimentally realize a new kind of bound states in the continuum (BICs) in a class of systems constructed by coupling multiple identical one-dimensional chains, each with inversion symmetry. In such systems, a specific separation of the Hilbert space into a topological and a nontopological subspace exists. Bulk-boundary correspondence in the topological subspace guarantees the existence of a localized interface state which can lie in the continuum of extended states in the nontopological subspace, forming a BIC. Such a topological BIC is observed experimentally in a system consisting of coupled acoustic resonators.

Strain-Induced Landau Levels in Arbitrary Dimensions with an Exact Spectrum

Certain nonuniform strain applied to graphene flakes has been shown to induce pseudo-Landau levels in the single-particle spectrum, which can be rationalized in terms of a pseudomagnetic field for electrons near the Dirac points. However, this Landau level structure is, in general, approximate and restricted to low energies. Here, we introduce a family of strained bipartite tight-binding models in arbitrary spatial dimension d and analytically prove that their entire spectrum consists of perfectly degenerate pseudo-Landau levels. This construction generalizes the case of triaxial strain on graphene's honeycomb lattice to arbitrary d; in d=3, our model corresponds to tetraxial strain on the diamond lattice. We discuss general aspects of pseudo-Landau levels in arbitrary d.

Geometrical spin manipulation in Dirac flakes

We investigate numerically the spin properties of electrons in flakes made of materials described by the Dirac equation, in the presence of intrinsic spin-orbit coupling (SOC). We show that electrons flowing along the borders of flakes via edge states become helically spin-polarized for strong SOC, for materials with and without a gap at the Fermi energy, corresponding to the massive and massless Dirac equation respectively. The helically spin-polarized electrons create spin-resolved transport, controlled by the flake's geometry in a multi-terminal device setup. A simple analytical model containing the basic ingredients of the problem is introduced to get an insight into the helical mechanism, along with our numerical results which are based on an effective tight-binding model.

Unusual electronic properties of clean and disordered zigzag graphene nanoribbons

We revisit the problem of electron transport in clean and disordered zigzag graphene nanoribbons, and expose numerous hitherto unknown peculiar properties of these systems at zero energy, where both sublattices decouple because of chiral symmetry. For clean ribbons, we give a quantitative description of the unusual power-law dispersion of the central energy bands and of its main consequences, including the strong divergence of the density of states near zero energy, and the vanishing of the transverse localization length of the corresponding edge states. In the presence of off-diagonal disorder, which respects the lattice chiral symmetry, all zero-energy localization properties are found to be anomalous. Recasting the problem in terms of coupled Brownian motions enables us to derive numerous asymptotic results by analytical means. In particular the typical conductance gN of a disordered sample of width N and length L is shown to decay as exp(-CNw√L), for arbitrary values of the disorder strength w, while the relative variance of ln gN approaches a non-trivial constant KN. The dependence of the constants CN and KN on the ribbon width N is predicted. From the mere viewpoint of the transfer-matrix formalism, zigzag ribbons provide a case study with many unusual features. The transfer matrix describing propagation through one unit cell of a clean ribbon is not diagonalizable at zero energy. In the disordered case, we encounter non-trivial random matrix products such that all Lyapunov exponents vanish identically.

Theoretical analysis of oxygen vacancies in layered sodium cobaltate, Na(x)CoO(2-δ)

Sodium cobaltate with high Na content is a promising thermoelectric material. It has recently been reported that oxygen vacancies can alter the material properties, reducing its figure of merit. However, experimental data concerning the oxygen stoichiometry are contradictory. We therefore studied the formation of oxygen vacancies in Na(x)CoO(2) with first principles calculations, focusing on x = 0.75. We show that a very low oxygen vacancy concentration is expected at the temperatures and partial pressures relevant for applications.

A few simple rules governing hydrogenation of graphene dots

We investigated binding of hydrogen atoms to small polycyclic aromatic hydrocarbons (PAHs)--i.e., graphene dots with hydrogen-terminated edges--using density functional theory and correlated wavefunction techniques. We considered a number of PAHs with three to seven hexagonal rings and computed binding energies for most of the symmetry unique sites, along with the minimum energy paths for significant cases. The chosen PAHs are small enough to not present radical character at their edges, yet show a clear preference for adsorption at the edge sites which can be attributed to electronic effects. We show how the results, as obtained at different levels of theory, can be rationalized in detail with the help of a few simple concepts derivable from a tight-binding model of the π electrons.

Adsorptions of hydrogen on graphene and other forms of carbon structures: First principle calculations

Carbon can exist in various structural forms (graphite, graphene, graphene-nanoribbon and flake) and these are technologically very important materials. On the other hand, hydrogen incorporation in these materials can significantly affect their structural and electronic properties. As it is difficult to observe hydrogenation processes directly in experiment and to measure the electronic states at atomic scale, first-principle calculations are widely used to investigate the interaction between hydrogen and various carbon-based structures in past years. In this article, we briefly review work done in recent years, theoretical understanding on the interaction between hydrogen and different forms of carbon materials and present a number of strategies to modify the properties of carbon-based systems.

Bandgap opening in graphene antidot lattices: the missing half

The electronic structure of graphene antidot lattices (GALs) with zigzag hole edges was studied with first-principles calculations. It was revealed that half of the possible GAL patterns were unintentionally missed in the usual construction models used in earlier studies. With the complete models, the bandgap of the GALs was sensitive to the width W of the wall between the neighboring holes. A nonzero bandgap was opened in hexagonal GALs with even W, while the bandgap remained closed in those with odd W. Similar alternating gap opening/closing with W was also demonstrated in rhombohedral GALs. Moreover, analytical solutions of single-walled GALs were derived based on a tight-binding model to determine the location of the Dirac points and the energy dispersion, which confirmed the unique effect in GALs.

Anomalies and Anderson localization: π-coupling of the energy bands

This work shows that delocalization phenomena in single-electron quasi-one-dimensional quantum chains may occur at points different from the center of the energy spectrum (E = 0) and in systems lacking the symmetry [Formula: see text]. It is found that the peaks appearing in the average conductance are controlled by the band structure of the periodic system underlying the disorder. The average conductance is expanded in powers of the disorder strength, allowing the conductance to be redefined as the sum of a regular and an anomalous contribution. The first non-vanishing term of the anomalous part is of the fourth order. The fourth-order term can be calculated for any number of coupled chains in terms of a matrix expression. For strictly one-dimensional systems the expansion is calculated up to the 12th order for both diagonal and real off-diagonal disorder and is compared with the numerical data. It is also found that the anomalous contribution defined here is responsible for an even-odd effect of the average conductance.

Localization-delocalization transition in a two-dimensional quantum percolation model

We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by calculating the transmission coefficient as a function of energy ( -2<E<2 in units of the hopping integral in the tight-binding Hamiltonian) and disorder, q (probability that a given site of the lattice is not available to the particle). Our study based on finite-size scaling suggests the existence of delocalized states that depends on energy and the amount of disorder present in the system. For energies away from the band center (E=0) , delocalized states appear only at low disorder (q<15%) . The transmission near the band center is generally very small for any amount of disorder and therefore makes it difficult to locate the transition to delocalized states if any, but our study does indicate a behavior that is weaker than power-law localization. Apart from this localization-delocalization transition, we also find the existence of two different kinds of localization regimes depending on energy and the amount of disorder. For a given energy, states are exponentially localized for sufficiently high disorder. As the disorder decreases, states first show power-law localization before showing a delocalized behavior.

Density of states in coupled chains with off-diagonal disorder

We compute the density of states rho(varepsilon) in N coupled chains with random hopping. At zero energy, rho(varepsilon) shows a singularity that strongly depends on the parity of N. For odd N, rho(varepsilon) approximately 1/|varepsilonln (3)varepsilon|, with and without time-reversal symmetry. For even N, rho(varepsilon) approximately |lnvarepsilon| in the presence of time-reversal symmetry, while there is a pseudogap, rho(varepsilon) approximately |varepsilonlnvarepsilon|, in the absence of time-reversal symmetry.