arXiv subjects

Anuradha Jagannathan

Publications and source records attributed to Anuradha Jagannathan.

At least 19 recordsLinked to original sources

arXiv2026

Metallic mean quasicrystals and their topological invariants

Topological invariants govern many important physical properties in condensed matter systems. In this work, we obtain the complete set of topological invariants for a family of one-dimensional quasicrystals. The first and best-studied member of the family is the Fibonacci chain, while the successive ones are known in the literature as silver, bronze... and collectively as the metallic mean chains. By considering rational approximants, and by making use of the relationship between these chains and two dimensional Quantum Hall problems, we write down a gap labeling scheme for finite systems, and extend it to the quasiperiodic limit. We show, by numerical computations on open chains, that the proposed scheme correctly yields the winding numbers of edge states in each of the gaps, in all of the quasicrystals. We observe that their relationship to the 2D model leads, in the strict 1D chains family, to spectra forming a simplified Hofstadter ``butterfly" diagram, with the analogues of Landau levels appearing in the asymptotic limit.

cond-mat.str-el↗

arXiv2026

Topological connections between the 2D Quantum Hall problem and the 1D quasicrystal

1D quasicrystals such as the Fibonacci chain have been said to ``inherit" their topological properties from the 2D Quantum Hall problem. Yet, a direct way to see the connection was lacking until a common ancestor, the Fibonacci-Hall model, was introduced recently \cite{aj2025}. This 2D ancestor model relates the role of the external magnetic flux in the Hall problem and that of a geometric flux which describes the winding of the quasicrystal in 2D, in the cut-and-project method. Doing this enables us to extend the notion of Chern numbers as defined in 2D, to the energy bands of the 1D chain by adiabatic continuity. The older notion of gap labels in the 1D system are now seen to be derivable from the Chern numbers of the 2D bands. The Fibonacci-Hall model thus provides an important link between physics of two paradigmatic models, the Fibonacci quasicrystal and the quantum Hall insulator. The generalization to other 1D quasiperiodic models is expected to be relatively straightforward. The extension to 2D cut-and-project tilings is left for future studies.

cond-mat.mes-hall↗

arXiv2026

Ground states of a family of frustrated spin models for quasicrystals and their approximants

Many new families of quasicrystal-forming magnetic alloys have been synthesized and studied in recent years. For small changes of composition, the alloys can go from quasiperiodic to periodic (approximant crystals) while conserving most of the local atomic environments. Experiments show that many of the periodic approximants order at low temperatures, with clear signatures of ferromagnetic or antiferromagnetic transitions, and also in some cases undergo non-equilibrium spin glass transitions. In contrast, the quasicrystals are mostly found to be spin glasses. Systematically studying these alloys could help elucidate the role played by quasiperiodicity in (de)stabilizing long range magnetic order. In this work, we study cluster spin models with the aim of understanding the mechanisms behind various types of long range magnetic ordering in approximants and quasicrystals. These models embody key features of real systems, and to some extent are analytically tractable, both for periodic and quasiperiodic cases. For the quasicrystal, we describe two novel magnetic phases with quasiperiodic ordering. Our results should serve to motivate further studies with detailed numerical explorations of this family of models.

cond-mat.str-el↗

arXiv2025

Missing link between the 2D Quantum Hall problem and 1D quasicrystals

This paper discusses a connection between two important classes of materials, namely quasicrystals and topological insulators as exemplified by the Quantum Hall problem. It has been remarked that the quasicrystal ``inherits" topological properties from the 2D Quantum Hall model. We show this explicitly by introducing the Fibonacci-Hall model as a link between a 1D quasicrystal and the magnetic problems. We show here how Chern numbers for bands in periodic approximants of quasicrystals can be computed, along with gap labels. The Chern numbers are thus seen as a consequence of a flux parameter $ϕ^S$ induced by the geometry of winding in 2D space of the quasicrystal. We show the existence of lines of Lifshitz transitions in the phase space of the model. These are marked by change of Chern number and disappearance of edge states. The proposed extrapolation method can be generalized to higher dimensional 2D and 3D quasicrystals, where higher order Chern numbers could be computed, and related to experimentally measurable transport quantities.

cond-mat.str-el↗

arXiv2025

Entropic selection of magnetization in a frustrated 2D magnetic model

We discuss the magnetic ground state and properties of a frustrated two-dimensional classical Heisenberg model of interacting hexagonal clusters of spins. The energy of the ground states is found exactly for arbitrary values of $J_1$ (intra-cluster couplings) and $J_2$ (inter-cluster couplings). Our main results concern a frustrated region of the phase diagram, where we show that the set of ground states has a degeneracy larger than that due to global rotation symmetry. Furthermore, the ground state manifold does not have a fixed total magnetization~: there is a range of allowed values. At finite temperature, our Monte-Carlo simulations show that the entropy selects the most probable value of the total magnetization, while the histogram of the Monte-Carlo time series is non-trivial. This model is a first step towards modelling properties of a class of frustrated magnetic structures composed of coupled spin clusters.

cond-mat.stat-mech↗

arXiv2024

Superconductivity in the Fibonacci Chain

Superconductivity was recently reported in several quasicrystalline systems. These are materials which are structurally ordered, but since they are not translationally invariant, the usual BCS theory does not apply. At the present time, the underlying mechanism and the properties of the superconducting phase are insufficiently understood. To gain a better understanding of quasiperiodic superconductors, we consider the attractive Hubbard model on the Fibonacci chain, and examine its low-temperature superconducting phase in detail using the Bogoliubov-de Gennes mean-field approach. We obtain superconducting solutions as a function of the parameters controlling the physical properties of the system: the strength of the Hubbard attraction $U$, the chemical potential $μ$, and the strength of the modulation of the Fibonacci Hamiltonian, $w$. We find that there is a bulk transition at a critical temperature that obeys a power law in $U$. The local superconducting order parameter is self-similar both in real and perpendicular space. The local densities of states vary from site to site, however, the width of the superconducting gap is the same on all sites. The interplay between the Hubbard attraction and the intrinsic gaps of the Fibonacci chain results in a complex zero-temperature $μ$-$U$ phase diagram with insulating domes surrounded by superconducting regions. Finally, we show that tuning $w$ from weak to strong quasicrystalline modulation gives rise to qualitatively different thermodynamic behaviors as could be observed by measuring the specific heat.

cond-mat.supr-con↗

arXiv2024

Properties of the Ammann-Beenker tiling and its square approximants

Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of particular importance -- in their own right, but also for information regarding properties of three dimensional systems. We provide here a users manual for those wishing to construct and study physical properties of the 8-fold Ammann-Beenker quasicrystal, a good starting point for investigations of two dimensional quasiperiodic systems. This tiling has a relatively straightforward construction. Thus, geometrical properties such as the type and number of local environments can be readily found by simple analytical computations. Transformations of sites under discrete scale changes -- called inflations and deflations -- are easier to establish compared to the celebrated Penrose tiling, for example. We have aimed to describe the methodology with a minimum of technicalities but in sufficient detail so as to enable non-specialists to generate quasiperiodic tilings and periodic approximants, with or without disorder. The discussion of properties includes some relations not previously published, and examples with figures.

cond-mat.str-el↗

arXiv2023

Supercurrent Distribution in Real-Space and Anomalous Paramagnetic Response in a Superconducting Quasicrystal

We theoretically study the real-space distribution of the supercurrent that flows under a uniform vector potential in a two-dimensional quasiperiodic structure. This is done by considering the attractive Hubbard model on the quasiperiodic Ammann-Beenker structure and studying the superconducting phase within the Bogoliubov-de Gennes mean-field theory. Decomposing the local supercurrent into the paramagnetic and diamagnetic components, we numerically investigate their dependencies on average electron density, temperature, and the angle of the applied vector potential. We find that the diamagnetic current locally violates the current conservation law, necessitating compensation from the paramagnetic current, even at zero temperature. The paramagnetic current shows exotic behaviors in the quasiperiodic structure, such as local currents which are oriented transversally or reversely to that of the applied vector potential.

cond-mat.supr-con↗

arXiv2023

Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal

The single electron spectrum and wavefunctions in quasicrystals continue to be a fascinating problem, with few known solutions, especially in two and higher dimensions. This paper investigates the energy spectra and gap structures in tight-binding models on a quasiperiodic tiling in two dimensions. By varying a continuous parameter, we follow the evolution of the band structure from the discrete molecular or atomic states, to the multifractal states well-known from previous studies. We propose a scheme for labeling gaps in finite approximants. It is equivalent in the limit of infinite systems to the one presented by Kellendonk and Putnam based on the algebraic structure of this quasiperiodic system.

cond-mat.str-el↗

arXiv2023

Electronic states of a disordered 2D quasiperiodic tiling: from critical states to Anderson localization

We consider critical eigenstates in a two dimensional quasicrystal and their evolution as a function of disorder. By exact diagonalization of finite size systems we show that the evolution of properties of a typical wave-function is non-monotonic. That is, disorder leads to states delocalizing, until a certain crossover disorder strength is attained, after which they start to localize. Although this non-monotonic behavior is only present in finite-size systems and vanishes in the thermodynamic limit, the crossover disorder strength decreases logarithmically slowly with system size, and is quite large even for very large approximants. The non-monotonic evolution of spatial properties of eigenstates can be observed in the anomalous dimensions of the wave-function amplitudes, in their multifractal spectra, and in their dynamical properties. We compute the two-point correlation functions of wave-function amplitudes and show that these follow power laws in distance and energy, consistent with the idea that wave-functions retain their multifractal structure on a scale which depends on disorder strength. Dynamical properties are studied as a function of disorder. We find that the diffusion exponents do not reflect the non-monotonic wave-function evolution. Instead, they are essentially independent of disorder until disorder increases beyond the crossover value, after which they decrease rapidly, until the strong localization regime is reached. The differences between our results and earlier studies on geometrically disordered ``phason-flip'' models lead us to propose that the two models are in different universality classes. We conclude by discussing some implications of our results for transport and a proposal for a Mott hopping mechanism between power law localized wave-functions, in moderately disordered quasicrystals.

cond-mat.dis-nn↗

arXiv2022

Edge and corner superconductivity in a 2D topological model

We consider a two-dimensional generalization of the Su-Schrieffer-Heeger model which is known to possess a non-trivial topological band structure. For this model, which is characterized by a single parameter, the hopping ratio $0 \leq r\leq 1$, the inhomogeneous superconducting phases induced by an attractive $U$ Hubbard interaction are studied using mean field theory. We show, analytically and by numerical diagonalization, that in lattices with open boundaries, phases with enhanced superconducting order on the corners or the edges can appear, depending on the filling. For finite samples at half filling, the corner site superconducting transition temperature can be much larger than that of the bulk. A novel proximity effect thus arises for $T_{c,bulk} < T<T_{c,corner}$, in which the corner site creates a nonzero tail of the superconducting order in the bulk. We show that such tails should be observable for a range of $r$ and $U$ values.

cond-mat.supr-con↗

arXiv2021

Bulk topological signatures of a quasicrystal

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the Chern number of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain -- the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

cond-mat.dis-nn↗

arXiv2021

The Fibonacci quasicrystal: case study of hidden dimensions and multifractality

The distinctive electronic properties of quasicrystals stem from their long range structural order, with invariance under rotations and under discrete scale change, but without translational invariance. d-dimensional quasicrystals can be described in terms of lattices of higher dimension $D>d$, and many of their properties can be simply derived from analyses that take into account the extra "hidden" dimensions. In particular, as recent theoretical and experimental studies have shown, quasicrystals can have topological properties inherited from the parent crystals. These properties are discussed here for the simplest of quasicrystals, the 1D Fibonacci chain. The Fibonacci noninteracting tight-binding Hamiltonians are characterized by multifractality of spectrum and states, which is manifested in many of its physical properties, notably in transport. Perturbations due to disorder and re-entrance phenomena are described, along with the crossover to strong Anderson localization. Perturbations due to boundary conditions also give information on the spatial and topological electronic properties, as is shown for the superconducting proximity effect. Related models including phonon and mixed Fibonacci models are discussed, as well as generalizations to other quasiperiodic chains and higher dimensional extensions. Interacting quasiperiodic systems and the case for many body localization are briefly discussed. Some experimental realizations of the 1D quasicrystal and their potential applications are described.

cond-mat.stat-mech↗

arXiv2021

Entropy driven formation of complex crystals in soft nanoparticle systems

We present a theoretical description of a mechanism for self assembly in binary soft nanoparticle systems of the type which were studied experimentally by Talapin et al [1]. We focus on, in particular, the conditions for formation of dodecagonal phases, and explain why these can be stabilized by the soft shells of the nanoparticles. We describe the different types of phase transition that are possible in terms of an effective free energy derived from n-body depletion potentials. A large variety of crystalline and several quasiperiodic structures are predicted to form, depending on the composition of the binary system and the size ratio of the particles. We show that this theory can qualitatively explain many of the experimentally seen structures, including striped, tetragonal, hexagonal and quasiperiodic phases. We also predict several new square triangle tilings corresponding to different packing fractions and clusters than the one dodecagonal phase that has been observed so far. Our theory can be tested in principle by detailed numerical investigations of the depletion forces in binary systems.

cond-mat.stat-mech↗

arXiv2020

Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems

We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real space Bogoliubov-de Gennes framework for three cases, namely, when states are i) extended, ii) localized or iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases i) and iii), stretched exponential in case ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable (case i) or of its logarithm (cases ii and iii). We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.

cond-mat.supr-con↗

arXiv2020

Infinite-pressure phase diagram of binary mixtures of (non)additive hard disks

One versatile route to the creation of two-dimensional crystal structures on the nanometer to micrometer scale is the self-assembly of colloidal particles at an interface. Here, we explore the crystal phases that can be expected from the self-assembly of mixtures of spherical particles of two different sizes, which we map to (additive or non-additive) hard-disk mixtures. We map out the infinite-pressure phase diagram for these mixtures, using Floppy Box Monte Carlo simulations to systematically sample candidate crystal structures with up to 12 disks in the unit cell. As a function of the size ratio and number ratio of the two species of particles, we find a rich variety of periodic crystal structures. Additionally, we identify random tiling regions to predict random tiling quasicrystal stability ranges. Increasing non-additivity both gives rise to additional crystal phases and broadens the stability regime for crystal structures involving a large number of large-small contacts, including random tilings. Our results provide useful guidelines for controlling the self-assembly of colloidal particles at interfaces.

cond-mat.soft↗

arXiv2019

Induced superconducting pair correlations in a quasicrystal coupled to a BCS superconductor

In this report, we describe the proximity effect which arises when a quasicrystal is placed in contact with a superconductor. We consider the simplest known model of a quasicrystal, the 1D Fibonacci chain, for which all states are known to be critical. A hybrid ring is made by connecting a finite piece of such a Fibonacci chain to a BCS-type superconductor. Solving the resulting Bogoliubov-de Gennes equations self-consistently, we show that the proximity effect in the Fibonacci chain is long ranged, and that the induced superconducting order carries information on topological properties, namely, the winding numbers of edge states of the Fibonacci chain.

cond-mat.supr-con↗

arXiv2019

The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring

We compute the real-space profile of the superconducting order parameter (OP) in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci chain using a self-consistent approach. In our study, the strength of the penetration, as measured by the order parameter at the center of the quasicrystal, depends on the structural parameter $ϕ$, or phason angle, that characterizes different realizations of the Fibonacci chains of a given length. We show that the penetration strength dependence on $ϕ$ reflects properties of the topological edge states of the Fibonacci chain. We show that the induced superconducting order parameter averaged over all chains has a power law decay as a function of distance from the S-N interface. More interestingly, we show that there are large OP fluctuations for individual chains and that the penetration strength in a finite Fibonacci chain can be significantly $larger$ than in a normal periodic conductor for special values of $ϕ$.

cond-mat.supr-con↗