arXiv subjects

Eric Akkermans

Publications and source records attributed to Eric Akkermans.

At least 19 recordsLinked to original sources

arXiv2026

Vacancy-Induced Topological Phase Transition via Valley Annihilation in an Anisotropic Honeycomb Lattice

A single missing atom can drive a topological phase transition in a lattice that is otherwise trivial for all values of its parameters. We demonstrate this in a two-dimensional honeycomb lattice with anisotropic nearest-neighbor hopping ratio $t'/t$. The pristine lattice is topologically trivial for all $t'/t$ by the Nielsen-Ninomiya fermion-doubling theorem: Dirac valleys appear in pairs whose topological charges cancel identically in any bulk invariant. A single vacancy breaks this cancelation, acting as an internal boundary with defect winding number $\nu_3=\mp 1$ for $t'/t<2$. At $t'/t=2$, the two Dirac valleys merge and annihilate; the number of active pseudospinor degrees of freedom drops from $m=2$ to $m=1$, violating the condition $d+D+1=2m$ required for a non-trivial winding number. The winding number collapses to $\nu_3=0$: a topological phase transition within a fixed symmetry class (BDI), driven entirely by a bulk Lifshitz transition and observable only through the vacancy. The defect zero mode crosses over from algebraic (${\sim}1/r$) to stronger spatial confinement, with its inverse participation ratio reaching a sharp minimum at criticality. Wavefront dislocations in the local density of states provide a direct, spatially resolved image of $\nu_3$, accessible in graphene and in photonic and cold-atom analogs.

cond-mat.mes-hall↗

arXiv2026

Local Defects and the Topology of the Haldane Model

We investigate the interplay between local defects and topology in the Haldane model within the framework of the tenfold classification. The Haldane model realizes a Chern-insulating phase characterized by an integer topological invariant ($C=\pm 1$) and supports chiral edge states. Introducing vacancies gives rise to localized states at the defect sites, classified by a $\mathbb{Z}_2$ invariant $\nu = C\cdot m,\mathrm{mod},2$, where $m=N_A-N_B$ is the net sublattice imbalance of the vacancy configuration: an odd imbalance hosts a protected zero-energy mode, whereas an even imbalance does not. We identify three independent experimental signatures that distinguish these topological defect states from trivial (adatom) defects. First, vacancy-induced states exhibit characteristic dislocations in their wavefunction profiles that track the phase winding associated with the defect. Second, a fractional charge of $e/2$ accumulates at vacancy sites, while no such charge appears at adatoms. Third, the probability current circulating around a vacancy-induced state flows in the opposite direction to that of chiral edge states, in direct analogy with the current reversal produced by a vortex in a $p$-wave superconductor. All three signatures are in quantitative agreement with the $\mathbb{Z}_2$ prediction.

cond-mat.mes-hall↗

arXiv2026

Topological sum rule for geometric phases of quantum gates

We establish a topological sum rule, $\nu_U = \frac{1}{2\pi}\sum_n\gamma_n = m\nu_H$, connecting the geometric phases accumulated by a two-qubit system over a complete basis of initial states to the winding number $\nu_H$ classifying its Hamiltonian. Implementations of the same gate from different topological classes must distribute these phases differently, making their distinction measurable through the Wootters concurrence. As a corollary, nontrivial topology is a necessary condition for entanglement: only Hamiltonians with access to $\nu_H \neq 0$ can generate it.

quant-ph↗

arXiv2025

Topological Winding Numbers from Wavefront Dislocations in Local Electronic Density

Topological materials are characterized by integer invariants that underpin robust quantized electronic properties, as exemplified by the Chern number in the integer quantum Hall effect. Yet, for most candidate systems, the observable linked to the topological invariant remains unknown, precluding direct verification of their topological nature. We present a general method to identify topological materials by connecting the local electronic density~$\delta\rho(\bm{r})$ to Atiyah-Singer index theorems. This method offers a concrete protocol for determining the winding number, the topological invariant associated with chiral-symmetric Hamiltonians. It also identifies a contour-independent wavefront dislocation pattern in $\delta\rho(\bm{r})$ arising from interference induced by topological defects and demonstrates its application to numerical simulations and to existing STM data. The method clearly distinguishes topological states from non-topological ones through a unified, standardized filtering step, offering a definitive approach for identifying and characterizing quantum topological states and opening the door to their use as robust, entangleable building blocks in quantum technologies.

cond-mat.mes-hall↗

arXiv2025

Engineering Topological Materials

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering materials to realize desired topological properties. In this work, we introduce a general method for designing topological materials by embedding defects or spatial textures, which alter symmetry or dimension. This enables controlled navigation across the tenfold table, allowing one to induce topological phase transitions on demand. We illustrate this approach through several nontrivial examples, demonstrating how local defects can generate phases with different symmetries and topological invariants.

cond-mat.mes-hall↗

arXiv2025

Defects Potentials for Two-Dimensional Topological Materials

For non-topological quantum materials, introducing defects can significantly alter their properties by modifying symmetry and generating a nonzero analytical index, thus transforming the material into a topological one. We present a method to construct the potential matrix configuration with the purpose of obtaining a non-zero analytical index, akin to a topological invariant like a winding or Chern number. We establish systematic connections between these potentials, expressed in the continuum limit, and their initial tight-binding model description. We apply our method to graphene with an adatom, a vacancy, and both as key examples illustrating our comprehensive description. This method enables analytical differentiation between topological and non-topological zero-energy modes and allows for the construction of defects that induce topology.

cond-mat.mes-hall↗

arXiv2025

Topological Tenfold Classification and the Entanglement of Two Qubits

We present a constructive method utilizing the Cartan decomposition to characterize topological properties and their connection to two-qubit quantum entanglement, in the framework of the tenfold classification and Wootters' concurrence. This relationship is comprehensively established for the 2-qubit system through the antiunitary time reversal (TR) operator. The TR operator is shown to identify concurrence and differentiate between entangling and non-entangling operators. This distinction is of a topological nature, as the inclusion or exclusion of certain operators alters topological characteristics. Proofs are presented which demonstrate that the 2-qubit system can be described in the framework of the tenfold classification, unveiling aspects of the connection between entanglement and a geometrical phase. Topological features are obtained systematically by a mapping to a quantum graph, allowing for a direct computation of topological integers and of the 2-qubit equivalent of topological zero-modes. An additional perspective is provided regarding the extension of this new approach to condensed matter systems, illustrated through examples involving indistinguishable fermions and arrays of quantum dots.

quant-ph↗

arXiv2023

Wavefronts Dislocations Measure Topology in Graphene with Defects

We present a general method to identify topological materials by studying the local electronic density $\delta \rho \left(\boldsymbol{r}\right)$. More specifically, certain types of defects or spatial textures such as vacancies, turn graphene into a topological material characterised by invariant Chern or winding numbers. We show that these numbers are directly accessible from a dislocation pattern of $\delta \rho \left(\boldsymbol{r}\right)$, resulting from an interference effect induced by topological defects. For non topological defects such as adatoms, this pattern is scrambled by Friedel oscillations absent in topological cases. A Kekule distortion is discussed and shown to be equivalent to a vacancy.

cond-mat.mes-hall↗

arXiv2023

Defects in Graphene : A Topological Description

Specific types of spatial defects or potentials can turn monolayer graphene into a topological material. These topological defects are classified by a spatial dimension $D$ and they are systematically obtained from the Hamiltonian by means of its symbol $\mathcal{H} (\boldsymbol{k}, \boldsymbol{r}) $, an operator which generalises the Bloch Hamiltonian and contains all topological information. This approach, when applied to Dirac operators, allows to recover the tenfold classification of insulators and superconductors. The existence of a stable $\mathbb{Z}$-topology is predicted as a condition on the dimension $D$, similar to the classification of defects in thermodynamic phase transitions. Kekule distortions, vacancies and adatoms in graphene are proposed as examples of such defects and their topological equivalence is discussed.

cond-mat.mes-hall↗

arXiv2022

Hydrodynamic description of Non-Equilibrium Radiation

Non-equilibrium radiation is addressed theoretically by means of a stochastic lattice-gas model. We consider a resonating transmission line composed of a chain of radiation resonators, each at a local equilibrium, whose boundaries are in thermal contact with two blackbody reservoirs at different temperatures. In the long chain limit, the stationary state of the non-equilibrium radiation is obtained in a closed form. The corresponding spectral energy density departs from the Planck expression, yet it obeys a useful scaling form. A macroscopic fluctuating hydrodynamic limit is obtained leading to a Langevin equation whose transport parameters are calculated. In this macroscopic limit, we identify a local temperature which characterises the spectral energy density. The generality of our approach is discussed and applications for the interaction of non-equilibrium radiation with matter are suggested.

cond-mat.stat-mech↗

arXiv2021

Winding Numbers and Topology of Aperiodic Tilings

We show that diffraction features of $1D$ quasicrystals can be retrieved from a single topological quantity, the \v{C}ech cohomology group, $\check{H}^{1}\cong\mathbb{Z}^2$, which encodes all relevant combinatorial information of tilings. We present a constructive way to calculate $\check{H}^{1}$ for a large variety of aperiodic tilings. By means of two winding numbers, we compare the diffraction features contained in $\check{H}^{1}$ to the gap labeling theorem, another topological tool used to label spectral gaps in the integrated density of states. In the light of this topological description, we discuss similarities and differences between families of aperiodic tilings, and the resilience of topological features against perturbations.

cond-mat.other↗

arXiv2020

Uncertainty Relations for Mesoscopic Coherent Light

Thermodynamic uncertainty relations unveil useful connections between fluctuations in thermal systems and entropy production. This work extends these ideas to the disparate field of \textit{zero temperature} quantum mesoscopic physics where fluctuations are due to coherent effects and entropy production is replaced by a cost function. The cost function arises naturally as a bound on fluctuations, induced by coherent effects -- a critical resource in quantum mesoscopic physics. Identifying the cost function as an important quantity demonstrates the potential of importing powerful methods from non-equilibrium statistical physics to quantum mesoscopics.

cond-mat.mes-hall↗

arXiv2020

Relating Diffraction and Spectral Data of Aperiodic Tilings: Towards a Bloch theorem

The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by \v{C}ech cohomology of the tiling space) and the spectral properties (of Hamiltonians defined on such tilings) defined by $K$-theory, and to show their equivalence in dimensions $\leq 3$. A theorem makes precise the conditions for this relationship to hold. It can be viewed as an extension of the "Bloch Theorem" to a large class of aperiodic tilings. The idea underlying this result is based on the relationship between cohomology and $K$-theory traces and their equivalence in low dimensions.

math-ph↗

arXiv2019

The breaking of continuous scale invariance to discrete scale invariance: a universal quantum phase transition

We provide a review on the physics associated with phase transitions in which continuous scale invariance is broken into discrete scale invariance. The rich features of this transition characterized by the abrupt formation of a geometric ladder of eigenstates, low energy universality without fixed points, scale anomalies and Berezinskii-Kosterlitz-Thouless scaling is described. The important role of this transition in various celebrated single and many body quantum systems is discussed along with recent experimental realizations. Particular focus is devoted to a recent realization in graphene.

cond-mat.mes-hall↗

arXiv2019

Fluctuating Forces Induced by Non Equilibrium and Coherent Light Flow

Casimir physics covers a wealth of phenomena where forces between macroscopic objects are induced by long range fluctuations of either classical or quantum origin. Fluctuations of the quantum electrodynamic vacuum epitomize this type of physics, but such fluctuation induced forces arise in a wide range of systems. Here we present a surprisingly never anticipated example of fluctuation induced radiation forces, stemming from spatially long ranged mesoscopic coherent fluctuations of light propagating in random media. Quite remarkably, spatially coherent light fluctuations can be thoroughly described by a hydrodynamic Langevin approach, where a properly tailored noise accounts for mesoscopic coherent effects. The light flow depends on two parameters only, the diffusion coefficient $D$ and the mobility $\sigma$, otherwise related by a Einstein relation. The mapping we present between coherent light flow and out of equilibrium hydrodynamics is easily generalisable to a large class of quantum or classical wave problems. A clear asset of this type of approach is in its dependence upon two parameters only thus making it a candidate to efficient machine learning algorithms. Moreover, the strength of these coherent fluctuating forces depends on a single and easily tunable dimensionless conductance $g$ -- analog of electronic conductance -- which encapsulates both the geometry and the scattering properties of the random medium. Hence coherent multiple light scattering offers setups where fluctuation induced forces are significantly enhanced compared to other known situations. The scarcity of measurable non equilibrium phenomena makes the present proposal particularly relevant to experimental inspections and applications, e.g. a wide variety of sensors in soft condensed matter, biophysics and quantum technologies.

cond-mat.mes-hall↗

arXiv2018

Vacancies in Graphene : Dirac Physics and Fractional Vacuum Charges

The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the symmetry between the two triangular graphene sublattices hence inducing zero energy states at the Dirac points. Here we show the fractional and pseudo-scalar nature of this vacancy charge. A continuous Dirac model is presented which relates zero modes to vacuum fractional charge and to a parity anomaly. This relation constitutes an Index theorem and is achieved by using particular chiral boundary conditions, which map the vacancy problem onto edge state physics. Vacancies in graphene thus allow to realize prominent features of $2+1$ quantum electrodynamics but without coupling to a gauge field. This essential difference makes vacancy physics relatively easy to implement and an interesting playground for topological switching.

cond-mat.mes-hall↗

arXiv2018

On the landscape of scale invariance in quantum mechanics

We consider the most general scale invariant radial Hamiltonian allowing for anisotropic scaling between space and time. We formulate a renormalisation group analysis of this system and demonstrate the existence of a quantum phase transition from a continuous scale invariant phase to a discrete scale invariant phase. Close to the critical point, the discrete scale invariant phase is characterised by an isolated, closed, attracting trajectory in renomalisation group space (a limit cycle). Moving in appropriate directions in the parameter space of couplings this picture is altered to one controlled by a quasi periodic attracting trajectory (a limit torus) or fixed points. We identify a direct relation between the critical point, the renormalisation group picture and the power laws characterising the zero energy wave functions.

hep-th↗

arXiv2017

Scale anomaly of a Lifshitz scalar: a universal quantum phase transition to discrete scale invariance

We demonstrate the existence of a universal transition from a continuous scale invariant phase to a discrete scale invariant phase for a class of one-dimensional quantum systems with anisotropic scaling symmetry between space and time. These systems describe a Lifshitz scalar interacting with a background potential. The transition occurs at a critical coupling $\lambda_{c}$ corresponding to a strongly attractive potential.

hep-th↗