arXiv subjects

Adam Yanis Chaou

Publications and source records attributed to Adam Yanis Chaou.

11 recordsLinked to original sources

arXiv2026

Simple invariants for band topology

Despite the exhaustive understanding gathered around non-interacting topological states of matter, there is no single method capable of systematically delivering simple, numerically efficient topological invariants that is applicable to all crystalline and non-crystalline systems alike. Here we revisit the spectral localizer operator, constructed from the Hamiltonian and position operators, and show how it can be treated it as an auxiliary zero-dimensional Hamiltonian whose topology encodes the higher dimensional phases of the parent Hamiltonian. Its classification reduces every topological invariant to a matrix signature or the sign of a Pfaffian for an appropriate localizer, both of which are simple to interpret and efficient to compute in real space. We validate this approach by deriving simple real-space invariants for weak and rotationally invariant crystalline phases that were previously beyond the grasp of the spectral localizer formalism, atomic limits that escape scattering invariants, phases that evade symmetry-based indicator methods, as well as phases that had no previously known invariant. Our work provides a systematic way to construct any non-interacting topological invariant for a crystalline or non-crystalline systems, opening avenues to classify and predict the topology of previously unexplored classes of materials.

cond-mat.mes-hall↗

arXiv2026

Topological Gyromorphs

Gyromorphs are a new class of disordered systems that combine an amorphous-like absence of translational order with quasi-long-range rotational order. Gyromorphs can outperform quasicrystals or hyperuniform arrangements in forming isotropic band gaps, suggesting an avenue to realize robust disordered topological phases. However, gyromorphs lack exact rotational symmetry, which is only realized on average, posing an obstacle for existing real-space invariants to correctly diagnose topological gyromorphs. In this work we show that gyromorphs can host higher-order topological insulating (HOTI) phases protected by average rotational symmetry, and we develop and systematically compare tools for diagnosing topological phases protected by such symmetry. We introduce symmetry indicators of the effective Hamiltonian based on average rotational symmetries which, when combined with the spectral localizer and a scattering invariant, draw a consistent topological phase diagram. Our work unlocks gyromorphs as a novel platform to study topological phases beyond crystals, quasicrystals, and amorphous materials.

cond-mat.dis-nn↗

arXiv2026

Symmetric approximant formalism for statistical topological matter

The standard approach to characterizing topological matter, computing topological invariants, fails when the symmetry protecting the topological phase is preserved only on average in a disordered system. Because topological invariants rely on enforcing the symmetry exactly, they can overcount phases by incorrectly identifying certain non-robust features as robust. Moreover, in intrinsic statistical topological insulators, enforcing the symmetry exactly is guaranteed to destroy the topological phase. We define a mapping that addresses both issues and provides a unified framework for describing disordered topological matter.

cond-mat.mes-hall↗

arXiv2025

Magnetotransport across Weyl semimetal grain boundaries

A clean interface between two Weyl semimetals features a universal, field-linear tunnel magnetoconductance of $(e^2/h)N_\mathrm{ho}$ per magnetic flux quantum, where $N_\mathrm{ho}$ is the number of chirality-preserving topological interface Fermi arcs. In this work we show that the linearity of the magnetoconductance is robust with to interface disorder. The slope of the magnetoconductance changes at a characteristic field strength $B_\mathrm{arc}$ -- the field strength for which the time taken to traverse the Fermi arc due to the Lorentz force is equal to the mean inter-arc scattering time. For fields much larger than $B_\mathrm{arc}$, the magnetoconductance is unaffected by disorder. For fields much smaller than $B_\mathrm{arc}$, the slope is no longer determined by $N_\mathrm{ho}$ but by the simple fraction $N_\mathrm{L} N_\mathrm{R}/(N_\mathrm{L}+N_\mathrm{R})$, where $N_\mathrm{L}$ and $N_\mathrm{R}$ are the numbers of Weyl-node pairs in the left and right Weyl semimetal, respectively. We also consider the effect of spatially correlated disorder potentials, where we find that $B_\mathrm{arc}$ decreases exponentially with increasing correlation length. Our results provide a possible explanation for the recently observed robustness of the negative linear magnetoresistance in grained Weyl semimetals.

cond-mat.mes-hall↗

arXiv2025

Proximity superconductivity in chiral kagome antiferromagnets

Recent experiments on the chiral kagome antiferromagnet Mn$_3$Ge have provided strong evidence of proximity-induced spin-polarized superconductivity. We introduce and explore a minimal model which exhibits a rich phase diagram as a function of chemical potential and spin canting. We find a valley-singlet superconducting phase for chemical potentials and canting consistent with the experimental system. This phase transitions into a Chern insulator at larger canting and gives way to topological superconducting phases with Chern numbers ${\cal C}_{\rm BdG} = \pm 1, \pm 3$ at other chemical potentials. Our results show that proximity-induced superconductivity in kagome antiferromagnets is a promising route towards exotic superconductivity with spin-polarized Cooper pairs, with potential applications in spintronics.

cond-mat.mes-hall↗

arXiv2024

On the band topology of the breathing kagome lattice

A two-dimensional second-order topological insulator exhibits topologically protected zero-energy states at its corners. In the literature, the breathing kagome lattice with nearest-neighbor hopping is often mentioned as an example of a two-dimensional second-order topological insulator. Here we show by explicit construction that the corner states of the breathing kagome lattice can be removed by a continuous change of the hopping parameters, without breaking any of the model's symmetries, without closing bulk and boundary gaps, and without introducing hopping terms not present in the original model. Furthermore, we topologically classify all three-band lattice models with the same crystalline symmetries as the breathing kagome lattice and show that though none of the phases have protected zero-energy corner states, some of the phases are obstructed atomic limits which exhibit a filling anomaly.

cond-mat.mes-hall↗

arXiv2024

Disordered topological crystalline phases

The imposition of crystalline symmetries is known to lead to a rich variety of insulating and superconducting topological phases. These include higher-order topological phases and obstructed atomic limits with and without filling anomalies. We here comprehensively classify such topological crystalline phases (TCPs) with mirror, twofold rotation, and inversion symmetries in the presence of disorder that preserves the crystalline symmetry on average. We find that the inclusion of disorder leads to a simplification of the classification in comparison to the clean case. We also find that, while clean TCPs evade a general bulk-boundary principle, disordered TCPs admit a complete bulk-boundary correspondence, according to which (bulk) topological phases are topologically equivalent if and only if they have the same anomalous boundary states and filling anomaly. We corroborate the stability of disordered TCPs by way of field-theoretic, numerical and symmetry-based analyses in various case studies. While the boundary signatures of most disordered TCPs are similar to their clean counterparts, the addition of disorder to certain mirror-symmetric TCPs results in novel higher-order statistical topological phases, in which zero-energy hinge states have critical wavefunction statistics, while remaining protected from Anderson localization.

cond-mat.mes-hall↗

arXiv2023

Quantum Oscillation Signatures of Fermi Arcs in Tunnel Magnetoconductance

Fermi-arc surface states of Weyl semimetals exhibit a unique combination of localization to a surface and connectivity to the bulk Weyl fermions that can move along the localization direction. We predict anomalous quantum-oscillation signatures of Fermi arcs in the tunnel mangetoconductance across an interface between two Weyl semimetals. These oscillations stem from a momentum-space analog of Aharonov-Bohm interference of electrons moving along the interface Fermi arcs, driven by an external magnetic field normal to the interface. The Fermi arcs' connectivity to the bulk enables their characterization via transport normal to the interface, while their localization manifests in a strong field-angle anisotropy of the oscillations. This combination distinguishes these anomalous oscillations from conventional Shubnikov-de Haas oscillations and makes them identifiable even in complex oscillation spectra of real materials.

cond-mat.mes-hall↗

arXiv2023

Magnetic Breakdown and Chiral Magnetic Effect at Weyl-Semimetal Tunnel Junctions

We investigate magnetotransport across an interface between two Weyl semimetals whose Weyl nodes project onto different interface momenta. Such an interface generically hosts Fermi arcs that connect Weyl nodes of identical chirality in different Weyl semimetals (homochiral connectivity) -- in contrast to surface Fermi arcs that connect opposite-chirality Weyl nodes within the same Weyl semimetal (heterochiral connectivity). We show that electron transport along the arcs with homochiral connectivity, in the presence of a longitudinal magnetic field, leads to a universal longitudinal magnetoconductance of $e^2/h$ per magnetic flux quantum. Furthermore, a weak tunnel coupling can result in a close encounter of two homochiral-connectivity Fermi arcs, enabling magnetic breakdown. Above the breakdown field the interface Fermi arc connectivity is effectively heterochiral, leading to a saturation of the conductance.

cond-mat.mes-hall↗

arXiv2023

Refining and relating fundamentals of functional theory

To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its possible natural variables and explain how symmetries could be exploited. In particular, for systems with time-reversal symmetry, we explain why there exist six equivalent universal functionals, prove concise relations among them and conclude that the important notion of $v$-representability is relative to the scope and choice of variable. All these fundamental concepts are then comprehensively discussed and illustrated for the Hubbard dimer and its generalization to arbitrary pair interactions $W$. For this, we derive by analytical means the pure and ensemble functionals with respect to both the real- and complex-valued Hilbert space. The comparison of various functionals allows us to solve the underlying $v$-representability problems analytically and the dependence of its solution on the pair interaction is demonstrated. Intriguingly, the gradient of each universal functional is found to always diverge repulsively on the boundary of the domain. In that sense, this key finding emphasizes the universal character of the fermionic exchange force, recently discovered and proven in the context of translationally-invariant one-band lattice models.

quant-ph↗

arXiv2022

Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer

Three-dimensional higher-order topological insulators can have topologically protected chiral modes propagating on their hinges. Hinges with two co-propagating chiral modes can serve as a "beam splitter" between hinges with only a single chiral mode. Here we show how such a crystal, with Ohmic contacts attached to its hinges, can be used to realize a Mach-Zehnder interferometer. We present concrete calculations for a lattice model of a first-order topological insulator in a magnetic field, which, for a suitable choice of parameters, is an extrinsic second-order topological insulator with the required configuration of chiral hinge modes.

cond-mat.mes-hall↗