arXiv subjects

Adolfo G. Grushin

Publications and source records attributed to Adolfo G. Grushin.

At least 19 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

Quantum-geometric bounds on Casimir repulsion

The quantum geometric tensor has been shown to bound the gap, optical absorption, and dielectric susceptibilities of materials. Here we derive new quantum-geometric bounds on the magnitude and sign of the Casimir force between two-dimensional plates in the long-distance limit. These bounds limit the previously attributed benefit of increasing the plate's Chern number to maximize repulsion, and give a quantum geometric origin to the stronger attractive force of metallic plates, regardless of their Chern number. These bounds allow us to infer that flat Chern bands that saturate geometric bounds, including Landau levels and moiré flat bands, enlarge the window where Casimir repulsion exists and bring the repulsive crossover to smaller, more experimentally relevant distances. We derive estimates for material platforms such as twisted MoTe$_2$. Our work shows that quantum-geometric bounds constrain repulsive Casimir forces beyond previously known theorems, and suggests new optimization strategies to observe repulsion.

quant-ph↗

arXiv2026

Non-Hermiticity-induced chirality imbalance of Weyl Landau levels

Weyl semimetals obey a global chirality constraint: the net chiral topological charge and any associated chiral spectral flow must vanish, as required by the Nielsen-Ninomiya theorem. Under magnetic fields, this constraint manifests through counter-propagating zeroth Landau levels associated with Weyl nodes of opposite chirality. Here, we experimentally demonstrate how non-Hermiticity can reshape this balance in a synthetic photonic Weyl semimetal. Using engineered gauge fields in one-dimensional multilayer structures, we realize both homogeneous and axial magnetic fields and directly probe the resulting Landau-level spectra. While a homogeneous field produces the expected chirality-balanced zeroth Landau levels, an axial field spatially separates the compensating chiral channels: co-propagating bulk pseudo-Landau levels carry one chirality, whereas the opposite chirality resides in boundary-localized surface states. We show that radiative boundary loss selectively suppresses these surface states, removing them from the long-lived observable spectrum and producing an experimentally accessible chirality imbalance. By reducing boundary loss, we recover the hidden chiral channel and reveal its surface-state origin. These results show that non-Hermiticity, present naturally in photonics, can control and relax fundamental chirality constraints in topological systems, enabling access to otherwise forbidden spectral responses.

cond-mat.mes-hall↗

arXiv2026

Explicit equivalence between the spectral localizer and local Chern and winding markers

Topological band insulators are classified using momentum-space topological invariants, such as Chern or winding numbers, when they feature translational symmetry. The lack of translation symmetry in disordered, quasicrystalline, or amorphous topological systems has motivated alternative, real-space definitions of topological invariants, including the local Chern marker and the spectral localizer invariant. However, the equivalence between these invariants is so far implicit. Here, we explicitly demonstrate their equivalence from a systematic perturbative expansion in powers of the spectral localizer's parameter $κ$. By leveraging only the Clifford algebra of the spectral localizer, we prove that Chern and winding markers emerge as leading-order terms in the expansion. It bypasses abstract topological machinery, offering a simple approach accessible to a broader physics audience.

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

Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires

Crystalline topological insulator nanowires with a magnetic flux threaded through their cross section display Aharanov-Bohm conductance oscillations. A characteristic of these oscillations is the perfectly transmitted mode present at certain values of the magnetic flux, due to the appearance of an effective time-reversal symmetry combined with the topological origin of the nanowire surface states. In contrast, amorphous nanowires display a varying cross section along the wire axis that breaks the effective time-reversal symmetry. In this work, we use transport calculations to study the stability of the Aharanov-Bohm oscillations and the perfectly transmitted mode in amorphous topological nanowires. We observe that at low energies and up to moderate amorphicity the transport is dominated, as in the crystalline case, by the presence of a perfectly transmitted mode. In an amorphous nanowire the perfectly transmitted mode is protected by chiral symmetry or, in its absence, by a statistical time-reversal symmetry. At high amorphicities the Aharanov-Bohm oscillations disappear and the conductance is dominated by nonquantized resonant peaks. We identify these resonances as bound states and relate their appearance to a topological phase transition that brings the nanowires into a trivial insulating phase.

cond-mat.mes-hall↗

arXiv2026

Topologically Protected Surface Altermagnetism on Antiferromagnets

Altermagnetism (AM) and its associated spin-transport phenomena are typically linked to spin-split electronic band structures in bulk materials. However, the crystal surface has a reduced symmetry with respect to the bulk, which can induce AM at the surface of conventional antiferromagnets (AFMs) $\unicode{x2013}$ a local effect which cannot be detected using bulk properties. In this work we define the symmetry conditions necessary for surface AM and show how it can be topologically protected, rendering it a robust effect. We provide a minimal model for one trivial and two topological examples of surface AM. We show that the spin spectral density, accessible by spin- and angle-resolved photoemission spectroscopy, can exhibit a $d$-wave-like altermagnetic character at the surface, even when the full band structure is completely spin degenerate. Our topological model describes the Dirac semimetal CuMnAs, which provides an existing realization of our theory. Our results identify crystal surfaces as a platform to realize robust, topology- and symmetry-driven unconventional magnetism beyond the bulk classification of magnetic materials.

cond-mat.str-el↗

arXiv2025

Beating the aliasing limit with aperiodic monotile arrays

Finding optimal wave sampling methods has far-reaching implications in wave physics, such as seismology, acoustics, and telecommunications. A key challenge is surpassing the Whittaker-Nyquist-Shannon (WNS) aliasing limit, establishing a frequency below which the signal cannot be faithfully reconstructed. However, the WNS limit applies only to periodic sampling, opening the door to bypass aliasing by aperiodic sampling. In this work, we investigate the efficiency of a recently discovered family of aperiodic monotile tilings, the Hat family, in overcoming the aliasing limit when spatially sampling a wavefield. By analyzing their spectral properties, we show that monotile aperiodic seismic (MAS) arrays, based on a subset of the Hat tiling family, are efficient in surpassing the WNS sampling limit. Our investigation leads us to propose MAS arrays as a novel design principle for seismic arrays. We show that MAS arrays can outperform regular and other aperiodic arrays in realistic beamforming scenarios using single and distributed sources, including station-position noise. While current seismic arrays optimize beamforming or imaging applications using spiral or regular arrays, MAS arrays can accommodate both, as they share properties with both periodic and aperiodic arrays. More generally, our work suggests that aperiodic monotiles can be an efficient design principle in various fields requiring wave sampling.

physics.geo-ph↗

arXiv2025

Geometry-Enforced Topological Chiral Fermions in Amorphous Chiral Metals

Since the prediction and observation of topological Weyl semimetals (chiral TSMs), there have been enormous efforts to characterize further condensed matter realizations of chiral fermions. These efforts were dramatically accelerated by the subsequent discovery of a profound link between low-energy topological and lattice chirality in structurally chiral crystals. Though TSMs are well understood in the limit of perfect translation symmetry, real solid-state materials host defects and disorder, and may even be rendered amorphous down to all but the smallest system length scales. Previous theoretical studies have concluded that chiral TSMs transition into trivial diffusive metals at moderate disorder scales, raising concerns that chiral TSM states may only be accessible in highly crystalline samples. In this work, we in contrast identify large families of chiral TSMs that persist under strong structural disorder - even into the amorphous regime. We show that amorphous chiral TSM phases can in particular be stabilized by the presence of long-range order in the local structural chirality. We present extensive analytic and numerical calculations demonstrating the existence of both Weyl and higher-charge chiral fermions in amorphous metals whose topology and spin and orbital angular momentum textures are tunable via the interplay of average symmetry and geometry. To distinguish and generate new realizations of strongly disordered chiral fermions, we introduce an analytic approach grounded in symmetry group theory. We then introduce an amorphous Wilson loop numerical method to characterize chiral fermions with quantized Berry curvature fluxes in metals with 3D structural disorder. Our findings bridge the crystalline and strongly disordered regimes of chiral TSMs, and indicate a clear route towards engineering geometry-enforced topology in non-crystalline materials and metamaterials.

cond-mat.mes-hall↗

arXiv2025

Chiral-helical junctions in screened graphene

Reproducibility and quantization in quantum spin Hall platforms is a persisting challenge, limiting their use in hybrid realizations of topological superconductivity. We report robust and reproducible quantized transport in a graphene quantum Hall topological insulator, stabilized at low magnetic fields by screening long-range Coulomb interactions with a metallic Bi$_2$Se$_3$ back gate. Beyond quantized resistance plateaus, we demonstrate mode-resolved control via gate-defined chiral-helical junctions that selectively transmit or backscatter a single helical channel, a capability inaccessible in time-reversal symmetric quantum spin Hall systems. Targeted experiments and simulations identify contact-induced doping, effectively creating unintended chiral-helical interfaces, as a generic mechanism for quantization breakdown, which is mitigated by large area contacts that enhance edge-channel equilibration. Our findings establish metal screened graphene as a gate-tunable, interaction-driven helical system with quantized transport, spatially separable helical channels, and compatibility with superconducting proximity for topological devices.

cond-mat.mes-hall↗

arXiv2025

Altermagnetism Without Crystal Symmetry

Altermagnetism is a collinear magnetic order in which opposite spin species are exchanged under a real-space rotation. Hence, the search for physical realizations has focussed on crystalline solids with specific rotational symmetry. Here, we show that altermagnetism can also emerge in non-crystalline systems, such as amorphous solids, despite the lack of global rotational symmetries. We construct a Hamiltonian with two directional orbitals per site on an amorphous lattice with interactions that are invariant under spin rotation. Altermagnetism then arises due to spontaneous symmetry breaking in the spin and orbital degrees of freedom around each atom, displaying a common point group symmetry. This form of altermagnetism exhibits anisotropic spin transport and spin spectral functions, both experimentally measurable. Our mechanism generalizes to any lattice and any altermagnetic order, opening the search for altermagnetic phenomena to non-crystalline systems.

cond-mat.str-el↗

arXiv2025

Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor

The strict geometric rules that define aperiodic tilings lead to the unique spectral and transport properties of quasicrystals, but also limit our ability to design them. In this Letter, we explore a novel example of a continuously tunable family of two-dimensional aperiodic tilings in which the underlying real-space geometry becomes a control knob of the wavefunction's quantum geometric tensor. The real-space geometry can be used to tune into topological phases occupying an expanded phase space compared to crystals, or into a disorder-driven topological Anderson insulator. The quantum metric can also be tuned continuously, opening new routes towards tunable single- and many-body physics in aperiodic solid-state and synthetic systems.

cond-mat.mes-hall↗

arXiv2025

Doping-induced nematic and stripe orders within the charge density wave state of TiSe$_2$

In this work, we present a theory to address conflicting experimental claims regarding the charge density wave (CDW) state in TiSe$_2$, including whether there is a single or multiple CDW transitions and whether threefold rotation symmetry ($C_3$) is broken. Using a continuum $\boldsymbol{k}\cdot\boldsymbol{p}$ model coupled to the CDW order parameter, we show how commonplace conduction band doping induces a nematic transition from a $C_3$-symmetric $3Q$ CDW to a $C_3$-breaking $3Q$ CDW, which is favored by the large ellipticity of the conduction bands of TiSe$_2$. We also find that a $1Q$ stripe CDW is generically stabilized for sufficiently high electron doping. We then show how both stripe and nematic CDW states emerge self-consistently from a minimal interacting tight-binding model, for both positive and negative initial gaps. Our theory provides a new scenario in which, as temperature is lowered, a second $C_3$-breaking transition may occur or not depending on the doping level, potentially explaining the experimental variability. These predictions can be further verified with a variety of probes including transport, photoemission and tunneling.

cond-mat.str-el↗

arXiv2025

A graphical diagnostic of topological order using ZX calculus

Establishing a universal diagnostic of topological order remains an open theoretical challenge. In particular, diagnosing long-range entanglement through the entropic area law suffers from spurious contributions, failing to unambiguously identify topological order. Here we devise a protocol based on the ZX calculus, a graphical tensor network, to determine the topological order of a state circumventing entropy calculations. The protocol takes as input real-space bipartitions of a state and returns a ZX contour diagram, $\mathcal{D}_{\partial A}$, displaying long-range graph connectivity only for long-range entangled states. We validate the protocol by showing that the contour diagrams of the toric and color codes are equivalent except for the number of non-local nodes, which differentiates their topological order. The number of these nodes is robust to the choice of the boundary and ground-state superposition, and they are absent for trivial states, even those with spurious entropy contributions. Our results single out ZX calculus as a tool to detect topological long-range entanglement by leveraging the advantages of diagrammatic reasoning against entropic diagnostics.

cond-mat.str-el↗

arXiv2025

Fractonic Fractional Quantum Hall Effect

In non-interacting systems, disorder can drive a trivial phase into a topological one. However little is known how to construct a fractional quantum Hall ground-state, a paradigmatic topologically ordered state, that exists both in crystalline and disordered lattices and is qualitatively different to known topological phases. Here, we propose a general method for building such a phase. This is done by coupling quantum wires placed aperiodically in real-space, where the spatial positioning allows us to tune the inter-wire couplings. We call the emergent phase the Fractonic Fractional Quantum Hall Effect as it displays a rich interplay of fractional quantum Hall physics with fractonic constraints, formed by coupling differently-fractionalised wires into a globally gapped phase. The ground state has an exponential degeneracy in system size, a signature of the emergence of fractons. It displays a rich phenomenology of excitations, which can either behave like anyons confined to move in one dimension (lineons), multiples of which can then hop between two wires (s-lineons) or be free to travel across the system (C-anyons), depending on the multiplicity. Both the ground state degeneracy and mutual statistics are directly determined by the real-space positions of the wires, which can be disordered. Our method provides an analytically solvable pathway to non-crystalline fractional quantum Hall effects and fractonic theories in two-dimensions, examples of which were lacking.

cond-mat.str-el↗

arXiv2024

Anomalous Casimir effect in an expanding ring

The Casimir effect is a macroscopic evidence of the quantum nature of the vacuum. On a ring, it leads to a finite size correction to the vacuum energy. In this work, we show that this vacuum's energy and pressure acquire additional, sizable corrections, when the ring's radius is increased fast enough, an experimentally accessible model of an expanding universe. This effect is distinct from the dynamical Casimir effect: it is a manifestation of the conformal anomaly, originating from the spacetime curvature induced by the increase of the ring's radius. This anomalous dynamical Casimir effect is measurable through the work necessary to increase the ring size, which becomes non-monotonous in time.

cond-mat.quant-gas↗

arXiv2024

Topological zero-modes of the spectral localizer of trivial metals

Topological insulators are described by topological invariants that can be computed by integrals over momentum space, but also as traces over local, real-space topological markers. These markers are useful to detect topological insulating phases in disordered crystals, quasicrystals and amorphous systems. Among these markers, only the spectral localizer operator can be used to distinguish topological metals, that show zero-modes of the localizer spectrum. However, it remains unclear whether trivial metals also display zero-modes, and if their localizer spectrum is distinguishable from topological ones. Here, we show that trivial metals generically display zero-modes of the localizer spectrum. The localizer zero-modes are determined by the zero-mode solutions of a Dirac equation with a varying mass parameter. We use this observation, valid in any dimension, to determine the difference between the localizer spectrum of trivial and topological metals, and conjecture the spectrum of the localizer for fractional quantum Hall edges. Because the localizer is a local, real-space operator, it may be used as a tool to differentiate between non-crystalline topological and trivial metals, and characterize strongly correlated systems, for which local topological markers are scarce.

cond-mat.mes-hall↗

arXiv2024

Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including six-fold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette ($ϕ$) is half of the flux quantum, zero-modes are found localized around the reflected `anti-hats'; and (v) its Hofstadter spectrum is periodic in $ϕ$, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.

cond-mat.mes-hall↗