arXiv subjects

Elizabeth J. Dresselhaus

Publications and source records attributed to Elizabeth J. Dresselhaus.

7 recordsLinked to original sources

arXiv2026

Textiles: from twisted yarn to topology and mechanics

While textiles have existed throughout much of human history as complex mechanical metamaterials, textile science has largely been overlooked by the physics community until recently. In this review, we consider the symmetry, topology, and mechanics of woven and knitted materials, showing that they represent a unique, if under-explored, corner of condensed matter. We start with the basic construction and elementary mechanical model of spun yarn, reviewing recent developments twisted bundle structures. We then introduce woven and knitted fabrics as materials with layer symmetries that can be topologically characterized as knots and links in the thickened torus. We finally discuss fabric mechanics and geometry, invoking recent results surrounding yarn-level and stitch-level geometry, deformations, and defect structures.

cond-mat.soft↗

arXiv2026

An Orbifold Framework for Classifying Layer Groups with an Application to Knitted Fabrics

Entangled structures such as textiles and architected materials are often doubly periodic. Due to this property and their finite transverse thickness, the symmetries of these materials are described by the crystallographic layer groups. While orbifold notation provides a compact topological description and classification of the planar wallpaper groups, no analogous framework has been available for the spatial layer groups. In this article we develop an orbifold theory in three dimensions and introduce a complete set of Conway-type symbols for all layer groups. To illustrate its applicability, we analyze several knitted fabric motifs and show how their layer-group symmetries are naturally expressed in this new orbifold notation. This work establishes a foundation for the topological classification of doubly periodic structures beyond the planar setting.

cond-mat.soft↗

arXiv2025

Return point memory in knitted fabrics

The tunable mechanical response of knitted fabrics underpins applications ranging from soft robotics and artificial muscles to morphing electromagnetic field sensors. Elasticity in fabrics emerges from the bending of yarn in the knitted structure; however, properties beyond elasticity are relatively unexplored. Here, we demonstrate that knitted fabrics subjected to cyclic uniaxial stress exhibit significant hysteresis and the remarkable ability to "remember" their response to previous deformations -- reminiscent of classical return point memory in magnetic systems. The hysteretic behavior deviates from the two standard models of hysteresis that usually apply to solid-state materials, viscoelasticity and plasticity. Thus, we develop a phenomenological extension of the Preisach model of hysteresis which well replicates our data, and discuss implications of these results on the underlying mechanisms of memory in knitted fabrics.

cond-mat.soft↗

arXiv2025

Anomalous tensorial properties of anisotropic 2D materials

Odd transport phenomena -- defined as a flux response orthogonal to an applied gradient -- have been recently observed in isotropic systems, with a multitude of proposed models and experiments to study these effects. Odd transport manifests in tensors that describe linear relations between fluxes and gradients that drive them, particularly when parity and time-reversal symmetries are broken. In this work, we identify such odd properties to be a subset of a broader class of major-symmetry-breaking behaviors, which we term ``anomalous." We develop a classification of anomalous properties described by $2^\mathrm{nd}$ and $4^\mathrm{th}$ order tensors in anisotropic 2D materials that maintain discrete rotational and reflection symmetries, characterized by the 17 wallpaper groups. To this end, we present representation theorems for these tensors, identifying which components are constrained for specific spatial symmetries and thereby allowing materials to be grouped into classes that exhibit anomalous responses or not. We focus our discussion on $2^\mathrm{nd}$ order tensors in the context of electrical resistivity and on $4^\mathrm{th}$ order tensors in the context of viscosity and elasticity. These findings are broadly applicable to the study of novel emergent material properties. To illustrate this, we discuss implications of our findings for two very different 2D materials that have recently garnered attention in condensed matter physics: knitted fabrics and twisted bilayer graphene.

cond-mat.soft↗

arXiv2025

A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a family of 2D models generalizing recent experiments on photonic systems. Models in this family reside on amorphous analogs of kagomé lattices with fixed coordination number, vary by a tunable synthetic field, and remarkabaly, permit exact results. We observe two kinds of localization that emerge in these models: Anderson localization by amorphous disorder, and the existence of compact, macroscopically degenerate localized states as in many crystalline flat bands. The flat-band-like degeneracy innate to kagomé lattices survives under amorphousness without on-site disorder. This phenomenon arises from the cooperation between the structure of the compact localized states and the geometry of the amorphous graph. More surprisingly, for particular values of the field, such states emerge in the amorphous system that were not present on the kagomé lattice in the same field. Outside the flat band, constrained amorphous graph geometry necessitates the existence of a fully delocalized state, near which we observe evidence of a localization-delocalization transition. Our platform serves as a demonstration of how the qualitative behavior of a disordered system can be tuned at fixed graph topology and lead to localization phenomena unique to amorphous systems that are not observed in their generically disordered counterparts.

cond-mat.dis-nn↗

arXiv2024

Coherent Magneto-Conductance Oscillations in Amorphous Topological Insulator Nanowires

Recent experiments on amorphous materials have established the existence of surface states similar to those of crystalline three-dimensional topological insulators (TIs). Amorphous topological insulators are also independently of interest for thermo-electric and other properties. To develop an understanding of transport in these systems, we carry out quantum transport calculations for a tight-binding model of an amorphous nano-wire pierced by an axial magnetic flux, then compare the results to known features in the case of crystalline models with disorder. Our calculations complement previous studies in the crystalline case that studied the surface or used a Green's function method. We find that the periodicity of the conductance signal with varying magnetic flux is comparable to the crystalline case, with maxima occurring at odd multiples of magnetic flux quanta. However, the expected amplitude of the oscillation decreases with increasing amorphousness, as defined and described in the main text. We characterize this deviation from the crystalline case by taking ensemble averages of the conductance signatures for various wires with measurements simulated at finite temperatures. This striking transport phenomenon offers a metric to characterize amorphous TIs and stimulate further experiments on this class of materials.

cond-mat.mes-hall↗

arXiv2021

Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition

Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al [Phys. Rev. B 50, 7526 (1994)] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. Here, we report the results of extensive numerics on the phase diagram and criticality of 2D-DDF in the unitary class. We find a critical line at m=0, with energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν_IQH = 2.56 - 2.62 from models of the IQHT. At E=0 however, we obtain ν_0 =2.30-2.36 incompatible with ν_IQH. This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.

cond-mat.mes-hall↗