A5087371028- Topological Materials and Phenomena
- Graphene research and applications
- Quantum many-body systems
- Advanced Condensed Matter Physics
- Cold Atom Physics and Bose-Einstein Condensates
- 2D Materials and Applications
- Physics of Superconductivity and Magnetism
- Quantum and electron transport phenomena
- Quantum Mechanics and Non-Hermitian Physics
- Quantum chaos and dynamical systems
- Advanced Chemical Physics Studies
- Quantum, superfluid, helium dynamics
- Theoretical and Computational Physics
- Algebraic structures and combinatorial models
- Rare-earth and actinide compounds
- Photorefractive and Nonlinear Optics
- Iron-based superconductors research
- Mechanical and Optical Resonators
- Chemical and Physical Properties of Materials
- Magnetic Properties of Alloys
- Noncommutative and Quantum Gravity Theories
- Liquid Crystal Research Advancements
- Magnetic properties of thin films
- Semiconductor Quantum Structures and Devices
- Nonlinear Dynamics and Pattern Formation
University of Cambridge
2020-2025
University of Manchester
2025
Cavendish Hospital
2025
Harvard University
2019-2023
Purdue University West Lafayette
2022
Max Planck Institute for the Physics of Complex Systems
2017-2019
Max Planck Society
2018
Leiden University
2012-2017
We consider conditions for the existence of boundary modes in non-Hermitian systems with edges arbitrary codimension. Through a universal formulation formation criteria terms local Green's functions, we outline generic perspective on appearance such and generate corresponding dispersion relations. In process, explain skin effect both topological nontopological systems, exhaustively generalizing bulk-boundary correspondence to different types gap conditions, prominent distinguishing feature...
The celebrated ``tenfold way'' provides a scheme for categorizing general topological states of matter, but it does not take into account the crystal symmetries that always exist in real materials. A new method extends this organization to allow categorization all topologically distinct electronic band structures materials with only any number physically relevant dimensions.
We present a general methodology towards the systematic characterization of crystalline topological insulating phases with time reversal symmetry (TRS).~In particular, taking two-dimensional spinful hexagonal lattice as proof principle we study windings Wilson loop spectra over cuts in Brillouin zone that are dictated by underlying symmetries.~Our approach finds prominent use elucidating and quantifying recently proposed ``topological quantum chemistry" (TQC) concept.~Namely, prove split an...
We show that the local in-gap Green's function of a band insulator ${\mathbf{G}}_{0}(\ensuremath{\epsilon},{\mathbf{k}}_{\ensuremath{\parallel}},{\mathbf{r}}_{\ensuremath{\perp}}=0)$, with ${\mathbf{r}}_{\ensuremath{\perp}}$ position perpendicular to codimension-1 or codimension-2 impurity, reveals topological nature phase. For insulator, eigenvalues this attain zeros in gap, whereas for trivial remain nonzero. This classification is related existence bound states along and impurities....
Out-of-plane polar domain structures have recently been discovered in strained and twisted bilayers of inversion symmetry broken systems such as hexagonal boron nitride. Here we show that this breaking also gives rise to an in-plane component polarization, the form total polarization is determined purely from considerations. The makes domains topologically non-trivial, forming a network merons antimerons (half-skyrmions half-antiskyrmions). For systems, are Bloch type whereas for they N\'eel...
While a significant fraction of topological materials has been characterized using symmetry requirements
We analyze quantum-geometric bounds on optical weights in topological phases with pairs of bands hosting nontrivial Euler class, a multigap invariant characterizing non-Abelian band topology. show how the constrain combined at different dopings and further restrict size adjacent gaps. In this process, we also consider associated interband contributions to dc conductivities flat-band limit. physically validate these results by recasting bound terms transition rates absorption light,...
The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures a new type topology -- Euler class such dynamical setting. enigmatic invariant $(\xi)$ falls outside conventional symmetry-eigenvalue indicated phases and, simplest incarnation, is described by triples bands that comprise gapless pair, featuring $2\xi$ stable band nodes, and gapped band. These nodes host non-Abelian charges can be further undone...
The study of topological bandstructures is an active area research in condensed matter physics and beyond. Here, we combine recent progress this field with developments machine-learning, another rising topic interest. Specifically, introduce unsupervised machine-learning approach that searches for retrieves paths adiabatic deformations between Hamiltonians, thereby clustering them according to their properties. algorithm general as it does not rely on a specific parameterization the...
We show that the π flux and dislocation represent topological observables probe two-dimensional order through binding of zero-energy modes. analytically demonstrate hosts a Kramers pair zero modes in Γ (Berry phase Skyrmion at momentum) M finite phases M-B model introduced for HgTe quantum spin Hall insulator. Furthermore, we acts as flux, but only so phase. Our numerical analysis confirms this bound to appearing only, further demonstrates robustness disorder Rashba coupling. Finally,...
We elucidate the general rule governing response of dislocation lines in three-dimensional topological band insulators. According to this $\mathbf{K}\text{\ensuremath{-}}\mathbf{b}\text{\ensuremath{-}}\mathbf{t}$ rule, lattice topology, represented by oriented direction $\mathbf{t}$ with Burgers vector $\mathbf{b}$, combines electronic-band characterized band-inversion momentum ${\mathbf{K}}_{\mathrm{inv}}$, produce gapless propagating modes when plane orthogonal line features a inversion...
We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on ${C}_{2}\mathcal{T}$-symmetric systems that have gained recent attention, for example, in context layered van-der-Waals graphene heterostructures, we relate these insights homotopy groups Grassmannians flag varieties, which turn correspond cohomology classes Wilson-flow...
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one quintessential ideas in physics topological quantum matter. Nevertheless, it has not been proven all generality and certain scenarios even shown to fail, depending on boundary profiles terminated system. Here, we introduce bulk numbers that capture exact number in-gap modes, without any such subtleties spatial dimension. Similarly, based these 1D numbers, define new 2D winding number, which...
A striking feature of time-reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when surface states gapped breaking perturbations. While TRS-protected TIs have become increasingly under control, magnetic analogs still largely unexplored territory with novel rich structures. In particular, can also host quantized axion term in presence lattice symmetries. Since these symmetries naturally broken...
Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by perturbative renormalization-group (RG) analysis shows that weak disorder is an irrelevant perturbation at semimetal(WSM)-insulator quantum critical point (QCP). But, metallic sets in through transition (QPT) strong across multicritical (MCP). field theoretic predictions for correlation length exponent...
The past years have seen rapid progress in the classification of topological materials. These diagnostical methods are increasingly getting explored pertinent context magnetic structures. We report on a general class electronic configurations within set anti-ferromagnetic-compatible space groups that necessarily topological. Interestingly, we find systematic correspondence between these anti-ferromagnetic phases to nontrivial ferro/ferrimagnetic counterparts readily obtained through...
Topological phases of matter have revolutionised the fundamental understanding band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies been extensively explored, a large number materials theoretically proposed experimentally observed. These ideas recently extended to multi-gap with nodes that carry non-Abelian charges, characterised by invariants arise momentum space braiding nodes. However, constraints...
We show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which superposition two circularly polarized waves with frequencies are integer multiples each other, traces out rose pattern the polarization plane can be chosen break selective symmetries, including spatial inversion. Using realistic low-energy model, we theoretically demonstrate three-dimensional Dirac semimetal Cd_{3}As_{2} promising platform for BCL...
Topological band theory has conventionally been concerned with the topology of bands around a single gap. Only recently non-Abelian topologies that thrive on involving multiple gaps were studied, unveiling new horizon in topological physics beyond conventional paradigm. Here, we report first experimental realization Euler insulator phase unique meronic characterization an acoustic metamaterial. We demonstrate this several nontrivial features: First, system cannot be described by theory, but...
This paper shows that the dynamics of two-band systems can be characterized by Hopf maps, where winding numbers are cast as linking numbers. finding opens doors towards both investigation insulators in experiments with ultracold atoms driven optical lattices and measurement Floquet topological invariants via observation post quench-dynamics
Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide condensed matter realization chiral anomaly, feature topologically protected Fermi arc surface states, and sustain sharp quasiparticles up to critical disorder at which continuous quantum phase transition (QPT) drives the system into metallic phase. We here numerically demonstrate that with increasing strength disorder, gradually loses its sharpness, close WSM-metal QPT it completely dissolves bath bulk....