arXiv subjects

Robert-Jan Slager

Publications and source records attributed to Robert-Jan Slager.

At least 91 records · Page 5Linked to original sources

arXiv2021

Subdimensional topologies, indicators and higher order phases

The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features. Within this context we recently reported on a class of unexplored topological structures that thrive on the concept of {\it sub-dimensional topology}. Although such phases have trivial indicators and band representations when evaluated over the complete Brillouin zone, they have stable or fragile topologies within sub-dimensional spaces, such as planes or lines. This perspective does not just refine classification pursuits, but can result in observable features in the full dimensional sense. In three spatial dimensions (3D), for example, sub-dimensional topologies can be characterized by non-trivial planes, having general topological invariants, that are compensated by Weyl nodes away from these planes. As a result, such phases have 3D stable characteristics such as Weyl nodes, Fermi arcs and edge states that can be systematically predicted by sub-dimensional analysis. Within this work we further elaborate on these concepts. We present refined representation counting schemes and address distinctive bulk-boundary effects, that include momentum depended (higher order) edge states that have a signature dependence on the perpendicular momentum. As such, we hope that these insights might spur on new activities to further deepen the understanding of these unexplored phases.

cond-mat.mes-hall↗

arXiv2020

Discovery of a weak topological insulating state and van Hove singularity in triclinic RhBi2

Time reversal symmetric (TRS) invariant topological insulators (TIs) fullfil a paradigmatic role in the field of topological materials, standing at the origin of its development. Apart from TRS protected 'strong' TIs, it was realized early on that more confounding weak topological insulators (WTI) exist. WTIs depend on translational symmetry and exhibit topological surface states only in certain directions making it significantly more difficult to match the experimental success of strong TIs. We here report on the discovery of a WTI state in RhBi2 that belongs to the optimal space group P1, which is the only space group where symmetry indicated eigenvalues enumerate all possible invariants due to absence of additional constraining crystalline symmetries. Our ARPES, DFT calculations, and effective model reveal topological surface states with saddle points that are located in the vicinity of a Dirac point resulting in a van Hove singularity (VHS) along the (100) direction close to the Fermi energy. Due to the combination of exotic features, this material offers great potential as a material platform for novel quantum effects.

cond-mat.str-el↗

arXiv2020

Topological Euler class as a dynamical observable in optical lattices

The last years have witnessed rapid progress in the topological characterization of out-of-equilibrium systems. We report on robust signatures of a new type of topology -- the Euler class -- in such a dynamical setting. The enigmatic invariant $(ξ)$ falls outside conventional symmetry-eigenvalue indicated phases and, in simplest incarnation, is described by triples of bands that comprise a gapless pair, featuring $2ξ$ stable band nodes, and a gapped band. These nodes host non-Abelian charges and can be further undone by converting their charge upon intricate braiding mechanisms, revealing that Euler class is a fragile topology. We theoretically demonstrate that quenching with non-trivial Euler Hamiltonian results in stable monopole-antimonopole pairs, which in turn induce a linking of momentum-time trajectories under the first Hopf map, making the invariant experimentally observable. Detailing explicit tomography protocols in a variety of cold-atom setups, our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.

cond-mat.quant-gas↗

arXiv2020

Geometric approach to fragile topology beyond symmetry indicators

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 the context of layered van-der-Waals graphene heterostructures, we relate these insights to homotopy groups of Grassmannians and flag varieties, which in turn correspond to cohomology classes and Wilson-flow approaches. We furthermore make use of a geometric construction, the so-called Plücker embedding, to induce windings in the band structure necessary to facilitate non-trivial topology. Specifically, this directly relates to the parametrization of the Grassmannian, which describes partitioning of an arbitrary band structure and is embedded in a better manageable exterior product space. From a physical perspective, our construction encapsulates and elucidates the concepts of fragile topological phases beyond symmetry indicators as well as non-Abelian reciprocal braiding of band nodes that arises when the multiple gaps are taken into account. The adopted geometric viewpoint most importantly culminates in a direct and easily implementable method to construct model Hamiltonians to study such phases, constituting a versatile theoretical tool.

cond-mat.mes-hall↗

arXiv2020

Selective branching, quenching, and converting of topological modes

A salient feature of topological phases are surface states and many of the widely studied physical properties are directly tied to their existence. Although less explored, a variety of topological phases can however similarly be distinguished by their response to localized flux defects, resulting in the binding of modes whose stability can be traced back to that of convectional edge states. The reduced dimensionality of these objects renders the possibility of arranging them in distinct geometries, such as arrays that branch or terminate in the bulk. We show that the prospect of hybridizing the modes in such new kinds of channels poses profound opportunities in a dynamical context. In particular, we find that creating junctions of $π$-flux chains or extending them as function of time can induce transistor and stop-and-go effects. Pending controllable initial conditions certain branches of the extended defect array can be actively biased. Discussing these physical effects within a generally applicable framework that relates to a variety of established artificial topological materials, such as mass-spring setups and LC circuits, our results offer an avenue to explore and manipulate new transport effects that are rooted in the topological characterization of the underlying system.

cond-mat.mes-hall↗

arXiv2020

Unsupervised machine learning and band topology

The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest. Specifically, we introduce an unsupervised machine-learning approach that searches for and retrieves paths of adiabatic deformations between Hamiltonians, thereby clustering them according to their topological properties. The algorithm is general as it does not rely on a specific parameterization of the Hamiltonian and is readily applicable to any symmetry class. We demonstrate the approach using several different models in both one and two spatial dimensions and for different symmetry classes with and without crystalline symmetries. Accordingly, it is also shown how trivial and topological phases can be diagnosed upon comparing with a generally designated set of trivial atomic insulators.

cond-mat.mes-hall↗

arXiv2019

Wannier representation of Floquet topological states

A universal feature of topological insulators is that they cannot be adiabatically connected to an atomic limit, where individual lattice sites are completely decoupled. This property is intimately related to a topological obstruction to constructing a localized Wannier function from Bloch states of an insulator. Here we generalize this characterization of topological phases toward periodically driven systems. We show that nontrivial connectivity of hybrid Wannier centers in momentum space and time can characterize various types of topology in periodically driven systems, which include Floquet topological insulators, anomalous Floquet topological insulators with micromotion-induced boundary states, and gapless Floquet states realized with topological Floquet operators. In particular, nontrivial time dependence of hybrid Wannier centers indicates impossibility of continuous deformation of a driven system into an undriven insulator, and a topological Floquet operator implies an obstruction to constructing a generalized Wannier function which is localized in real and frequency spaces. Our results pave a way to a unified understanding of topological states in periodically driven systems as a topological obstruction in Floquet states.

cond-mat.mes-hall↗

arXiv2019

Intrinsic axion insulating behavior in antiferromagnetic MnBi$_6$Te$_{10}$

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 the surface states are gapped by time reversal breaking perturbations. While time reversal symmetry (TRS) protected TIs have become increasingly under control, magnetic analogs are still largely unexplored territories with novel rich structures. In particular, topological magnetic insulators can also host a quantized axion term in the presence of lattice symmetries. Since these symmetries are naturally broken on the boundary, the surface states can develop a gap without external manipulation. In this work, we combine theoretical analysis, density functional calculations and experimental evidence to reveal intrinsic axion insulating behavior in MnBi6Te10. The quantized axion term arises from the simplest possible mechanism in the antiferromagnetic regime where it is protected by inversion symmetry and a fractional translation symmetry. The anticipated gapping of the Dirac surface state at the edge is subsequently experimentally established using Angle Resolved Spectroscopy. As a result, this system provides the magnetic analogue of the simplest TRS protected TI with a single, gapped Dirac cone at the surface.

cond-mat.mtrl-sci↗

arXiv2019

Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry

We present a general methodology towards the systematic characterization of crystalline topological insulating phases with time reversal symmetry (TRS).~In particular, taking the two-dimensional spinful hexagonal lattice as a proof of principle we study windings of Wilson loop spectra over cuts in the Brillouin zone that are dictated by the underlying lattice symmetries.~Our approach finds a prominent use in elucidating and quantifying the recently proposed ``topological quantum chemistry" (TQC) concept.~Namely, we prove that the split of an elementary band representation (EBR) by a band gap must lead to a topological phase.~For this we first show that in addition to the Fu-Kane-Mele $\mathbb{Z}_2$ classification, there is $C_2\mathcal{T}$-symmetry protected $\mathbb{Z}$ classification of two-band subspaces that is obstructed by the other crystalline symmetries, i.e.~forbidding the trivial phase. This accounts for all nontrivial Wilson loop windings of split EBRs \textit{that are independent of the parameterization of the flow of Wilson loops}.~Then, we show that while Wilson loop winding of split EBRs can unwind when embedded in higher-dimensional band space, two-band subspaces that remain separated by a band gap from the other bands conserve their Wilson loop winding, hence revealing that split EBRs are at least "stably trivial", i.e. necessarily non-trivial in the non-stable (few-band) limit but possibly trivial in the stable (many-band) limit.~This clarifies the nature of \textit{fragile} topology that has appeared very recently.~We then argue that in the many-band limit the stable Wilson loop winding is only determined by the Fu-Kane-Mele $\mathbb{Z}_2$ invariant implying that further stable topological phases must belong to the class of higher-order topological insulators.

cond-mat.mes-hall↗

arXiv2019

Hopf characterization of two-dimensional Floquet topological insulators

We present a topological characterization of time-periodically driven two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity of the Floquet system with respect to both time and the underlying two-dimensional momentum space constitutes a map from a three dimensional torus to the Bloch sphere. As a result, we find that the driven system can be understood by appealing to a Hopf map that is directly constructed from the micromotion of the drive. Previously found winding numbers are shown to correspond to Hopf invariants, which are associated with linking numbers describing the topology of knots in three dimensions. Moreover, after being cast as a Hopf insulator, not only the Chern numbers, but also the winding numbers of the Floquet topological insulator become accessible in experiments as linking numbers. We exploit this description to propose a feasible scheme for measuring the complete set of their Floquet topological invariants in optical lattices.

cond-mat.quant-gas↗

arXiv2019

Non-Hermitian Boundary Modes

We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline a generic perspective on the appearance of such modes and generate corresponding dispersion relations. In the process, we explain the skin effect in both topological and non-topological systems, exhaustively generalizing bulk-boundary correspondence in the presence of non-Hermiticity. This is accomplished via a doubled Green's function, inspired by doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work constitutes a general tool, as well as, a unifying perspective for this rapidly evolving field. Indeed, as a concrete application we find that our method can expose novel non-Hermitian topological regimes beyond the reach of previous methods.

cond-mat.mes-hall↗

arXiv2019

$π$-fluxes, semi-metals and flat bands in artificial materials

The possibility of engineering experimentally viable systems that realize gauge fluxes within plaquettes of hopping have been subject of search for decades due to vast amounts of theoretical study. This is of particular interest for topological band insulators, where it is known that such fluxes bind protected mid-gap states. These modes can hybridize in extended flux lattices, giving rise to semi-metallic bands that are highly tunable. We demonstrate that within artificial materials, local $π$-fluxes can be naturally realized. Consequently, we provide concrete set-ups to access this physics and analyze similar self-organized band structures and physical properties. Our work therefore does not only pinpoint simple systems exhibiting flat bands, but also opens up a route to study flux lattice models and associated effective theories in a novel scene.

cond-mat.mes-hall↗

arXiv2018

Dynamical synchronization transition in interacting electron systems

Synchronization is a ubiquitous phenomenon in nature and we propose its new perspective in ultrafast dynamics in interacting electron systems. In particular, using graphene irradiated by an intense bi-circular pulse laser as a prototypical and experimental viable example, we theoretically investigate how to selectively generate a coherent oscillation of electronic order such as charge density waves (CDW). The key is to use tailored fields that match the crystalline symmetry broken by the target order. After the pump, a macroscopic number of electrons start oscillating and coherence is built up through a transition. The resulting physics is detectable as a coherent light emission at the synchronization frequency and may be used as a purely electronic way of realizing Floquet states respecting exotic space time crystalline symmetries. In the process, we also explore possible flipping of existing static CDW orders and generation of higher harmonics. The general framework for the coherent electronic order is found to be analogous with the celebrated Kuramoto model, describing the classical synchronization of coupled pendulums.

cond-mat.str-el↗

arXiv2018

Spin Hall effect in 2D metallic delafossite PtCoO$_2$ and vicinity topology

The two-dimensional (2D) metal PtCoO$_2$ is renowned for the lowest room temperature resistivity among all oxides, close to that of the top two materials Ag and Cu. In addition, we theoretically predict a strong intrinsic spin Hall effect. This originates from six strongly-tilted Dirac cones that we find in the electronic structure near the Fermi surface, where a gap is opened by large spin-orbit coupling (SOC). This is underpinned by rich topological properties; in particular, the phenomenology of a mirror Chern metal is realized not exactly, but very accurately, on account of an approximate crystalline symmetry. We expect that such 'vicinity topology' to be a feature of relevance well beyond this material. Our Wilson loop analysis indicates further elaborate features such as fragile topology. These findings highlight PtCoO$_2$ as a promising material for spintronic applications as well as a platform to study the interplay of symmetry and topology.

cond-mat.mes-hall↗

arXiv2018

Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality

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 a perturbative renormalization-group (RG) analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal(WSM)-insulator quantum critical point (QCP). But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point (MCP). The field theoretic predictions for the correlation length exponent $ν=2$ and dynamic scaling exponent $z=5/4$ at this MCP are in good agreement with the ones extracted numerically, yielding $ν=1.98 \pm 0.10$ and $z=1.26 \pm 0.05$, from the scaling of the average density of states (DOS). Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT. We here demonstrate that in the presence of generic, but strong disorder the WSM-metal QPT is ultimately always characterized by the exponents $ν=1$ and $z=3/2$ (to one-loop order), originating from intra-node or chiral symmetric (e.g., regular and axial potential) disorder. We here anchor such emergent \emph{chiral superuniversality} through complementary RG calculations, controlled via $ε$-expansions, and numerical analysis of average DOS across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy. The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Gr$\ddot{\mbox{u}}$neisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid are discussed.

cond-mat.mes-hall↗

arXiv2017

Dissolution of topological Fermi arcs in a dirty Weyl semimetal

Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder the Fermi arc gradually looses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. Predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can directly be observed in angle-resolved-photo-emmision-spectroscopy (ARPES) and Fourier transformed scanning-tunneling-microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.

cond-mat.mes-hall↗

arXiv2017

Unified bulk-boundary correspondence for band insulators

The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has in certain scenarios even been shown to fail, depending on the boundary profiles of the terminated system. Here, we introduce bulk numbers that capture the exact number of in-gap modes, without any such subtleties in one spatial dimension. Similarly, based on these 1D bulk numbers, we define a new 2D winding number, which we call the pole winding number, that specifies the number of robust metallic surface bands in the gap as well as their topological character. The underlying general methodology relies on a simple continuous extrapolation from the bulk to the boundary, while tracking the evolution of Green's function's poles in the vicinity of the bulk band edges. As a main result we find that all the obtained numbers can be applied to the known insulating phases in a unified manner regardless of the specific symmetries. Additionally, from a computational point of view, these numbers can be effectively evaluated without any gauge fixing problems. In particular, we directly apply our bulk-boundary correspondence construction to various systems, including 1D examples without a traditional bulk-boundary correspondence, and predict the existence of boundary modes on various experimentally studied graphene edges, such as open boundaries and grain boundaries. Finally, we sketch the 3D generalization of the pole winding number by in the context of topological insulators.

cond-mat.str-el↗

arXiv2017

The translational side of topological band insulators

Spin-orbit coupled materials have attracted revived prominent research interest as of late, especially due their direct connection with topological notions. Arguably, a hallmark of this pursuit is formed by the concept of the topological band insulator (TBI). In these incompressible systems band inversions, often driven by strong spin-orbit coupling, result in a state that is topologically distinct from the usual insulator as long as time reversal symmetry is maintained. More generally, topological states that arise by virtue of a protecting symmetry have resulted in a flourishing research field on both the experimental as well as theoretical side of the condensed matter agenda. As a prime signature topological band insulators can exhibit protected spin filtered edge states, whose time reversal invariant partner is spatially separated on the other edge. While these edge states have resultantly been identified with many exotic physical phenomena, we here wish to provide a perspective on the equally rich, although far less explored, aspects of the bulk. That is, we will focus on the role of lattice defects, dislocations in particular, and their relation with the topological nature of the bulk.

cond-mat.mes-hall↗