Reactivity to sustainability metrics: A configurational study of motivation and capacity

Previous research on reactivity – defined as changing organisational behaviour to better conform to the criteria of measurement in response to being measured – has found significant variation in company responses towards sustainability metrics. We propose that reactivity is driven by dialogue, motivation and capacity in a configurational way. Empirically, we use fuzzy set Qualitative Comparative Analysis (fsQCA) to analyse company responses to the sustainability index FTSE4Good. We find evidence of complimentary and substitute effects between motivation and capacity. Based on these effects we develop a typology of reactivity to sustainability metrics, which also theorises the use of metrics as tools for performance feedback and the building of calculative capacity. We show that when reactivity is studied configurationally, we can identify previously underacknowledged types of responses. We discuss the theoretical and practical implications for studying and using sustainability metrics as governance tools for responsible behaviour

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.Comment: 6 pages, 3 figures + 2 pages, 1 figure supplementar

Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation lines oriented in direction ${\bf t}$ with Burgers vector ${\bf b}$, combines with the electronic-band topology, characterized by the band-inversion momentum ${\bf K}_{\rm inv}$, to produce gapless propagating modes when the plane orthogonal to the dislocation line features a band inversion with a nontrivial ensuing flux $\Phi={\bf K}_{\rm inv}\cdot {\bf b}\,\, ({\rm mod\,\,2\pi})$. Although it has already been discovered by Y. Ran {\it et al.}, Nature Phys. {\bf 5}, 298 (2009), that dislocation lines host propagating modes, the exact mechanism of their appearance in conjunction with the crystal symmetries of a topological state is provided by the ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule . Finally, we discuss possible experimentally consequential examples in which the modes are oblivious for the direction of propagation, such as the recently proposed topologically-insulating state in electron-doped BaBiO$_3$.Comment: Main text + supplementary material, published versio

The translational side of topological band insulators

Spin-orbit coupled materials have attracted revived prominent research interest as of late, especially due their connection with topological materials. A hallmark of this pursuit is arguably formed by the advent of topological band insulators (TBIs). Whereas such topological systems are often characterized by the presence of metallic edge states, we here provide a review on the equally rich, although far less explored, aspects of the bulk. Starting from the fact that pi fluxes unambiguously probe the nontrivial nature of time reversal invariant TBIs upon binding special excitations, we summarize the criteria for the formation of similar localized modes in the presence of crystal dislocations. These criteria under which dislocations act as effective fluxes directly relate to their status as unique probes of translational symmetry breaking and as such pinpoint an indexing of TBIs beyond the standard tenfold way. Apart from elucidating refined classification schemes that include crystal symmetries, we also review why the predicted dislocation physics may be perceived compelling in its own right. For example, the study of these defects could result in new routes to explore spin-charge separated excitations. Similarly, arrays of dislocations, as realizable in ordinary grain boundaries, can be shown to host self organized semimetals that have distinct transport properties. Most importantly, however, research efforts on the material side as well as recent experimental signatures further indicate that the outlined perspective can very well provide for an attractive, timely and experimentally viable research agenda beyond the edge state focussed activities

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.Comment: 15 pages, 4 figures. Supplement added. Substantial extension of result

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.Comment: 27 pages, 13 figures, v2: minor corrections, new references included, v3: metastable topology of split EBRs emphasized, v4: prepared for publicatio

Self-organized pseudo-graphene on grain boundaries in topological band insulators

Semi-metals are characterized by nodal band structures that give rise to exotic electronic properties. The stability of Dirac semi-metals, such as graphene in two spatial dimensions (2D), requires the presence of lattice symmetries, while akin to the surface states of topological band insulators, Weyl semi-metals in three spatial dimensions (3D) are protected by band topology. Here we show that in the bulk of topological band insulators, self-organized topologically protected semi-metals can emerge along a grain boundary, a ubiquitous extended lattice defect in any crystalline material. In addition to experimentally accessible electronic transport measurements, these states exhibit valley anomaly in 2D influencing edge spin transport, whereas in 3D they appear as graphene-like states that may exhibit an odd-integer quantum Hall effect. The general mechanism underlying these novel semi-metals -- the hybridization of spinon modes bound to the grain boundary -- suggests that topological semi-metals can emerge in any topological material where lattice dislocations bind localized topological modes.Comment: 14 pages, 6 figures. Improved discussion compared to the earlier versio

Banking across Borders

Deze studie analyseert internationalisatie strategieën van de grootste banken ter wereld tussen 1980 en 2000. Deze banken hebben de internationalisatie activiteiten gedomineerd; in totaal worden 44 banken uit 8 landen onderzocht. Overeenkomsten en verschillen in strategieën worden bepaald op basis van een typologie die in deze studie ontwikkeld is. De belangrijkste onderzoeksvraag richt zich op de effectiviteit van deze internationalisatie strategieën. Met behulp van een zelf ontwikkelde internationalisatie database worden verschillen in binnenlands en buitenlands rendement berekend, en effecten van internationalisatie op aandeelhoudersrendement. Over het algemeen heeft meer internationalisatie een negatief effect op het rendement van de bank gehad. Op dezelfde manier hebben aandeelhouders niet geprofiteerd van meer internationalisatie. Banken die hun internationalisatie beperkten genereerden het meeste aandeelhoudersrendement, net als banken met een langdurige aanwezigheid in het buitenland. Banken die daarentegen hun buitenlandse activiteiten over een langere periode (sterk) uitbreidden hebben het minste rendement voor aandeelhouders gegenereerd. De studie richt zich ook op toekomstige ontwikkelingen in het internationaal bankieren - welke strategieën zullen de banken hanteren? Mogelijkheden voor verdere binnenlandse financiële deregulering, onzekerheid over het internationale regulerings raamwerk, en de gekozen business mix van banken spelen een belangrijke rol in de richting van toekomstige internationalisatie strategieën en de mogelijkheden voor extra rendement.The study examines the internationalization strategies of the world’s largest banks between 1980 and 2000. These banks have dominated the internationalization of banking. For 44 banks, commonalities and differences are identified on the basis of a strategic typology developed for this study. The central research question deals with the effectiveness of internationalization. Using a self constructed internationalization database, differences are estimated between foreign and domestic performance, and the effects on shareholder return. A higher degree of internationalization has on average contributed negatively to bank performance. Similarly, shareholders have not gained by more internationalization. Banks who retreated from their internationalization or banks with a long established internationalization strategy generated the highest total shareholder return. Banks who (strongly) increased their internationalization generated the least returns. The study also addresses the future outlook for international banking - how will the internationalization of banks proceed? The potential for further financial deregulation in the home country, uncertainty on the international regulatory regime, and the business mix of the bank are likely drivers for the bank's future internationalization strategy and profitability enhancement