Weyl semimetals exhibit a myriad of exotic transport responses, among which, the Goos-Hänchen (GH) and Imbert-Fedorov (IF) effects have recently garnered substantial attention. Besides the usual parametric dependence inherited from the underlying Hamiltonian to describe a Weyl system, the IF shift particularly carries a topological identity—it depends on the chirality of the Weyl cones. Observing such signatures following the trail of theoretical predictions applied to clean systems can be severely obfuscated by surface potentials induced by localized impurities that are naturally present in real materials hosting the semimetallic phase. Classifying these potentials, we study their effects on GH and IF shifts to provide useful guidance to experiments that are tuned to the objective of characterizing Weyl semimetals and leveraging them to provide the basis for future technological advances. A transfer matrix-based approach is proposed to study the profile of Weyl wave functions scattering from the impurity potentials. As we unfold, the presence of such potentials can lead to several remarkable effects such as the complete nullification of the IF shift and valley inversion.

Theoretical models of a spin-polarized voltage probe (SPVP) tunnel-coupled to the helical edge states (HES) of a quantum spin Hall system (QSHS) are studied. Our first model of the SPVP comprises Np spin-polarized modes (subprobes), each of which is locally tunnel-coupled to the HES, while the SPVP, as a whole, is subjected to a self-consistency condition ensuring zero average current on the probe. We carry out a numerical analysis which shows that the optimal situation for reading off spin-resolved voltage from the HES depends on the interplay of the probe-edge tunnel-coupling and the number of modes in the probe (Np). We further investigate the stability of our findings by introducing Gaussian fluctuations in (i) the tunnel-coupling between the subprobes and the HES about a chosen average value and (ii) spin-polarization of the subprobes about a chosen direction of the net polarization of SPVP. We also perform a numerical analysis corresponding to the situation where four such SPVPs are implemented in a self-consistent fashion across a ferromagnetic barrier on the HES and demonstrate that this model facilitates the measurements of spin-resolved four-probe voltage drops across the ferromagnetic barrier. As a second model, we employ the edge state of a quantum anomalous Hall state (QAHS) as the SPVP which is tunnel-coupled over an extended region with the HES. A two-dimensional lattice simulation for the quantum transport of the proposed device setup comprising a junction of QSHS and QAHS is considered and a feasibility study of using the edge of the QAHS as an efficient spin-polarized voltage probe is carried out including disorder.

Kibble-Zurek theory (KZ) stands out as the most robust theory of defect generation in the dynamics of phase transitions. KZ utilizes the structure of equilibrium states away from the transition point to estimate the excitations due to the transition using adiabatic and impulse approximations. Here we show, the actual nonequilibrium dynamics lead to a qualitatively different scenario from KZ, as far correlations between the defects (rather than their densities) are concerned. For a quantum Ising chain, we show, this gives rise to a Gaussian spatial decay in the domain wall (kinks) correlations, while KZ would predict an exponential fall. We propose a simple but general framework on top of KZ, based on the “quantum coarsening” dynamics of local correlators in the supposed impulse regime. We outline how our picture extends to generic interacting situations.

We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both bosonic and fermionic Gaussian states in terms of so-called linear complex structures J. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our findings in one- and two-dimensional systems, including the paradigmatic Kitaev honeycomb model. While typically supersymmetry preserves features like area law scaling of the entanglement entropies on either side, we find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy (super area law) in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.

Many advancements have been made in the field of topological mechanics. The majority of the work, however, concerns the topological invariant in a linear theory. In this Letter, we present a generic prescription to define topological indices that accommodates nonlinear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of a topological index in differential geometry known as the Poincare-Hopf index, which features the topological invariant of nonlinear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected nonlinear ZMs in the future.

Topological protection of edge state in quantum spin Hall systems relies only on time-reversal symmetry. Hence, S-z conservation on the edge can be relaxed which can have an interferometric manifestation in terms of spin Berry phase. Primarily it could lead to the generation of spin Berry phase arising from a closed loop dynamics of electrons. Our work provides a minimal framework to generate and detect these effects by employing both spin-unpolarized and spin-polarized leads. We show that spin-polarized leads could lead to resonances or antiresonances in the two-terminal conductance of the interferometer. We further show that the positions of these antiresonances (as a function of energy of the incident electron) get shifted owing to the presence of spin Berry phase. Finally, we present simulations of a device setup using KWANT package which put our theoretical predictions on a firm footing.