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Bound states in the continuum (BICs) garnered significant research interest in the field of sensors due to their exceptionally high-quality factors. However, the wide-band continuum in BICs are noise to the bound states, and it is difficult to control and filter. Therefore, we constructed a top-bottom symmetric cavity containing three high permittivity rectangular columns. The cavity supports a symmetry-protected (SP) superbound state (SBS) mode and an accidental (AC) SBS mode within the bandgap. With a period size of 5 × 15, the bandgap effectively filters out the continuum, allowing only the bound states to exist. This configuration enabled us to achieve a high signal-to-noise ratio and a wide free-spectral-range. The AC SBS and the SP SBS can be converted into quasi-SBS by adjusting different parameters. Consequently, the cavity can function as a single-band sensor or a dual-band sensor. The achieved bulk sensitivity was 38 µm/RIU in terahertz wave band, and a record-high FOM reached 2.8 × 108 RIU−1. The effect of fabrication error on the performance for sensor application was also discussed, showing that the application was feasible. Moreover, for experimental realization, a 3D schematic was presented. These achievements pave the way for compact, high-sensitivity biosensing, multi-wavelength sensing, and other promising applications.

We investigate single and multiple defects embedded in a superconducting host, studying the interplay between the proximity-induced pairing and interactions. We explore the influence of the spin–orbit coupling on energies, polarization and spatial patterns of the bound (Yu–Shiba–Rusinov) states of magnetic impurities in a two-dimensional square lattice. We also address the peculiar bound states in the proximitized Rashba chain, resembling the Majorana quasiparticles, focusing on their magnetic polarization that has been recently reported by S. Jeon et al. ( Science 2017, 358, 772). Finally, we study leakage of these polarized Majorana quasiparticles into side-attached nanoscopic regions and confront them with the subgap Kondo effect near to the singlet–doublet phase transition.

Hybrid superconductor–semiconductor nanowires with Rashba spin–orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor–normal–superconductor junctions made of nanowires with strong Rashba spin–orbit coupling, where an external Zeeman field is applied perpendicular to the spin–orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current–phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current–phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

Under certain conditions, a fermion in a superconductor can separate in space into two parts known as Majorana zero modes, which are immune to decoherence from local noise sources and are attractive building blocks for quantum computers. Promising experimental progress has been made to demonstrate Majorana zero modes in materials with strong spin–orbit coupling proximity coupled to superconductors. Here we report signatures of Majorana zero modes in a material platform utilizing the surface states of gold. Using scanning tunneling microscope to probe EuS islands grown on top of gold nanowires, we observe two well-separated zero-bias tunneling conductance peaks aligned along the direction of the applied magnetic field, as expected for a pair of Majorana zero modes. This platform has the advantage of having a robust energy scale and the possibility of realizing complex designs using lithographic methods.

The most well-known example of an ordered quantum state—superconductivity—is caused by the formation and condensation of pairs of electrons. Fundamentally, what distinguishes a superconducting state from a normal state is a spontaneously broken symmetry corresponding to the long-range coherence of pairs of electrons, leading to zero resistivity and diamagnetism. Here we report a set of experimental observations in hole-doped Ba1−xKxFe2As2. Our specific-heat measurements indicate the formation of fermionic bound states when the temperature is lowered from the normal state. However, when the doping level is x ≈ 0.8, instead of the characteristic onset of diamagnetic screening and zero resistance expected below the superconducting phase transition, we observe the opposite effect: the generation of self-induced magnetic fields in the resistive state, measured by spontaneous Nernst effect and muon spin rotation experiments. This combined evidence indicates the existence of a bosonic metal state in which Cooper pairs of electrons lack coherence, but the system spontaneously breaks time-reversal symmetry. The observations are consistent with the theory of a state with fermionic quadrupling, in which long-range order exists not between Cooper pairs but only between pairs of pairs.A state that breaks time-reversal symmetry is observed in the normal phase above the superconducting critical temperature in a multiband superconductor. This could be explained by correlations between the Cooper pairs formed in different bands.

In a recent experiment (Hou et al 2025 Phys. Rev. X 15 011027), a new type of necklace-like vortex bound state (VBS) was observed and attributed to disorder induced interference among different Caroli–de Gennes–Matricon (CdGM) states within one single vortex. In this work, we further investigate the possibilities of quantum interference among the CdGM states from different vortices in clean superconductors, which may become significant near the upper critical field. We find a series of interference patterns in the local density of states (LDOS) due to the overlap between spatially separated individual CdGM states. On a vortex lattice, the interference can also lead to a necklace-like LDOS, hence, providing an alternative and intrinsic mechanism to observe the novel necklace-like, or other spatially modulated VBS more generally, in experiments. These results can be understood quite well within an effective tight-binding model constructed from the individual CdGM states, and can be checked in future experiments.

Andreev bound states are an expression of quantum coherence between particles and holes in hybrid structures composed of superconducting and non-superconducting metallic parts. Their spectrum carries important information on the nature of the pairing, and determines the current in Josephson devices. Here, I focus on Andreev bound states in systems involving superconductors and ferromagnets with strong spin-polarization. I provide a general framework for non-local Andreev phenomena in such structures in terms of coherence functions, and show how the latter link wave function and Green-function based theories. This article is part of the theme issue 'Andreev bound states'.

This paper proposes an adaptive super-twisting control design method to solve tracking problems for a class of perturbed MIMO nonlinear systems under the condition of input constraints. A partial state’s observer is firstly designed to estimate the unmeasurable states. Then, one designs a sliding surface function and crafts an adaptive super-twisting sliding mode controller under the constraints of input saturation for solving the tracking problems. The signs of the upper and lower bounds of the input saturation functions are not restricted to positive and negative respectively. Under certain conditions, the tracking errors and state estimation errors are all tend to zero within a finite time. Furthermore, there is no need to know the upper bounds of perturbations beforehand due to the usage of adaptive mechanisms embedded control both in the scheme and the state’s observer. An application example is given to demonstrate feasibility and effectiveness of the proposed control scheme.

Optical heating of resonant nanostructures is one of the key issues in modern nanophotonics, being either harmful or desirable effect depending on the applications. Despite a linear regime of light-to-heat conversion being well-studied both for metal and semiconductor resonant systems is generalized as a critical coupling condition, the clear strategy to optimize optical heating upon high-intensity light irradiation is still missing. This work proposes a simple analytical model for such a problem, taking into account material properties changes caused by the heating. It allows us to derive a new general critical coupling condition for the nonlinear case, requiring a counterintuitive initial spectral mismatch between the pumping light frequency and the resonant one. Based on the suggested strategy, we develop an optimized design for efficient nonlinear optical heating, which employs a cylindrical nanoparticle supporting the quasi bound state in the continuum mode (quasi-BIC or so-called ‘super-cavity mode’) excited by the incident azimuthal vector beam. Our approach provides a background for various nonlinear experiments related to optical heating and bistability, where self-action of the intense laser beam can change resonant properties of the irradiated nanostructure.

Superconductivity and magnetism are competing effects that can coexist in certain regimes. Their co-existence leads to unexpected new behaviors that include the onset of exotic electron pair mechanisms and topological phases. In this work, we study the properties of a Josephson junction between two spin-split superconductors. The spin-splitting in the superconductors can arise from either the coupling to a ferromagnetic material or an external magnetic field. The properties of the junction are dominated by the Andreev bound states that are also split. One of these states can cross the superconductor’s Fermi level, leading to a ground-state transition characterized by a suppressed supercurrent. We interpret the supercurrent blockade as coming from a dominance of p-wave pairing close to the junction, where the electrons are at both sides. To support this interpretation, we analyze the different pairing channels and show that p-wave pairing is favored in the case where the magnetization of the two superconductors is parallel and suppressed in the anti-parallel case. We also analyze the noise spectrum that shows signatures of the ground-state transition in the form of an elevated zero-frequency noise.