We experimentally investigate supercurrent through Coulomb islands, where island and leads are fabricated from semiconducting nanowires with fully surrounding superconducting shells. Applying flux along the wire yields a series of destructive Little-Parks lobes with reentrant supercurrent. We find Coulomb blockade with $2e$ peak spacing in the zeroth lobe and $1e$ average spacing, with regions of significant even-odd modulation, in the first lobe. Evolution of Coulomb-peak amplitude through the first lobe is consistent with a theoretical model of supercurrent carried predominantly by zero-energy states in the leads and the island.

Despite fascinating experimental results, the influence of defects and elastic strains on the physical state of nanosized ferroelectrics is still poorly explored theoretically. One of the unresolved theoretical problems is the analytical description of the strongly enhanced spontaneous polarization, piezoelectric response, and dielectric properties of ferroelectric oxide thin films and core-shell nanoparticles induced by elastic strains and stresses. In particular, the 10-nm quasi-spherical $\mathrm{BaTi}{\mathrm{O}}_3$ core-shell nanoparticles reveal a giant spontaneous polarization up to $130\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$, where the physical origin is a large Ti off-centering. The available theoretical description cannot explain the giant spontaneous polarization observed in these spherical nanoparticles. This work analyzes polar properties of $\mathrm{BaTi}{\mathrm{O}}_3$ core-shell spherical nanoparticles using the Landau-Ginzburg-Devonshire approach, which considers the nonlinear electrostriction coupling and large Vegard strains in the shell. We reveal that a spontaneous polarization greater than $50\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$ can be stable in a (10–100)-nm $\mathrm{BaTi}{\mathrm{O}}_3$ core at room temperature, where a 5-nm paraelectric shell is stretched by (3–6)% due to Vegard strains, which contribute to the elastic mismatch at the core-shell interface. The polarization value $50\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$ corresponds to high tetragonality ratios (1.02–1.04), which is further increased up to $100\mu \mathrm{C}/\mathrm{c}{\mathrm{m}}^2$ by higher Vegard strains and/or intrinsic surface stresses leading to unphysically high tetragonality ratios (1.08–1.16). The nonlinear electrostriction coupling and the elastic mismatch at the core-shell interface are key physical factors of the spontaneous polarization enhancement in the core. Doping with the highly polarized core-shell nanoparticles can be useful in optoelectronics and nonlinear optics to increase beam coupling efficiency, electric field enhancement, reduced switching voltages, ionic contamination elimination, catalysis, and electrocaloric nanocoolers.

Layered thermoelectric ${\mathrm{Mg}}_3{\mathrm{Sb}}_2$ has inspired increasing interest due to its inherently peculiar phonon and electron properties. Here, we propose the crucial role of temperature-induced renormalization of phonon and electron transports in the thermal, electronic, and thermoelectric performance by considering the peculiar temperature-dependent anharmonic phonon vibrational modes. After the phonon renormalization is included, the lattice thermal conductivity has a very weak temperature dependence of $\sim T^{-0.62}$ that agrees better with the experimental results than other theoretical pictures, in sharp contrast to the traditional harmonic $T^{-1}$ trend. This is because the strong quartic anharmonicity induces significant hardening of low-lying acoustic phonon modes at the Brillouin zone boundary with temperature and finally suppresses the scattering rate by reducing the phonon scattering phase space. The fundamental band gap anomalously increases with temperature rather than decreasing as in most semiconductors because the greatly strengthened electron-acoustic-phonon coupling by locally asymmetric atomic vibrations drops the valence band maximum significantly. Furthermore, the temperature dependence of thermopower is effectively improved by the temperature-renormalized electronic structures, and then, combined with the phonon renormalization, excellent thermoelectric performance in good agreement with the experimental data is described. Our work establishes the relationship of temperature-renormalized phonon and electron transports versus intrinsic anharmonic acoustic phonon modes, which is helpful for describing the related physical properties more precisely at elevated temperatures.

Topological qubits composed of unpaired Majorana zero modes are under intense experimental and theoretical scrutiny in efforts to realize practical quantum computation schemes. In this work, we show that the minimum four unpaired Majorana zero modes required for a topological qubit according to braiding schemes and control of entanglement for gate operations are inherent to multiplicative topological phases, which realize symmetry-protected tensor products—and maximally entangled Bell states—of unpaired Majorana zero modes. We construct and characterize both one-dimensional and two-dimensional multiplicative topological phases with two parent Kitaev chain Hamiltonians. We furthermore characterize topology in the bulk and on the boundary with established methods while also introducing techniques to overcome challenges in characterizing multiplicative topology. In the process, we explore the potential of these multiplicative topological phases for an alternative to braiding-based topological quantum computation schemes, in which gate operations are performed through topological phase transitions.

A phase transition is found in ${\mathrm{Ti}}_3{\mathrm{C}}_2{\mathrm{T}}_x$ MXene at 350 K, by measuring the complex Young's modulus of self-standing thick films. A steplike softening and increase of the mechanical losses is found below 350 K, indicative of a phase transition, where the square of the order parameter is coupled to strain. It is argued that it should be a ferroelectric transition, most likely of the sliding (moiré) type, due to charge transfer between facing flakes sliding with respect to each other. If the transition will be confirmed to be ferroelectric, ${\mathrm{Ti}}_3{\mathrm{C}}_2{\mathrm{T}}_x$ will be added to the class of metallic ferroelectrics and open new perspectives of applications, in addition to the numerous already studied.

The melting curve of pure silica (${\mathrm{SiO}}_2$) was determined using ab initio density functional theory together with the solid-liquid coexisting approach, thermodynamic integration, and the Z method. The melting curves are consistent with a smooth, slow increase in a large region from 50 GPa ($dT/dP \approx 15$ K/GPa) to about 500 GPa ($dT/dP \approx 5$ K/GPa) without any abrupt changes at around 120 and 300 GPa as seen in some recent experimental and computational studies. The topography of the melting curve above 50 GPa is consistent with a gradual change in the distribution of the Si coordination numbers in the liquid state and the absence of large changes in the density following solid-solid phase transitions. The pair distribution functions show that the structural correlation in the liquid is mainly short range and that the Si-O bond is stiff. The densification of the melt structure with pressure above 50 GPa is therefore due to an increase in seven- and eightfold coordinated silicon.

In this paper, the effects of rotation on a phononic crystal (PnC) operated in whispering-gallery modes (WGMs) are investigated for the first time. According to the results of a finite element method, the vibration pattern of the WGMs under the action of rotation will undergo a linear precession with the integral of rotation, which agrees with the theoretical models. In addition, the precession of WGMs will linearly induce a phase difference between the transmissive waves with a fixed phase gain. The difference displacement is utilized to characterize the effects of rotation on the transmissive wave, showing periodicity, linearity, and directionality as theoretical predictions. These findings offer a rate-integrating scheme to sense rotation and have promising applications, especially in high-performance SAW gyroscopes.

The THz Kerr effect measures the birefringence induced in an otherwise isotropic material by a strong THz pulse driving the Raman-active excitations of the systems. Here we provide experimental evidence of a sizable Kerr response in insulating ${\mathrm{SrTiO}}_3$ due to infrared-active lattice vibrations. Such a signal, named the ionic Kerr effect, is associated with the simultaneous excitation of multiple phonons. Thanks to a theoretical modeling of the time, polarization, and temperature dependence of the birefrengence, we can disentangle the ionic Kerr effect from the off-resonant electronic excitations, providing an alternative tunable mechanism to modulate the refractive index on ultrashort timescales via infrared active phonons.

The rise of spintronic terahertz (THz) emitters has captured considerable attention owing to their potential for delivering high-intensity broadband THz pulses. The quest for enhancing their performance has largely concentrated on two key aspects: the out-coupling of THz radiation and its generation within the material system. A thorough understanding of THz generation and its interaction with photoexcited, out-of-equilibrium materials is pivotal for achieving further progress. Ultrafast optical excitations elicit a range of dynamic responses within the picosecond timescale, aligning with the THz frequency range. Although existing methodologies, such as optical-pump THz-probe experiments, offer valuable insights, the intricate details of spin current generation in spintronic THz emitters, including the possible delay between energy rise and spin current generation, continue to be somewhat obscure. To address this gap, we theoretically propose two approaches to extract the subpicosecond timescales involved in the complex process of converting a laser excitation to a THz pulse in spintronics THz emitter use. In doing so we leverage the interference of the THz-probe pulse interacting with time-varying material properties and the THz pulse generated by the spin-to-charge conversion process. To describe such processes and theoretically support the experimental approaches we suggest, we introduce the perturbative transfer matrix method to take into account both the interaction of a THz probe with a multilayer undergoing subpicosecond dynamics and the production of THz radiation within some of the layers.

The ability to selectively excite light with fixed handedness is crucial for circularly polarized light emission. It is commonly believed that the luminescent material chirality determines the emitted light handedness, regardless of the light emitting direction. In this paper, we propose an anomalous circular polarized light emission (ACPLE) whose handedness actually relies on the emission direction and current direction in electroluminescence. In a solid semiconductor, the ACPLE originates in the band structure topology characterized by the optical Berry curvature dipole. ACPLE exists in inversion-symmetry breaking materials including chiral materials. We exemplify the ACPLE by estimating the high circular polarization ratio in monolayer ${\mathrm{WS}}_2$. In addition, the ACPLE can be further generalized to magnetic semiconductors in which the optical Berry curvature plays a leading role instead. Our finding reveals intriguing consequences of band topology in light emission and promises optoelectric applications.

In the $R\mathrm{Al}$(Si,Ge) ($R$: lanthanides) family, both spatial inversion and time-reversal symmetries are broken. This may offer opportunities to study Weyl-fermion physics in nontrivial spin structures emerging from a noncentrosymmetric crystal structure. In this study, we investigated the anomalous Hall effect (AHE) in NdAlGe via magnetotransport, magnetization, and magnetic torque measurements down to 40 mK (0.4 K for magnetization). The single crystals grown by a laser-heated floating-zone method exhibit a single magnetic phase transition at $T_{\mathrm{M}}=13.5$ K, where the $T_{\mathrm{M}}$ is the transition temperature. With the magnetic field parallel to the easy $\left[001\right]$ axis, the AHE gradually evolves as the temperature decreases below $T_{\mathrm{M}}$. The anomalous Hall conductivity (AHC) reaches $\sim 320 {\mathrm{\Omega }}^{-1} {\mathrm{cm}}^{-1}$ at 40 mK in the magnetically saturated state. Except in low-temperature low-field plateau phases, the AHC and magnetization are proportional, and their ratio agrees with the ratios for conventional ferromagnets, suggesting that the intrinsic AHE occurs by the Karplus-Luttinger mechanism. Below $\sim 0.6\mathrm{K}$, the curves of Hall resistivity against the field exhibit plateaus at low fields below $\sim 0.5\mathrm{T}$, correlating with the plateaus in the magnetization curve. For the first plateau, the magnetization is one order of magnitude smaller than the magnetically saturated state, whereas the AHE is more than half that in the saturated state. This finding under well below $T_{\mathrm{M}}$ suggests that the AHE at the first plateau is not governed by the magnetization and may be interpreted based on a multipole or spin chirality.

Nonsymmorphic chiral superconductors, like ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$, are promising candidates to explore parity mixing and multifold degenerate fermions. However, only ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$ and ${\mathrm{W}}_3{\mathrm{Al}}_2\mathrm{C}$ in the ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$ family have been identified up to now. We carry out a high-throughput materials screening procedure on ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$-like crystals based on first principles calculations. We report 21 crystals in this family based on systematic stability evaluations and perform electron-phonon coupling strength calculations for all of them. Additionally, the band structures of these compounds indicate that almost all of these compounds can hold multiple fermions near the Fermi level. This study may contribute to the discovery of more novel NCSs with multiple degenerate fermions.

Higher-order topological properties of two-dimensional (2D) magnetic materials have recently been proposed. In 2D ferromagnetic Janus materials, we find that ScClI is a second-order topological insulator. Using the tight-binding approximation, we develop a multiorbital model that adequately describes the high-order topological states of ScClI. Further, we give the complete high-order topological phase diagram of ScClI, based on the external field modulation of the magnetovalley coupling and energy levels. The 2D ScClI has a pronounced valley polarization. This type of magnetovalleytronics results in different insulating phases to exhibit completely different anomalous Nernst conductance. Through valleytronics, we establish a link between the topological insulator and the valley Nernst effect, thus constructing an anomalous valley Nernst conductance map that corresponds to the topological phase diagram. We utilize the characteristics of valley electronics to link higher-order topological materials with the anomalous Nernst effect, which has potential implications for high-order topological insulators and valley electronics.

Black phosphorus (BP) stands out from other two-dimensional (2D) materials by the wide amplitude of the band-gap energy $\left(E_g\right)$ that sweeps an optical window from visible to infrared wavelengths, depending on the layer thickness. This singularity made optical and excitonic properties of BP difficult to map. Here we report a comprehensive study of the intrinsic (i.e., measured at 4 K) optical properties of 79 passivated BP flakes obtained by mechanical exfoliation of thickness ranging from 4 to 700 nm. By following single- or multistamp exfoliation protocols and by combining micro-Raman and photoluminescence experiments, we demonstrate that the exfoliation step induces line like defects which open radiative recombination paths alternative to those of the crystalline bulk and that actually dominate the emission process. We also show that the evolution of the photoluminescence energy versus thickness follows an inverse square law. We relate this to a quantum well model whose validity is discussed and justified at intermediate thickness. Finally, we report that the emission energy of BP slabs placed in different 2D heterostructures is not significantly modulated by the dielectric environment.

The dislocation skin effect exhibits the capacity of topological defects to trap an extensive number of modes in two-dimensional non-Hermitian systems. Similar to the corresponding skin effects caused by system boundaries, this phenomenon also originates from nontrivial topology. However, finding the relationship between the dislocation skin effect and nonzero topological invariants, especially in disordered systems, can be obscure and challenging. Here, we introduce a real-space topological invariant based on the spectral localizer to characterize the skin effect on two-dimensional lattices. We demonstrate that this invariant consistently predicts the occurrence and location of both boundary and dislocation skin effects, offering a unified approach applicable to both ordered and disordered systems. Our work demonstrates a general approach that can be utilized to diagnose the topological nature of various types of skin effects, particularly in the absence of translational symmetry when momentum-space descriptions are inapplicable.

We establish a general Rashba Hamiltonian for trilayer graphene (TLG) by introducing an extrinsic layer-dependent Rashba spin-orbit coupling (SOC) arising from the off-plane inversion symmetry breaking. Our results indicate that the band spin splitting depends strongly on the layer distribution and sign of Rashba SOC as well as the ABA or ABC stacking order of TLG. We find that spin splitting is significantly enhanced as the number of layers of the Rashba SOC with the same sign and magnitude increases. For the spatially separated two Rashba SOCs of the same magnitude but the opposite sign, no spin splitting arises in ABC-TLG due to the preservation of inversion symmetry that ensures the complete cancellation of contributions from the opposite layers, whereas nonzero spin splitting is observed for ABA-TLG due to its own lack of inversion symmetry. We further illustrate that gate voltage is effective to modulate the spin-polarized states near the band edges. Moreover, we use density-functional-theory calculations to verify the Rashba splitting effect in the example of TLG interfaced by Au layer(s), which induce simultaneously the effective terms of Rashba SOC and gate voltage. Our results demonstrate the significance of layer and symmetry in manipulating spin and can be extended to multilayer graphene or other van der Waals interface systems.

Topological phase transitions fall outside of the symmetry-breaking paradigm and therefore elude many traditional analytical methods. In particular, significant geometric features found in the set of reduced density matrices (RDMs) disappear in symmetry-preserving topological systems. By returning to the fundamental properties of phase transitions, such as the divergence of correlation length and energy surface discontinuities, we demonstrate that the set of RDMs captures the critical behavior of systems with topological order. We find signatures of the gapless transition in the discontinuous movement of the ground-state RDMs. Additionally, the correlation length divergence near critical points appears in the off-diagonal character of RDMs, which is quantified through spectral and linear fitting analyses. This framework generalizes the quantum information approach to RDM critical theory, allowing for classification and visualization of all of the phases of the system—both topological and trivial—in the convex set of RDMs.

Quadratic nodal point (QNP) in two dimensions has so far been reported only in nonmagnetic materials and in the absence of spin-orbit coupling. Here, by first-principles calculations and symmetry analysis, we predict stable QNP near Fermi level in a two-dimensional kagome metal-organic framework material, ${\mathrm{Cr}}_3$(HAB)${}_2$, which features noncollinear antiferromagnetic ordering and sizable spin-orbit coupling. Effective $k·p$ and lattice models are constructed to capture such magnetic QNPs. Besides QNP, we find ${\mathrm{Cr}}_3$(HAB)${}_2$ also hosts six magnetic linear nodal points protected by mirror as well as $C_{2z}T$ symmetry. Properties associated to these nodal points, such as topological edge states and quantized optical absorbance, are discussed.

We present a series of detailed images of the distribution of kinetic energy among frequencies and wave vectors in the bulk of an MgO crystal as it is heated slowly until it melts. These spectra, which are Fourier transforms of mass-weighted velocity-velocity correlation functions calculated from accurate molecular dynamics (MD) simulations, provide a valuable perspective on the growth of thermal disorder in ionic crystals. We use them to explain why the most striking and rapidly progressing departures from a band structure occur among longitudinal optical (LO) modes, which would be the least active modes at low temperature ($T$) if phonons did not interact. The degradation of the LO band begins, at low $T$, as an anomalously large broadening of modes near the center of the Brillouin zone (BZ), which gradually spreads towards the BZ boundary. The LO band all but vanishes before the crystal melts, and transverse optical (TO) modes' spectral peaks become so broad that the TO branches no longer appear band-like. Acoustic bands remain relatively well defined until melting of the crystal manifests in the spectra as their sudden disappearance. We argue that, even at high $T$, the long wavelength acoustic (LWA) phonons of an ionic crystal can remain partially immune to disorder generated by its LO phonons; whereas, even at low $T$, its LO phonons can be strongly affected by LWA phonons. This is because LO displacements average out in much less than the period of an LWA phonon; whereas during each period of an LO phonon, an LWA phonon appears as a quasistatic perturbation of the crystal, which warps the LO mode's intrinsic electric field. LO phonons are highly sensitive to acoustic warping of their intrinsic fields because their frequencies depend strongly on them: They cause the large frequency difference between LO and TO bands known as LO-TO splitting. We calculate vibrational spectra from MD trajectories using a method that we show to be classically exact and therefore applicable, with equal validity, to any solid or liquid in any thermal or nonthermal state. By demonstrating its power and generality, we show that it has become possible to go far beyond the reach of perturbation theories and mean-field theories in the study of vibrations in materials.

We numerically investigate the stability of the skyrmion crystals in a system without the Dzyaloshinskii-Moriya interaction by focusing on the role of magnetic frustration arising from the multi-sublattice degree of freedom. By analyzing an effective three-sublattice spin model with the antiferromagnetic exchange interaction between different sublattices and the momentum-resolved exchange interaction between the same sublattice based on the simulated annealing, we find that various skyrmion crystal phases with sublattice-dependent skyrmion numbers are stabilized with and without an external magnetic field depending on the model parameters: two ferro-type skyrmion crystal phases with the skyrmion numbers of one and two, two ferri-type skyrmion crystal phases, and one antiferro-type skyrmion crystal phase. Our results indicate that the multi-sublattice degree of freedom brings a further intriguing possibility of inducing exotic skyrmion crystal phases.