Majorana bound states are zero-energy excitations of topological superconductors that obey non-Abelian exchange statistics and are basic building blocks for topological quantum computation. To observe and exploit their extraordinary properties, we need to be able to properly manipulate them, for instance by braiding a couple of them in real space. We propose a setup based on the helical edges of two-dimensional topological insulators (2DTIs) that allows for a high degree of tunability by only controlling a handful of superconducting phases. In particular, our setup allows us to move the Majoranas along a single edge and to move them across two different edges coupled by a quantum point contact. Robustness against nonoptimal control of the phases is also discussed. This proposal constitutes an essential step forward toward realizing 2DTI-based architectures capable of performing braiding of Majoranas in a feasible way.

We present an edge-based framework for the study of geometric elastic network models to model mechanical interactions in physical systems. We use a formulation in the edge space, instead of the usual node-centric approach, to characterize edge fluctuations of geometric networks defined in $d$-dimensional space and define the edge mechanical embeddedness, an edge mechanical susceptibility measuring the force felt on each edge given a force applied on the whole system. We further show that this formulation can be directly related to the infinitesimal rigidity of the network, which additionally permits three- and four-center forces to be included in the network description. We exemplify the approach in protein systems, at both the residue and atomistic levels of description.

It is generally accepted that the nonlinear, dynamical evolution of magnetic fields in the interior of neutron stars plays a key role in the explanation of the observed phenomenology. Understanding the transfer of energy between toroidal and poloidal components, or between different scales, is of particular relevance. In this Rapid Communication, we present the first three-dimensional (3D) simulations of the Hall instability in a neutron star crust, confirming its existence for typical magnetar conditions. We compare our results to estimates obtained by a linear perturbation analysis, which discards any interpretation as numerical instabilities and confirms its physical origin. Interestingly, the Hall instability creates locally strong magnetic structures that occasionally can make the crust yield to the magnetic stresses and generates coronal loops, similar to the way solar coronal loops find their way out through the photosphere. This supports the viability of the mechanism, which has been proposed to explain magnetar outbursts.

Higher-order topological (HOT) phases feature boundary (such as corner and hinge) modes of codimension $d_c>1$. We here identify an antiunitary operator that ensures the spectral symmetry of a two-dimensional HOT insulator and the existence of cornered localized states ($d_c=2$) at precise zero energy. Such an antiunitary symmetry allows us to construct a generalized HOT insulator that continues to host corner modes even in the presence of a weak anomalous Hall insulator and spin-orbital density-wave orderings, and is characterized by a quantized quadrupolar moment $Q_{xy}=0.5$. Similar conclusions can be drawn for the time-reversal symmetry breaking HOT $p+id$ superconductor and the corner localized Majorana zero modes survive even in the presence of weak Zeeman coupling and $s$-wave pairing. Such HOT insulators also serve as the building blocks of three-dimensional second-order Weyl semimetals, supporting one-dimensional hinge modes.

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows one to infer topological properties of the mechanical system, such as the occurrence of “floppy” boundary modes, from the associated electronic band structure. Here, we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g., electronic) degrees of freedom. As examples we discuss mechanical analogs of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines a set of topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.

The recently discovered superconductivity in ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$ provides a new opportunity for studying strongly correlated unconventional superconductivity. The single-hole ${\mathrm{Ni}}^{+}$ $\left(3d^9\right)$ configuration in the parent compound ${\mathrm{NdNiO}}_2$ is similar to that of ${\mathrm{Cu}}^{2+}$ in cuprates. We suggest that after doping, the intraorbital spin-singlet and interorbital spin-triplet double-hole (doublon) configurations of ${\mathrm{Ni}}^{2+}$ are competing, and we construct a two-band Hubbard model by including both the $3d_{x^2-y^2}$ and $3d_{xy}$ orbitals. The effective spin-orbital superexchange model in the undoped case is a variant of the $\text{SU}\left(4\right)$ Kugel-Khomskii model augmented by symmetry-breaking terms. Upon doping, the effective exchange interactions between spin-$\frac{1}{2}$ single holes, spin-1 (triplet) doublons, and singlet doublons are derived. Possible superconducting pairing symmetries are classified in accordance to the $D_{4h}$ crystalline symmetry, and their connections to the superexchange interactions are analyzed.

Higher-order topological (HOT) states, hosting topologically protected modes on lower-dimensional boundaries, such as hinges and corners, have recently extended the realm of the static topological phases. Here we demonstrate the possibility of realizing a two-dimensional Floquet second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment $Q_{xy}^{\mathrm{Flq}}=0.5$, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold ($C_4$) and time-reversal ($\mathcal{T}$) symmetry breaking Dirac mass perturbation. Furthermore, we show that $Q_{xy}^{\mathrm{Flq}}$ becomes independent of the choice of origin as the system approaches the thermodynamic limit. We also analyze the dynamics of a corner mode after a sudden quench, when the $C_4$ and $\mathcal{T}$ symmetry breaking perturbation is switched off, and find that the corresponding survival probability displays periodic appearances of complete, partial and no revival for long time, encoding the signature of corner modes in a QSHI. Our protocol is sufficiently general to explore the territory of dynamical HOT phases in insulators and gapless systems.

We demonstrate that the Lifshitz interaction energy (excluding the self-energies of the inner and outer spherical regions) for three concentric spherical dielectric media can be evaluated easily using the immense computation power in recent processors relative to those of a few decades ago. As a prototype, we compute the Lifshitz interaction energy for a spherical shell of water immersed in water vapor of infinite extent while enclosing a spherical ball of ice inside the shell such that two concentric spherical interfaces are formed: one between solid ice and liquid water and the other between liquid water and gaseous vapor. We evaluate the Lifshitz interaction energy for the above configuration at the triple point of water when the solid, liquid, and gaseous states of water coexist and thus extend the analysis of Elbaum and Schick [M. Elbaum and M. Schick, Phys. Rev. Lett. 66, 1713 (1991)] to spherical configurations. We find that when the Lifshitz energy contributes dominantly to the total energy of this system, which is often the case when electrostatic interactions are absent, a drop of water surrounded by vapor of infinite extent is not stable at the triple point. This instability, which is a manifestation of the quantum fluctuations in the medium, will promote the formation of ice in water, which will then grow in size indefinitely. This is a consequence of the finding here that the Lifshitz energy is minimized for a large (micrometer-size) radius of the ice ball and small (nanometer size) thickness of the water shell surrounding the ice. These results might be relevant to the formation of hail in thunderclouds. These results are tentative in that the self-energies are omitted; surface tension and nucleation energy are not considered.

Sharp features in the primordial power spectrum are a powerful window into the inflationary epoch. To date, the cosmic microwave background (CMB) has offered the most sensitive avenue to search for these signatures. In this paper, we demonstrate the power of large-scale structure observations to surpass the CMB as a probe of primordial features. We show that the signatures in galaxy surveys can be separated from the broadband power spectrum and are as robust to the nonlinear evolution of matter as the standard baryon acoustic oscillations. As a result, analyses can exploit a significant range of scales beyond the linear regime available in the data sets. We develop a feature search for large-scale structure, apply it to the final data release of the Baryon Oscillation Spectroscopic Survey and find new bounds on oscillatory features that exceed the sensitivity of Planck for a significant range of frequencies. Moreover, we forecast that the next generation of galaxy surveys, such as DESI and Euclid, will be able to improve current constraints by up to an order of magnitude over an expanded frequency range.

We consider a general problem of a Josephson contact between two multiband superconductors with coexisting superconducting and magnetic phases. As a particular example, we use the quasiclassical theory of superconductivity to study the properties of a Josephson contact between two disordered $s^{\pm }$-wave superconductors allowing for the coexistence between superconductivity and spin-density-wave orders. The intra- and interband disorder-induced scattering is treated within the self-consistent Born approximation. We calculate the spatial profile of the corresponding order parameters on both sides of the interface with a finite reflection coefficient and use our results to evaluate the local density of states at the interface as well as critical supercurrent through the junction as a function of phase or applied voltage. Our methods are particularly well suited for describing spatially inhomogeneous states of iron-based superconductors where controlled structural disorder can be created by an electron irradiation. We reveal the connection between our theory and the circuit theory of Andreev reflection and extend it to superconducting junctions of arbitrary nature. Lastly, we outline directions for further developments in the context of proximity circuits of correlated electron systems.

Majorana fermions are predicted to arise at the ends of nanowire devices which combine superconductivity, strong spin-orbit coupling, and an external magnetic field. By manipulating networks of these devices with suitable gating, it has been suggested that braiding operations may be performed which act as logic operations, suitable for quantum computation. However, the unavoidable misalignment of the magnetic field in any realistic device geometry has raised questions about the feasibility of such braiding. In this paper, we numerically simulate braiding operations in devices with Y-junction and tuning-fork geometries using an experimentally motivated nanowire model. We study how the static and dynamical features vary with geometric parameters and identify parameter choices that optimize the probability of a successful braid. Notably, we find that there is an optimal Y-junction half-angle (about ${20}^{\circ }$ for our parameter values), which balances two competing mechanisms that reduce the energy gap to excitations. In addition, we find that a tuning-fork geometry has significant advantages over a Y-junction geometry, as it substantially reduces the effect of dynamical phase oscillations that complicate the braiding process. Our results suggest that performing a successful braid is in principle possible with such devices and is within experimental reach.

We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals noninteracting and interacting fixed points, which draws an analogy to the ${\varphi }^4$ theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid.

This work explored an elementwise approach to model transcranial MRI-guided focused ultrasound (TcMRgFUS) thermal ablation, a noninvasive approach to neurosurgery. Each element of the phased array transducer was simulated individually and could be simultaneously loaded into computer memory, allowing for rapid $(\sim 2.5\mathrm{s})$ calculation of the pressure field for different phase offsets used for beam steering and aberration correction. We simulated the pressure distribution for 431 sonications in 32 patients, applied the phase and magnitude values used during treatment, and estimated the resulting temperature rise. We systematically varied the relationship between CT (computerized tomography)-derived skull density and the acoustic attenuation and sound speed to obtain the best agreement between the predictions and MR temperature imaging (MRTI). The optimization was validated with simulations of 396 sonications from 40 additional treatments. After optimization, the predicted and measured heating agreed well $(R^2$: 0.74 patients 1–32; 0.71 patients 33–72). The dimensions and obliquity of the heating in the simulated temperature maps were correlated with the MRTI $(R^2$: 0.62, 0.74, respectively), but the measured heating was more spatially diffuse. The energy needed to achieve ablation varied by an order of magnitude (3.3–36.1 kJ). While this elementwise approach required more computation time up front (the combined simulation matrices were approximately 4.6 times higher than a single large simulation), it could be performed in parallel on a computing cluster. It allows for rapid calculation of the three-dimensional heating at the focus for different phase and magnitude values on the array. We also show how this approach can be used to optimize the relationship between CT-derived skull density and acoustic properties. While the relationships found here need further validation in a larger patient population, these results demonstrate the promise of this approach to model TcMRgFUS.

The topological features of quantum many-body wave functions are known to have profound consequences for the physics of ground-states and their low-energy excitations. We describe how topology influences the dynamics of many-body systems when driven far from equilibrium. Our results are succinctly captured by a nonequilibrium topological classification that can be used to predict universal aspects of generic isolated quantum systems as they evolve unitarily in time. By analogy to the classifications used to describe systems in equilibrium, we consider two short-ranged entangled wave functions to be topologically equivalent if they can be interconverted via finite-time unitary evolution governed by a symmetry-respecting Hamiltonian. We demonstrate that this definition captures the salient features of these systems in a broad range of nonequilibrium scenarios. As well as providing conceptual insights into the constraints imposed by topology on many-body dynamics, we discuss the practical implications of our findings. In particular, we show that the characteristic zero-frequency spectroscopic peaks associated with topologically protected edge modes will be broadened by external noise only when the system is trivial in the nonequilibrium classification.

We present a proof of concept of elastic immersive wave experimentation. A physical experiment of finite volume is connected with a numerical domain via the novel theory of immersive boundary conditions. We show that by applying the incident traction measured at the free surface of a solid target, we can completely cancel unwanted boundary reflections in the physical domain. The propagating waves can then seamlessly interact with a virtual, numerical domain while we fully account for long-range interactions between the two domains. Utilizing a laser Doppler vibrometer, we can accurately record the three-component particle motion of the wave field at the surface of a thin aluminum beam. The recordings are used to iteratively construct the immersive boundary conditions which are applied to the lateral ends of the beam by three-component piezoelectric actuators. Our one-dimensional experimental results show that we can actively cancel the waves reflected at the free-surface end of the aluminum beam for individually excited, broadband longitudinal and flexural wave modes, as well as for the simultaneous excitation of the two. Finally, we introduce interactions between the physical and a desired numerical domain, thereby virtually extending the physical aluminum beam.

As they do not rely on the presence of any crystal symmetry, Weyl nodes are robust topological features of an electronic structure that can occur at any momentum and energy. Acting as sinks and sources of Berry curvature, Weyl nodes have been predicted to strongly affect the transverse electronic response, like in the anomalous Hall or Nernst effects. However, to observe large anomalous effects the Weyl nodes need to be close to or at the Fermi level, which implies the band structure must be tuned by an external parameter, e.g., chemical doping. Here we show that in a ferromagnetic metal tuning of the Weyl node energy and momentum can be achieved by rotation of the magnetization. First, taking as example the elementary magnet hcp-Co, we use electronic structure calculations based on density-functional theory to show that by canting the magnetization away from the easy axis, Weyl nodes can be driven exactly to the Fermi surface. Second, we show that the same phenomenology applies to the kagome ferromagnet ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, in which we additionally show how the dynamics in energy and momentum of the Weyl nodes affects the calculated anomalous Hall and Nernst conductivities. Our results highlight how the intrinsic magnetic anisotropy can be used to engineer Weyl physics.

We analyze the dynamics of periodically driven (Floquet) Hamiltonians with short and long-range interactions, finding clear evidence for a thermalization time, ${\tau }^{*}$, that increases exponentially with the drive frequency. Using a combination of heating and entanglement dynamics, we explicitly extract the effective energy scale controlling the rate of thermalization. Finally, we demonstrate that for times shorter than ${\tau }^{*}$, the dynamics of the system is well approximated by evolution under a time-independent Hamiltonian, $D_{\text{eff}}$, for both short-range interacting systems, in agreement with recent rigorous bounds, as well as for long-range interacting systems, where such results do not exist at present.

We study vortex motion using a Hopf flow on a 3-sphere, in place of the standard 3-torus defined by periodic boundary conditions. Although both of these underlying manifolds look locally like ${\mathbb{R}}^3$, the vortex behavior differs significantly. This raises the question of how well calculations on the 3-torus correspond to behavior in ${\mathbb{R}}^3$, for this problem or others. We find that, on both the 3-sphere and 3-torus, vortex tangles appear, with their line density related to the strength of the driving velocity field. However, tangles on the 3-sphere are highly anisotropic, with vortices tending to align along the flow direction. Standard power-law dependences change accordingly from their values in more isotropic tangles. The line length density $\langle L\rangle$ is proportional to $v_{ns}^{1.28}$, where $v_{ns}$ is the drive velocity, and the reconnection rate depends roughly on ${\langle L\rangle }^2$. These compare to $v_{ns}^2$ and ${\langle L\rangle }^{2.5}$ for the more isotropic tangles on the 3-torus. In addition, in simulations using the local induction approximation rather than the full Biot-Savart law, the tangle collapses so that all vortices are nearly aligned with a single flow line. By contrast, vortices on the 3-torus become perpendicular to the driving velocity.

We study here how phase transitions are induced in colloidal suspensions by a pointlike heat source, an optically trapped metal-oxide-particle absorbing light. We find that thermophoresis increases the number density of colloids around the oxide particle, leading to the appearance of solid clusters. Our analysis based on thermophoresis reveals that the solid-fluid interface position is purely determined by the relationship of the particle concentration profile in the fluid state with the volume fraction of the phase transition, and no other effect of thermodynamics is seen in the cluster sizes. In this system, we observe the formation of face-centered-cubic crystals, amorphous states, and structures with icosahedral order. This shows a rich possibility of nontrivial orderings under spatially controlled heterogeneous growth in external semisoft potentials that are softer than walls but with substantial variations at the scale of a few particle diameters. Because of the tunable rate of the addition of particles to the clusters, we propose that this method could be used to study the complex interplay of densification with local spatial confinement effects, kinetics, and ordering.

Macroscale continuum mechanics simulations rely on material properties stemming from the microscale, which are normally described using predetermined phenomenological equations of state (EOS), which depend on physical parameters usually obtained from experiments. A method is proposed for the automatic generation of first-principles unconstrained EOSs using a Gaussian process on a set of ab initio molecular dynamics simulations, thereby closing the continuum equations with the accuracy determined by the underlying first-principles theory. The method is validated for bulk silicon using density-functional theory (DFT) by comparing planar (one-dimensional) shock waves with experiment, and also with an explicit first-principles molecular dynamics simulation, both in the hyperelastic regime. Its applicability is then illustrated it for two-dimensional shock waves in DFT bulk silicon, following their nonlinear, temperature-dependent, anisotropic dynamics after a cylindrical region is instantaneously heated. The method is applicable to condensed matter systems in other regimes, using well-known continuum techniques and/or molecular dynamics simulations at larger scales.