We propose using tunneling spectroscopy with a superconducting electrode to probe the collective modes of unconventional superconductors. The modes are predicted to appear as peaks in $dI/dV$ at voltages given by $eV={\omega }_i/2$ where ${\omega }_i$ denotes the mode frequencies. This may prove to be a powerful tool to investigate the pairing symmetry of unconventional superconductors. The peaks associated with the collective modes appear at fourth order in the single-particle tunneling-matrix element. At the same fourth order, multiple Andreev reflection (MAR) leads to peaks at voltage equal to the energy gaps, which, in BCS superconductors, coincides with the expected position of the amplitude (Higgs) mode. The peaks stemming from the collective modes of unconventional superconductors do not suffer from this coincidence. For scanning tunneling microscopes, we estimate that the magnitude of the collective mode contribution is smaller than the MAR contribution by the ratio of the energy gap to the Fermi energy. Moreover, there is no access to the mode dispersion. Conversely, for planar tunnel junctions the collective mode peak is expected to dominate over the MAR peak, and the mode dispersion can be measured. We discuss systems where the search for such collective modes is promising.

Lanthanum hydride is the superconductor with the highest known critical temperature. It is believed that the superconductivity is of standard BCS type, with electrons forming Cooper pairs and opening the superconducting band gap. Here, we show that the BCS electron pairing is in competition with an alternative pairing: covalent bonding. We show that the covalent pairing is favored at lower pressures, and the superconducting cubic phase becomes unstable as pressure is reduced. Previous calculations based on static relaxation neglect three factors, all of which are important in stabilizing the cubic phase. Finite temperature plays a role, and two quantum effects are also important—the nuclear wave function contributes to destabilizing the ${\mathrm{H}}_2$ molecules, and the zero-point pressure means that calculated pressures are significantly overestimated by standard methods. We demonstrate these phenomena using Born-Oppenheimer and path-integral molecular dynamics: These give the same qualitative picture, with nuclear quantum effects increasing the transition pressure significantly. This competition between molecularization and superconducting gap formation is the fundamental reason why hydride superconductors have so far been found only at high pressure.

Bringing magnetic metals into superconducting states represents an important approach for realizing unconventional superconductors and potentially even topological superconductors. Altermagnetism, classified as a third basic collinear magnetic phase, gives rise to intriguing momentum-dependent spin-splitting of the band structure and results in an even number of spin-polarized Fermi surfaces due to the symmetry-enforced zero net magnetization. In this work, we investigate the effect of this new magnetic order on the superconductivity of a two-dimensional metal with $d$-wave altermagnetism and Rashba spin-orbital coupling. Specifically we consider an extended attractive Hubbard interaction and determine the types of superconducting pairing that can occur in this system and ascertain whether they possess topological properties. Through self-consistent mean-field calculations, we find that the system in general favors a mixture of spin-singlet $s$-wave and spin-triplet $p$-wave pairings and that the altermagnetism is beneficial to the latter. Using symmetry arguments supported by detailed calculations, we show that a number of topological superconductors, including both first-order and second-order ones, can emerge when the $p$-wave pairing dominates. In particular, we find that the second-order topological superconductor is enforced by a ${\mathcal{C}}_{4z}\mathcal{T}$ symmetry, which renders the spin polarization of Majorana corner modes into a unique entangled structure. Our study demonstrates that altermagnetic metals are fascinating platforms for the exploration of intrinsic unconventional superconductivity and topological superconductivity.

We derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result given by Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution operator governed by the Fermi-Hubbard Hamiltonian on one-dimensional and two-dimensional square and triangular lattices. The main technical contribution of our work is a symbolic evaluation of nested commutators between hopping and interaction terms for a given lattice geometry. The calculations result in explicit expressions for the error bounds in terms of the time step and Hamiltonian coefficients. Comparison with the actual Trotter error (evaluated on a small system) indicates that the bounds still overestimate the error.

The edge state of the topological insulator coupled to a superconductor system is able to simulate the Majorana fermion in zero-energy mode since the Kitaev-type pairing is induced by exchanging quasi-excitations in electron tunneling. However, this is not always the case. The present study has revealed that this physical simulation is not valid for a larger surface gap, which is the energy gap of the insulator's surface states. A refined pairing term that depends on the surface gap has been obtained as a second-order effect of the proximity effect, whereas the lowest order produces a constant pairing strength. By carefully considering the dependence of pairing strength on the surface gap, the Majorana phase diagram is re-achieved and a significant difference from previous work is observed, where the pairing strength was assumed to be independent of the surface gap and resulted in a conical phase boundary.

We consider superconductor-normal-superconductor-normal-superconductor (SNSNS) planar Josephson junctions in hole systems with spin-orbit interaction that is cubic in momentum (CSOI). Using only the superconducting phase difference, we find parameter regimes where junctions of experimentally achievable transparency can enter a topological superconducting phase with Majorana bound states (MBSs) at the junction ends. In planar germanium heterostructures CSOI can be the dominant form of SOI and extremely strong. We show analytically and numerically that, within experimental regimes, our results provide an achievable roadmap for a new MBS platform with low disorder, minimal magnetic fields, and very strong spin-orbit interaction, overcoming many of the key deficiencies that have so far prevented the conclusive observation of MBSs.

Hermitian Dirac points play a fundamental role in topological phenomena. The introduction of gain or loss leads to non-Hermitian systems, where Dirac points transform into pairs of exceptional points connected by a Fermi arc. Open non-Hermitian systems also manifest bound states in the continuum (BICs), which are nonradiating resonances located within the band of radiation states. So far, exceptional points have been shown to be robust when interacting with BICs. However, our work unveils that the intersection of two BICs from distinct energy bands along the Fermi arc can prevent the formation of exceptional points, restoring a genuine Hermitian Dirac point instead, albeit surrounded by non-Hermitian states. This represents a different mechanism for the formation of Dirac points embedded in the continuum of radiation, which combines the physics associated to Dirac points and the resonant properties of BICs in non-Hermitian systems. The concept is analyzed using a general model and further explored in a waveguiding photonic system based on hyperbolic dispersion media.

Spin-orbit coupling (SOC) plays a significant role in the development of topological physics. For example, considering the SOC effect would lead to the formation of a topological insulator with band inversion in a time-reversal symmetry-preserved system and the realization of a Chern phase in a time-reversal symmetry-broken system. Here, by using angle-resolved photoemission spectroscopy combined with first-principles electronic structure calculations, we report SOC-induced “hidden” Dirac bands near the Fermi level in the nonsymmorphic topological semimetal InBi. We clearly observe Dirac-like bulk band crossings located at the corner and boundary of the Brillouin zone, providing compelling evidence for three-dimensional Dirac semimetal states. By means of in situ potassium dosing on the crystal surface, we are able to reveal a partial Dirac nodal line along the $k_z$ direction formed by Dirac fermions close to the Fermi level. Our results not only demonstrate the rich topological states in InBi but also offer a good platform for engineering topologically nontrivial phases.

Half-metallic ferromagnets (HMFs) are ferromagnetic metallic compounds with 100% spin polarization at the Fermi level $\left(E_F\right)$, and thus they are of particular interest in the field of spintronics, but the identification of HMFs with experiments is a challenging task. In principle, temperature-dependent electrical transport measurements should sensitively probe the half-metallic ferromagnetism since the spin-flip electron-magnon scattering mechanism is expected to be absent. In this work, we perform a systematic temperature-dependent electrical transport measurement on the ferromagnetic full Heusler compound ${\mathrm{Co}}_2\mathrm{MnGe}$. Our experimental results reveal that ${\mathrm{Co}}_2\mathrm{MnGe}$ exhibits an exponential suppression of spin-flip electron-magnon scattering below a characteristic crossover temperature $(\mathrm{\Delta }\sim 79 \mathrm{K})$, which suggests that this material possesses a perfect spin polarization at the low temperature. The energy gap $\left(k_B\mathrm{\Delta }\right)$ characterizing the suppression of spin-flip electron-magnon scattering is $\sim 7\mathrm{meV}$. This key finding is further established by a sign change in magnetoresistance at $T\gtrsim \mathrm{\Delta }$. Moreover, we have also studied the anomalous Hall effect (AHE) of the present compound. We find a notable change in the ordinary Hall coefficient $\left(R_0\right)$ and in the carrier density $\left(n\right)$ at $T\lesssim \mathrm{\Delta }$, which is consistent with the complete absence of minority-spin states at the $E_F$. The anomalous Hall resistivity $\left({\rho }_{yx}^A\right)$ is observed to scale near quadratically with the longitudinal resistivity $\left({\rho }_{xx}\right)$, and further experimental analysis indicates that the AHE in ${\mathrm{Co}}_2\mathrm{MnGe}$ is dominated by the intrinsic Karplus-Luttinger Berry phase mechanism. These findings imply that the ${\mathrm{Co}}_2\mathrm{MnGe}$ is a rare ferromagnetic full Heusler compound in which half-metallicity coexists with the topology-driven AHE.

Hybrid Josephson junctions realized on a two-dimensional electron gas are considered promising candidates for developing topological elements that are easily controllable and scalable. Here, we theoretically study the possibility of the detection of topological superconductivity via the nonlocal spectroscopy technique. We show that the nonlocal conductance is related to the system's band structure, allowing probe of the gap closing and reopening related to the topological transition. We demonstrate that the topological transition induces a change in the sign of the nonlocal conductance at zero energy due to the change in the quasiparticle character of the dispersion at zero momentum. Importantly, we find that the tunability of the superconducting phase difference via flux in hybrid Josephson junctions systems is strongly influenced by the strength of the Zeeman interaction, which leads to considerable modifications in the complete phase diagram that can be measured under realistic experimental conditions.

Three-dimensional topological semimetals have attracted tremendous attention across multiple disciplines. Recently, a novel class of nodal-line semimetals hosting fourfold nodal hinges has been proposed, which manifests as four-band degeneracies pinning at the hinges of the three-dimensional Brillouin zone. Markedly different from the conventional nodal line featuring a nontrivial $\pi$ Berry phase that brings about drumhead surface modes, the fourfold nodal hinge carries a Berry phase of $2\pi$ and yields exotic toruslike surface modes. However, this fascinating nodal-line semimetal phase has not yet been reached experimentally. Here, we report a concrete construction of acoustic metamaterials with such symmetry-enforced fourfold nodal hinges and present convincing experimental evidence for the highly desired topological objects and the consequent toruslike surface modes. In addition, we also identify the twofold nodal walls and hourglass nodal lines in this system, where the latter feature drumhead surface states as usual. Our study may offer new possibilities for manipulating acoustic surface waves and exploring unique topological semimetal phases.

We study ferroelectric domain walls in barium titanate-type systems with perfect electric screening. We search for structurally nontrivial so-called non-Ising domain walls, where the polarization is nontrivial for all components. Our approach enables us to find solutions for domain walls in any orientation, and the existence and energy of these walls depend on their particular orientation. We find that, across all phases of the material, there are orientations where the non-Ising walls have lower energy than Ising walls. The most interesting property of these domain walls is their nonmonotonic interaction forces, allowing them to form stable domain-wall clusters rather than following standard behavior where domain walls annihilate or repel each other. We find the required external electric field to create the non-Ising configurations. Besides theoretical interest, this unconventional property of domain walls makes them a good candidate for memory applications.

As an analog to a magnetic tunneling junction, a magnon junction composed of a ferromagnetic insulator (FMI)/antiferromagnetic insulator (AFMI)/ferromagnetic insulator heterostructure has been proposed in recent years. In a magnon junction, the magnon current transmission can be adjusted by manipulating the angle of magnetic moments in the two FM layers. However, the mechanism of this magnon junction effect is still not quite clear. In this paper, we numerically calculate the bulk acoustic wave-induced magnon junction effect. Our results emphasize the crucial role played by variations in magnetic structures within the AFMI spacer when the alignments of magnetic moments in the two FMI layers are adjusted between the parallel and antiparallel state. These differences significantly influence the modulation of magnon current transmission. This is different from the chirality-relevant magnon scattering mechanism as assumed in previous works.

After removal of an applied magnetic field, artificial square spin ice can be left in a metastable remanent state, with nonzero residual magnetization and excess energy above the ground state. Using a model of magnetic islands with dipoles of fixed magnitude and local anisotropies, the remanent states are precisely determined here, including all long-range dipole interactions. Small deviations away from remanent states are analyzed and the frequencies of modes of oscillation are determined. Some modes reach zero frequency at high-symmetry wave vectors, such that the stability limits are found, as determined by the local anisotropy strength relative to the dipolar coupling strength.

We investigated the magnetic phase transitions of ${\mathrm{ErCrO}}_3$ using single-crystal and powder samples. Neutron powder diffraction showed that the ${\mathrm{Cr}}^{3+}$ orders at $T_N=133\mathrm{K}$ with the irreducible representation of ${\mathrm{\Gamma }}_4(G_x,F_z)$. ${\mathrm{ErCrO}}_3$ exhibits a mixed ${\mathrm{\Gamma }}_4(G_x;F_z^R)$ and ${\mathrm{\Gamma }}_1(G_y;C_z^R)$ phase just below 10 K. The ${\mathrm{\Gamma }}_1(G_y;C_z^R)$ phase becomes dominate at the base temperature. On the other hand, the transition from ${\mathrm{\Gamma }}_4(G_x,F_z)$ to ${\mathrm{\Gamma }}_1(G_y;C_z^R)$ is sharp in the single-crystal sample. The scattered intensity of the (110) Bragg peak, which indicates the ferromagnetic component along the $c$ axis, displays continuous growth upon cooling and dropped starting at $T_{SR}=9.6\mathrm{K}$ when the spin reorientation of ${\mathrm{Cr}}^{3+}$ occurs. The temperature-dependent magnetization measurement of the single-crystal sample showed the ferromagnetic moment is along the $c$ axis appearing at $T_N\approx 133\mathrm{K}$ with a sharp drop at $T_{{\text{Er}}^{3+}}=10\mathrm{K}$. The specific heat shows a sharp peak at $T_{{\text{Er}}^{3+}}=9.3\mathrm{K}$ for the single crystal while the polycrystalline sample does not. The crystal-field excitation of the first Kramers doublet above the ground state of ${}^{4}I_{15/2}$ of ${\mathrm{Er}}^{3+}$ is observed at $\approx 1.19\left(1\right)\mathrm{meV} (=13.80\mathrm{K})$, which is close to the Schottky anomaly observed as $\mathrm{\Delta }=13.23\mathrm{K}$ from the lowest-lying crystal-field states in the specific heat. It is not yet clear whether the near coincidence of $T_{SR}$ and $T_{{\text{Er}}^{3+}}$ is an accident or not.

Topological insulators are unique materials possessing forbidden topological gap and behaving similar to usual insulators in their bulk, but at the same time supporting localized in-gap states at their edges that demonstrate exceptional robustness, because they are protected by topology of the system and cannot be destroyed by local disorder or edge perturbations. Topological insulators discovered in different areas of physics, including optics, acoustics, and physics of Bose-Einstein and polariton condensates, usually employ potential landscapes (or lattices), designed such as to feature specific degeneracies in their linear modal spectra, that can be lifted by various physical effects or controllable deformations of the potential, leading to opening of the topological gap, where edge states appear. In this work, using binary Bose-Einstein condensate we propose a type of topological insulator that does not explicitly use specially designed potential landscape, but instead utilizes spatially inhomogeneous Rabi coupling between two components, in the form of a one- or two-dimensional Su-Schrieffer-Heeger structure, combined with Zeeman splitting. Such Rabi lattices reveal the appearance of topologically nontrivial phases (including higher-order ones) controlled by spatial shift of the domains with enhanced coupling between condensates within unit cells of the structure, where localized topological states appear at the edges or in the corners of truncated Rabi lattice. We also show that the properties of edge states, their spatial localization, and location of their chemical potential within topological gap can be controlled by interatomic interactions that lead to formation of gap topological edge solitons bifurcating from linear edge states. Such solitons in condensates with inhomogeneous Rabi coupling appear as very robust nonlinear topological objects that do not require any threshold norm for their formation even in two-dimensional geometries, and that can exist in stable form for both attractive and repulsive interactions. Our results demonstrate considerable enhancement of stability of solitons in topological Rabi lattices in comparison with trivial Rabi lattices. They open additional prospects for realization of topologically nontrivial phases by spatial engineering of coupling in multicomponent systems.

Laser radiation incident on a ferromagnetic sample produces excited electrons and currents whose spin polarization must not be aligned with the magnetization—an effect due to spin-orbit coupling that is ubiquitous in spin- and angle-resolved photoemission. In this paper, we report on a systematic investigation of the dynamics of spin polarization and spin-polarized currents produced by femtosecond laser pulses, modeled within our theoretical framework evolve. The spin polarization depends strongly on the properties of the laser pulse and on the sample composition, as shown by comparing results for Cu(100), Co(100), and a Co/Cu heterostructure. We find a transition from coherence before the laser pulse's maximum to incoherence thereafter. Moreover, the time dependence of the spin-polarization components induced by spin-orbit coupling differ significantly in Cu and Co: in Cu, we find long-period oscillations with tiny rapid modulations, whereas in Co prominent rapid oscillations with long-period ones are superimposed. The pronounced spatial dependences of the signals underline the importance of inhomogeneities; in particular, magnetic/nonmagnetic interfaces act as a source for ultrafast spin-polarization effects. Our investigation provides detailed insight into electron dynamics during and shortly after a femtosecond laser excitation.

We examine spin density wave and triplet superconductivity as possible ground states of the Bernal bilayer graphene. The spin density wave is stable for the unbiased and undoped bilayer. Both the doping and the applied bias voltage destroy this phase. We show that, when biased and slightly doped, a bilayer can host a triplet superconducting phase. The mechanisms for both ordered phases rely on the renormalized Coulomb interaction. The consistency of our theoretical conclusions with recent experimental results is discussed.

Tuning superconductivity in topological materials by means of chemical substitution, electrostatic gating, or pressure is thought to be an effective route towards realizing topological superconductivity with their inherent Majorana fermions, the manipulation of which may form the basis for future topological quantum computing. It has recently been established that the pseudo-binary chalcogenides (${ACh)}_m{\left(P{n}_{2}C{h}_3\right)}_n$ ($A=\text{Ge}$, Mn, Pb, etc.; $Pn=\text{Sb}$ or Bi; $Ch=\text{Te}$, Se) may host novel topological quantum states such as the quantum anomalous Hall effect and topological axion states. Here we map out the phase diagram of one member in this series, the topological insulator candidate ${\mathrm{GeSb}}_4{\mathrm{Te}}_7$ up to pressures of $\sim 35$ GPa, through a combination of electrical resistance measurements, Raman spectroscopy, as well as first-principles calculations. Three distinct superconducting phases emerge under the pressure above $\sim 11, \sim 17$, and $\sim 31$ GPa, which are accompanied by concomitant structural transitions, evidenced from the changes in the Raman modes. The first-principles calculations validate the existence of a topological insulating state at ambient pressure and predict two possible structural transitions at 10 and 17 GPa, in agreement with the experimental observations. Overall, our results establish the ${\mathrm{GeSb}}_4{\mathrm{Te}}_7$ family of materials as a fertile arena for further exploring various topological phenomena, including topological phase transitions and putative topological superconductivity.