The local electric field gradients and magnetic dynamics of ${\mathrm{TaSb}}_2$ have been studied using ${}^{121}\mathrm{Sb}$, ${}^{123}\mathrm{Sb}$, and ${}^{181}\mathrm{Ta}$ nuclear quadrupole resonance (NQR) with density functional theory (DFT) calculations using XRD-determined crystal structures. By measuring all structurally expected 13 NQR lines, the nuclear quadrupole coupling constant $\left({\nu }_Q\right)$ and asymmetric parameter $\left(\eta \right)$ for Ta, Sb(1), and Sb(2) sites were obtained. These values are all in good agreement with the presented DFT calculations. Principal axes of the electric field gradients was determined for a single-crystal sample by measuring the angular dependencies of NMR frequency under a weak magnetic field. The unusual temperature dependence of $\eta \left(T\right)$ of Sb(2) hints at the suppressed thermal expansion along the $a$ axis. Spin-lattice relaxation rate $(1/T_{1}T)$ measurements reveal an activated-type behavior and an upturn below 30 K. Neither the low-temperature upturn nor the high-temperature activation-type behaviors are reproduced by the calculated $1/T_{1}T$ based on the calculated density of states (DOS). On the other hand, the agreement between the calculated DOS and specific heat measurements indicates that the band renormalization is small. This fact indicates that ${\mathrm{TaSb}}_2$ deviates from the simple semimetal scenario, and magnetic excitations are not captured by Fermi liquid theory.

We consider flux equilibrium in dissipative nonlinear wave systems subject to external energy pumping. In such systems, the elementary excitations, or quasiparticles, can create a Bose-Einstein condensate. We develop a theory on the Bose-Einstein condensation of quasiparticles for various regimes of external excitation, ranging from weak and stationary to ultrastrong pumping, enabling us to determine the number of quasiparticles near the bottom of the energy spectrum and their distribution along wave vectors. We identify physical phenomena leading to condensation in each of the regimes. For weak stationary pumping, where the distribution of quasiparticles deviates only slightly from thermodynamic equilibrium, we define a range of pumping parameters where the condensation occurs and estimate the density of the condensate and the fraction of the condensed quasiparticles. As the pumping amplitude increases, a powerful influx of injected quasiparticles is created by the Kolmogorov-Zakharov scattering cascade, leading to their Bose-Einstein condensation. With even stronger pumping, kinetic instability may occur, resulting in a direct transfer of injected quasiparticles to the bottom of the spectrum. For the case of ultrastrong parametric pumping, we have developed a stationary nonlinear theory of kinetic instability. The theory agrees qualitatively with experimental data obtained using Brillouin light scattering spectroscopy during parametric pumping of magnons in room-temperature films of yttrium-iron garnet.

A core-level crossing (CLC) resulting from extreme compression has been calculated to occur in Ir metal at 80 GPa, analogous to a transition previously reported in Os at 392 GPa. We present results from static high-pressure diffraction experiments and theoretical investigations on the compressive behavior of Ir up to 159 GPa, well above the calculated CLC transition pressure. Neither our experimental nor computational results find evidence for a CLC over this pressure range, and instead, our first-principles calculations suggest that the CLC occurs in Ir at the much higher pressure of 400 GPa. Furthermore, computational analysis of the CLC in Ir, combined with previous work on Os, indicates that CLCs at high pressure are not experimentally detectable.

In an altermagnet, the symmetry that relates configurations with flipped magnetic moments is a rotation. This makes it qualitatively different from a ferromagnet, where no such symmetry exists, or a collinear antiferromagnet, where this symmetry is a lattice translation. In this paper, we investigate the impact of the crystalline environment, enabled by the spin-orbit coupling, on the magnetic and electronic properties of an altermagnet. We find that, because each component of the magnetization acquires its own angular dependence, the Zeeman splitting of the bands has symmetry-protected nodal lines residing on mirror planes of the crystal. Upon crossing the Fermi surface, these nodal lines give rise to pinch points that behave as single or double type-II Weyl nodes. We show that an external magnetic field perpendicular to these mirror planes can only move the nodal lines, such that a critical field value is necessary to collapse the nodes and make the Weyl pinch points annihilate. This unveils the topological nature of the transition from a nodal to a nodeless Zeeman splitting of the bands. We also classify the altermagnetic states of common crystallographic point groups in the presence of spin-orbit coupling, revealing that a broad family of magnetic orthorhombic perovskites can realize altermagnetism.

Spatial dispersion (SD) is a nonlocal effect that can introduce optical anisotropy in an otherwise isotropic material, causing the electromagnetic response at a given point to depend not only on the local field, but also on the field in the vicinity of that point. In this study, we investigate the impact of SD on a cubic semiconductorlike silicon, which is typically considered a negligible effect due to the small size of the lattice parameters with respect to the wavelength of light. However, our findings demonstrate that SD can be significant above the band gap, where transmission measurements are not feasible and reflection measurements are required for characterization. We utilize Mueller matrix ellipsometry spectroscopy to quantify the anisotropy caused by SD in (110) and (100) silicon wafers, and determine the complete permittivity tensor of silicon when spatial dispersion is included. In the most general case, this tensor is found to depend on two complex parameters.

Andreev bound states are fermionic states localized in weak links between superconductors which can be occupied with spinful quasiparticles. Microwave experiments using superconducting circuits with InAs/Al nanowire Josephson junctions have recently enabled probing and coherent manipulation of Andreev states but have remained limited to zero or small magnetic fields. Here, we use a flux-tunable superconducting circuit compatible in magnetic fields up to $1\mathrm{T}$ to perform spectroscopy of spin-polarized Andreev states up to $\sim 250\mathrm{m}\mathrm{T}$, beyond which the spectrum becomes gapless. We identify singlet and triplet states of two quasiparticles occupying different Andreev states through their dispersion in magnetic field. These states are split by exchange interaction and couple via spin-orbit coupling, analogously to two-electron states in quantum dots. We also show that the magnetic field allows to drive a direct spin-flip transition of a single quasiparticle trapped in the junction. Finally, we measure a gate- and field-dependent anomalous phase shift of the Andreev spectrum, of magnitude up to $\sim 0.7\pi$. Our observations demonstrate alternative ways to manipulate Andreev states in a magnetic field and reveal spin-polarized triplet states that carry supercurrent.

The eigenstate thermalization hypothesis (ETH) represents a cornerstone in the theoretical understanding of the emergence of thermal behavior in closed quantum systems. The ETH asserts that expectation values of simple observables in energy eigenstates are accurately described by smooth functions of the thermodynamic parameters, with fluctuations and off-diagonal matrix elements exponentially suppressed in the entropy. We investigate to what extent the ETH holds in non-Hermitian many-body systems and come to the surprising conclusion that the fluctuations between eigenstates are of equal order to the average, indicating no eigenstate thermalization. We support this conclusion with mathematically rigorous results in the Ginibre ensemble and numerical results in other random matrix ensembles, the non-Hermitian Sachdev-Ye-Kitaev model, and a local non-Hermitian spin chain, indicating universality in a broad class of chaotic non-Hermitian quantum systems.

Microwave impedance microscopy (MIM) has been utilized to directly visualize topological edge states in many quantum materials. While the microwave response for conventional metals and insulators can be accurately quantified using simple lumped-element circuits, whose applicability to more exotic quantum systems remain limited. In this work, we present a general theoretical framework of the MIM response of arbitrary quantum materials. Applying it to topological edge states in a Chern insulator predicts an enhanced MIM response at the crystal boundaries due to collective edge magnetoplasmon (EMP) excitations. The unique resonance frequency of these plasmonic modes allows one to disentangle the signatures of topological versus trivial edge states. To benchmark our analytical predictions, we experimentally probe the MIM response of quantum anomalous Hall edge states in a Cr-doped ${(\mathrm{Bi},\mathrm{Sb})}_2{\mathrm{Te}}_3$ topological insulator and perform numerical simulations using a classical formulation of the EMP modes based on this realistic tip-sample geometry, both of which yield results consistent with our theoretical picture. We also show how the technique of MIM can be used to quantitatively extract the topological invariant of a Chern insulator and shed light on the microscopic nature of dissipation along the crystal boundaries.

Controlling the phase and amplitude of spin waves in magnetic insulators with an electric field opens the way to fast logic circuits with ultralow power consumption. One way to achieve such control is to manipulate the magnetization of the medium via magnetoelectric effects. In experiments with magnetostatic spin waves in an yttrium iron garnet film, we have obtained evidence of a theoretically predicted phenomenon: the change of the spin-wave phase due to the magnonic Aharonov-Casher effect—the geometric accumulation of the magnon phase as these quasiparticles propagate through an electric field region.

Motivated by unexpected reports of a 26 K superconducting transition in elemental titanium at high pressure, we carry out an accurate ab initio study of its properties to understand the rationale for this observation. The critical superconducting temperatures ($T_c$'s) predicted under the assumption of a phononic pairing mechanism are found to be significantly lower than those experimentally observed. We argue that this disagreement cannot be explained by an unconventional coupling, as previously suggested, or by the existence of competing metastable structural phases. As a physically meaningful hypothesis to reconcile experimental and theoretical results, we assume the presence of Ti vacancies in the lattice. Our first-principles calculations indeed show that lattice vacancies can cause pressure-dependent phonon softening and substantially increase the electron-phonon coupling at high pressure, yielding computed $T_c$'s in agreement with the experimental measurements over the full pressure range 150-300 GPa. We expect the proposed $T_c$ enhancement mechanism to occur on a general basis in simple high-symmetry metals for various types of defects.

Recent experiments on the twisted semiconductor bilayer system $t{\mathrm{MoTe}}_2$ have observed integer and fractional quantum anomalous Hall effects, which occur in topological moiré bands at zero magnetic field. Here, we present a global phase diagram of $t{\mathrm{MoTe}}_2$ throughout the filling range $0<n\le 1$ substantiated by exact diagonalization calculations. At a magic angle, we find that the system resembles the lowest Landau level (LLL) to a remarkable degree, exhibiting an abundance of incompressible fractional quantum anomalous Hall states and compressible anomalous composite Fermi liquid states. Away from the magic angle, particle-hole symmetry is strongly broken. Some LLL-like features remain robust near half-filling, while others are replaced, predominantly by charge density waves near $n=0$ and anomalous Hall Fermi liquids near $n=1$. Among LLL-like phases, we find the anomalous composite Fermi liquid at $n=\frac{1}{2}$ to be most robust against deviations from the magic angle. Within the band-projected model, we show that strong particle-hole asymmetry above the magic angle results from interaction-enhanced quasiparticle dispersion near $n=1$. Our paper sets the stage for future exploration of LLL-like and beyond-LLL phases in fractional quantum anomalous Hall systems.

We report the crystal and electronic structures, charge density wave (CDW), and superconductivity of polycrystalline $4H_{\mathrm{a}}\text{−}{\mathrm{NbSe}}_2$ studied by x-ray diffraction, ab initio calculations, electrical resistivity, magnetization, and specific heat. $4H_{\mathrm{a}}\text{−}{\mathrm{NbSe}}_2$ has no central inversion symmetry (space group $P\text{−}6m2$), and the stacking-fault structure was observed in the crystal lattice. The weak CDW transition at $T_{\mathrm{CDW}}\sim 43\mathrm{K}$ thermodynamically is of second order. $4H_{\mathrm{a}}\text{−}{\mathrm{NbSe}}_2$ has a superconducting critical temperature $T_{\mathrm{c}}\sim 6.4$ K, which is a moderately coupled BCS superconductor with two-gap $s+s$-wave-like pairing. The upper critical field ${\mu }_0{H}_{\mathrm{c}2}\left(0\right)$ is as high as 26.5 T which far exceeds the Pauli paramagnetic limit and this violation is mostly attributed to the breaking of the central inversion symmetry. Second magnetization peaks can be observed in the system with weak flux pinning. Electronic structure calculations reveal that the $\text{Nb}4d$ orbitals dominate the bands near the Fermi level with different degree of hybridization between the Nb $4d$ and Se $4p$ orbitals in $2H$- and $4H_{\mathrm{a}}\text{−}{\mathrm{NbSe}}_2$, and the band structures of $4H_{\mathrm{a}}\text{−}{\mathrm{NbSe}}_2$ favor a higher $T_{\mathrm{CDW}}$. The higher $T_{\mathrm{CDW}}$ but lower $T_{\mathrm{c}}$ compared to $2H-{\mathrm{NbSe}}_2$ leads us to conclude that the two collective electronic states are competitive on the Fermi surface in this system. The large ${\mu }_0{H}_{\mathrm{c}2}\left(0\right)$ derived from $4H_{\mathrm{a}}\text{−}{\mathrm{NbSe}}_2$ is expected to stimulate the explorations for high-field superconductor applications from a noncentrosymmetric structural strategy.

The field of optical detection and manipulation of transient states with ultrafast lasers is rapidly growing and shows great promise. In this field, new states can be generated through photodoping or optical-induced strain. However, traditional ultrafast measurements have been plagued by the challenge of inhomogeneous excitation, which is difficult to avoid. Nevertheless, recent developments suggest that this situation might change and open up more possibilities for the ultrafast manipulation of materials. One such possibility involves introducing nonuniform order parameter fields, like carrier density gradients. In this study, we demonstrate the potential to manipulate the coherent photoacoustic wave in $2H\text{−}\mathrm{Mo}{\mathrm{Te}}_2$ by adjusting the homogeneity of laser excitation, which is closely linked to the thickness of the flake. Our ultrafast electron diffraction experiments reveal that, as the flake thickness increases, the photoacoustic wave transforms from a standing wave with breathing motions to a solitonlike traveling wave. This transformation is characterized by distinct diffraction intensity oscillations. For flake thicknesses below the critical value of approximately 40 nm, homogeneous excitation results in out of phase intensity oscillations of the Friedel pairs, and only a fundamental frequency component is detected. On the other hand, in thicker flakes, inhomogeneous excitation leads to in-phase intensity oscillations and the emergence of a second harmonic component. Overall, our findings highlight the unique aspects of inhomogeneous excitation and its implications for the optical control of exotic properties in strain-related transient states.

A superconductor emerges as a condensate of electron pairs, which bind despite their strong Coulomb repulsion. Eliashberg's theory elucidates the mechanisms enabling them to overcome this repulsion and predicts the transition temperature and pairing correlations. However, a comprehensive understanding of how repulsion impacts the phenomenology of the resulting superconductor remains elusive. We present a formalism that addresses this challenge by applying the Hubbard-Stratonovich transformation to an interaction including instantaneous repulsion and retarded attraction. We first decompose the interaction into frequency scattering channels and then integrate out the fermions. The resulting bosonic action is complex and the saddle point corresponding to Eliashberg's equations generally extends into the complex plane and away from the physical axis. We numerically determine this saddle point using the gradient descent method, which is particularly well-suited for the case of strong repulsion. We then turn to consider fluctuations around this complex saddle point. The matrix controlling fluctuations about the saddle point is found to be a non-Hermitian symmetric matrix, which generally suffers from exceptional points that are tuned by different parameters. These exceptional points may influence the thermodynamics of the superconductor. For example, within the quadratic approximation, the upper critical field sharply peaks at a critical value of the repulsion strength related to an exceptional point appearing at $T_c$. Our work facilitates the mapping between microscopic and phenomenological theories of superconductivity, particularly in the presence of strong repulsion. It has the potential to enhance the accuracy of theoretical predictions for experiments in systems where the pairing mechanism is unknown.

We investigate the neutralization of charged defects in a ${\mathrm{Cu}}_2\mathrm{O}$ crystal experimentally with a continuous-wave two-color pump-probe setup. We demonstrate that the excitation of high-lying Rydberg excitons at low densities generates an enhancement of exciton absorption up to a factor of 3. The result is an overall improvement of the absorption spectrum's quality in terms of increased oscillator strengths and narrower linewidths, referred to as purification. The reduction of the amount of charged impurities in the crystal is further verified by a thorough analysis of impurity photoluminescence signals.

Proximity-induced phenomena in van der Waals heterostructures have emerged as a platform to tailor the electronic, spin, optical, and topological properties in two-dimensional materials. A crucial degree of freedom, which has only recently been recognized, is the relative twist angle between the monolayers. While partial results exist in the literature, we present here a comprehensive first-principles-based investigation of the twist-angle-dependent proximity spin-orbit coupling (SOC) in graphene in contact with, or encapsulated by, monolayer transition metal dichalcogenides (TMDCs) ${\mathrm{MoS}}_2$, ${\mathrm{MoSe}}_2$, ${\mathrm{WS}}_2$, and ${\mathrm{WSe}}_2$. Crucially, our commensurate supercells comprise monolayers with strains of less than 2.5%, minimizing band-offset artifacts. We confirm earlier DFT results that for Mo-based TMDCs the proximity valley–Zeeman SOC exhibits a maximum at around ${15}^{\circ }–{20}^{\circ }$ and vanishes at ${30}^{\circ }$ for symmetry reasons. Although such a maximum was also predicted by tight-binding simulations for W-based TMDCs, we find an almost linear decrease of proximity valley–Zeeman SOC in graphene/${\mathrm{WSe}}_2$ and graphene/${\mathrm{WS}}_2$ when twisting from $0^{\circ }$ to ${30}^{\circ }$. We also refine previous DFT simulations and show that the induced Rashba SOC is rather insensitive to twisting, while acquiring a nonzero Rashba phase angle $\phi$ which measures the deviation of the electron spin from in-plane transverse direction to the momentum, for twist angles different from $0^{\circ }$ and ${30}^{\circ }$. The Rashba phase angle $\mathrm{var}\varphi$ varies from $-{20}^{\circ }$ to ${40}^{\circ }$, with the largest variation (${40}^{\circ }$) found for ${\mathrm{MoS}}_2$ at a twist angle of ${20}^{\circ }$. This finding contradicts earlier tight-binding predictions that the Rashba angle can be ${90}^{\circ }$ in the studied systems. In addition, we study the influence of a transverse electric field, vertical and lateral shifts, and TMDC encapsulation on the proximity SOC for selected twist angles. Within our investigated electric field limits of $\pm 2$ V/nm, mainly the Rashba SOC can be tuned by about 50%. The interlayer distance provides a giant tunability, since the proximity-induced SOC can be increased by a factor of 2–3, when reducing the distance by only about 10%. When encapsulating graphene between two TMDCs, both twist angles are important to control the interference of the individual proximity-induced SOCs, allowing to precisely tailor the proximity-induced valley-Zeeman SOC in graphene, while the Rashba SOC becomes suppressed. Finally, based on our effective Hamiltonians with fitted parameters to low-energy ab initio band structures, we calculate experimentally measurable quantities such as spin lifetime anisotropy and charge-to-spin conversion efficiencies. The spin lifetime anisotropy—being the ratio between out-of-plane and in-plane spin lifetimes—can become giant (up to 100), depending on the TMDC, twist angle, transverse electric field, and the interlayer distance. The charge-to-spin conversion can be divided into three components which are due to spin-Hall and Rashba-Edelstein effects with nonequilibrium spin-density polarizations that are perpendicular and parallel to the applied charge current. All conversion efficiencies are highly tunable by the twist angle and the Fermi level.

We investigated temperature ($T$)-dependent ultrafast near-infrared (NIR) transient reflectivity dynamics in coexisting superconducting (SC) and charge density wave (CDW) phases of layered $2H\text{−}{\mathrm{NbSe}}_2$ using NIR and visible excitations. With visible pump-photon excitation (400 nm) we find a slow high-energy quasiparticle relaxation channel, which is present in all phases. In the CDW phase, we observe a distinctive transient response component, irrespective of the pump-photon energy. The component is marked by the absence of coherent amplitude mode oscillations and a relatively slow, picosecond rise time, which is different than in most of the typical CDW materials. In the SC phase, another tiny component emerges that is associated with optical suppression of the SC phase. The transient reflectivity relaxation in the CDW phase is dominated by phonon diffusive processes with an estimated low-$T$ heat diffusion constant anisotropy of $\sim 30$. Strong excitation of the CDW phase reveals a weakly nonthermal CDW order parameter (OP) suppression. Unlike CDW systems with a larger gap, where the optical OP suppression involves only a small fraction of phonon degrees of freedom, the OP suppression in $2H\text{−}{\mathrm{NbSe}}_2$ is characterized by the excitation of a large number of phonon degrees of freedom and significantly slower dynamics.

A unidirectional “density” wave order in an otherwise isotropic environment is guaranteed to display a smecticlike Goldstone mode. Examples of such soft states include conventional smectic liquid crystals, putative Fulde-Ferrell-Larkin-Ovchinnikov superfluids, and helical states of frustrated bosons and spins. Here we develop generalized spin-smectic $\sigma$-models that break $O\left(N\right)$ internal symmetry in addition to the $d$-dimensional rotational and uniaxial translational symmetries. We explore long-wavelength properties of such strongly fluctuating states, show that they are characterized by a “double-power-law” static structure peak, and analyze their asymptotic symmetry-reduced crossover to conventional low-energy modes. We also present the associated Ginzburg-Landau theory, describing the phase transition into such spin-smectic states, and we discuss experimental realization of such models.

We present a theoretical study of the interaction between an atom characterized by a degenerate ground state and a reciprocal environment, such as a semiconductor nanoparticle, without the presence of external bias. Our analysis reveals that the combined influence of the electron's intrinsic spin magnetic moment on the environment and the chiral atomic dipolar transitions may lead to either the spontaneous breaking of time-reversal symmetry or the emergence of time-crystal-like states with remarkably long relaxation times. The different behavior is ruled by the handedness of the precession motion of the atom's spin vector, which is induced by virtual chiral-dipolar transitions. Specifically, when the relative orientation of the precession angular velocity and the electron spin vector is as in a spinning top, the system manifests time-crystal-like states. Conversely, with the opposite relative orientation, the system experiences spontaneous symmetry breaking of time reversal symmetry. Our findings introduce a mechanism for the spontaneous breaking of time-reversal symmetry in atomic systems, and unveil an exciting opportunity to engineer a nonreciprocal response at the nanoscale, exclusively driven by the quantum vacuum fluctuations.

We examined the magnetic ground state of the pyrochlore spin-ice compounds ${\mathrm{Pr}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ and ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ by means of specific-heat, magnetization, and ac-susceptibility measurements in the mK regime. At these low temperatures, we observe an unexpected large specific heat and corresponding entropy, which diminish in applied magnetic fields. This evidences the presence of additional states beyond the electronic spin and orbital degrees of freedom. We can qualitatively explain the large specific heat by the coupling of the nuclear spins of ${}^{141}\mathrm{Pr}$ and ${}^{165}\mathrm{Ho}$ with their electronic counterparts, which leads to a complex hyperfine-coupled term scheme. With increasing fields, the nuclear and electronic spins decouple leaving only the electronic excitations in the measured temperature window. At intermediate fields, a rather evolved term scheme emerges that may explain the unusual hysteretic magnetization and a remarkable state with a negative magnetization found for ${\mathrm{Ho}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. Our findings bring deep insights to the complex ground state of pyrochlore spin-ice compounds and their low-energy excitations.