Mirror-symmetric twisted trilayer graphene (tTLG) is composed of even-parity twisted bilayer graphene (tBLG)-like bands and odd-parity Dirac-like bands. Here, we study the mirror-symmetric and mirror-asymmetric Hofstadter moiré (HM) fractal bands of tTLG. A quantum parity Hall state is identified in mirror-symmetric tTLG at experimentally accessible charge densities. This mirror-symmetry-protected topological phase exhibits simultaneous quantized Hall and longitudinal resistances. The effects of the displacement field on the HM fractal bands of tTLG and topological phase transitions are also studied. The application of an electric displacement field results in an emergent weakly dispersive band at the charge neutrality point for a range of twist angles. This zero-energy state resides in the middle layer. It is isolated from the HM spectrum by an energy gap that scales proportional to the applied displacement field, making it a prime candidate to host correlated topological states.

Recent years have witnessed a surge of research on the non-Hermitian skin effect (NHSE) in one-dimensional lattices with finite-range couplings. In this work, we show that the long-range couplings that decay as $1/l^{\alpha }$ at distance $l$ can fundamentally modify the behavior of NHSE and the scaling of quantum entanglement in the presence of nonreciprocity. At $\alpha =0$, the nonlocality of couplings gives rise to the scale-free skin modes, whose localization length is proportional to the system size. Increasing the exponent $\alpha$ drives a complex-to-real spectral transition and a crossover from a scalefree to constant localization length. Furthermore, the scaling of nonequilibrium steady-state entanglement entropy exhibits a subextensive law due to the nonlocality and the complex spectrum, in contrast to an area law arising from NHSE. Our results provide a theoretical understanding on the interplay between long-range couplings and non-Hermiticity.

The study of abnormal Wilson transitions from metal to nonmetal states in simple electronic systems under high pressure plays an important role in understanding the profound physical mechanisms associated with the electronic structures of materials. Moreover, such studies serve as important references for understanding complex electronic systems. Of particular interest is that Li-O systems have been demonstrated to exhibit both normal and abnormal Wilson transition behaviors at high pressure depending on the Li to O ratio, and that Li-O compounds also exhibit superconductivity. However, the pressure-induced phase transformations and superconducting properties of these materials have not been comprehensively studied, particularly for Li-rich oxides. The present work addresses this issue by conducting ab initio structural relaxations of ${\mathrm{Li}}_m{\mathrm{O}}_n$ compounds $\left(m\le 8,n\le 2\right)$ at selected pressures ranging from 1 atm to 200 GPa using density-functional theory. Accordingly, we obtain detailed structural information for all stable compounds based on their formation enthalpies with respect to decomposition into other Li-O compounds or elemental Li and O solids. The results demonstrate that the parity of $m$ in Li-rich ${\mathrm{Li}}_m\mathrm{O}$ compounds determines their metallization or antimetallization features under applied pressures rather than the magnitude of $m$. The $C2/c$ phase of ${\mathrm{Li}}_8\mathrm{O}$, which exhibits an antimetallization feature with increasing pressure, is found to be superconducting at a temperature of 5.54 K under an applied pressure of 100 GPa. In stark contrast to other Li-rich compounds and most hydrides whose superconductivity is primarily affected by the electron density of states at the Fermi level, the superconductivity of $C2/c$-phase ${\mathrm{Li}}_8\mathrm{O}$ is mainly affected by an increasing average electron-phonon matrix element over the Fermi surface and a decreasing average phonon frequency with increasing pressure.

Quantum oscillations (QOs) describe the periodic variation of physical observables as a function of inverse magnetic field in metals. The Onsager relation connects the basic QO frequencies with the extremal areas of closed Fermi surface pockets, and the theory of magnetic breakdown explains the observation of sums of QO frequencies at high magnetic fields. Here we develop a quantitative theory of difference-frequency QOs in two- and three-dimensional metals with multiple Fermi pockets with parabolic or linearly dispersing excitations. We show that a nonlinear interband coupling, e.g., in the form of interband impurity scattering, can give rise to otherwise forbidden QO frequencies which can persist to much higher temperatures compared to the basis frequencies. We discuss the experimental implications of our findings for various material candidates, for example multifold fermion systems, like CoSi, and the relation to magneto-intersubband oscillations known for coupled two-dimensional electron gases.

Phasons are collective low-energy modes that appear in disparate condensed matter systems such as quasicrystals, incommensurate structures, fluctuating charge density waves, and moiré superlattices. They share several similarities with acoustic phonon modes, but they are not protected by any exact translational symmetry. As a consequence, they are subject to a wave-vector-independent damping, and they develop a finite pinning frequency, which destroy their acoustic linearly propagating dispersion. Under a few simple, well-motivated assumptions, we compute the phason density of states, and we derive the phason heat capacity as a function of the temperature. Finally, imagining a hypothetical $s$-wave pairing channel with electrons, we compute the critical temperature $T_c$ of the corresponding superconducting state as a function of phason damping using the Eliashberg formalism. We find that for large phason damping, the heat capacity is linear in temperature, showing a distinctive glasslike behavior. Additionally, we observe that the phason damping can strongly enhance the effective Eliashberg coupling, and we reveal a sharp nonmonotonic dependence of the superconducting temperature $T_c$ on the phason damping, with a maximum located at the underdamped-to-overdamped-crossover scale. Our simple computations confirm the potential role of overdamped modes not only in explaining the glassy properties of incommensurate structures but also in possibly inducing strongly coupled superconductivity therein and enhancing the corresponding $T_c$.

We investigate the steady-state phase transitions in an all-to-all transverse-field Ising model subjected to an environment. The considered model is composed of two ingredient Hamiltonians. The orientation of the external field, which is perpendicular to the spin interaction, can be tuned to be along either $x$ direction or $z$ direction in each ingredient Hamiltonian, while the dissipations always tend to flip the spins down to the $z$ direction. By means of mean-field approximation, we find that the quasicontinuous steady-state phase transition is presented as a consequence of the merging of two branches of steady-state solutions. The emergence of bistability is confirmed by analyzing the steady-state behaviors of a set of finite-size systems, which is also revealed by the Liouvillian spectrum.

Nanolaminated ${\mathrm{Mn}}_2\mathrm{GaC}$ epitaxial films crystallizing in the hexagonal structure belong to the family of MAX phase compounds and display complex magnetic interactions. While the critical temperature of the order-disorder transition is 507 K, at around 214 K this compound undergoes a first-order phase transition with the magnetic structure below the transition point not being fully resolved. Previous studies indicated a noncollinear spin arrangement, but a specific magnetic structure could not be defined. In this work we present the results of ${}^{69}\mathrm{Ga}, {}^{71}\mathrm{Ga}$, and ${}^{55}\mathrm{Mn}$ NMR experiments performed at 4.2 K in an external in-plane magnetic field up to 1 T. The in-depth analysis of the experimental results shows a helical magnetic structure consisting of the ferromagnetically coupled Mn-C-Mn slabs that are twisted across the Ga layer by $167.2^{\circ }$ with respect to the next Mn-C-Mn slab. As a result, the magnetic structure presents a spiral propagating along the out-of-plane direction (hexagonal $c$ axis) with a pitch of around 14 lattice constants.

We analyze the nature of the modulated magnetic states in a micromagnetic model for the monoaxial chiral magnet ${\mathrm{MnNb}}_3{\mathrm{S}}_6$, for which the Dzyaloshinskii-Moriya interaction and the dipolar interaction compete evenly. We show that the interplay between these interactions lead to a complex phase diagram including ferromagnetic states, fanlike states, in-plane stripes patterns, and chiral soliton lattices. In particular, stripe patterns and chiral soliton lattices comprise nontrivial topological states with fixed chirality. The obtained phase diagram exhibits a strong dependency on the thickness and on the strength of the Dzyaloshinskii-Moriya interaction. Our results can help to understand the magnetic properties of systems such as ${\mathrm{MnNb}}_3{\mathrm{S}}_6$.

Here we report the investigation on correlation between the transport properties and the corresponding stability of the lattice structure for $\mathrm{CaK}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Ni}}_x\right)}_4{\mathrm{As}}_4$ ($x=0.04$ and 0), a new type of putative topological superconductors with and without a spin-vortex crystal (SVC) state in a wide pressure range involving superconducting (SC) to nonsuperconducting (NSC) transition and the half to full collapse of tetragonal [half-collapsed tetragonal (h-cT) and full-collapsed tetragonal (f-cT)] phases by the complementary measurements of high-pressure resistance, Hall coefficient, and synchrotron x-ray diffraction. The three critical pressures are identified: $P_{ch}^{\mathrm{on}}$ that is the turn-on critical pressure of the h-cT phase transition and it coincides with the critical pressure for the sign change of Hall coefficient from positive to negative, a manifestation of the Fermi surface reconstruction; $P_{ch}^{\mathrm{off}}$ that is the turn-off pressure of the h-cT phase transition; and $P_{cf}$ that is the critical pressure of the f-cT phase transition. By comparing the high-pressure results measured from the two kinds of samples, we find a distinct “left-shift” of the $P_{ch}^{\mathrm{on}}$ for the doped sample, at the pressure of which its SVC state is fully suppressed, however, the $P_{ch}^{\mathrm{off}}$ and the $P_{cf}$ remain the same as that of the undoped one. Our results not only provide a consistent understanding on the results reported before, but also demonstrate the importance of the Fe-As bonding in stabilizing the superconductivity of the iron pnictide superconductors through the “pressure window.”

We apply the static auxiliary field Monte Carlo approach to study phase correlations of the pairing fields in a model with spin-singlet pairing interaction. We find that the short- and long-distance phase correlations are well captured by the phase mutual information, which allows us to construct a theoretical phase diagram containing the uniform $d$-wave superconducting region, the phase fluctuating region, the local pairing region, and the disordered region. We show that the gradual development of phase coherence has a number of consequences on spectroscopic measurements, such as the development of the Fermi arc and the anisotropy in the angle-resolved spectra, scattering rate, entropy, specific heat, and quasiparticle dispersion, in good agreement with experimental observations. For strong coupling, our Monte Carlo simulation reveals an unexpected charge-4$e$ plaquette state with $d$-wave bonds, which competes with the uniform $d$-wave superconductivity and exhibits a U-shaped density of states.

We report Raman studies of GdN and LuN, two of the rare-earth mononitrides that form a series of mostly intrinsic ferromagnetic semiconductors. Their rock-salt structure supports no first-order Raman scattering, but, nonetheless, we find a density-of-modes pattern expected for nearly point-defect scattering, an intrinsic two-phonon scattering spectrum, and an LO feature that appears independent of defect concentration. The results are compared with the phonon dispersion calculated within a density functional theory treatment indicating that computed phonon frequencies are smaller than measured, with the disagreement rising to $\sim 30\%$ for the TA branch. Contrary to the previous assumption of defect-induced scattering at the $L$ point, we propose that the observed LO feature arises from $\mathrm{LO}(\mathrm{\Gamma }$) scattering induced by the Fröhlich interaction, similar to what has been observed in YbS.

We theoretically study the Dzyaloshinskii-Moriya interaction (DMI) mediated by band electrons with strong spin-orbit coupling (SOC). We first derive a general formula for the coefficient ${\mathit{D}}_i$ of the DMI in free energy in terms of Green's functions, and we examine its variations in relation to physical quantities. In general, the DMI coefficient can vary depending on physical quantities, i.e., whether one is looking at equilibrium spin structure (${\mathit{D}}_i$) or spin-wave dispersion (${\mathit{D}}_i^{\left(2\right)}$), and the obtained formula helps to elucidate their relations. By explicit evaluations for a magnetic topological insulator and a Rashba ferromagnet with perpendicular magnetization, we observe ${\mathit{D}}_i^{\left(2\right)}\ne {\mathit{D}}_i$ in general. In the latter model, or more generally, when the magnetization and the spin-orbit field are mutually orthogonal, ${\mathit{D}}_i$ is exactly related to the equilibrium spin current for arbitrary strength of SOC, generalizing the similar relation for systems with weak SOC. Among various systems with strong SOC, magnetic Weyl semimetals are special in that ${\mathit{D}}_i^{\left(2\right)}={\mathit{D}}_i$, and in fact, the DMI in this system arises as the chiral anomaly.

Nanoscale magnetic domains with controllable configurations could be used for classical and quantum applications, where the switching of magnetization configurations is an essential operation for information processing. Here, we report that the magnetic domain reorientation in a notched ferromagnetic nanotrack can be realized and effectively controlled by applying uniform magnetic field pulses in a fixed in-plane direction perpendicular to the nanotrack. Our micromagnetic simulation results show that the configurations of magnetic domains in the notched nanotrack can be switched between a head-to-head state and a tail-to-tail state in a reversible manner driven by magnetic field pulses, while it is unnecessary to reverse the direction of the magnetic field. Such a unique magnetic domain reorientation dynamics is found to depend on magnetic parameters and nanotrack geometries. The reorientation dynamics of magnetic domains also depends on the strength and length of the applied magnetic-field pulse. In addition, we point out that the notches at the center of the nanotrack play an important role for the stabilization of the head-to-head and tail-to-tail states during the magnetic domain reorientation. We also qualitatively explain the field-induced reorientation phenomenon with a simplified two-dimensional macrospin model. Our results may make it possible to build spintronic devices driven by a fixed magnetic field. Our findings may also motivate future studies to investigate the classical and quantum applications based on nanoscale magnetic domains.

We present a comprehensive first-principles investigation of the La-F system in rare-earth fluorides under pressures ranging from 50 to 300 GPa. Our study reveals the existence of novel F-rich phases $\mathrm{La}{\mathrm{F}}_5$ and $\mathrm{La}{\mathrm{F}}_6$ with $F\text{−}43m$ and $R3$ symmetry, respectively, in addition to the known insulating $\mathrm{La}{\mathrm{F}}_3$. $\mathrm{La}{\mathrm{F}}_5$, a binary derivative of half-Heusler alloys, exhibits half-metallic ferromagnetism between 14 and 100 GPa, with large band gaps of 5.7–6.9 eV of the spin-up channel and high Curie temperatures of 673–505 K. Electronic analysis attributes the ferromagnetic and half-metallic properties to F atoms in tetrahedral motifs. Furthermore, we predict that trigonal $\mathrm{La}{\mathrm{F}}_6$, characterized by layered stacking structures, exhibits superconductivity with a critical temperature $\left(T_{\mathrm{c}}\right)$ of 5 K at 50 GPa. Our findings provide valuable insights into the high-pressure behavior of rare-earth fluorides and their potential applications in advanced materials and devices.

Theoretical studies predicted possible superconductivity in electron-doped chromium pnictides isostructural to their iron counterparts. Here, we report the synthesis and characterization of a ZrCuSiAs-type Cr-based compound ThCrAsN, as well as its oxygen-doped variants. All samples of ${\mathrm{ThCrAsN}}_{1-x}{\mathrm{O}}_x$ show metallic conduction, but no superconductivity is observed above 30 mK even though the oxygen substitution reaches 75%. The magnetic structure of ThCrAsN is determined to be G-type antiferromagnetic by magnetization measurements and first-principles calculations jointly. The calculations also indicate that the in-plane Cr-Cr direct interaction of ThCrAsN is robust against the heavy electron doping. The calculated density of states of the orbital occupations of Cr for ThCrAs(N,O) is strongly spin polarized. Our results suggest the similarities between chromium pnictides and iron-based superconductors should not be overestimated.

A recent study [S. Yoshizawa et al., Nat. Commun. 12, 1462 (2021)] reported the occurrence of field-resilient superconductivity, that is, enhancement of the in-plane critical magnetic field $H_{\mathrm{c}2}^{\left|\right|}$ beyond the paramagnetic limiting field, in atomic-layer crystalline ($\sqrt{7}\times \sqrt{3}$)-In on a Si(111) substrate. The present article elucidates the origin of the observed field-resilient noncentrosymmetric superconductivity in this highly crystalline two-dimensional material. We develop the quasiclassical theory of superconductivity by incorporating the Fermi surface anisotropy together with an anisotropic spin splitting and texture specific to atomic-layer crystalline systems. In Si(111)-($\sqrt{7}\times \sqrt{3}$)-In, a typical material with a large antisymmetric spin-orbit coupling (ASOC), we show an example where the combination of the ASOC and disorder effect suppresses the paramagnetic depairing and can lead to an enhancement of $H_{\mathrm{c}2}^{\left|\right|}$ compared to an isotropic system only when a magnetic field is applied in a particular direction due to an anisotropic spin texture. We also study the parity-mixing effect to demonstrate that the enhancement of $H_{\mathrm{c}2}^{\left|\right|}$ is limited in the moderately clean regime because of the fragile $s+p$-wave pairing against nonmagnetic scattering in the case of the dominant odd-parity component of a pair wave function. Furthermore, from analysis of the transition line, we identify the field-resilience factor taking account of the scattering and suppression of paramagnetic effects and discuss the origin of the field-resilient superconductivity. Through fitting of the $H_{\mathrm{c}2}^{\left|\right|}$ data, the normal-state electron scattering is discussed with a prime focus on the role of atomic steps on a Si(111) surface.

The anomalous Nernst effect is studied by $\mathit{ab}$ initio calculations in substituted iron nitrides with antiperovskite structure ${\mathrm{Fe}}_3{M}^1\mathrm{N}$ and ${\mathrm{Fe}}_2{M}^1{M}^2\mathrm{N}$ ($M^1$ = $4d$ or $5d$, and $M^2$ = $3d$ transition metals), considering the intrinsic Berry curvature-related mechanism depending only on the band structure. The highest absolute anomalous Nernst conductivity (ANC) $8{\mathrm{A}\mathrm{K}}^{-1}{\mathrm{m}}^{-1}$ with a negative sign is calculated for ruthenium substituted ferromagnetic phase ${\mathrm{Fe}}_3\mathrm{RuN}$. A similar maximum ANC is determined for ferrimagnetic phase ${\mathrm{Fe}}_2\mathrm{RuCrN}$, yet the advantage of this doubly substituted phase is that the high ANC values persist over a wider temperature range. Comparable ANCs have so far only been determined for compounds with critical temperatures of magnetic ordering below room temperature, while substituted iron nitrides exhibit $T_C$ well above room temperature. Therefore, we propose ${\mathrm{Fe}}_2\mathrm{RuCrN}$, composed from nontoxic, and except for Ru, also fairly abundant elements, as a starting stoichiometry for further experimental study of candidates for devices possessing a high ANC and suitable for room- and high-temperature applications.

Quantum many-body scar is a recently discovered phenomenon weakly violating eigenstate thermalization hypothesis, and it has been extensively studied across various models. However, experimental realizations are mainly based on constrained models such as the PXP model. Inspired by recent experimental observations on the superconducting platform in the works by Zhang et al. [Nat. Phys. 19, 120 (2023)] and Yao et al. [Nat. Phys. (2023)], we study a distinct class of quantum many-body scars based on a half-filling hard-core Bose-Hubbard model, which is generic to describe in many experimental platforms. It is the so-called Hilbert-space quantum scar as it originates from a subspace with a hypercube geometry weakly connecting to other thermalization regions in Hilbert space. Within the hypercube, a pair of collective Fock states do not directly connect to the thermalization region, resulting in slow thermalization dynamics with remarkable fidelity revivals with distinct differences from dynamics of other initial states. This mechanism is generic in various real-space lattice configurations, including one-dimensional Su-Schrieffer-Heeger chain, comb lattice, and even random dimer clusters consisting of dimers. In addition, we develop a toy model based on Hilbert hypercube decay approximation, to explain the spectrum overlap between the collective states and all eigenstates. Furthermore, we explore the Hilbert-space quantum scar in two- and three-dimensional Su-Schrieffer-Heeger many-body systems, consisting of tetramers or octamers, respectively. This study makes quantum many-body scar state more realistic in applications such as quantum sensing and quantum metrology.