Larkin-Ovchinnikov superconducting state has spontaneous modulation of Cooper pair density, while Fulde-Ferrell state has a spontaneous modulation in the phase of the order parameter. We report that a quasi-two-dimensional Dirac metal, under certain conditions has principally different inhomogeneous superconducting states that by contrast have spontaneous modulation in a submanifold of a multiple-symmetries-breaking order parameter. The first state we find can be viewed as a nematic superconductor where the nematicity vector spontaneously breaks rotational and translational symmetries due to spatial modulation. The other demonstrated state is a chiral superconductor with spontaneously broken time-reversal and translational symmetries. It is characterized by an order parameter, which forms a lattice pattern of alternating chiralities.

In hybrid improper ferroelectric systems, polarization arises from the onset of successive nonpolar lattice modes. In this work, measurements and modeling were performed to determine the spatial symmetries of the phases involved in the transitions to these modes. Structural and optical measurements reveal that the tilt and rotation distortions of the $\mathrm{Mn}{\mathrm{O}}_6$ or $\mathrm{Ti}{\mathrm{O}}_6$ polyhedra relative to the high symmetry phases driving ferroelectricity in the hybrid improper $\mathrm{C}{\mathrm{a}}_3{X}_2{\mathrm{O}}_7$ system $(X=\mathrm{Mn}$ and Ti) condense at different temperatures. The tilt angle vanishes abruptly at $T_{\mathrm{T}}\sim 400$ K for $\mathrm{C}{\mathrm{a}}_3\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_7$ (and continuously for $X=\mathrm{Ti})$ and the rotation mode amplitude is suppressed at much higher temperatures $T_{\mathrm{R}}\sim 1060$ K. Moreover, Raman measurements in $\mathrm{C}{\mathrm{a}}_3\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_7$ under isotropic pressure reveal that the polyhedral tilts can be suppressed by very low pressures (between 1.4 and 2.3 GPa) indicating their softness. These results indicate that the $\mathrm{C}{\mathrm{a}}_3\mathrm{M}{\mathrm{n}}_2{\mathrm{O}}_7$ system provides a platform for strain engineering of ferroelectric properties in film-based systems with substrate-induced strain.

We study the current-driven motion of metastable localized spin structures with various topological charges in a $\left({\mathrm{Pt}}_{0.95}{\mathrm{Ir}}_{0.05}\right)$/Fe bilayer on a Pd(111) surface by combining atomistic spin model simulations with an approach based on the generalized Thiele equation. We demonstrate that besides a distinct dependence on the topological charge itself the dynamic response of skyrmionic structures with topological charges $Q=-1$ and $Q=3$ to a spin-polarized current exhibits an orientation dependence. We further show that such an orientation dependence can be induced by applying an in-plane external field, possibly opening up a different pathway to the manipulation of skyrmion dynamics.

Using a tight-binding two-orbital ($d_{x^2-y^2}, d_{3z^2-r^2}$) model and a random phase approximation treatment of the spin-fluctuation pairing vertex, we calculate the pairing strengths for a cuprate model in which the hole doping varies from ${\mathrm{Cu}}^{2+}$ to ${\mathrm{Cu}}^{3+}$. We find two domes of pairing strength: one corresponding to the traditional low hole doping regime and the other to the extremely overdoped regime discussed by Geballe and Marezio [Physica C 469, 680 (2009)]. In the overdoped regime we find that there is significant pairing strength in both the $d$-wave and $s^{\pm }$ channels.

The two-dimensional Hubbard model is studied for small values of the interaction strength ($U$ of the order of the hopping amplitude $t$), using a variational ansatz well suited for this regime. The wave function, a refined Gutzwiller ansatz, has a BCS mean-field state with $d$-wave symmetry as its reference state. Superconducting order is found for densities $n<1$ (but not for $n=1$). This resolves a discrepancy between results obtained with the functional renormalization group, which do predict superconducting order for small values of $U$, and numerical simulations, which did not find superconductivity for $U\lesssim 4t$. Both the gap parameter and the order parameter have a domelike shape as a function of $n$ with a maximum for $n\approx 0.8$. Expectation values for the energy, the particle number, and the superconducting order parameter are calculated using a linked-cluster expansion up to second order in $U$. In this way large systems (millions of sites) can be readily treated and well converged results are obtained. A big size is indeed required to see that the gap becomes very small at half filling and probably tends to zero in the thermodynamic limit, whereas away from half filling a finite asymptotic limit is reached. For a lattice of a given size the order parameter becomes finite only above a minimal coupling strength $U_c$. This threshold value decreases steadily with increasing system size, which indicates that superconductivity exists for arbitrarily small $U$ for an infinite system. For moderately large systems the size dependence is quite irregular, due to variations in level spacings at the Fermi energy. The fluctuations die out if the gap parameter spans several level spacings.

The origin of simultaneous electronic, structural, and magnetic transitions in bulk rare-earth nickelates $\left(RE{\mathrm{NiO}}_3\right)$ remains puzzling with multiple conflicting reports on the nature of these entangled phase transitions. Heterostructure engineering of these materials offers unique opportunity to decouple the metal-insulator transition (MIT) from the magnetic transition. However, the evolution of underlying electronic properties across these decoupled transitions remains largely unexplored. In order to address this, we have measured Hall effect on a series of epitaxial ${\mathrm{NdNiO}}_3$ films, spanning a variety of electronic and magnetic phases. We find that the MIT results in only a partially gapped Fermi surface, whereas the full insulating phase forms below the magnetic transition. In addition, we also find a systematic reduction of the Hall coefficient $R_H$ in the metallic phase of these films with epitaxial strain and also a surprising transition to a negative value at large compressive strain. The partially gapped, weakly insulating, paramagnetic phase is reminiscence of pseudogap behavior of high-$T_c$ cuprates. The precursor metallic phase, which undergoes transition to the insulating phase, is a non-Fermi liquid with a temperature exponent $n$ of resistivity of 1, whereas the exponent increases to 4/3 in the noninsulating samples. Such a nickelate phase diagram with sign reversal of $R_H$, a pseudogap phase, and non-Fermi-liquid behavior is intriguingly similar to high-$T_c$ cuprates, giving important guidelines to engineer unconventional superconductivity in oxide heterostructures.

It is shown that the symmetry-enforced Dirac points exist at some time-reversal symmetric momenta in the antiferromagnetic compound ${\mathrm{GdB}}_4$. These Dirac points may be controlled by the external magnetic field or by the deformation of the crystal. Application of the external magnetic field leads to splitting of these points into Weyl points or to opening of a gap depending on the field direction. The application of the symmetry-breaking deformation also opens a gap in the spectrum. Suppression of the antiferromagnetic order leads to the formation of the nodal line instead of the Dirac points. This indicates that the symmetry-enforced Dirac semimetals may be effectively used in different spintronic devices.

We report studies of the Seebeck coefficient $S$ of the quasi-one-dimensional compound $\mathrm{Nb}{\mathrm{S}}_3$, together with the temperature dependence of its specific conductivity ${\sigma }_{\mathrm{s}}$ and heat capacity $c_p$. The monoclinic phase $(\mathrm{Nb}{\mathrm{S}}_3$-II) is studied over the temperature range $T=80–400$ K, which covers two charge density wave (CDW) transitions at $T_{\mathrm{P}1}=360$ K (CDW-1) and $T_{\mathrm{P}2}=150$ K (CDW-2). The $S\left(T\right)$ curves show features in the vicinities of both CDW transitions and appear to be correlated with the value of ${\sigma }_{\mathrm{s}}\left(300\mathrm{K}\right)$: The increase of $S$ below $T_{\mathrm{P}1}$ in the high-Ohmic samples reveals a complete dielectrization of the electronic spectrum, while in the low-Ohmic samples $S$ decreases below $T_{\mathrm{P}1}$ and even becomes negative below $T_{\mathrm{P}2}$. The magnitude of $S$ in low-Ohmic samples at $T<T_{\mathrm{P}2}$ is well below $k_{\mathrm{B}}/e\approx 86\mu \mathrm{V}/\mathrm{K},k_B$ being the Boltzmann constant and $e$ the elementary charge, which is surprisingly low for a usual CDW semiconducting state. Our results suggest that at $T_{\mathrm{P}1}$ the main electronic band with $p$-type carriers becomes gapped, while some $n$-type carriers can remain in a separate band with low density of states. These carriers, whose concentration is defined by the compositional doping, are gapped at $T_{\mathrm{P}2}$. We also report $S$ for the triclinic dielectric phase of $\mathrm{Nb}{\mathrm{S}}_3\left(\mathrm{Nb}{\mathrm{S}}_3\text{−}\mathrm{I}\right)$. Its low absolute value, $\sim k_{\mathrm{B}}/e$, and the anomalous temperature dependence demonstrate that $\mathrm{Nb}{\mathrm{S}}_3\text{−}\mathrm{I}$ is neither a semiconductor nor a CDW conductor in the usual sense.

We propose a setup based on (solid-state) qubits coupled to a common multimode transmission line, which allows for coherent spin-spin interactions over macroscopic on-chip distances, without any ground-state cooling requirements for the data bus. Our approach allows for the realization of fast deterministic nonlocal quantum gates, the simulation of quantum spin models with engineered (long-range) interactions, and provides a flexible architecture for the implementation of quantum approximate optimization algorithms.

We report the experimental observation of strong electrical magnetochiral anisotropy in trigonal tellurium ($t$-Te) crystals. We introduce the tensorial character of the effect and determine several tensor elements. We present a simple model based on the band structure of $t$-Te and the Boltzmann relaxation time approximation which gives a reasonable description of the principal results.

We propose a Haldane-BCS-Hubbard model on a honeycomb lattice which is composed of two copies of the Haldane model of the quantum anomalous Hall effect, an equal-spin pairing term, and an on-site Hubbard interaction term. For any interaction strength, this model is exactly solvable along the symmetric line where the hopping and pairing amplitudes are equal to each other. The ground state of the Haldane-BCS-Hubbard model is a topological superconducting state at weak interaction with two chiral Majorana edge states. A strong interaction drives the system across a topological quantum phase transition to a topologically trivial superconductor. A ${\mathbb{Z}}_2$ symmetry of the Hamiltonian, which is a composition of the bond-centered inversion and a gauge transformation, is spontaneously broken by the interaction, resulting in a finite antiferromagnetic order in the $y$ direction.

Three types (three-band, two-band, and one-band) of effective Hamiltonians for ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$ and three-band effective Hamiltonian for ${\mathrm{La}}_2{\mathrm{CuO}}_4$ are derived by improving the constrained-$GW$ approximation combined with the self-interaction correction ($\mathrm{c}GW-\text{SIC}$) formulated by Hirayama et al. [Phys. Rev. B 98, 134501 (2018)]. The improved treatment of the interband Hartree energy in the present paper turns out to be crucially important, because the solution of the present improved Hamiltonian shows excellent agreement with the experimental results, for instance, for the charge gap (2 eV) and antiferromagnetic ordered moment $\left(0.6{\mu }_{\text{B}}\right)$ of the mother compound of ${\mathrm{La}}_2{\mathrm{CuO}}_4$, in sharp contrast to the estimates by the previous Hamiltonian, 4.5 eV and $0.8{\mu }_{\text{B}}$, respectively. To our knowledge, this is the first simultaneous and quantitative reproduction of these quantities by $\mathit{ab}\mathit{initio}$ methods without introducing adjustable parameters. We also predict that the Mott gap and the magnetic ordered moment for ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$ is about 0.7 eV and $0.4{\mu }_{\text{B}}$, respectively, if the mother compound becomes available, indicating weaker electron correlations than ${\mathrm{La}}_2{\mathrm{CuO}}_4$. Surprisingly, we find that while carriers are doped only in the highest antibonding band, only the Cu $3d_{x^2-y^2}$ (O $2p$) carriers look doped in the electron (hole) doped side around the zero doping in the atomic orbital basis, implying that the Mott-Hubbard (single-band) and charge transfer (three-band) descriptions are both correct. The obtained Hamiltonians will serve to further clarify the electronic structures of these copper oxide superconductors and to elucidate the superconducting mechanism in an ab initio fashion.

Many rotational invariants for crystal structure representations have been used to describe the structure-property relationship by machine learning. The machine learning interatomic potential (MLIP) is one of the applications of rotational invariants, which provides the relationship between the energy and the crystal structure. Therefore, the enumeration of rotational invariants should be useful for constructing MLIPs with the desired accuracy. In this study, we introduce high-order linearly independent rotational invariants up to the sixth order based on spherical harmonics and apply them to linearized MLIPs for elemental aluminum. A set of rotational invariants is derived by the general process of reducing the Kronecker products of irreducible representations for the SO(3) group using a group-theoretical projector method. A high predictive power for a wide range of structures is accomplished by using high-order invariants with low-order invariants equivalent to pair and angular structural features.

In this work, we measured N self-diffusion in the Co-N system and found an unexpected result that N diffuses out almost completely around 500 K, leaving behind fcc Co irrespective of the amount of N used to deposit Co-N. On the other hand, in previous attempts the ${\mathrm{Co}}_4\mathrm{N}$ phase has always been grown at 550 K or above. In view of our finding, it appears that fcc Co could have been mistaken for ${\mathrm{Co}}_4\mathrm{N}$, probably due to the closeness of their lattice parameters (LP; fcc Co = 3.54 $\AA$, ${\mathrm{Co}}_4\mathrm{N}$= 3.74 $\AA$). Therefore, ${\mathrm{Co}}_4\mathrm{N}$ – an interesting material for its high spin-polarization ratio and high magnetic moment remained unexplored. By bringing down the growth temperature, we report the growth of stoichiometric ${\mathrm{Co}}_4\mathrm{N}$ epitaxial thin films. Films were grown using a direct current reactive magnetron sputtering process on ${\mathrm{LaAlO}}_3$ (LAO mismatch $1.4\%$) and MgO (mismatch $11.3\%$) substrates and their structural and magnetic properties were studied. Precise magnetic moment ($M_s$) of ${\mathrm{Co}}_4\mathrm{N}$ samples were measured using polarized neutron reflectivity and compared with bulk magnetization results. We found that the $M_s$ of ${\mathrm{Co}}_4\mathrm{N}$ is higher due to a magnetovolume effect. Unlike previous findings, we observed that substrates induce misfit strain and strain inhomogeneity is the cause of modifications in magnetic ensemble such as coercivity, saturation magnetization, and magnetic anisotropy. A consequence of incoherent strain present in our samples is also reflected in the magnetic anisotropy leading to a superposition of strong fourfold and a small fraction of uniaxial magnetic anisotropy. Obtained results are presented and discussed in this work.

A helix has a wave vector along the $z$ axis with the magnetic moments ferromagnetically aligned within $xy$ planes with a turn angle $kd$ between the moments in adjacent planes in transverse field $\mathbf{H}=H_x\widehat{\mathbf{i}}=0$. The magnetic structure and $x$-axis average magnetization per spin of this system in a classical XY anisotropy field $H_{\mathrm{A}}$ is studied versus $kd$, $H_{\mathrm{A}}$, and large $H_x$ at zero temperature. For values of $H_{\mathrm{A}}$ below a $kd$-dependent maximum value, the $xy$ helix phase transitions with increasing $H_x$ into a spin-flop (SF) phase where the ordered moments have $x$, $y$, and $z$ components. The moments in the SF phase are taken to be distributed on either one or two $xyz$ spherical ellipses. The minor axes of the ellipses are oriented along the $z$ axis and the major axes along the $y$ axis where the ellipses are flattened along the $z$ axis due to the presence of the XY anisotropy. From energy minimization of the SF spherical ellipse parameters for given values of $kd$, $H_{\mathrm{A}}$, and $H_x$, four $kd$-dependent SF phases are found: either one or two $xyz$ spherical ellipses and either one or two $xy$ fans, in addition to the $xy$ helix/fan phase and the paramagnetic (PM) phase with all moments aligned along H. The PM phase occurs via second-order transitions from the $xy$ fan and SF phases with increasing $H_x$. Phase diagrams in the $H_x\text{−}{H}_{\mathrm{A}}$ plane are constructed by energy minimization with respect to the SF phases, the $xy$ helix/fan phase, and the $xy$ SF fan phase for five $kd$ values. One of these five phase diagrams is compared with the magnetic properties found experimentally for the model helical Heisenberg antiferromagnet ${\mathrm{EuCo}}_2{\mathrm{P}}_2$ and semiquantitative agreement is found.

The Mermin-Wagner theorem prevents the stabilization of long-range magnetic order in two-dimensional layered materials, such as the pnictide superconductors, unless the magnetism is associated with a discrete symmetry breaking. A typical known example is the discrete row and column collinear magnetic state that emerges in doped iron pnictide materials due to an order-by-disorder mechanism. In these compounds, the magnetic state competes with superconductivity and the mechanism that stabilizes magnetism remains controversial. In this work, we report the phase diagram of a doped frustrated Heisenberg model obtained through Monte Carlo simulations combined with a parallel tempering simulation technique. The emergence of long-range magnetic order is stabilized by interactions between the magnetic dopant impurities.

We report numerical simulations of the nonlinear dynamics of Josephson vortices driven by strong dc currents in layered superconductors. Dynamic equations for interlayer phase differences in a stack of coupled superconducting layers were solved to calculate a drag coefficient $\eta \left(J\right)$ of the vortex as a function of the perpendicular dc current density $J$. It is shown that Cherenkov radiation produced by a moving vortex causes significant radiation drag increasing $\eta \left(v\right)$ at high vortex velocities $v$ and striking instabilities of driven Josephson vortices moving faster than a terminal velocity $v_c$. The steady-state flux flow breaks down at $v>v_c$ as the vortex starts producing a cascade of expanding vortex-antivortex pairs evolving into either planar macrovortex structures or branching flux patterns propagating both along and across the layers. This vortex-antivortex pair production triggered by a rapidly moving vortex is most pronounced in a stack of underdamped planar junctions where it can occur at $J>J_s$ well below the interlayer Josephson critical current density. Both $v_c$ and $J_s$ were calculated as functions of the quasiparticle damping parameter, and the dc magnetic field was applied parallel to the layers. The effects of vortex interaction on the Cherenkov instability of moving vortex chains and lattices in annular stacks of Josephson junctions were considered. It is shown that a vortex driven by a current density $J>J_s$ in a multilayer of finite length excites self-sustained large-amplitude standing waves of magnetic flux, resulting in temporal oscillations of the total magnetic moment. We evaluated a contribution of this effect to the power $W$ radiated by the sample and showed that $W$ increases strongly as the number of layers increases. These mechanisms can result in nonlinearity of the $c$-axis electromagnetic response and contribute to THz radiation from the layered cuprates at high dc current densities flowing perpendicular to the $ab$ planes.

Acoustic analogies of topological insulators reside at the frontier of ongoing metamaterials research. Of particular interest are the topological interface states that are determined by the Zak phase, which is the geometric phase characterizing the topological property of the bands in one-dimensional systems. Here we design double-channel Mie resonators based on the so-called labyrinth acoustic metamaterials, which can be considered equivalent to a ultraslow medium of large refractive index, inevitably containing structural features on a subwavelength scale. The metamolecule containing two cells is engineered to host the degenerated states through a zone-folding mechanism, whereupon the Zak phase transition takes place when the interval between two cells changes from shrunk to expanded. Furthermore, the topological interface state displays strong robustness against randomly introduced perturbations whose acoustic intensity is enhanced by nearly a factor 1600 in comparison to an ordinary waveguide.

X-ray photon correlation is used to probe the slow dynamics of the glass-former ${\mathrm{B}}_2{\mathrm{O}}_3$ across the glass transition. In the undercooled liquid phase, the decay times of the measured correlation functions are consistent with visible light-scattering results and independent of the incoming flux; in the glass they are instead temperature independent and show a definite dependence on the x-ray flux since here the dynamics is artificially induced by the interaction with the x-ray beam. The decay times in this regime provide a measure of the number of atoms that rearrange on a length scale on the order of the inverse of the exchanged wave vector following an absorption event. Quite surprisingly, this number for the ${\mathrm{B}}_2{\mathrm{O}}_3$ glass is on the order of thousands of atoms. The induced dynamics persists also at higher temperatures until, close to the glass transition, it gets much slower than the intrinsic relaxation of the material. We suggest a possible scenario in which the single absorbed photon induces a collective motion of a volume of the glass with a size of the order of the nanometer.