Discrete time crystals (DTCs) are nonequilibrium phases of matter characterized by robust subharmonic order parameter dynamics. We report a type of DTC in a periodically driven surface code, the subharmonic signature of which is only observable with respect to some nonlocal order parameter. By modifying the commonly used metrics for characterizing ordinary DTCs, i.e., the spectral functions, spin-glass order parameters, and two-point correlators, we further numerically demonstrate the rich phases of the proposed system. Specifically, depending on the system parameters and boundary conditions, we find that the system may fall into either a “surface code” phase, trivial paramagnet phase, nonlocal period-doubling DTC phase, or nonlocal period-quadrupling DTC phase. Our work thus demonstrates the prospect of exploring topological codes for discovering novel phases of matter.

The $\mathrm{Mn}{\left({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x\right)}_2{\mathrm{Te}}_4$ series is purported to span from an antiferromagnetic (AF) topological insulator at $x=0$ to a trivial AF insulator at $x=1$. Here we report on neutron diffraction and inelastic neutron scattering studies of the magnetic interactions across this series. All compounds measured possess ferromagnetic (FM) triangular layers and we find a crossover from AF to FM interlayer coupling near $x=1$ for our samples. The large spin gap at $x=0$ closes rapidly and the average FM exchange interactions within the triangular layer increase with Sb substitution. Similar to a previous study of ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$, we find severe spectral broadening which increases dramatically across the compositional series. In addition to broadening, we observe an additional sharp magnetic excitation in ${\mathrm{MnSb}}_2{\mathrm{Te}}_4$ that may indicate the development of local magnetic modes originating from antisite disorder between Mn and Sb sublattices. The results suggest that both substitutional and antisite disorder contribute substantially to the magnetism in $\mathrm{Mn}{\left({\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x\right)}_2{\mathrm{Te}}_4$.

Although cuprate superconductors have been intensively studied for the past decades, there is no consensus regarding the microscopic origin of their superconductivity. In this paper, we measure the low-energy electrodynamic response of slightly underdoped and overdoped ${\mathrm{La}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ thin films using time-domain terahertz (THz) spectroscopy to determine the temperature and field dependence of the superfluid spectral weight. We show that the temperature dependence obeys the relation ${\mathrm{n}}_s$ $\propto 1-{(T/T_c)}^2$, typical for dirty limit BCS-like $d$-wave superconductors. Furthermore, the magnetic field dependence was found to follow a sublinear $\sqrt{B}$ form, which supports predictions based on a $d$-wave symmetry for the superconducting gap. These observations imply that the superconducting order in these electron-doped cuprates can be well described in terms of a disordered BCS $d$-wave formalism.

We employ the phenomenological Lawrence-Doniach model to compute the contributions of the superconducting fluctuations to the third-harmonic magnetic response, denoted here by $\overline{M_3}$, which can be measured in a precise way using ac magnetic fields and lock-in techniques. We show that, in an intermediate temperature regime, this quantity behaves as the third-order nonlinear susceptibility, which shows a power-law dependence with the reduced temperature $\epsilon =\frac{T-T_c}{T_c}$ as ${\epsilon }^{-5/2}$. Very close to $T_c$, however, $\overline{M_3}$ saturates due to the nonzero amplitude of the ac field. We compare our theoretical results with experimental data for three conventional superconductors—lead, niobium, and vanadium—and for the unconventional superconductor ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ (SRO). We find good agreement between theory and experiment for the elemental superconductors, although the theoretical values for the critical field systematically deviate from the experimental ones. In the case of SRO, however, the phenomenological model completely fails to describe the data, as the third-harmonic response remains sizable over a much wider reduced temperature range compared to Pb, Nb, and V. We show that an inhomogeneous distribution of $T_c$ across the sample can partially account for this discrepancy, since regions with a locally higher $T_c$ contribute to the fluctuation $\overline{M_3}$ significantly more than regions with the “nominal” $T_c$ of the clean system. However, the exponential temperature dependence of $\overline{M_3}$ first reported by Pelc et al. [Nat. Commun. 10, 2729 (2019)] is not captured by the model with inhomogeneity. We conclude that, while inhomogeneity is an important ingredient to understand the superconducting fluctuations of SRO and other perovskite superconductors, additional effects may be at play, such as non-Gaussian fluctuations or rare-region effects.

Dirac electrons in graphene are to lowest order spin 1/2 particles, owing to the orbital symmetries at the Fermi level. However, anisotropic corrections in the $g$ factor appear due to the intricate spin-valley-orbit coupling of chiral electrons. We resolve experimentally the $g$ factor along the three orthogonal directions in a large-scale graphene sample. We employ a Hall bar structure with an external magnetic field of arbitrary direction, and extract the effective $g$ tensor via resistively detected electron spin resonance. We employ a theoretical perturbative approach to identify the intrinsic and extrinsic spin orbit coupling and obtain a fundamental parameter inherent to the atomic structure of ${}^{12}\mathrm{C}$, commonly used in ab initio models.

The production of entangled pairs of electrons in ferromagnet-superconductor-ferromagnet or normal metal-superconductor-normal metal three-terminal structures has aroused considerable interest in the last twenty years. In these studies, the distance between the contacts is limited by the zero-energy superconducting coherence length. Here, we demonstrate nonlocality and quantum correlations in voltage-biased three-terminal Josephson junctions over the ultralong distance that exceeds the superconducting coherence length by orders of magnitude. The effect relies on the interplay between the time-periodic Floquet-Josephson dynamics, Cooper pair splitting, and long-range coupling similar to the two-terminal Tomasch effect. We find crossover between the “Floquet-Andreev quartets” (if the spatial separation is smaller than the superconducting coherence length) and the “ultralong-distance Floquet-Tomasch clusters of Cooper pairs” if the separation exceeds the superconducting coherence length, possibly reaching the same $\simeq 30\mu \mathrm{m}$ as in the Tomasch experiments. The effect can be detected with DC-transport and zero-frequency quantum current-noise cross-correlation experiments, and it can be used for fundamental studies of superconducting quasiparticle quantum coherence in the circuits of quantum engineering.

The relation between the Kondo spin-relaxation rate ${{\tau }_{sK}}^{-1}$ and the Kondo momentum-relaxation rate ${{\tau }_{eK}}^{-1}$ is explored by using nonlocal spin valves with submicron copper channels that contain dilute iron impurities. A linear relation between ${{\tau }_{sK}}^{-1}$ and ${{\tau }_{eK}}^{-1}$ is established under varying temperatures for any given device. Among 20 devices, however, ${{\tau }_{sK}}^{-1}$ remains nearly constant, despite variation of ${{\tau }_{eK}}^{-1}$ by a factor of 10. This surprising relation can be understood by considering spin relaxation through overlapping Kondo screening clouds and supports the physical existence of the elusive Kondo clouds.

We study the ground-state properties, the electronic excitations, and lattice dynamics in spin-liquid candidate ${\mathrm{TbInO}}_3$. By employing polarization-resolved Raman spectroscopy we define the intermultiplet and intramultiplet excitations, and establish the low-energy crystal-field (CF) level scheme. In particular, we demonstrate that the ground state of the ${\mathrm{Tb}}^{3+}$ ions is a non-Kramers doublet, and relate the enhanced linewidth of the CF modes to the magnetic fluctuations near the spin-liquid ground state. We identify the 38 allowed Raman-active phonon modes at low temperature. Moreover, we observe hybrid vibronic excitations involving coupled CF and low-lying phonon modes, suggesting strong spin-lattice dynamics. We develop a model for vibronic states and obtain the parameters of the bare responses and coupling strength. We further demonstrate that the obtained CF level scheme is consistent with specific-heat data.

Non-Hermitian nonreciprocal systems are known to be extremely sensitive to boundary conditions, exhibiting diverse localizing behaviors and spectrum structures when translational invariance is locally broken, either by tuning the boundary coupling strength, or by introducing an effective boundary using impurities or defects. In this work we consider the single impurity problem in the Hatano-Nelson model and the Su-Schreieffer-Heeger model, which can be exactly solved with the single impurity being treated as an effective boundary of the system. From our exact solutions for finite-size systems, we unveil that increasing the impurity strength can lead to a transition of the bulk states from nonskin states to skin states, accompanied by the change of the spectrum structure from an ellipse in the complex plane to a segment along the real axis. These exact results indicate that the critical value of impurity strength is size dependent, and increases exponentially with the lattice size when the impurity is strong or the system is large enough. Our exact solutions are also useful for determining the spectral topological transition in the concerned models.

We propose energy band engineering to enhance tunneling electroresistance (TER) in ferroelectric tunnel junctions (FTJs). We predict that an ultrathin dielectric layer with a smaller band gap, embedded into a ferroelectric barrier layer, acts as a switch controlling high- and low-conductance states of an FTJ depending on polarization orientation. Using first-principles modeling based on density functional theory, we investigate this phenomenon for a prototypical $\mathrm{SrRu}{\mathrm{O}}_3\text{/}\mathrm{BaTi}{\mathrm{O}}_3\text{/}\mathrm{SrRu}{\mathrm{O}}_3$ FTJ with a $\mathrm{BaSn}{\mathrm{O}}_3$ monolayer embedded in the $\mathrm{BaTi}{\mathrm{O}}_3$ barrier. We show that in such a composite-barrier FTJ, ferroelectric polarization of $\mathrm{BaTi}{\mathrm{O}}_3$ shifts the conduction-band minimum of the $\mathrm{BaSn}{\mathrm{O}}_3$ monolayer above or below the Fermi energy depending on polarization orientation. The resulting switching between direct and resonant tunneling leads to a TER effect with a giant ON/OFF conductance ratio. The proposed resonant band engineering of FTJs can serve as a viable tool to enhance their performance, useful for device applications.

Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the hourglass dispersion can be jointly protected by symmorphic and nonsymmorphic symmetries, instead of the conventional nonsymmorphic symmetry. Moreover, using first-principles calculations, we realize our proposal in the phonon spectra of realistic materials that share an antiperovskite structure with space group $P4$/nmm. Importantly, the neck points of these hourglass dispersions trace out two nodal rings tangential to four nodal lines, forming a unique hourglass nodal cage in the bulk Brillouin zone. The Berry phase analysis reveals the nontrivial topology of these nodal rings and nodal lines. Furthermore, nontrivial surface states and isofrequency surface arcs are visible, facilitating their experimental confirmation of such exotic quasiparticles. work not only offers different insights into the hourglass dispersion, but also expands aspects for studying promising topological quasiparticles in condensed-matter systems.

We propose that noncollinear magnetic order in magnetic systems can harbor a higher-order topological magnon phase with non-Hermitian topology and hinge magnon modes. We consider a three-dimensional system of interacting local moments on stacked layers of honeycomb lattice. It initially favors a collinear magnetic order along an in-plane direction, which turns into a noncollinear order upon applying an external magnetic field perpendicular to the easy axis. We exploit the non-Hermitian nature of the magnon Hamiltonian to show that this field-induced transition corresponds to the transformation from a topological magnon insulator to a higher-order topological magnon state with a one-dimensional hinge mode. As a concrete example, we discuss the recently discovered monoclinic phase of thin chromium trihalides, which we propose as a promising material candidate of the higher-order topological magnon phase.

Anomalous nematic states, recently discovered in ultraclean two-dimensional electron gas, emerge from quantum Hall stripe phases upon further cooling. These states are hallmarked by a local minimum (maximum) in the hard (easy) longitudinal resistance and by an incipient plateau in the Hall resistance in nearly half-filled Landau levels. Here, we demonstrate that a modest in-plane magnetic field, applied either along $\langle 110\rangle$ or $\langle 1\overline{1}0\rangle$ crystal axis of GaAs, destroys anomalous nematic states and restores quantum Hall stripe phases aligned along their native $\langle 110\rangle$ direction. These findings confirm that anomalous nematic states are distinct from other ground states and will assist future theories to identify their origin.

Different from the chiral edge states, antichiral edge states propagating in the same direction on the opposite edges are theoretically proposed based on the modified Haldane model, which is recently experimentally realized in photonic crystal and electric lattice systems. Here, we instead present that the antichiral edge states in the two-dimensional system can also be achieved based on the original Haldane model by combining two subsystems with the opposite chirality. Most importantly, by stacking these two-dimensional systems into three-dimension, it is found that the copropagating antichiral hinge states localized on the two opposite diagonal hinge cases of the system can be implemented. Interestingly, the location of antichiral hinge states can be tuned via hopping parameters along the third dimension. By investigating the local Chern number/layer Chern number and transmission against random disorders, we confirm that the proposed antichiral edge states and hinge states are topologically protected and robust against disorders. Our proposed model systems are expected to be realized in photonic crystal and electric lattice systems.

Spin and spatial dimensionalities are universal concepts, essential for describing both phase transitions and dynamics in magnetic materials. Lately, these ideas have been adopted to describe magnetic properties of metamaterials, replicating the properties of their atomic counterparts as well as exploring properties of ensembles of mesospins belonging to different universality classes. Here, we take the next step when investigating magnetic metamaterials not conforming to the conventional framework of continuous phase transitions. Instead of a continuous decrease in the moment with temperature, discrete steps are possible, resulting in a binary transition in the interactions of the elements. The transition is enabled by nucleation and annihilation of vortex cores, shifting topological charges between the interior and the edges of the elements. Consequently, the mesospins can be viewed as shifting their spin dimensionality, from 2 (XY-like) to 0 (vortices), at the transition. The results provide insight into how dynamics at different length scales couple, which can lead to thermally driven topological transitions in magnetic metamaterials.

We investigate the phonon spectrum of pure and rare-earth substituted langasites. For electric fields oriented along the $c$ axis, a strong low-frequency phonon is observed, softening at lower temperature in all samples studied. The dielectric contribution and temperature dependence of this mode is the primary source of the large $\left[\varepsilon \right(0)\sim 100]$ static dielectric permittivity observed in these systems. Softening of this mode with increasing mass of the rare-earth substitutes further suggests that langasites are close to a structural instability at low temperatures. The application of a magnetic field to a diluted Ho-langasite sample reveals a shift in the strong absorption band at THz frequencies associated with this soft lattice mode, suggesting spin-lattice effects may also be at play in these systems.

We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of ${}^3\mathrm{He}$ confined in highly anisotropic Nafen aerogel. Superfluidity of ${}^3\mathrm{He}$ confined in Nafen is the realization of a “nematic superfluid” with Cooper pairs condensed into a single $p$-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second “chiral” phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid ${}^3\mathrm{He}$. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of ${}^3\mathrm{He}$-Nafen.

Although several impurity solvers in the dynamical mean field theory (DMFT) have been proposed, especially in multiband systems, there are practical difficulties arising from a trade-off between numerical costs and reliability. In this study, we reinterpret the iterative perturbation theory (IPT) as an approximation which captures the strong correlation effects by mimicking the particular frequency structures of the exact full vertex, and extend it such that it can have efficiency and reliability simultaneously by modifying IPT vertex using the parquet equations. We apply this method to several models to evaluate their validity. We confirm that our method shows good agreements with the numerically exact continuous-time quantum Monte Carlo method in the single-site DMFT calculation.

We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding model exhibit many characteristic features, including a flat band which is ubiquitous among frustrated lattices. On the flat band, we elucidate its origin by using the molecular-orbital representation and also find localized exact eigenstates called compact localized states. In addition to the flat band, we also find two spin-1 Dirac cones with different energies. These spin-1 Dirac cones are not described by the simplest effective Dirac Hamiltonian because the middle band is bended and the energy spectrum is particle-hole asymmetric. We also investigated the Hofstadter problem on a square kagome lattice in the presence of an external field and find that the profile of the Chern numbers around the modified spin-1 Dirac cones coincides with the conventional one.