We develop a three-phase field model for the simulation of eutectic and eutectoid transformations on the basis of a nondiagonal model obeying Onsager relations for a kinetic cross coupling between diffusion and the phase fields. This model overcomes the limitations of existing phase field models concerning the fulfillment of local equilibrium boundary conditions at the transformation fronts in the case of a finite diffusional contrast between the phases. We benchmark our model in the well understood one-sided case with diffusion only in the parent phase against results from the literature. In addition to this solidification scenario, the case of solid-state transformations with diffusion in the growing phases is investigated. Our simulations validate the relevance of the theory developed by Ankit et al. [Acta Mater. 61, 4245 (2013)], that describes in a single frame the two limiting regimes where diffusion mainly takes place whether in the mother phase or in the growing phases. In both the one-sided and two-sided cases, we verify the necessity of the kinetic cross coupling for quantitative phase field simulations.

Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization, and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks the limit for quantum systems. However, we report in this paper a periodically-modulated nonlinear Schrödinger system, in which we interestingly find a way of OTOCs' growth: super-EG. We show that the quantum OTOCs, which stems from the quantum chaotic dynamics, will increase in a super-exponential way. We also find that in the classical limit, the hyper-chaos revealed by a linearly-increasing Lyapunov exponent actually triggers the super-EG of classical OTOCs. The results in this paper break the restraints of EG as the limit for quantum systems, which give us insight into the nature of quantum chaos in various fields of physics from black hole to many-body system.

We describe how to construct generalized string-net models, a class of exactly solvable lattice models that realize a large family of two-dimensional topologically ordered phases of matter. The ground states of these models can be thought of as superpositions of different “string-net configurations,” where each string-net configuration is a trivalent graph with labeled edges, drawn in the $xy$ plane. What makes this construction more general than the original string-net construction is that, unlike the original construction, tetrahedral reflection symmetry is not assumed, nor is it assumed that the ground-state wave function $\mathrm{\Phi }$ is “isotropic”: i.e., in the generalized setup, two string-net configurations $X_1,X_2$ that can be continuously deformed into one another can have different ground-state amplitudes $\mathrm{\Phi }\left(X_1\right)\ne \mathrm{\Phi }\left(X_2\right)$. As a result, generalized string-net models can realize topological phases that are inaccessible to the original construction. In this paper, we provide a more detailed discussion of ground-state wave functions, Hamiltonians, and minimal self-consistency conditions for generalized string-net models than what exists in the previous literature. We also show how to construct string operators that create anyon excitations in these models, and we show how to compute the braiding statistics of these excitations. Finally, we derive necessary and sufficient conditions for generalized string-net models to have isotropic ground-state wave functions on the plane or the sphere, a property that may be useful in some applications.

We have investigated charge and spin transport in $n$-type metallic GaAs nanowires ($\approx {10}^{17}{\mathrm{cm}}^{-3}$ doping level) grown by hydride vapor phase epitaxy (HVPE) on Si substrates. For this doping level, charge and spin transport might appear difficult because of the expected localization of minority holes in the valence band potential fluctuations generated by statistical fluctuations of the donor concentration. In contrast with these expectations, it is found, using spatially and spectrally resolved investigation of the luminescence intensity and circular polarization under laser excitation, that (i) establishment of a charge thermodynamic equilibrium between the photoelectrons and the Fermi sea occurs over a distance from the excitation spot of $2\mu \mathrm{m}$. At this distance, the spin polarization is still observed, implying that photoelectrons have preserved their spin orientation and that the two spin reservoirs remain distinct. (ii) Charge can be transported over record distances larger than $20\mu \mathrm{m}$ at 6 K. (iii) Spatially-resolved investigations show that a photoelectron spin polarization of $20\%$ can be transported over a record distance of more than $20\mu \mathrm{m}$. This long distance transport occurs because of the presence of large internal electric fields of ambipolar origin, further enhanced by the spatial redistribution of the Fermi sea. These findings have potential applications for long distance spin transport in $n$-type doped nanowires.

Two-dimensional (2D) layered III–VI semiconductors such as GaSe have attracted a lot of attention in recent years. Bulk GaSe consists of stacks of layers held together by weak interlayer interaction generally assumed to be of van der Waals type. However, proper justification of this assumption has been lacking in the reported studies. In this paper, we explore in detail the interlayer coupling in GaSe by studying lattice dynamics using first-principles density functional theory. Our study strongly suggests that contrary to common assumption, the contribution of Coulomb interaction in interlayer coupling can be significantly higher than that of van der Waals interaction in GaSe and other similar 2D layered semiconductors. The suggested predominance of electrostatic over van der Waals interaction in interlayer coupling may have important implications for various physical properties of GaSe and related layered semiconductors. Further, we study polarized Raman spectra, infrared (IR) activities, mode symmetry assignments, and Born-effective charge tensors for bulk GaSe polytypes (β, ε, γ). The Raman mode intensities are calculated for different light polarization setups and signature Raman and IR active modes are identified for each GaSe polytype (structure). In addition, the influence of film thickness and strain on Raman and IR mode frequencies and intensities of GaSe are explored and compared with available experiments.

Structural symmetry breaking in two-dimensional materials can lead to superior physical properties and introduce an additional degree of piezoelectricity. In the present paper, we propose three structural phases ($1H, 1T$, and $1T^{\prime }$) of Janus $\mathrm{W}X\mathrm{O}$ ($X=\mathrm{S}$, Se, and Te) monolayers and investigate their vibrational, thermal, elastic, piezoelectric, and electronic properties by using first-principles methods. Phonon spectra analysis reveals that while the $1H$ phase is dynamically stable, the $1T$ phase exhibits imaginary frequencies and transforms to the distorted $1T^{\prime }$ phase. Ab initio molecular dynamics simulations confirm that $1H$- and $1T^{\prime }\text{−}\mathrm{W}X\mathrm{O}$ monolayers are thermally stable even at high temperatures without any significant structural deformations. Different from binary systems, additional Raman active modes appear upon the formation of Janus monolayers. Although the mechanical properties of $1H\text{−}\mathrm{W}X\mathrm{O}$ are found to be isotropic, they are orientation dependent for $1T^{\prime }\text{−}\mathrm{W}X\mathrm{O}$. It is also shown that $1H\text{−}\mathrm{W}X\mathrm{O}$ monolayers are indirect band-gap semiconductors and the band gap narrows down the chalcogen group. Except $1T^{\prime }$-WSO, $1T^{\prime }\text{−}\mathrm{W}X\mathrm{O}$ monolayers have a narrow band gap correlated with the Peierls distortion. The effect of spin-orbit coupling on the band structure is also examined for both phases and the alteration in the band gap is estimated. The versatile mechanical and electronic properties of Janus $\mathrm{W}X\mathrm{O}$ monolayers together with their large piezoelectric response imply that these systems are interesting for several nanoelectronic applications.

Motivated by the relevance of Hund's coupling in the context of multiorbital superconductors, we revisit the problem of a multiorbital Kondo impurity with Hund's interaction. Using dynamical large-$N$ techniques, we propose an efficient approach that retains the essential physics at play, while providing a pathway to scalable quantum impurity solvers. We are able to follow the ground state, dynamic, and thermodynamic properties of this system over many decades of temperature. Our approach captures the emergence of large moments and follows the stretched evolution of the physics down to their exponentially suppressed Kondo temperature. We focus our analysis on the intermediate finite temperature phase which presents an alternate paramagnetic state due to the emergent moment and discuss the relevance of this regime to Hund's metals.

Superconductivity arises mostly at energy and temperature scales that are much smaller than the typical bare electronic energies. Since the computational effort of diagrammatic many-body techniques increases with the number of required Matsubara frequencies and thus with the inverse temperature, phase transitions that occur at low temperatures are typically hard to address numerically. In this work, we implement a fluctuation exchange (FLEX) approach to spin fluctuations and superconductivity using the “intermediate representation basis” (IR) [Shinaoka et al., Phys. Rev. B 96, 035147 (2017)] for Matsubara Green functions. This $\mathrm{FLEX}+\mathrm{IR}$ approach is numerically very efficient and enables us to reach temperatures on the order of ${10}^{-4}$ in units of the electronic bandwidth in multiorbital systems. After benchmarking the method in the doped repulsive Hubbard model on the square lattice, we study the possibility of spin-fluctuation-mediated superconductivity in the hydrated sodium cobalt material ${\mathrm{Na}}_x{\mathrm{CoO}}_2·{y\mathrm{H}}_2\mathrm{O}$ reaching the scale of the experimental transition temperature $T_{\mathrm{c}}=4.5\mathrm{K}$ and below.

We use conformal field theory to construct model wave functions for a gapless interface between lattice versions of a bosonic Laughlin state and a fermionic Moore-Read state, both at $\nu =1/2$. The properties of the resulting model state, such as particle density, correlation function, and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wave functions also for anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge, and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some anyons (the Laughlin Abelian ones) can cross the interface, while others (the non-Abelian ones) lose their anyonic character in such a process. Also, we argue that, under an assumption of local particle exchange, multiple interfaces give rise to a topological degeneracy, which can be interpreted as originating from Majorana zero modes.

We investigate the temperature evolution of the magnetic structure of ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ using neutron diffraction techniques. We find that ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ has two propagation vectors: ${\mathbf{k}}_{\mathbf{0}}=(0,0,0)$ and ${\mathbf{k}}_{\mathbf{1}}=(0,0,\frac{1}{3})$. The ${\mathbf{k}}_{\mathbf{0}}$ vector can be associated with an antiferromagnetic ordering of in-plane moments with a refined value of $0.90\left(5\right){\mu }_{\mathrm{B}}$, and ${\mathbf{k}}_{\mathbf{1}}$ can be associated with moments along the $c$ axis in an up-down-down configuration with refined values of $1.21\left(12\right){\mu }_{\mathrm{B}}$ and $0.61\left(6\right){\mu }_{\mathrm{B}}$. Both ${\mathbf{k}}_{\mathbf{0}}$ and ${\mathbf{k}}_{\mathbf{1}}$ magnetic components couple with an out-of-plane ferromagnetic moment consistent with magnetization data. Furthermore, single-crystal neutron diffraction shows evidence of diffuse magnetic scattering between the (010) and ($01\pm \frac{1}{3}$) Bragg peaks. We also characterize the field and temperature evolution of the magnetic structure in ${\mathrm{V}}_{1/3}{\mathrm{NbS}}_2$ by magnetic susceptibility and heat capacity measurements. The dc susceptibility measurements give an antiferromagnetic transition temperature of $T_{\mathrm{N}}=50$ K, and the field scans reveal that the moment does not saturate at magnetic fields up to 100 kOe.

We provide a microscopic-level derivation of earlier results showing that in the critical vicinity of the superconductor-to-insulator transition (SIT), disorder and localization become negligible and the structure of the emergent phases is determined by topological effects arising from the competition between two quantum orders, superconductivity and superinsulation. We find that around the critical point the ground state is a composite incompressible quantum fluid of Cooper pairs and vortices coexisting with an intertwined Wigner crystal comprising the excesses of both types of excitations with respect to integer filling.

In the novel stoichiometric iron-based material ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$, superconductivity coexists with a peculiar long-range magnetic order of Eu 4f states. Using angle-resolved photoemission spectroscopy, we reveal a complex three-dimensional electronic structure and compare it with density functional theory calculations. Multiple superconducting gaps were measured on various sheets of the Fermi surface. High-resolution resonant photoemission spectroscopy reveals magnetic order of the Eu 4f states deep into the superconducting phase. Both the absolute values and the anisotropy of the superconducting gaps are remarkably similar to the sibling compound without Eu, indicating that Eu magnetism does not affect the pairing of electrons. A complete decoupling between Fe- and Eu-derived states was established from their evolution with temperature, thus unambiguously demonstrating that superconducting and a long-range magnetic orders exist independently from each other. The established electronic structure of ${\mathrm{RbEuFe}}_4{\mathrm{As}}_4$ opens opportunities for the future studies of the highly unorthodox electron pairing and phase competition in this family of iron-based superconductors with doping.

In the recent publication [Phys. Rev. B 102, 144420 (2020)], Cabrera-Baez et al., present a study of the effects of Cd substitution for Zn in the ferromagnetic compound ${\mathrm{GdFe}}_2{\mathrm{Zn}}_{20}$. As part of this paper they claim that for ${\mathrm{GdFe}}_2{\mathrm{Zn}}_{18.6}{\mathrm{Cd}}_{1.4}$ the effective moment of Gd is reduced by 25%, and the saturated moment of Gd is reduced by over 40%. We regrew representative members of the ${\mathrm{GdFe}}_2{\mathrm{Zn}}_{20-x}{\mathrm{Cd}}_x$ series and did not find any such reductions. In addition, we measured several crystals from the growth batch that was used by Cabrera-Baez et al. and did not see such reductions. Although there is a modest increase in $T_C$ with Cd substitution, there is no significant change in the Gd effective moment or the saturated moment associated with the low-temperature ferromagnetic state.

The $R{T}_2{\mathrm{Zn}}_{20}$ family offers an incredible versatility to tune diverse ground states through small modifications of their composition. In our recent publication [Phys. Rev. B 102, 144420 (2020)] we have reported an enhancement of the FM transition temperature due to negative chemical pressure from 86 to 96 K for $x=0.0$ and $x=1.4$, respectively, with an also unexpected, however, suspicious reduction of the effective and saturation magnetic moment that was inconsistent with our ESR data [Phys. Rev. B 102, 144420 (2020)]. In a comment of our work by Canfield (preceding paper [Phys. Rev. B 103, 176401 (2021)]), they have confirmed our finding about the enhancement of the FM temperature, however, with appreciable differences in the $M$($H$) and $M$($T$) curves for the Cd doped samples. We agree with their analysis of the magnetization data, the saturation of those samples is between $6{\mu }_B$ and $7{\mu }_B$ instead of $4{\mu }_B$ as we have reported. It is indeed likely that we have used a mass value of the measured samples that includes Cd-doped $\mathrm{Gd}{\mathrm{Fe}}_2{\mathrm{Zn}}_{20}$ and a second-phase contamination of the non-magnetic Zn flux (please observe the XRD data in the original paper [Phys. Rev. B 102, 144420 (2020)]). Therefore, we agree with the comment by Canfield et al. (preceding paper [Phys. Rev. B 103, 176401 (2021)]) about the thorough analysis of the $M$($T$) and $M$($H$) for the Cd-doped samples (Fig. 2 of their Comment). The erratum clarifies and corrects [Phys. Rev. B 103, 179903(E) (2021)].

We report on the synthesis and electronic properties of epitaxial perovskite ${\mathrm{La}}_{1\text{−}x}{\mathrm{Sr}}_x\mathrm{Rh}{\mathrm{O}}_3$ thin films. Thin films with a Sr content ranging from $x=0$ to 0.5 have been grown using molecular beam epitaxy. Transport and x-ray photoemission spectroscopy data reveal an insulator-metal-insulator transition, accompanied by a $p$- to $n$-type carrier change observed in Hall measurements. Combined with theoretical calculations, we find that the addition of Sr does not directly dope carriers into the conduction band, but rather induces localized Rh $4d$ states within the $\mathrm{La}\mathrm{Rh}{\mathrm{O}}_3$ band gap. The bandwidth of the impurity band increases with Sr content, eventually causing the valence band (VB) and the localized Rh $4d$ band to overlap, which explains the first insulator-to-metal transition occurring at $x=0.35$. For Sr content $x>0.4$, possible cation ordering results in an increase of the gap between the VB and the Rh $4d$ band, leading to the second metal-to-insulator transition. We map out the electronic phase diagram of the Sr-doped $\mathrm{La}\mathrm{Rh}{\mathrm{O}}_3$ system and suggest strategies to engineer the electronic states in rhodate systems via delocalizing the ${\mathrm{Rh}}^{3+}$ states.

The Fermi surface properties of the nontrivial system YSi are investigated by de Haas–van Alphen (dHvA) oscillation measurements combined with the first-principles calculations. Three main frequencies ($\alpha , \beta , \gamma$) are probed up to a magnetic field of 14 T in dHvA oscillations. The $\alpha$ branch possesses nontrivial topological character with a Berry phase of $0.52\pi$ for $B\parallel \left[100\right]$ and $1.39\pi$ for $B\parallel \left[001\right]$ direction. The linear dispersion of $\alpha$ branch along $\mathrm{\Gamma }$ to $Z$ direction corroborates the light mass of charge carriers. The effective mass of $\alpha$ branch is estimated to be 0.069 $m_e$ for $B\parallel \left[100\right]$, with third-lowest Landau level $(n=2)$ up to 14 T. The $\gamma$ pocket of 295 T frequency exhibits two-dimensional character and a high Fermi velocity of $6.7\times {10}^5{\mathrm{m}\mathrm{s}}^{-1}$. The band structure calculations reveal multiple nodal crossings in the vicinity of Fermi energy $E_{\mathrm{F}}$ without spin-orbit coupling (SOC). Inclusion of SOC opens a small gap at the nodal crossings and results in nonsymmorphic symmetry enforced Dirac points at some high symmetry points, suggesting YSi is a symmetry enforced topological metal.

The spin relaxation of a strongly correlated electron system hosted in a narrow AlAs quantum well is studied experimentally in the regime of the quantum Hall ferromagnet, i.e., near odd fillings of the integer quantum Hall effect. The relaxation rate is evaluated by analyzing the linewidth of the electrically detected electron-spin resonance. The measured spin dynamics is shown to undergo a radical modification in tilted magnetic fields. Increasing of the tilt angle resulted not only in the decrease of the relaxation time at the exact odd fillings by almost an order of magnitude, but also in the essentially different dependence of the relaxation rate on the filling factor at highest tilt angles. In the case of a perpendicular magnetic field the relaxation rate reached its minimal value near the exact odd filling and slowly increased when the filling factor $\nu$ was altered. In contrast, at large tilt angles relaxation turned out to be the fastest at some $\nu$ in close vicinity of the exactly odd number. The observed effects may be ascribed to the renormalization of the spin excitation spectra by the strong e-e interaction.

Topological nodal-line semimetals exhibit double or fourfold degenerate nodal lines, which are protected by symmetries. Here, we investigate the possibility of the existence of triply degenerate nodal lines in metals. We present two types of triply degenerate nodal lines, one topologically trivial and the other nontrivial. The first type is stacked by two-dimensional pseudospin-1 fermions, which can be viewed as an critical case of a tunable band-crossing line structure that contains a symmetry-protected quadratic band-crossing line and a nondegenerate band, and can split into four Weyl nodal lines under perturbations. We find that surface states of the nodal line structure are dependent on the geometry of the lattice and the surface termination. Such a metal has a nesting of Fermi surface in a range of filling, resulting in a density-wave state when interaction is included. The second type is a vortex ring of pseudospin-1 fermions. In this system, the pseudospins form Skyrmion textures, and the surface states are fully extended topological Fermi arcs so that the model exhibits 3D quantum anomalous Hall effect with a maximal Hall conductivity. The vortex ring can evolve into a pair of vortex lines that are not closed in the first Brillouin zone. A vortex line cannot singly exist in the lattice model if it is the only nodal feature of the system.

The debate whether uranium $5f$ electrons are closer to being localized or itinerant in the ferromagnetic compound $\mathrm{U}{\mathrm{Ga}}_2$ is not yet fully settled. The experimentally determined magnetic moments are large, approximately $3{\mu }_{\mathrm{B}}$, suggesting the localized character of the $5f$ electrons. In the same time, one can identify signs of itinerant as well as localized behavior in various spectroscopic observations. The band theory, employing local exchange-correlation functionals, is biased toward itinerant $5f$ states and severely underestimates the moments. Using material-specific dynamical mean-field theory (DMFT), we probe how a less approximate description of electron-electron correlations improves the picture. We present two variants of the theory: starting either from spin-restricted (LDA) or spin-polarized (LSDA) band structure. We show that the L(S)$\mathrm{DA}+\mathrm{DMFT}$ method can accurately describe the magnetic moments in $\mathrm{U}{\mathrm{Ga}}_2$ as long as the exchange interaction between the uranium $6d$ and $5f$ electrons is preserved by a judicious choice of the spin-polarized double-counting correction. We discuss the computed electronic structure in relation to photoemission experiments and show how the correlations reduce the Sommerfeld coefficient of the electronic specific heat by shifting the $5f$ states slightly away from the Fermi level.