Relaxor ferroelectrics, well known for their large dielectric and piezoelectric response, are attracting growing interest in thin-film form driven by a need for miniaturized devices. Fundamental understanding and control of the performance of relaxors as thin films, however, is underdeveloped relative to studies of bulk versions. One obvious challenge is substrate clamping, which reduces the dielectric and piezoelectric response, yet systematic comparisons of the effect of substrate clamping on different relaxor materials is missing. Here, the impact of epitaxial constraint on the relaxor behavior and properties of both homovalent ${\mathrm{BaZr}}_{0.5}{\mathrm{Ti}}_{0.5}{\mathrm{O}}_3$ and heterovalent $\mathrm{Pb}{\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3$ relaxors is studied in (001)-, (011)-, and (111)-oriented thin films. While the different orientations of $\mathrm{Pb}{\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3$ heterostructures show little variation in dielectric permittivity, a strong orientational effect is observed in ${\mathrm{BaZr}}_{0.5}{\mathrm{Ti}}_{0.5}{\mathrm{O}}_3$ heterostructures, with (111)-oriented films exhibiting a 67% higher dielectric permittivity than (001)-oriented films, a difference that is attributed to how substrate clamping along different crystallographic axes interacts with the polar-structure nucleation and growth. Measurements of dielectric anisotropy in (001)-oriented films confirm the trend—with $\mathrm{Pb}{\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}{\mathrm{O}}_3$ heterostructures exhibiting just half as much anisotropy in dielectric permittivity than ${\mathrm{BaZr}}_{0.5}{\mathrm{Ti}}_{0.5}{\mathrm{O}}_3$ heterostructures. These results indicate a higher susceptibility to substrate clamping in homovalent relaxors as compared to heterovalent relaxors, implying that the random fields in the heterovalent relaxors could be advantageous for materials in such geometries and applications.

We present a new, large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the distribution of the local density of states (LDoS) down to very small probability tails as small as ${10}^{-50}$, which are completely out of reach for standard numerical techniques. We perform a thorough analysis of the functional form of the tails of the probability distributions of the LDoS, which turn out to be very well described by the functional form predicted by the supersymmetric formalism and yields a direct and transparent estimation of the correlation volume very close to the Anderson transition. Such a correlation volume is found to diverge exponentially when the localization is approached from the delocalized regime, in a singular way that is compatible with the analytic predictions of the supersymmetric treatment.

Applied magnetic fields can couple to atomic displacements via generalized Lorentz forces, which are commonly expressed as gyromagnetic $g$ factors. We develop an efficient first-principles methodology based on density functional perturbation theory to calculate this effect in both molecules and solids to linear order in the applied field. Our methodology is based on two linear-response quantities: the macroscopic polarization response to an atomic displacement (i.e., Born effective charge tensor), and the antisymmetric part of its first real-space moment (the symmetric part corresponding to the dynamical quadrupole tensor). The latter quantity is calculated via an analytical expansion of the current induced by a long-wavelength phonon perturbation, and compared to numerical derivatives of finite-wave-vector calculations. We validate our methodology in finite systems by computing the gyromagnetic $g$ factor of several simple molecules, demonstrating excellent agreement with experiment and previous density functional theory and quantum chemistry calculations. In addition, we demonstrate the utility of our method in extended systems by computing the energy splitting of the low-frequency transverse-optical phonon mode of cubic ${\mathrm{SrTiO}}_3$ in the presence of a magnetic field.

The superconductors with the Ginzburg-Landau (G-L) parameter $\left(\kappa \right)$ $\sim 1/\sqrt{2}$ exist near a critical Bogomolnyi (B) point where they show intertype domains between type-I and type-II superconductivity. While such physics is well understood for isotropic superconductors, the experimental investigation of the physics of anisotropic superconductors near a critical B point remains an unattained goal, mainly due to the unavailability of model material systems. Theoretically, such superconductors are expected to show type-I or type-II behavior for definite directions of an applied magnetic field. Here, from directional point-contact Andreev reflection spectroscopy and field-angle-dependent ac magnetic susceptibility measurements, we show that ${\mathrm{ZrB}}_{12}$ is an anisotropic superconductor and it exhibits field-direction-dependent type-I and type-II behavior. These observations match remarkably well with the theoretical expectations for an anisotropic superconductor near a critical B point. Therefore our results project ${\mathrm{ZrB}}_{12}$ as a model material system where the physics of intertype anisotropic superconductivity can be explored experimentally.

Understanding the phase-transition processes of van der Waals (vdW) materials plays a vital role in their performance control and application development. Here, we investigate the structural transitions and Raman identifications of the monoclinic and orthorhombic phases of the layered vdW magnet ${\mathrm{CrI}}_2$. At present, the characterization of these two phases remains a challenge, and our first-principles calculations show that they each have a specific Raman spectrum, which proposes a reliable method to identify them. Moreover, we discover that ${\mathrm{CrI}}_2$ with orthorhombic phase exhibits both ferroelectricity and magnetism simultaneously due to its unique interlayer stacking order, indicating that it will provide a platform for the popular sliding ferroelectricity and multiferroicity.

Structural as well as magnetization studies have been carried out on graphite samples irradiated by neutrons for over 50 years in the CIRUS research reactor at Trombay, India. Neutron diffraction studies reveal that the defects in irradiated graphite samples are not well annealed and remain significant up to high temperatures much greater than 653 K where the Wigner energy is completely released. We infer that the remnant defects may be intralayer Frenkel defects, which do not store large energy, unlike the interlayer Frenkel defects that store the Wigner energy. Magnetization studies on the irradiated graphite show ferromagnetic behavior that persists up to ∼850 K and a large additional paramagnetic contribution. Ab initio calculations based on the spin-polarized density-functional theory show that the magnetism in defected graphite is essentially confined to a single twofold-coordinated carbon atom that is located around a vacancy in the hexagonal layer.

We study magnetic properties of the half-filled Hubbard model on the two-dimensional hexagonal golden-mean tiling. We find that the vertex model of the tiling is bipartite, with a sublattice imbalance of $\sqrt{5}/\left(6{\tau }^3\right)$ (where $\tau$ is the golden mean), and that the noninteracting tight-binding model gives macroscopically degenerate states at $E=0$. We clarify that each sublattice has specific types of confined states, which in turn leads to an interesting spatial pattern in the local magnetizations in the weak coupling regime. Furthermore, this allows us to analytically obtain the lower bound on the fraction of the confined states as $(\tau +9)/\left(6{\tau }^6\right)\sim 0.0986$, which is conjectured to be the exact fraction. These results imply that a ferrimagnetically ordered state is realized even in the weak coupling limit. The introduction of the Coulomb interaction lifts the macroscopic degeneracy at the Fermi level and induces finite staggered magnetization as well as uniform magnetization. Likewise, the spatial distribution of the magnetizations continuously changes with increasing interaction strength. The crossover behavior in the magnetically ordered states is also addressed in terms of the perpendicular space analysis.

The procedure of magnetization density reconstruction in locally anisotropic magnetics with unquenched orbital moment is developed, based on the iterative entropy maximization and the site susceptibility approach. The procedure provides simultaneously model-free site susceptibility parameters of the $R$ ions and the shape of the magnetization distribution. The reconstruction of a noncollinear magnetic moment distribution was applied to rare-earth pyrochlore compounds $R_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ $(R=\text{Tb}, \mathrm{Ho}, \mathrm{Er}, \mathrm{Yb})$, which revealed an oblate asphericity of the ${\mathrm{Tb}}^{3+}$ magnetization density and a prolate one for the ${\mathrm{Ho}}^{3+}$ and ${\mathrm{Yb}}^{3+}$ ions. The noncollinear magnetic moment distributions are compared with these predicted by the single-ion anisotropy model, shedding light on the anisotropy of lanthanides with an unquenched orbital moment.

AuBe is a chiral, noncentrosymmetric superconductor with transition temperature $T_C\simeq 3.25$ K. The broken inversion symmetry in its crystal structure makes AuBe a possible candidate to host a mixed singlet-triplet pairing symmetry in its superconducting order parameter ($\mathrm{\Delta }$). This possibility was investigated by transport, thermodynamic, and muon-spin rotation/relaxation experiments in AuBe. However, this issue was not addressed using direct spectroscopic probes so far. In addition, certain ambiguities exist in the description of superconductivity in AuBe based on $\mu \mathrm{S}\mathrm{R}$ experiments reported earlier. Here we report scanning tunneling spectroscopy (STS) on AuBe down to 300 mK. We found a signature of two superconducting gaps (with $2{\mathrm{\Delta }}_1/k_B{T}_C=4.37$ and $2{\mathrm{\Delta }}_2/k_B{T}_C=2.46$, respectively) and a clean BCS-like temperature dependence of both the gaps. We have also performed band structure calculations to identify the different bands that might give rise to the observed two-gap superconductivity in AuBe.

In an unconventional superconductor, the interplay of scattering off impurities and Andreev processes may lead to different scattering times for electronlike and holelike quasiparticles. Such electron-hole asymmetry appears when the impurity scattering phase shift is intermediate between the Born and unitary limits and leads to an expectation for large thermoelectric effects. Here, we examine the thermoelectric response of a $d$-wave superconductor connected to normal-metal reservoirs under a temperature bias using a fully self-consistent quasiclassical theory. The thermoelectrically induced quasiparticle current is cancelled by superflow in an open circuit setup, but at the cost of a charge imbalance induced at the contacts and extending across the structure. We investigate the resulting thermopower and thermophase and their dependencies on scattering phase shift, mean free path, and interface transparency. For crystal-axis orientations such that surface-bound zero-energy Andreev states are formed, the thermoelectric effect is reduced as a result of locally reduced electron-hole asymmetry. For a semiballistic superconductor with good contacts, we find thermopowers of order several $\mu \mathrm{V}/\mathrm{K}$, suggesting a thermovoltage measurement as a promising path to investigate thermoelectricity in unconventional superconductors.

We demonstrate the existence of novel interaction effects in hole-doped semiconductor quantum wells which are connected to dramatic changes in the Fermi surface geometry occurring upon variation of the doping. We present band structure calculations showing that quantum wells formed in $p$-type cubic semiconductors develop perfectly nested Fermi surfaces at a critical hole density $p\sim 1/d^2$ set by the width $d$ of the quantum well. Nesting gives rise to competing superconducting and charge or spin density wave order, which we analyze using the perturbative renormalization group method. The correlated phases may be created or destroyed by tuning the hole density towards or away from the critical density. Our results establish $p$-type semiconductor quantum wells as a platform for novel correlated phases, which may be precisely controlled using electrostatic gating and external magnetic fields.

It is well known that the unavoidable variation of the heights and widths of the barriers (structural disorder) in semiconductor superlattices and superlattices based on two-dimensional materials degrades important physical properties such as the electronic transport and the thermoelectric response. Here, we show that the structural disorder contrary to what is expected improves the magnetoresistive and spin-valleytronic properties of magnetic silicene superlattices. We reach this conclusion by studying the impact of the random variations of the width and strength of the magnetic barriers on the tunneling magnetoresistance and spin-valley polarization. The theoretical treatment is based on a Dirac-like Hamiltonian, the transfer matrix method, and the Landauer-Büttiker formalism to describe silicene electrons, to obtain the transmittance, and to obtain the conductance, respectively. Our results indicate that structural disorder effects improve the magnetoresistance response and the spin-valley polarization by eliminating the conductance oscillations caused by the periodic magnetic modulation as well as by differentiating the response of the conductance for the parallel and antiparallel magnetization configuration. These results could be useful in designing versatile devices with magnetoresistive and spin-valleytronic capabilities. Particularly, magnetic silicene superlattices with moderate structural disorder are more convenient than perfect or nearly perfect ones.

We present a complete microscopic Fermi-liquid description for next-to-leading order transport through an Anderson impurity under a finite bias voltage $V$. It is applicable to multilevel quantum dots without particle-hole or time-reversal symmetry and is constructed based on the nonequilibrium Keldysh formalism, taking into account the current conservation between electrons in the impurity levels and the conduction bands. Specifically, we derive the formula for the current noise generated in the steady flow up to terms of order ${\left(eV\right)}^3$ at zero temperature $T=0$. To this end, we calculate the Keldysh vertex functions ${\mathrm{\Gamma }}_{\sigma {\sigma }^{\prime };{\sigma }^{\prime }\sigma }^{{\nu }_1{\nu }_2;{\nu }_3{\nu }_4}(\omega ,{\omega }^{\prime };{\omega }^{\prime },\omega )$, which depend on branches ${\nu }_1,{\nu }_2,{\nu }_3$, and ${\nu }_4$ of the time-loop contour and on spin degrees of freedom $\sigma$ and ${\sigma }^{\prime }$, up to linear order terms with respect to $eV$, $T$, and frequencies $\omega$ and ${\omega }^{\prime }$. The coefficients of these linear order terms are determined by a set of the parameters, defined with respect to the equilibrium ground state: the phase shift, static susceptibilities, and nonlinear three-body susceptibilities of the impurity electrons. The low-energy expressions of the vertex components are shown to satisfy the Ward identities with the Keldysh Green's functions expanded up to terms of order ${\omega }^2$, ${\left(eV\right)}^2$, and $T^2$. We also find that the imaginary part of the Ward identities can be described in terms of the $eV$-dependent collision integrals for a single-quasiparticle excitation and that for a single quasiparticle-quasihole pair excitation. These collision integrals ensure the current conservation of the next-to-leading order Fermi-liquid transport due to the quasiparticles with a finite damping rate.

We report on the long-range antiferromagnetic ordering with two successive phase transitions at $T_{\mathrm{N}1}=4.0\mathrm{K}$, $T_{\mathrm{N}2}\approx 1.3\mathrm{K}$ and the heavy-fermion-like behaviors in PrPdAl, a Kondo lattice with kagome-like structure of non-Kramers Pr ions in the hexagonal basal plane. The ground-state antiferromagnetism forms by two-thirds Pr ions with nearly full magnetic moment and one-third with strongly frustrated and reduced moment. The easy magnetization axis points along $c$ whereas the ordered Pr $4f$ moments reside in the basal plane, mirroring the important effect of spin frustrations. The electronic specific-heat coefficient is strongly enhanced to $\sim 940\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$, and the Kadowaki-Woods ratio is factor-of-25 smaller than that of conventional heavy-fermion compounds with Kramers doublet ground state. The effective Grüneisen ratio estimated from thermal expansion reveals large values in the vicinity of the broadened phase transition at $T_{\mathrm{N}2}$, manifesting its instability against pressure. Accordingly, PrNiAl, a chemically pressurized analog of the titled compound, was found to reveal only one antiferromagnetic transition at a considerably higher temperature of 6.9 K. These results demonstrate that PrPdAl and related homologues can offer excellent cases for investigating competing ground states in frustrated Kondo lattices formed by non-Kramers magnetic ions.

We develop a systematic theory of symmetry fractionalization for fermionic topological phases of matter in $(2+1)\mathrm{D}$ with a general fermionic symmetry group $G_f$. In general, $G_f$ is a central extension of the bosonic symmetry group $G_b$ by fermion parity, ${(-1)}^F$, characterized by a nontrivial cohomology class $\left[{\omega }_2\right]\in {\mathcal{H}}^2(G_b,{\mathbb{Z}}_2)$. We show how the presence of local fermions places a number of constraints on the algebraic data that defines the action of the symmetry on the supermodular tensor category that characterizes the anyon content. We find two separate obstructions to defining symmetry fractionalization, which we refer to as the bosonic and fermionic symmetry localization obstructions. The former is valued in ${\mathcal{H}}^3(G_b,K\left(\mathcal{C}\right))$, while the latter is valued in either ${\mathcal{H}}^3(G_b,\mathcal{A}/\{1,\psi \})$ or $Z^2(G_b,{\mathbb{Z}}_2)$ depending on additional details of the theory. $K\left(\mathcal{C}\right)$ is the Abelian group of functions from anyons to $\mathrm{U}\left(1\right)$ phases obeying the fusion rules, $\mathcal{A}$ is the Abelian group defined by fusion of Abelian anyons, and $\psi$ is the fermion. When these obstructions vanish, we show that distinct symmetry fractionalization patterns form a torsor over ${\mathcal{H}}^2(G_b,\mathcal{A}/\{1,\psi \})$. We study a number of examples in detail; in particular, we provide a characterization of fermionic Kramers degeneracy arising in symmetry class DIII within this general framework, and we discuss fractional quantum Hall and ${\mathbb{Z}}_2$ quantum spin liquid states of electrons.

Applications of epitaxial antiferroelectrics face scientific challenges, such as limited understanding of degraded (in comparison to bulk) switching behavior and its relation to nanoscale structural organization. We report on an unusual structural response of ${\mathrm{PbZrO}}_3/{\mathrm{SrRuO}}_3/{\mathrm{SrTiO}}_3$ (001) heterostructures to precritical (lower than required for switching) electric fields. In situ x-ray diffraction shows a ferrielectric-like structure, which forms gradually upon increasing the applied field and makes up a heterophase state with the host antiferroelectric phase. The field-induced structure is similar to the antiferroelectric parent phase in the octahedral-tilt pattern, but differs from it in the lead-ion displacement pattern. The latter can be encoded as $\uparrow \uparrow \uparrow \uparrow \downarrow \uparrow \uparrow \downarrow$ provided that the antiferroelectric structure is encoded as $\downarrow \downarrow \uparrow \uparrow$. We propose that the unusual commensurateness (as opposed to the more ubiquitous incommensuration in similar materials) between the modulation periods of host and guest phases can be explained by accounting for the energy of heterophase boundaries, which is important in dense nanostructures due to the high surface-to-bulk ratio of nanodomains. An analysis using the ab-initio-correlated, but empirical (parametrized) energy model suggests that the observed field-induced structure is likely to be selected in ${\mathrm{PbZrO}}_3$ instead of the others in the case when the above commensuration effect is at play. The results point to the mechanism leading to the smearing of polarization-field loops in such heterostructures and suggest a perspective for the controlled creation of delicate dipolar orderings for ferroic-based memory.

Similar to light polarization that is selected by a superposition of the optical basis, the electron spin direction can be controlled through a superposition of the spin basis. We investigate such a spin interference occurring in the photoemission of a spin-orbit coupled surface state in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ by using spin- and angle-resolved photoemission spectroscopy combined with a laser light source (laser-SARPES). Our laser-SARPES with three-dimensional spin detection and tunable laser polarization including elliptical and circular polarization enables us to directly visualize how the direction of the fully polarized photoelectron spin changes according to the optical phase and orientation of the incident laser polarization. By this advantage of our laser-SARPES, we demonstrate that such optical information can be projected to the three-dimensional spin vector of the photoelectrons. Our results therefore present a spin-polarized electron source permitting us to optically control the pure spin state pointing to an arbitrary direction.

Out-of-time-order correlators (OTOCs) progressively play an important role in different fields of physics, particularly in the nonequilibrium quantum many-body systems. In this paper, we show that OTOCs can be used to probe the Floquet dynamical quantum phase transitions (FDQPTs). We investigate the OTOCs of two exactly solvable Floquet spin models, namely, Floquet XY chain and synchronized Floquet XY model. We show that the border of driving frequency range, over which the Floquet XY model shows FDQPT, is signaled by the global minimum of the infinite-temperature time averaged OTOC. Moreover, our results manifest that OTOCs decay algebraically in the long time, for which the decay exponent in the FDQPT region is different from that in the region where the system does not show FDQPTs. In addition, for the synchronized Floquet XY model, which reveals FDQPT at any driving frequency depending on the initial infinite or finite temperature, the imaginary part of the OTOCs becomes zero whenever the system shows FDQPT.