For orthorhombic superconductors we define thermodynamic anisotropy $N\equiv d{T}_c/d{\epsilon }_{22}-d{T}_c/d{\epsilon }_{11}$ as the difference in how superconducting $T_c$ varies with strains ${\epsilon }_{ii}$, $i=(1,2)$, along the in-plane directions. We study the hole doping $\left(p\right)$ dependence of $N$ on detwinned single crystals of underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ (YBCO) using the ultrasound technique. While the structural orthorhombicity of YBCO reduces monotonically with decreasing doping over $0.065<p<0.16$, we find that the thermodynamic anisotropy shows an intriguing enhancement at the intermediate doping level, which is of electronic origin. Our theoretical analysis shows that the enhancement of the electronic anisotropy can be related to the pseudogap potential in the electronic spectrum that itself increases when the Mott insulating state is approached. Our results imply that the pseudogap is controlled by a local energy scale that can be tuned by varying the nearest-neighbor Cu-Cu bond length. Our work opens the possibility to strain engineer the pseudogap potential to enhance the superconducting $T_c$.

The effect of the Dirac cone tilt of anisotropic two-dimensional materials on the time evolution of coherent electron states in the presence of electric and magnetic fields is studied. We propose a canonical transformation that maps the anisotropic Dirac-Weyl Hamiltonian with tilted Dirac cones to an effective and isotropic Dirac Hamiltonian under these fields. In this way, the well-known Landau level spectra and wave functions allow calculating the Wigner matrix representation of Landau and coherent states. We found a valley dependency in the behavior of the Wigner function for both Landau and coherent electron states. The time evolution shows that the interplay of the Dirac cone tilt and the electric field keeps the uncertainties of both position and momentum in one valley significantly lower than in the other valley. The increment of quantum noise correlates with the emergence of negative values in the Wigner function. These results may help us to understand the generation of coherent electron states under the interaction with electromagnetic fields. The reported valley-dependent signatures in the Wigner function of materials with tilted Dirac cones may be revealed by quantum tomography experiments, even in the absence of electric fields.

We present a universal and extremely efficient tree search algorithm for irreducible site-occupancy configurations (implemented in disorder code) that partially avoids the barrier from the combinatorial explosion and allows us to model the compositionally complex materials. The tree search algorithm is developed based on our original algorithm and is leveraging the idea of stopping descending further down the branches of the tree that do not meet the requirements. Meanwhile, the wrongly counted degeneracies of the irreducible site-occupancy configurations, caused by the skipping of some branches of the tree, can be corrected by a degeneracy correction procedure. Using binary face-centered cubic alloys, ternary body-centered cubic alloys, and quaternary simple cubic alloys as examples, we demonstrate that, compared with our original algorithm, the overall efficiency of the tree search algorithm is improved by more than 2 times for binary site occupancy, 70 times for ternary site occupancy, and 50 times for quaternary site occupancy, which is far beyond other similar algorithms. The tree search algorithm developed here can be broadly useful for the modeling of high-entropy alloys and provides support for other methods, such as special quasirandom structures and small set of ordered structures, that require enumerating a set of site-occupancy configurations.

Spin textures in perfectly ordered antiferromagnetic ultrathin films are evaluated on the basis of atomistic simulations and compared to the results of recent extensions of the ($\mathbf{l},\mathbf{m}$) decomposition model. A comparison between similar textures supported by either a bcc or a fcc lattice shows that the sole inclusion of symmetric Heisenberg exchange interactions suffices to provide, when geometry commands, a natural canting between neighboring ${\mathbf{s}}_{\uparrow }$ and ${\mathbf{s}}_{\downarrow }$ spins within a texture. Moreover, a pure “at lattice points” dipole model leads to natural symmetries, in clear disagreement with expectations from the ($\mathbf{l},\mathbf{m}$) model. Inversely, properties such as wall mobility under spin-orbit torques depending mostly on wall geometrical characteristics such as chirality and chirality axis orientation prove, as anticipated, primarily lattice immune.

The mechanisms underlying the enhancement of magnetic anisotropies (MAs) of Sm ions, owing to valence electrons at the Sm site and the screened nuclear charges of ligands, are clarified using a detailed analysis of crystal fields (CF). In order to investigate the finite-temperature magnetic properties, we developed an effective spin model for $\mathrm{Sm}{\mathrm{Fe}}_{12}X$ ($X$=H, B, C, and N) and $\mathrm{Sm}{\mathrm{Fe}}_{11}M$ ($M$=Ti, V, and Co), where the magnetic moments, CF parameters, and exchange fields were determined by first-principle calculations. Using this model, the MA constants and magnetization curves at finite temperatures were investigated using a recently introduced analytical method [Yoshioka, Tsuchiura, and Novák, Phys. Rev. B 102, 184410 (2020)]. In $\mathrm{Sm}{\mathrm{Fe}}_{12}X$, the doped light elements $X$ are assumed to be at the $2b$ site, and in $\mathrm{Sm}{\mathrm{Fe}}_{11}M$, the substitution site of Fe is systematically investigated for all inequivalent $8f, 8i$, and $8j$ sites. We found that the first-order MA constant $K_1$ is increased by a factor of about two when hydrogen is doped to the $2b$ site and when Fe is replaced by Ti or V at the $8j$ site, owing to the attraction of the prolate $4f$ electron cloud to the screened positive charges of the surrounding ligand ions. We found that when Fe is replaced by Co, the MA increases at all temperatures regardless of the substitution site. The substituted Co attracts electrons, which reduces the electron density in the region from the Sm site to the empty $2b$ site. This causes the $4f$ electron cloud at the Sm site to be fixed along the $c$-axis direction, which improves the MA. The calculated temperature dependence of $K_1\left(T\right)$ and $K_2\left(T\right)$ in $\mathrm{Sm}{\mathrm{Fe}}_{11}\mathrm{Co}$ qualitatively reproduces the experimental results in the case of $\mathrm{Sm}{\left({\mathrm{Co}}_x{\mathrm{Fe}}_{1-x}\right)}_{12}$ for $x=0.1$ and 0.07. The first-order magnetization process is observed at low temperatures in $\mathrm{Sm}{\mathrm{Fe}}_{12}$ itself and in many variations of $\mathrm{Sm}{\mathrm{Fe}}_{12}$-based compounds prepared using element doping and substitution. This is mainly due to the competition between the conditions $K_1>0$ and $K_2<0$, and that of $K_1<-6K_2$ owing to the ${\mathrm{ThMn}}_{12}$ structure having a vacancy at the $2b$ site.

Rutile-type ${\mathrm{RuO}}_2$ likely supports a simple antiferromagnetic structure which can be verified by x-ray Bragg diffraction. Three magnetic motifs that do not break translation symmetry are explored in calculations of amplitudes suitable for diffraction enhanced by tuning the primary x-ray energy to a ruthenium atomic resonance. Coupling to x-ray helicity through a charge-magnetic interference is common to all motifs, together with magnetic and charge intensities in quadrature in the rotated channel of polarization. Necessary conditions for these diffraction phenomena are a centrosymmetric crystal structure, null magnetic propagation vector, and absence of a linear magnetoelectric effect. Published x-ray diffraction data for ${\mathrm{RuO}}_2$ were analyzed by the authors against a magnetic motif that does not satisfy the conditions. A polarized neutron study of antiferromagnetic domains can be achieved with a sample that meets the stated crystal and magnetic symmetries.

Recent observations of two nodeless gaps in superconducting $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$ have raised intensive debates as to its exact gap structure of either sign-reversal ($s^{+-}$) or sign-preserving ($s^{++}$) pairing. Here, we investigate the quasiparticle interference (QPI) using realistic Fermi surface topology for both weak and strong interband impurity scatterings. Our calculations of the QPI and integrated antisymmetrized local density of states reveal qualitative distinctions between $s^{+-}$ and $s^{++}$ pairing states, which include the intragap impurity resonance and a significant energy-dependence difference between two gap energies. Our predictions provide a guide for phase-sensitive QPI measurements to uncover decisively the true pairing symmetry in the heavy-fermion superconductor $\mathrm{Ce}{\mathrm{Cu}}_2{\mathrm{Si}}_2$.

The Higgs mode associated with amplitude fluctuations of the superconducting gap in uniform superconductors is usually heavy, which makes its excitation and detection difficult. We report on the existence of a gapless Higgs mode in the Fulde-Ferrell-Larkin-Ovchinnikov states. This feature originates from the Goldstone mode associated with translation-symmetry breaking. The existence of the gapless Higgs mode is demonstrated by using both a phenomenological model and microscopic Bardeen-Cooper-Schrieffer (BCS) theory. The gapless Higgs mode can avoid the decay into other low-energy excitations, which renders it stable and detectable.

In this paper, we discuss strong coupling limits of topological quantum critical points (TQCPs) where quantum phase transitions between two topological distinct superconducting states take place. We illustrate that while superconducting phases on both sides of TQCPs spontaneously break the same symmetries, universality classes of critical states can be identified only when global symmetries in topological states are further specified. In dimensions $d=2\text{and}3$, we find that continuous $(d+1)\mathrm{th}$-order transitions at weakly interacting TQCPs that were pointed out previously in the presence of the emergent Lorentz symmetry can be terminated by strongly interacting fixed points of Majorana fields. For $2d$ time reversal symmetry breaking TQCPs, termination points are supersymmetric with $\mathcal{N}=4N_f=1$ (where $N_f$ is the number of four-component Dirac fermions and $\mathcal{N}$ is the number of two-component real fermions) beyond which transitions are discontinuous first-order ones. For $2d$ time reversal symmetric TQCPs without other global symmetries, termination points of $(d+1)\mathrm{th}$-order continuous transition lines are generically conformal invariant without supersymmetry. Beyond these strong coupling fixed points, there are first-order discontinuous transitions as far as the protecting symmetry is not spontaneously broken but no direct transitions if the protecting symmetry is spontaneously broken in the presence of strong interactions. In this case, termination points can become supersymmetric with $\mathcal{N}=4N_f=2$ only when interacting Majorana fermions further display an emergent global $\text{U}\left(1\right)$ symmetry. In $3d$, strong coupling termination points can be further effectively represented by new emergent gapless real bosons weakly coupled with free gapless Majorana fermions. However, in $1d$, time reversal symmetric $(d+1)\mathrm{th}$ continuous transition lines of TQCPs are terminated by simple free Majorana fermion fixed points.

Under a static electric field, we present the scanning nanobeam x-ray diffraction of a relaxor ferroelectric single crystal. The x-ray intensity distributions of a Bragg peak in reciprocal space diffracted from local volumes on the surface of a $0.7\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3-0.3\mathrm{PbTi}{\mathrm{O}}_3$ (PMN-30PT) single crystal show position and electric field dependence. While the spatially averaged intensity distribution has a single peak corresponding to the average crystal structure, intensity distributions from each local volume have several strong sharp peaks and a weak broad peak, and show strong position dependence as the translation symmetry is broken in nano- to microscale. A static local lattice strain with spatially valuable lattice constants and nanodomains is responsible for peak splitting and heterogeneous crystal structure. The locally strained lattice exhibits a significant tensile lattice strain caused by an electric field, which is compatible with its large piezoelectric constant of approximately $2\times {10}^3\mathrm{pC}/\mathrm{N}$. When the electric field surpasses the coercive field of 3 kV/cm, polarization switching causes a substantial shear lattice strain with intensity redistribution. Position dependence can also be seen in the piezoelectric constants and coercive fields calculated from x-ray diffraction data for each local location. The standard deviation of the local lattice strain distribution is $3\times {10}^{-3}$ regardless of the electric field, which is greater than the piezoelectric lattice strain of $1\times {10}^{-3}$ caused by an electric field of 8 kV/cm. The enormous electric field induced lattice strain and fatigue-free polarization switching are enabled and facilitated by the nano- to microscale heterogeneous crystal structure with widely and continuously distributed local lattice strain.

We study the many-body localization (MBL) transition of Floquet eigenstates in a driven, interacting fermionic chain with an incommensurate Aubry-André potential and a time-periodic hopping amplitude as a function of the drive frequency ${\omega }_D$ using exact diagonalization (ED). We find that the nature of the Floquet eigenstates change from ergodic to Floquet-MBL with increasing frequency; moreover, for a significant range of intermediate ${\omega }_D$, the Floquet eigenstates exhibit nontrivial fractal dimensions. We find a possible transition from the ergodic to this multifractal phase followed by a gradual crossover to the MBL phase as the drive frequency is increased. We also study the fermion autocorrelation function, entanglement entropy, normalized participation ratio (NPR), fermion transport, and the inverse participation ratio (IPR) as a function of ${\omega }_D$. We show that the autocorrelation, fermion transport, and NPR display qualitatively different characteristics (compared to their behavior in the ergodic and MBL regions) for the range of ${\omega }_D$ which supports multifractal eigenstates. In contrast, the entanglement growth in this frequency range tend to have similar features as in the MBL regime; its rate of growth is controlled by ${\omega }_D$. Our analysis thus indicates that the multifractal nature of Floquet-MBL eigenstates can be detected by studying autocorrelation function and fermionic transport of these driven chains. We support our numerical results with a semianalytic expression of the Floquet Hamiltonian obtained using Floquet perturbation theory (FPT) and discuss possible experiments which can test our predictions.

Large symmetry groups in quantum many-body systems could strongly enhance quantum fluctuations and thereby stabilize exotic quantum phases. Frustrated interactions were long known to have similar effects. Here we intertwine the large $\mathrm{SU}(N$) symmetry and the frustration in a $J_1\text{−}{J}_2\mathrm{SU}(N$) Heisenberg model on a honeycomb lattice, where $J_1$ is the nearest-neighbor coupling and $J_2$ is the next-nearest-neighbor coupling. With a large-$N$ analysis, we obtain a rich phase diagram by varying both $N$ and the ratio $J_2/J_1$. The ground states include Dirac spin liquid, chiral spin liquid, valence cluster solids, flux ordered state, and stripe states. The physical properties of each phase are discussed.

The manipulation of magnetic anisotropy via interface is crucial for spintronics, but its mechanism is still controversial due to the parasitic problem of strain and the chemistry environment. We have independently controlled the interfacial chemistry of the epitaxially grown Ni film on ${\mathrm{Cu}}_3\mathrm{Au}\left(001\right)$ by inserting the thickness wedged Cu layer. The Ni layer is confirmed to be fully strained until 8 ML by the analysis of LEED I-V spectra, which guarantees that the strain contributions to the magnetic anisotropies are identical. Our results clearly show that the chemistry contribution of Au atoms at $\mathrm{Ni}/{\mathrm{Cu}}_3\mathrm{Au}$ interface plays a major role for its perpendicular magnetic anisotropy. We provide a method to quantitatively separate and extract the chemistry and strain contributions to the interfacial magnetic anisotropy, which is helpful for clarifying its mechanism and developing high performance spintronic materials and devices.

We investigate coherent phonon oscillations of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ using optical pump-probe spectroscopy. Time-resolved optical reflectivity shows periodic modulations due to the $A_{1g}$ coherent phonon of $c$-axis arsenic vibrations. Optical probe beams polarized along the orthorhombic $a$ and $b$ axes reveal that the initial phase of coherent oscillations shows a systematic deviation as a function of temperature, although these oscillations arise from the same $c$-axis arsenic vibrations. The oscillation phase remains anisotropic even in the tetragonal structure, reflecting a nematic response of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. Our study suggests that investigations on the phase of coherent phonon oscillations in optical reflectivity can offer unique evidence of a nematic order strongly coupled to a lattice instability.

A measure-preserving formalism (MPF) is constructed and applied to spin/band models, which yield observations about pumping. It occurs at the topological phase transition, i.e., a $Z_2$ flip, suggesting that $Z_2$ can imply bulk effects. The model's asymptotic behavior is analytically solved via MPF. The pumping probability is geometric, fractional, and has a ceiling of $\frac{1}{2}$. Intriguingly, theorems are proved about occurrence conditions, which are linked to the system's dimension and the distinction between rational and irrational numbers. Experimental detection is discussed.

In this paper, we show that the introduction of long-range hoppings in one-dimensional topological insulator models implies that different possibilities of site indexing must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended Su-Schrieffer-Heeger chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of “influence” of different chiral symmetries. Furthermore, edge states become a linear combination of edgelike states with different localization lengths and reflect the gradual transition between these different chiral symmetries.

The realization of the quantum anomalous Hall (QAH) effect without magnetic doping attracts intensive interest since magnetically doped topological insulators usually possess inhomogeneity of ferromagnetic order. Here, we propose a different strategy to realize intriguing QAH states arising from the interplay of light and nonmagnetic disorder in two-dimensional topologically trivial systems. By combining the Born approximation and Floquet theory, we show that a time-reversal-invariant disorder-induced topological insulator, known as the topological Anderson insulator (TAI), would evolve into a time-reversal-broken TAI and then into a QAH insulator by shining circularly polarized light. We utilize spin and charge Hall conductivities, which can be measured in experiments directly, to distinguish these three different topological phases. This work not only offers an exciting opportunity to realize the high-temperature QAH effect without magnetic orders, but also is important for applications of topological states to spintronics.

$\mathrm{Eu}{\mathrm{B}}_6$ has for a long time captured the attention of the physics community, as it shows a ferromagnetic phase transition leading to a insulator the metal transition together with colossal magnetoresistance (CMR). $\mathrm{Eu}{\mathrm{B}}_6$ has a very low carrier density, which is known to drastically change the interaction between the localised Eu moments and the conduction electrons. One of early triumphs of the quantum theory in condensed matter was the presence of Fermi surface, which is intimately linked to the symmetry of the underlying crystal lattice. This symmetry can be probed by angle dependent magnetoresistance oscillations (AMRO) measurements. Here, we present AMRO measurements that show that in $\mathrm{Eu}{\mathrm{B}}_6$ this symmetry is broken, possibly indicating the presence of a quantum nematic phase. We identify the region in the temperature-magnetic field phase diagram where the magnetoresistance shows twofold oscillations instead of the expected fourfold pattern. Quantum nematic phases are analogous to classical liquid crystals. Like liquid crystals, which break the rotational symmetry of space, their quantum analogs break the point-group symmetry of the crystal due to strong electron-electron interactions, as in quantum Hall states, ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, and high-temperature superconductors. This is the same region where magnetic polarons were previously observed, suggesting that they drive the nematicity in $\mathrm{Eu}{\mathrm{B}}_6$. This is also the region of the phase diagram where $\mathrm{Eu}{\mathrm{B}}_6$ shows a colossal magnetoresistance (CMR). This novel interplay between magnetic and electronic properties could thus be harnessed for spintronic applications.

We show an application of the functional-renormalization-group aided density functional theory to the homogeneous electron gas with arbitrary spin polarization, which gives an energy density functional in the local spin density approximation. The correlation energy per particle is calculated at arbitrary Wigner–Seitz radius $r_{\text{s}}$ and spin polarization $\zeta$. In the high-density region, our result shows good agreement with Monte Carlo (MC) data. The agreement with MC data is better in the case of small spin polarization, while the discrepancy increases as the spin polarization increases. The magnetic properties given by our numerical results are also discussed.