We characterize the single-electron energies and the wave-function structure of arrays with two, three, and four phosphorus atoms in silicon by implementing atomistic tight-binding calculations and analyzing wave-function overlaps to identify the single-dopant states that hybridize to make the array states. The energy spectrum and wave-function overlap variation as a function of dopant separation for these arrays shows that hybridization mostly occurs between single-dopant states of the same type, with some cross hybridization between $A_1$ and $E$ states occurring at short separations. We also observe energy crossings between hybrid states of different types as a function of impurity separation. We then extract tunneling rates for electrons in different dopants by mapping the state energies into hopping Hamiltonians in the site representation. Significantly, we find that diagonal and nearest-neighbor tunneling rates are similar in magnitude in a square array. Our analysis also accounts for the shift of the on-site energy at each phosphorus atom resulting from the nuclear potential of the other dopants. This approach constitutes a solid protocol to map the electron energies and wave-function structure into Fermi-Hubbard Hamiltonians needed to implement and validate analog quantum simulations in these devices.

Lattice strains of appropriate symmetry have served as an excellent tool to explore the interaction of superconductivity in the iron-based superconductors with orthorhombic-nematic and stripe spin-density-wave (SSDW) order. In this Letter, we contribute to a broader understanding of the coupling of strain to superconductivity and competing normal-state orders by studying ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ under large, in-plane strains of $B_{1g}$ and $B_{2g}$ symmetry. In contrast to the majority of iron-based superconductors, pure ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$ exhibits superconductivity with a relatively high transition temperature of $T_c\sim 35\mathrm{K}$ in proximity of a noncollinear, tetragonal, hedgehog spin-vortex crystal (SVC) order. Through experiments and calculations, we demonstrate an anisotropic in-plane strain response of $T_c$ and the favored SVC configuration in ${\mathrm{CaKFe}}_4{\mathrm{As}}_4$. This supports a scenario, in which the change in spin fluctuations dominates the strain response of superconducting $T_c$. Overall, by suggesting moderate $B_{2g}$ strains as an effective parameter to change the stability of SVC and SSDW, we outline a pathway to a unified phase diagram of iron-based superconductivity.

Topological semimetals, such as the Weyl and Dirac semimetals, represent one of the most active research fields in modern condensed-matter physics. The peculiar physical properties of these systems mainly originate from their underlying symmetries, emergent relativistic dispersion, and band topology. In this Letter, we present a different class of gapless systems in three dimensions, dubbed geometric semimetals. These semimetals are protected by the generalized chiral and rotation symmetries, but are topologically trivial. Nevertheless, we show that their band geometry is nontrivial, as evidenced by the nonzero quantum metric trace with possible quantization. The possible realization in synthetic-matter experiments is also discussed.

We investigate rare-earth magnetic Weyl semimetals through first-principles simulations, analyzing the connection between incommensurate magnetic order and the presence of Weyl nodes in the electronic band structure. Focusing on PrAlSi, NdAlSi, and SmAlSi, we demonstrate that the reported helical ordering does not originate from the nesting of topological features at the Fermi surface or the Dzyaloshinskii-Moriya interaction. Instead, the helical order arises from frustrated isotropic short-range superexchange between the $4f$ moments facilitated by $pd$ hybridization with the main group elements. Employing a spin Hamiltonian with isotropic exchange and single-ion anisotropy we replicate the experimentally observed helical modulation.

Amorphous materials exhibit various characteristics that are not featured by crystals and can sometimes be tuned by their degree of disorder (DOD). Here, we report results on the mechanical properties of monolayer amorphous carbon (MAC) and monolayer amorphous boron nitride (maBN) with different DOD. The pertinent structures are obtained by kinetic Monte Carlo (kMC) simulations using machine-learning potentials with density-functional theory-level accuracy. An intuitive order parameter, namely, the areal fraction $F_{\mathrm{x}}$ occupied by crystallites within the continuous random network, is proposed to describe the DOD. We find that $F_{\mathrm{x}}$ captures the essence of the DOD: Samples with the same $F_{\mathrm{x}}$ but different sizes and arrangements of crystallites, obtained using two distinct kMC procedures, have virtually identical radial distribution functions as well as bond-length and bond-angle distributions. Furthermore, by simulating the fracture process with molecular dynamics, we found that the mechanical responses of MAC and maBN before fracture are mainly determined by $F_{\mathrm{x}}$ and are insensitive to the sizes and specific arrangements and to some extent the numbers and area distributions of the crystallites. The behavior of cracks in the two materials is analyzed and found to mainly propagate in meandering paths in the continuous random network region and to be influenced by crystallites in distinct ways that toughen the material. The present results reveal the relation between structure and mechanical properties in amorphous monolayers and may provide a universal toughening strategy for two-dimensional materials.

We study a non-Anderson disorder driven quantum phase transition in a semi-infinite Dirac semimetal with a flat boundary. The conformally invariant boundary conditions, which include those that are time-reversal invariant, lead to nodal-like surface states on the boundary. In this case the boundary becomes metallic at a critical disorder that is weaker than that for the semimetal-diffusive metal transition in the bulk. The latter transition takes place in the presence of a metallic surface; in the language of surface critical phenomena this corresponds to the so-called extraordinary transition. The lines of the surface and the extraordinary transitions meet at the special transition point. To elucidate universal properties at different transitions on the phase diagram, we employ renormalization group methods and compute the corresponding surface critical exponents using $\varepsilon$ expansion.

Ternary Li halides, such as ${\mathrm{Li}}_3{\text{Me}X}_6$ with, e.g., Me = In, Sc, Y and $X$ = Cl, Br, are the center of attention for battery applications, as these materials might serve as ionic electrolytes. To fulfill their function, such electrolytes must have an extraordinarily high ionic ${\mathrm{Li}}^{+}$ conductivity. Layer-structured ${\mathrm{Li}}_3{\mathrm{InCl}}_6$ represents such a candidate; however, understanding the origin of the rapid ${\mathrm{Li}}^{+}$ exchange processes needs further investigation. Spatially restricted, that is, low-dimensional particle diffusion, might offer an explanation for fast ion dynamics. It is, however, challenging to provide evidence for 2D diffusion at the atomic scale when dealing with polycrystalline powder samples. Here, we use purely diffusion-induced ${}^7\mathrm{Li}$ nuclear magnetic spin relaxation to detect anomalies that unambiguously show that 2D Li diffusion is chiefly responsible for the dynamic processes in a ${\mathrm{Li}}_3{\mathrm{InCl}}_6$ powder sample the present paper focusses on. The change of the spin-lattice relaxation rate $1/T_1$ as a function of inverse temperature $1/T$ passes through a rate peak that strictly follows asymmetric behavior. This feature is in excellent agreement with the model of P. M. Richards [Solid State Commun. 25, 1019 (1978)], suggesting a logarithmic spectral density function $J$ to fully describe 2D diffusion. Hence, ${\mathrm{Li}}_3{\mathrm{InCl}}_6$ belongs to the very rare examples for which 2D ${\mathrm{Li}}^{+}$ diffusion has been immaculately verified.

We report on strong coupling between light in open cavities formed by arrays of gold microparticles and the carbonyl molecular vibration in poly(methyl methacrilate). These arrays sustain surface lattice resonances (SLRs), which are optical modes generated by the enhanced radiative coupling of the localized resonances in single scatterers by the diffraction in the array. Using the high-coherence beam of a free-electron laser, we measure the vibrational strong coupling and find a Rabi splitting into an upper and lower vibropolariton band. We observe the narrowing of the lower polariton band when the SLR is resonant with the molecular vibration. This behavior of the lower polariton linewidth can be modeled taking into account motional narrowing due to the spatial averaging of delocalized molecular vibrations in the strong coupling regime. The presence of motional narrowing in vibropolaritons in plasmonic arrays gives insight into the strong coupling of molecular vibrations, and introduces a different platform to investigate polaritonic chemistry, where reactions are not governed by individual molecules but by collective coupled vibrations.

The pseudo-fermion functional renormalization group is generalized to treat spin Hamiltonians with finite magnetic fields, enabling its application to arbitrary spin lattice models with linear and bilinear terms in the spin operators. We discuss in detail an efficient numerical implementation of this approach making use of the system's symmetries. Particularly, we demonstrate that the inclusion of small symmetry-breaking magnetic seed fields regularizes divergences of the susceptibility at magnetic phase transitions. This allows the investigation of spin models within magnetically ordered phases at $T=0$ in the physical limit of vanishing renormalization group parameter $\mathrm{\Lambda }$. We explore the capabilities and limitations of this method extension for Heisenberg models on the square, honeycomb, and triangular lattices. While the zero-field magnetizations of these systems are systematically overestimated, the types of magnetic orders are correctly captured, even if the local orientations of the seed field are chosen differently than the spin orientations of the realized magnetic order. Furthermore, the magnetization curve of the square lattice Heisenberg antiferromagnet shows good agreement with error controlled methods. In the future, the inclusion of magnetic fields in the pseudo-fermion functional renormalization group, which is also possible in three-dimensional spin systems, will enable a variety of additional interesting applications such as the investigation of magnetization plateaus.

In this work, we examine the extraordinary behavior of polarization and spin angular momentum density in the vicinity of longitudinal field zeros in three-dimensional monochromatic acoustic fields. We demonstrate that, as governed by the continuity equation, the velocity fields of arbitrary acoustic sources maintain nondiffractive elliptical polarization structures that enclose longitudinal field zeros, despite having divergent transverse spatial profiles of intensity. Furthermore, embedded in these nonparaxial field contours, for infinite distance, are threads of circular polarization singularities. We illuminate these inherent properties in acoustic vortex fields, dipole arrays, and the famous Young's double-slit experiment. Our results reveal spin characteristics of sound waves that provide a platform for future studies and applications of structured acoustic waves and chiral acoustic phenomena.

We present a study of the lattice dynamical properties of $\mathrm{M}{\mathrm{n}}_{1-x}\mathrm{F}{\mathrm{e}}_x\mathrm{Si}$ with $0\le x\le 0.22$. Employing time-of-flight neutron spectroscopy and inelastic x-ray scattering, we investigate the doping dependence of phonon energies, $E_{\mathrm{ph}}$, and linewidths, ${\mathrm{\Gamma }}_{\mathrm{ph}}$. We find anomalous softening and broadening of a phonon mode propagating along the [111] direction. Ab initio lattice dynamical calculations link this softening to an enhanced electron-phonon coupling due to the doping-dependent changes of the Fermi surface. We discuss an interplay of increased electron-phonon coupling and reduced ordered magnetic moments in $\mathrm{M}{\mathrm{n}}_{1-x}\mathrm{F}{\mathrm{e}}_x\mathrm{Si}$.

The rare-earth (RE) based Shastry-Sutherland lattice (SSL) materials have attracted recent attention for exploring the exotic magnetic phases of $4f$ electrons. Here, we present a comparative study on low-temperature magnetization and specific-heat results of two tetragonal structure compounds ${RE}_2\mathrm{B}{\mathrm{e}}_2\mathrm{Ge}{\mathrm{O}}_7$ ($RE=\mathrm{Pr}$, Nd), where the non-Kramers $\mathrm{P}{\mathrm{r}}^{3+}$ ($J=4$) ions and Kramers $\mathrm{N}{\mathrm{d}}^{3+}$ ($J=9/2$) ions are located on the SSL geometry with “AA”-type stacking fashion along the [001] axis. Temperature-dependent magnetic susceptibility and isothermal field-dependent magnetization $M$($B$) measurements reveal that these two compounds share a similar Ising-like magnetic anisotropy with easy magnetization along the [001] axis and additional fourfold symmetry within the $ab$ plane. For their magnetic ground states, $\mathrm{N}{\mathrm{d}}_2\mathrm{B}{\mathrm{e}}_2\mathrm{Ge}{\mathrm{O}}_7$ exhibits the coexistence of short-range spin correlation and long-range magnetic order with $T_{\mathrm{N}}=0.26$ K in zero magnetic field, while $\mathrm{P}{\mathrm{r}}_2\mathrm{B}{\mathrm{e}}_2\mathrm{Ge}{\mathrm{O}}_7$ does not show any signature of long-range magnetic ordering at temperatures as low as 0.08 K. The ac susceptibility and specific-heat analysis of $\mathrm{P}{\mathrm{r}}_2\mathrm{B}{\mathrm{e}}_2\mathrm{Ge}{\mathrm{O}}_7$ reveal a dynamic spin-freezing behavior below ∼0.22 K similar to that observed in Pr-based pyrochlore spin-ice systems.

The nature of the normal state of cuprate superconductors continues to stimulate considerable speculation. Of particular interest has been the linear temperature dependence of the in-plane resistivity in the low-temperature limit, which violates the prediction for a Fermi liquid. We present measurements of anisotropic resistivity in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ that confirm the strange-metal behavior for crystals with doped-hole concentration $p=x>p^{*}\sim 0.19$ and contrast with the nonmetallic behavior for $p<p^{*}$. We propose that the changes at $p^{*}$ are associated with a first-order transition from doped Mott insulator to conventional metal; the transition appears as a crossover due to intrinsic dopant disorder. We consider results from the literature that support this picture; in particular, we present a simulation of the impact of the disorder on the first-order transition and the doping dependence of stripe correlations. Below $p^{*}$, the strong electronic interactions result in charge and spin stripe correlations that percolate across the ${\mathrm{CuO}}_2$ planes; above $p^{*}$, residual stripe correlations are restricted to isolated puddles. We suggest that the $T$-linear resistivity results from scattering of quasiparticles from antiferromagnetic spin fluctuations within the correlated puddles. This is a modest effect compared to the case at $p<p^{*}$, where the data suggest that there are no coherent quasiparticles in the normal state.

Doublon-holon dynamics is investigated in a pumped one-dimensional Hubbard model with a staggered on-site Coulomb interaction at half-filling. When the system parameters are set to be in the Mott-insulating regime the equilibrium sublattice density of states exhibits several characteristic peaks, corresponding to the lower and upper Hubbard bands as well as hybridization bands. We study the linear absorption spectrum and find two main peaks characterizing the photon frequencies which excite the ground state to an excited state. For a system driven by a laser pulse with general intensity and frequency, both the energy absorption and the doublon-holon dynamics exhibit distinct behaviors as a function of laser amplitude and frequency. Single-photon processes are observed at low laser intensity where the energy is absorbed for resonant laser frequencies. For strong laser intensity multiphoton-induced dynamics are observed in the system that are confirmed by an evaluation of the Loschmidt amplitude. The contribution of multiphoton processes to site-resolved double occupancy is also characterized by the generalized Loschmidt amplitude. The site-resolved doublon-holon dynamics are observed in both the one and multiphoton processes and the site-resolved behavior is explained within a quasiparticle picture. Our study suggests strategies to optically engineer the doublon-holon dynamics in one-dimensional strongly correlated many-body systems.

We carry out large-scale quantum Monte Carlo simulations of a candidate field theory for the onset of superconductivity in magic-angle twisted bilayer graphene. The correlated insulating state at charge neutrality spontaneously breaks U(1) Moiré valley symmetry. Owing to the topological nature of the bands, skyrmion defects of the order parameter carry charge $2e$ and condense upon doping. In our calculations we encode the U(1) symmetry by an internal degree of freedom such that it is not broken upon lattice regularization. Furthermore, the skyrmion carries the same charge. The nature of the doping-induced phase transitions depends on the strength of the easy-plane anisotropy that reduces the SU(2) valley symmetry to $\mathrm{U}\left(1\right)\times {\mathbb{Z}}_2$. For large anisotropy, we observe two distinct transitions separated by phase coexistence. While the insulator to superconducting transition is of mean-field character, the U(1) transition is consistent with three-dimensional $XY$ criticality. Hence, the coupling between the gapless charge excitations of the superconducting phase and the $XY$ order parameter is irrelevant. At small anisotropy, we observe a first-order transition characterized by phase separation.

Floquet engineering offers a unique approach to generate nonequilibrium topological phases in which the unbounded nature of a quasienergy band allows two kinds of topological edge modes, one of them traversing the 0 gap and another one traversing the $\pi$ gap. Characterizing of these two modes is the main topic of Floquet topological insulators, where they are usually characterized by different topological invariants. However, in this paper, for a specific protocol of Floquet engineering where the Dirac mass term of the Chern insulator is periodically kicked, its topological phases are characterized with the Floquet Chern number $C_F$. Specifically, in our illustrative example, the periodically kicked Qi-Wu-Zhang model, there are six different topological phases in total, denoted as $C_F=\{-1_0,-2,-1_{\pi },1_{\pi },2,1_0\}$. Topological phases with larger topological number are observed, i.e., $C_F=\pm 2$, where the chiral edge modes traversing the 0 gap and those traversing $\pi$ gap have the opposite chirality. The mechanism of its topology is revealed by studying the corresponding low-energy effective Dirac Hamiltonian, and the phase boundaries between different topological phases are explicitly found. Additionally, we investigate the orders of phase transitions between different topological phases by studying the von Neumann entropy of the Floquet steady state (FSS), where the FSS corresponds to a stationary state of the Floquet system that is coupled to a Markovian environment. The hallmark of a periodically kicked Dirac mass term is uncovered in this paper, which may inspire further explorations of the physical effects of periodically kicked Dirac mass terms in other systems.

Expanding the two-particle Green's functions determines the self-energy and the polarization as well as the response function on the same footing. The correlation energy is calculated with the help of the extended quasiparticle picture, which accounts for off-shell effects. The corresponding response function leads to the same correlation energy as the self-energy in agreement with perturbation theory, provided one works in the extended quasiparticle picture. A one-dimensional quantum wire of fermions is considered and ground-state properties are calculated in the high-density regime within the extended quasiparticle picture and Born approximation. While the on-shell selfenergies are strictly zero due to Pauli-blocking of elastic scattering, the off-shell behavior shows a rich structure of a gap in the damping of excitation, which is closed when the momentum approaches the Fermi one. The consistent spectral function is presented, completing the first two energy-weighted sum rules. The excitation spectrum shows a splitting due to holons and antiholons as non-Fermi liquid behavior. A renormalization procedure is proposed by subtracting an energy constant to render the Fock exchange energy finite. The effective mass derived from meanfield approximation shows a dip analogous to the onset of Peierls instability. The reduced density matrix or momentum distribution is calculated with the help of a Padé regularization repairing deficiencies of the perturbation theory. A seemingly finite step at the Fermi energy indicating Fermi-liquid behavior is repaired in this way.

We investigate an intriguing phenomenon, the nonlinear chiral thermoelectric (NCTE) Hall effect, where electric current flows parallel to the outer product of an applied electric field and temperature gradient. We develop a general microscopic formulation and confirm the effect in a chiral crystal. Significantly, we find that the contribution of the orbital magnetic moment, which has been previously overlooked, is as crucial as the conventional Berry curvature dipole term. We further demonstrate a substantial NCTE Hall effect in a chiral Weyl semimetal. Our results shed new light on nonlinear transport phenomena and have broad implications for condensed matter physics.

We propose a novel scheme for combining efficiently the truncated-unity functional renormalization group (TUFRG) and the mean-field theory. It follows the method of Wang, Eberlein, and Metzner that uses only the two-particle channel-irreducible part of the vertex as an input for the mean-field treatment. In the TUFRG, the neglect of fluctuation effects from other channels in the symmetry-broken regime is represented by applying the random phase approximation (RPA) in each individual channel, below the divergence scale. Then the Bethe-Salpeter equation for the four-point vertex is translated into the RPA matrix equations for the bosonic propagators that relates the singular and irreducible singular modes of the propagators. The universal symmetries for the irreducible singular modes are obtained from the antisymmetry of Grassmann variables. The mean-field equation based on these modes is derived by the saddle-point approximation in the framework of the path-integral formalism. By using our scheme, the power of the TUFRG, as a diagrammatically unbiased tool for identifying the many-body instabilities, could be elevated to a quantitatively reasonable level, and its application would be extended to a quantitatively reasonable analysis of the coexisting orders. As an illustration, we employ this scheme to study the coexistence phase of the chiral superconductivity and the chiral spin-density wave, predicted near van Hove filling of the honeycomb lattice.