Motivated by the experimental observation that superconductivity in bulk doped ${\mathrm{SrTiO}}_3$ is enhanced as a putative ferroelectric quantum critical point (FE-QCP) is approached, we study the pairing instability of a cubic system in which electrons exchange low-energy ferroelectric fluctuations. Instead of the gradient coupling to the lattice distortion associated with ferroelectricity, we consider direct coupling between the electrons and the bosonic ferroelectric field that appears in the presence of spin-orbit coupling. Working in the weak-coupling regime, we find that the pairing interaction is dominated by the soft transverse optical (TO) mode, resulting in a $T_c$ enhancement upon approaching the FE-QCP. Focusing on even-parity states, we find that although the $s$-wave state always wins, states with higher Cooper-pair angular momentum become close competitors as the TO mode softens. We show that the cubic anisotropy of the FE fluctuations mixes the $s$-wave and $g$-wave states, resulting in a characteristic anisotropy of the gap function. The gap anisotropy behaves nonmonotonically as the FE-QCP is approached: upon decreasing the TO mode frequency, the gap anisotropy first changes sign and then increases in magnitude. We discuss the possible applications of our results to the superconducting state of ${\mathrm{SrTiO}}_3$.

Wave propagation in a two-dimensional periodic fluid-saturated porous metamaterial (FSPM) is investigated. The constitutive relation considered for fluid-saturated porous materials is based on Biot's homogeneization theory. Such media generally support two shear and two longitudinal elastic waves. Anisotropic wave propagation results both from anisotropy of the solid matrix and from the periodic structure of the metamaterial. Special attention is devoted to the dispersion and attenuation of evanescent Bloch waves in a FSPM whose matrix is transversely isotropic in which case in-plane elastic waves are a superposition of one shear wave and of two longitudinal waves. Bloch waves, complex band structures, and transmission properties are obtained numerically using finite element analysis. The case of homogeneous fluid-saturated porous media is considered since numerical simulations can be compared directly with analytic results in this case. The effects of material anisotropy and of fluid viscosity on wave propagation in two-dimensional FSPM are then discussed. It is found that wave-number band gaps appear in the complex band structure of the lossless FSPM due to the interference of waves with different but nonorthogonal polarizations. Wave-number band gaps are connected continuously by complex-frequency bands, hence, defining stop bands in the time domain. No complete frequency band gaps are found in two-dimensional lossless FSPM, in contrast to the one-dimensional case [Y.-F. Wang et al. Phys. Rev. B 99, 134304 (2019)] due to the presence of the additional quasishear wave accompanying the two quasilongitudinal waves. Both the complex band structure and the transmission properties are affected by the anisotropy of the solid matrix. Wide transmission dips come up when viscosity is introduced as a result of the strong attenuation and the coupling of all wave polarizations. Concurrently, wave-number band gaps are washed out by viscosity. This theoretical paper has relevance to practical applications of fluid-saturated porous metamaterials, e.g., in concrete structures and geological soils.

We present an ab initio density-functional-theory approach for calculating electron-phonon interactions within the projector augmented-wave (PAW) method. The required electron-phonon matrix elements are defined as the second derivative of the one-electron energies in the PAW method. As the PAW method leads to a generalized eigenvalue problem, the resulting electron-phonon matrix elements lack some symmetries that are usually present for simple eigenvalue problems and all-electron formulations. We discuss the relation between our definition of the electron-phonon matrix element and other formulations. To allow for efficient evaluation of physical properties, we introduce a Wannier-interpolation scheme, again adapted to generalized eigenvalue problems. To explore the method's numerical characteristics, the temperature-dependent band-gap renormalization of diamond is calculated and compared with previous publications. Furthermore, we apply the method to selected binary compounds and show that the obtained zero-point renormalizations agree well with other values found in literature and experiments.

We have performed ${}^{13}\mathrm{C}$ NMR measurements on $\lambda -{(\mathrm{BEDT}-\mathrm{STF})}_2{\mathrm{FeCl}}_4$ to reveal the mechanism of unconventional paramagneticlike behavior observed in $\lambda$-type molecular $\pi -d$ systems. ${}^{13}\mathrm{C}$ NMR spectra and nuclear spin-lattice relaxation rate $1/T_1$ revealed that the $\pi$ and $3d$ electron systems undergo an antiferromagnetic transition simultaneously at 16 K with the assistance of the $\pi -d$ interaction. We found that the sublattice magnetizations of the $\pi$ and $3d$ spins show different temperature dependence below $T_{\mathrm{N}}$, which is derived from the magnetic coupling between the two sublattice systems with different magnetic natures. We discuss the relationship between the two different magnetization processes and the unconventional magnetic behavior in $\lambda$-type molecular $\pi -d$ system.

The delafossite series of layered oxides includes some of the highest conductivity metals ever discovered. Of these, ${\mathrm{PtCoO}}_2$, with a room-temperature resistivity of 1.8 $\mu \mathrm{\Omega }\mathrm{cm}$ for in-plane transport, is the most conducting of all. The high conduction takes place in triangular lattice Pt layers, separated by layers of Co-O octahedra, and the electronic structure is determined by the interplay of the two types of layers. We present a detailed study of quantum oscillations in ${\mathrm{PtCoO}}_2$, at temperatures down to 35 mK and magnetic fields up to 30 T. As for ${\mathrm{PdCoO}}_2$ and ${\mathrm{PdRhO}}_2$, the Fermi surface consists of a single cylinder with mainly Pt character and an effective mass close to the free-electron value. Due to Fermi-surface warping, two close-lying high frequencies are observed. Additionally, a pronounced difference frequency appears. By analyzing the detailed angular dependence of the quantum-oscillation frequencies, we establish the warping parameters of the Fermi surface. We compare these results to the predictions of first-principles electronic-structure calculations including spin-orbit coupling on Pt and Co and on-site correlation $U$ on Co, and hence demonstrate that electronic correlations in the Co-O layers play an important role in determining characteristic features of the electronic structure of ${\mathrm{PtCoO}}_2$.

Using first-principles density functional theory ($\mathrm{DFT}+U$), we have investigated the possibility to tune the electronic and magnetic properties of the graphone/Ni(111) interface through O intercalation. Our study shows that the interaction of graphone becomes stronger with the Ni(111) surface as the coverage of intercalating O atoms is increased. Moreover, we find that as a function of O coverage, there is an interplay between the energy gained by O intercalation and the instability in the graphene sheet due to the presence of unsaturated C atoms which drives the reconstruction of the Ni surface at O coverages below 0.5 ML. With the increase in O coverage we find that there is huge enhancement in the magnetic moments on the Ni atoms at the interface. Most interestingly, for the interface at half a monolayer O coverage, we find that there is a significant enhancement in the magnetic moment of the graphone sheet that otherwise is quenched when adsorbed on the Ni(111) surface in absence of oxygen.

Chern insulators are states of matter characterized by their quantized Hall conductance but also by their singular response to monopole configurations of an external electromagnetic field. In this paper, we exploit this response to provide a classification for these states. We demonstrate that for each Chern-insulator state, including the trivial state, the response defines an associated operator that can be interpreted as the insertion of local charges and monopoles at two points separated in space. This operator decays algebraically in the monopole separation distance only for its associated state but exponentially in all other states. Crucially, the operators do not depend on any microscopic properties, and therefore constitute a general set of nonlocal order parameters. We support this claim with numerical evaluation of the order parameters in a simple lattice model, and find excellent agreement. Our construction is well suited for generalization to other states with topological electromagnetic response, and we use the states with a quantized magnetoelectric effect in three dimensions as an example. Aside from providing insights into topological states of matter, our construction can also be exploited to efficiently diagnose such states numerically.

The Green's function (GF) of two localized magnetic moments embedded in the electron gas is calculated exactly. The electrons are treated in the effective mass approximation and the magnetic moments are coupled with electrons by a deltalike $s\text{−}d$ interaction. The resulting GF is obtained as a result of the exact summation of the Born series using a generalization of the method developed by Slater-Koster and Ziman to noncommuting spin operators with the use of the Woodbury identities. For small $s\text{−}d$ coupling $J$ the exact GF reduces to the Ruderman-Kittel-Kasuya-Yosida (RKKY) case, for which the first two terms of the Born series are included. In contrast to the standard RKKY, for the exact GF there is no symmetry between positive and negative values of $J$. The exact GF crucially depends on the value of the one-electron Green's function at the origin, denoted as $g_0$. The Born series is convergent only if $g_0$ is finite, which holds for electrons in parabolic energy bands in one dimension, but not in two and three dimensions. For this reason, a simple model of RKKY interaction deserves to be reconsidered since the second term of the perturbation series is finite, and gives the standard RKKY interaction, while the sum of remaining terms is divergent. A finite value of $g_0$ can be obtained once a cutoff for the energy integration is introduced. The exact GF includes nonlinear combination of localized spin operators and a method of calculating matrix elements of these operators is given. For spins ${\widehat{S}}_a,{\widehat{S}}_b=\frac{1}{2}$ the exact GF is expressed as a linear combination of components of ${\widehat{S}}_a,{\widehat{S}}_b$, and the exact range function $\mathcal{J}\left(r_{ab}\right)$ is obtained as a double integral over analytical expression. For electron energy $E=0$ and $J{g}_0/2\simeq 2$ or $J{g}_0/2\simeq -\frac{2}{3}$, the range function and GF are singular. Poles of GF occur in the vicinities of singularity points and the resulting energies of bound states are calculated. The origin of asymmetry between positive and negative $J$ values is explained. For small $\left|J\right|$ the range function $\mathcal{J}\left(r_{ab}\right)$ resembles the RKKY one: it has the same period $\pi /k_F$, the same decay character, and a slightly different amplitude, usually within a few percent. This regime occurs most frequently in the nature. For $\left|J\right|$ comparable to $|g_0{|}^{-1}$, the exact range function has much larger amplitude and nonoscillatory character. For $\left|J\right|\gg |g_0{|}^{-1}$, the exact range function oscillates with the same period and powerlike decay as the usual RKKY function but it has much lower amplitude decaying with growing $\left|J\right|$. In the limiting case of $\left|J\right|\to \infty$, the range function vanishes. A range of validity of the proposed model to real systems is discussed.

The nonlocal nature of the Majorana zero modes implies an inherent teleportation channel and unique transport signatures for Majorana identification. In this work we make an effort to eliminate some inconsistencies between the Bogoliubov–de Gennes equation based treatment and the method using the associated regular fermion-number states of occupation within the “second quantization” framework. We first consider a rather simple “quantum dot–Majorana wire–quantum dot” system, then a more experimentally relevant setup by replacing the quantum dots with transport leads. For the latter setup, based on the dynamical evolution of electron-hole excitations, we develop a single-particle wave-function approach to quantum transport, which renders both the conventional quantum scattering theory and the steady-state nonequilibrium Green's function formalism as its stationary limit. Further, we revisit the issue of Majorana tunneling spectroscopy and consider in particular the two-lead coupling setup. We present comprehensive discussions with detailed comparisons, and predict a zero-bias-limit conductance of $e^2/h$ (for symmetric coupling to the leads), which is a half of the popular result of the zero-bias peak or the so-called Majorana quantized conductance ($2e^2/h$). This work may arouse a need to reexamine some existing studies and the proposed treatment is expected to be involved in analyzing future experiments in this fast developing field.

We describe an efficient near-field to far-field transformation for optical quasinormal modes, which are the dissipative modes of open cavities and plasmonic resonators with complex eigenfrequencies. As an application of the theory, we show how one can compute the reservoir modes (or regularized quasinormal modes) outside the resonator, which are essential to use in both classical and quantum optics. We subsequently demonstrate how to efficiently compute the quantum optical parameters necessary in the theory of quantized quasinormal modes [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. To confirm the accuracy of our technique, we directly compare with a Dyson equation approach (in regimes where this is possible), and we demonstrate several order of magnitude improvement for the calculation runtimes. We also introduce an efficient pole approximation for computing the quantized quasinormal mode parameters. Using this approach, we show how to compute regularized quasinormal modes and quantum optical parameters for a full 3D metal dimer (with various material losses) in under one minute on a standard desktop computer. Our technique is exemplified by studying the quasinormal modes of metal dimers and a hybrid structure consisting of a gold dimer on top of a photonic crystal beam, designed to yield a Purcell factor in excess of 1 million. In the latter example, we show how to compute the quantized mode parameters that describe a pronounced Fano resonance, using structural geometries that cannot practically be solved using a Dyson equation approach. All calculations for the spontaneous emission rates are confirmed with full-dipole calculations in Maxwell's equations and are shown to be in excellent agreement.

We analyze the localization properties of the disordered Hubbard model in the presence of a synthetic magnetic field. An analysis of level spacing ratios shows a clear transition from ergodic to many-body localized phase. The transition shifts to larger disorder strengths with increasing magnetic flux. Study of dynamics of local correlations and entanglement entropy indicates that charge excitations remain localized whereas spin degree of freedom gets delocalized in the presence of the synthetic flux. This residual ergodicity is enhanced by the presence of the magnetic field with dynamical observables suggesting incomplete localization at large disorder strengths. Furthermore, we examine the effect of quantum statistics on the local correlations and show that the long-time spin oscillations of a hard-core boson system are destroyed as opposed to the fermionic case.

We propose to simultaneously determine bulk and interfacial Dzyaloshinskii-Moriya interactions (DMIs) by using the in-plane field dependence of the precessional flow of chiral domain walls (DWs). It is found that the effective fields of bulk and interfacial DMIs have respectively transverse and longitudinal components that affect differently the motion of chiral DWs in magnetic narrow heterostructure strips. The in-plane field dependence of the average precessional wall velocity can take either a dome shape or a canyon shape, depending on whether the driving force is an in-plane current or an out-of-plane magnetic field. The responses of their center shifts to the reversal of topological wall charge and current/field direction uniquely determine the nature and strength of DMI therein. Operable procedures are proposed and applied to explain existing experimental data.

The wavelike processes of crystallization and melting or crystallization waves are well known to exist at the crystal ${}^4\mathrm{He}$ surface in its rough state. Below the roughening transition temperature the crystalline surface experiences the transition to the smooth faceted state and the crystallization waves represent the propagation of a train of crystalline steps at the velocity depending on the crystal step height. Here we analyze the transmission and reflection of crystallization waves which propagate across the crystal edge separating the crystalline surfaces in the rough and faceted states.

The characterization of quantum magnetism in a large spin ($\ge 1$) system naturally involves both spin vectors and spin tensors. While certain types of spin-vector (e.g., ferromagnetic, spiral) and spin-tensor (e.g., nematic in frustrated lattices) orders have been investigated separately, the coexistence and correlation between them have not been well explored. Here, we propose a quantum spiral spin-tensor order on a spin-1 Heisenberg chain subject to a spiral spin-tensor Zeeman field, which can be experimentally realized using a Raman-dressed cold atom optical lattice. We develop a method to fully characterize quantum phases of such spiral tensor magnetism with the coexistence of spin-vector and spin-tensor orders as well as their correlations using eight geometric parameters. Our method provides a powerful tool for characterizing spin-1 quantum magnetism and opens an avenue for exploring magnetic orders and spin-tensor electronics and atomtronics in large-spin systems.

We report thermodynamic and neutron diffraction measurements on a $S=1/2$ metal-organic kagome compound ${\left\{\right[{\mathrm{Cu}}_3\left({\mathrm{CO}}_3\right){}_2{\left(\mathrm{bpe}\right)}_3]·{2\mathrm{ClO}}_4\}}_n$ [bpe=1,2-bis(4-pyridyl)ethane] with a Curie-Weiss temperature of $\sim -2.9\pm 0.9\mathrm{K}$. The dc and ac magnetization measurements as well as neutron diffraction study show no long-range magnetic order down to 1.5 K. The temperature dependence of specific heat also shows no signature of long-range magnetic order down to 86 mK, as expected for an ideal Heisenberg kagome lattice with a nearest-neighbor antiferromagnetic exchange interaction. The frequency-independent flattening behavior observed in the real part of the ac susceptibility in a zero applied magnetic field below $\sim 6$ K rules out the presence of a spin glass state and indicates a slowing down of the spin dynamics at low temperatures. Our results suggest that strong quantum fluctuations enhanced by geometrical frustration suppress the long-range magnetic order and a ground state with quasistatic short-range canted antiferromagnetic-type order is realized in the ${\left\{\right[{\mathrm{Cu}}_3\left({\mathrm{CO}}_3\right){}_2{\left(\mathrm{bpe}\right)}_3]·{2\mathrm{ClO}}_4\}}_n$ [bpe=1,2-bis(4-pyridyl)ethane]. The ground state is fragile against external magnetic fields. An applied magnetic field of 125 Oe (and higher) induces ferromagneticlike spin-spin correlations.

We apply the efficient two-optimized references thermodynamic integration using Langevin dynamics method [Phys. Rev. B 96, 224202 (2017)] to calculate highly accurate melting properties of Al and magnetic Ni from first principles. For Ni we carefully investigate the impact of magnetism on the liquid and solid free energies including longitudinal spin fluctuations and the reverse influence of atomic vibrations on magnetic properties. We show that magnetic fluctuations are effectively canceling out for both phases and are thus not altering the predicted melting temperature. For both elements, the generalized gradient approximation (GGA) and the local-density approximation (LDA) are used for the exchange-correlation functional revealing a reliable ab initio confidence interval capturing the respective experimental melting point, enthalpy of fusion, and entropy of fusion.

Silicon carbide is a very promising platform for quantum applications because of the extraordinary spin and optical properties of point defects in this technologically friendly material. These properties are strongly influenced by crystal vibrations, but the exact relationship between them and the behavior of spin qubits is not fully investigated. We uncover the local vibrational modes of the Si vacancy spin qubits in as-grown 4H-SiC. We apply microwave-assisted spectroscopy to isolate the contribution from one particular type of defects, the so-called V2 center, and observe the zero-phonon line together with seven equally separated phonon replicas. Furthermore, we present first-principles calculations of the photoluminescence line shape, which are in excellent agreement with our experimental data. To boost up the calculation accuracy and decrease the computation time, we extract the force constants using machine-learning algorithms. This allows us to identify the dominant modes in the lattice vibrations coupled to an excited electron during optical emission in the Si vacancy. A resonance phonon energy of 36 meV and a Debye-Waller factor of about $6\%$ are obtained. We establish experimentally that the activation energy of the optically induced spin polarization is given by the local vibrational energy. Our findings give insight into the coupling of electronic states to vibrational modes in SiC spin qubits, which is essential to predict their spin, optical, mechanical, and thermal properties. The approach described can be applied to a large variety of spin defects with spectrally overlapped contributions in SiC as well as in other three- and two-dimensional materials.

The relaxation of a many-body system is still a challenging problem that has not been well understood. In this work we exactly calculate the dynamics of the quantum $XY$ model with boundary dissipation, in which the density matrix in terms of Majorana operators can be decoupled into independent subspaces ${\mathcal{K}}_i$ represented by different number of Majorana fermions. The relaxation is characterized by multiple timescales, and in the long-time limit it is determined by the single-particle relaxation process in a typical timescale $T^{*}$. For the bulk bands, we find $T^{*}\propto N^3/\gamma n^2$ in the weak dissipation limit and $T^{*}\propto \gamma N^3/n^2$ in the strong dissipation limit, where $N$ is the chain length, $\gamma$ is the dissipation rate, and $n$ is the band index. For the edge modes, $T^{*}\propto 1/\gamma$ indicates the most vulnerable to dissipation in the long-chain limit. These results are counterintuitive because it means any weak dissipation can induce strong relaxation, while strong dissipation can induce weak relaxation. We find that these two limits correspond to two different physics, which are explained based on the first- and second-order perturbation theory in an equivalent non-Hermitian model. Finally, we show that even in the long-chain limit with weak dissipation, the relaxation may exhibit strong odd-even effect, which can be washed out by the strong dissipation. These results shed new insight into the dynamics of topological qubits in the environment, and the mechanism for many-body dissipation may also have universal significance in understanding the many-body dissipation in the other models.