We describe a nonempirical procedure for achieving accurate band gaps of extended systems through the insertion of suitably defined potential probes. By enforcing Koopmans' condition on the resulting localized electronic states, we determine the optimal fraction of Fock exchange to be used in the adopted hybrid functional. As potential probes, we consider point defects, the hydrogen interstitial, and various adjustable potentials that allow us to vary the energy level of the localized state in the band gap. By monitoring the delocalized screening charge, we achieve a measure of the degree of hybridization with the band states, which can be used to improve the band-gap estimate. Application of this methodology to AlP, C, and MgO yields band gaps differing by less than 0.2 eV from experiment.

The ground-state phase diagram of a spin $S=\frac{1}{2}\text{XXZ}$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya interaction $\mathcal{H}={\sum }_n\{J\left(S_n^x{S}_{n+1}^x+S_n^y{S}_{n+1}^y\right)+J_z{S}_n^z{S}_{n+1}^z+[D_0+{(-1)}^n{D}_1](S_n^x{S}_{n+1}^y-S_n^y{S}_{n+1}^x)\}$ is studied using the continuum-limit bosonization approach and extensive density-matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double-frequency sine-Gordon model (DSG) where the frequencies, i.e., the scaling dimensions of the two competing cosine perturbation terms, depend on the effective anisotropy parameter ${\gamma }^{*}=J_z/\sqrt{J^2+D_0^2+D_1^2}$. Exploring the ground-state properties of the DSG model we show that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at ${\gamma }^{*}\le -1$; (ii) the gapless Luttinger-liquid (LL) phase at $-1<{\gamma }^{*}<{\gamma }_{\text{C1}}^{*}=-1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\epsilon \sim {(-1)}^n\left({\mathbf{S}}_n{\mathbf{S}}_{n+1}\right)$ with the LRO alternating spin chirality pattern $\kappa \sim {(-1)}^n\left(S_n^x{S}_{n+1}^y-S_n^y{S}_{n+1}^x\right)$ at ${\gamma }_{\text{C1}}^{*}<{\gamma }^{*}<{\gamma }_{\text{C2}}^{*}$; and (iv) at ${\gamma }^{*}>{\gamma }_{\text{C2}}^{*}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at ${\gamma }_{\text{C1}}^{*}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at ${\gamma }^{*}={\gamma }_{\text{C2}}^{*}$ from C1 to C2 phase is of the Ising type.

Recent experiments have found that monolayer $1H\text{−}{\mathrm{TaS}}_2$ grown on Au(111) lacks the charge density wave (CDW) instability exhibited by bulk $2H\text{−}{\mathrm{TaS}}_2$. Additionally, angle-resolved photoemission spectroscopy measurements suggest that the monolayer becomes strongly electron doped by the substrate. While density functional theory (DFT) calculations have shown that electron doping can suppress the CDW instability in monolayer $1H\text{−}{\mathrm{TaS}}_2$, it has been suggested that the actual charge transfer from the substrate may be much smaller than the apparent doping deduced from photoemission data. We present DFT calculations of monolayer $1H\text{−}{\mathrm{TaS}}_2$ on Au(111) to explore substrate effects beyond doping. We find that the CDW instability is suppressed primarily by strong S-Au interactions rather than by doping. The S-Au interaction results in a structural distortion of the ${\mathrm{TaS}}_2$ monolayer characterized by both lateral and out-of-plane atomic displacements and a $7\times 7$ periodicity dictated by the commensurate interface with Au. Simulated STM images of this $7\times 7$ distorted structure are consistent with experimental STM images. In contrast, we find a robust $3\times 3$ CDW phase in monolayer $1H\text{−}{\mathrm{TaS}}_2$ on a graphene substrate with which there is minimal interaction.

The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modeled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas Maxwell-Boltzmann molecules distribution of velocities at thermodynamic equilibrium. The calculation of the skyrmion configurational entropy, due to thermally induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. These results can be employed to advance the field of skyrmionics.

It has been suggested by theoretical works that equal-spin triplet pair correlations can be generated in Josephson junctions containing both a ferromagnet and a source of spin-orbit coupling. Our recent experimental work suggested that such triplet correlations were not generated by a Pt spin-orbit coupling layer when the ferromagnetic weak link had entirely in-plane anisotropy [Satchell and Birge, Phys. Rev. B 97, 214509 (2018)]. Here, we revisit the experiment using Pt again as a source for spin-orbit coupling and a ${\left[\mathrm{Co}\right(0.4\mathrm{nm})/\mathrm{Ni}(0.4\mathrm{nm}\left)\right]}_{\times 8}/\mathrm{Co}\left(0.4\mathrm{nm}\right)$ ferromagnetic weak link with both in-plane and out-of-plane magnetization components (canted magnetization). The canted magnetization more closely matches theoretical predictions than our previous experimental work. Our results suggest that there is no supercurrent contribution in our junctions from equal-spin triplet pair correlations. In addition, this work includes systematic study of supercurrent dependence on Cu interlayer thickness, a common additional layer used to buffer the growth of the ferromagnet and which for Co may significantly improve the growth morphology. We report that the supercurrent in the ${\left[\mathrm{Co}\right(0.4\mathrm{nm})/\mathrm{Ni}(0.4\mathrm{nm}\left)\right]}_{\times 8}/\mathrm{Co}\left(0.4\mathrm{nm}\right)$ ferromagnetic weak links can be enhanced by over two orders of magnitude by tuning the Cu interlayer thickness. This result has important application in superconducting spintronics, where large critical currents are desirable for devices.

We show that an in-plane Zeeman field applied to noncentrosymmetric Ising superconductors converts singlet $s$-wave Cooper pairs to equal-spin triplet $if$ pairs. Singlets are converted to triplets as spins originally polarized by spin-orbit interaction are reoriented by the Zeeman field. We demonstrate that the pairing in the triplet $f$ channel(s) decisively affects the critical field. While attraction enhances the critical field, repulsion suppresses it. The singlet to triplet conversion phenomenon has a geometrical origin, and the discussion applies universally to Ising superconductors with generic band structure such as, e.g., monolayer transition metal dichalcogenides.

The central approximation made in classical molecular dynamics simulation of materials is the interatomic potential used to calculate the forces on the atoms. Great effort and ingenuity is required to construct viable functional forms and find accurate parametrizations for potentials using traditional approaches. Machine learning has emerged as an effective alternative approach to develop accurate and robust interatomic potentials. Starting with a very general model form, the potential is learned directly from a database of electronic structure calculations and therefore can be viewed as a multiscale link between quantum and classical atomistic simulations. Risk of inaccurate extrapolation exists outside the narrow range of time and length scales where the two methods can be directly compared. In this work, we use the spectral neighbor analysis potential (SNAP) and show how a fit can be produced with minimal interpolation errors which is also robust in extrapolating beyond training. To demonstrate the method, we have developed a tungsten-beryllium potential suitable for the full range of binary compositions. Subsequently, large-scale molecular dynamics simulations were performed of high energy Be atom implantation onto the (001) surface of solid tungsten. The machine learned W-Be potential generates a population of implantation structures consistent with quantum calculations of defect formation energies. A very shallow ($<2\mathrm{nm}$) average Be implantation depth is predicted which may explain ITER diverter degradation in the presence of beryllium.

We study a model in (2 + 1)-dimensional space-time that is realized by an array of chains, each of which realizes relativistic Majorana fields in (1 + 1)-dimensional space-time, coupled via current-current interactions. The model is shown to have a lattice realization as an array of coupled quantum spin-1/2 ladders. We study this model both in the presence and in the absence of time-reversal symmetry within a mean-field approximation. We find regimes in coupling space where Abelian and non-Abelian spin-liquid phases are stable. In the case when the Hamiltonian is time-reversal symmetric, we find regimes where gapped Abelian and non-Abelian chiral phases appear as a result of spontaneous breaking of time-reversal symmetry. These gapped phases are separated by a discontinuous phase transition. More interestingly, we find a regime for which a nonchiral gapless non-Abelian spin liquid is stable. The excitations in this regime are described by relativistic Majorana fields in (2 + 1)-dimensional space-time, much as those appearing in the Kitaev honeycomb model but here emerging in a model of coupled spin ladders that do not break the $SU\left(2\right)$ spin-rotation symmetry.

The recently developed stochastic gradient method combined with Monte Carlo sampling techniques [W. Y. Liu et al., Phys. Rev. B 95, 195154 (2017)] offers a low scaling and accurate method to optimize the projected entangled pair states (PEPS). We extended this method to the fermionic PEPS (fPEPS). To simplify the implementation, we introduce a Fermi arrow notation to specify the order of the fermion operators in the virtual entangled EPR pairs. By defining some local operation rules associated with the Fermi arrows, one can implement fPEPS algorithms very similar to that of standard PEPS. We benchmark the method for the interacting spinless fermion models and the $t\text{−}J$ models. The numerical calculations show that the gradient optimization greatly improves the results of simple update method. Furthermore, very large virtual bond dimensions ($D$) and truncation dimensions ($D_c$) are necessary to converge the results of these models. The method therefore offers a powerful tool to simulate fermion systems because it has much lower scaling than the direct contraction methods.

Based on first-principles calculations and $k·p$ effective models, we report physical properties of ferroelectriclike hexagonal polar metals with $P{6}_{3}mc$ symmetry, which are distinct from those of conventional metals with spatial inversion symmetry. Spin textures exist on the Fermi surface of polar metals (e.g., ternary LiGaGe and elemental polar metal of Bi) and spin-momentum locking exist on accidental Dirac cones on the sixfold rotational axis, due to the spin-orbit coupling and lack of inversion symmetry in polar space group. This effect has potential applications in spin-orbitronics. Dirac points are also predicted in LiGaGe.

Magnesium in silicon primarily occupies an interstitial site, where it acts as a moderately deep double donor. It has recently been shown that interstitial magnesium can pair with the substitutional acceptor boron to form a shallow single-donor center. In this work, we demonstrate analogous complexing with the other group-III acceptors Ga, In, and Al. We observe the odd-parity excited states of each shallow donor complex in absorption spectra, from which the ionization energies are obtained. These complexes can localize excitons, and we observe the donor bound exciton transitions of all four centers in photoluminescence spectra. The Mg-acceptor complexes are found to obey Haynes rule, which predicts a linear relationship between donor ionization energy and donor bound exciton localization energy.

We theoretically investigate the impact of excited states on the dynamics of the exciton ground state in diluted magnetic semiconductor quantum wells. Exploiting the giant Zeeman shift in these materials, an external magnetic field is used to bring transitions between the exciton ground state and excited states close to resonance. It turns out that, when treating the exciton dynamics in terms of a quantum kinetic theory beyond the Markov approximation, higher exciton states are populated already well below the critical magnetic field required to bring the exciton ground state in resonance to an excited state. This behavior is explained by exciton-impurity correlations that can bridge energy differences on the order of a few meV and require a quantum kinetic description beyond the independent-particle picture. Of particular interest is the significant spin transfer toward states on the optically dark $2p$ exciton parabola which are protected against radiative decay.

We propose a physical mechanism to generate and selectively amplify anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between two local spins. The idea is to combine the deflection of the carrier velocity by a $p-n$ interface and the locking of this velocity to the carrier spin orientation via spin-orbit coupling. We provide analytical and numerical results to demonstrate this mechanism on the surface of a topological insulator $p-n$ junction. This work identifies the $p-n$ interface as a second knob which, together with the carrier density, enables independent control of the strength and anisotropy of the RKKY interaction over a wide range. These findings may be relevant to scalable quantum computation and two-impurity quantum criticality.

We study the pyrochlore series (${\mathrm{Eu}}_{1-x}{\mathrm{Bi}}_x{)}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ for $0\le x\le 1$. We show that for small $x$, the lattice undergoes an anomalous contraction but the time reversal symmetry breaking all-in/all-out state remains robust and the resistivity approaches a $1/T$ dependence at low $T$, suggesting proximity to the Weyl semimetallic phase. At the boundary near 10% Bi doping, a qualitatively different ground state emerges, which is characterized by a metallic behavior and the absence of magnetic ordering at least down to $0.02\mathrm{K}$. For higher Bi doping, the resistivity remains metallic, and evolves gradually from $T$ linear to $T^2$ to $T^{3/2}$, suggesting the possibilities of myriad different electronic phases between ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ and ${\mathrm{Bi}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$.

We study finite-temperature topological properties of the Kitaev's spin-honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate fermionization procedure to study the system as a two-band $p$-wave superconductor described by a Bogoliubov–de Gennes Hamiltonian. This allows us to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time-reversal symmetry. The introduction of such an external perturbation opens up a gap in the phase of the system characterized by non-Abelian statistics. The resulting model belongs to a symmetry-protected class, so that the Uhlmann number can be analyzed. We first consider the Berry curvature on a particular evolution line over the phase diagram. The mean Uhlmann curvature and the Uhlmann number are then analyzed by assuming a thermal state. The mean Uhlmann curvature describes a crossover effect as temperature rises. In the trivial phase, a nonmonotonic dependence of the Uhlmann number, as temperature increases, is reported and explained.

Dynamical mean-field theory (DMFT) is one of the most widely-used methods to treat accurately electron correlation effects in ab-initio real material calculations. Many modern large-scale implementations of DMFT in electronic structure codes involve solving a quantum impurity model with a continuous-time quantum Monte Carlo (CT-QMC) solver [Rubtsov et al., Phys. Rev. B 72, 035122 (2005); Werner et al., Phys. Rev. Lett. 97, 076405 (2006); Werner and Millis, Phys. Rev. B 74, 155107 (2006); Gull et al., Rev. Mod. Phys. 83, 349 (2011)]. The main advantage of CT-QMC is that, unlike standard quantum Monte Carlo approaches, it is able to generate the local Green's functions $G\left(\tau \right)$ of the correlated system on an arbitrarily fine imaginary time $\tau$ grid, and is free of any systematic errors. In this work, we extend a hybrid QMC solver proposed by Khatami et al. [Phys. Rev. E 81, 056703 (2010)] and Rost et al. [Phys. Rev. E 87, 053305 (2013)] to a multiorbital context. This has the advantage of enabling impurity solver QMC calculations to scale linearly with inverse temperature $\beta$, and permit its application to $d$- and $f$-band materials. In addition, we present a Green's-function processing scheme which generates accurate quasicontinuous imaginary time solutions of the impurity problem which overcome errors inherent to standard QMC approaches. This solver and processing scheme are incorporated into a full DFT+DMFT calculation using the castep DFT code [Clark et al., Z. Kristallogr. 220, 567 (2005)]. Benchmark calculations for ${\mathrm{SrVO}}_3$ properties are presented. The computational efficiency of this method is also demonstrated.

A recent observation of the thermal Hall effect of magnetic origin in underdoped cuprates calls for critical reexamination of low-energy magnetic dynamics in an undoped antiferromagnetic compound on square lattice, where traditional, renormalized spin-wave theory was believed to work well. Using the Holstein-Primakoff boson formalism, we find that magnon-based theories can lead to finite Berry curvature in the magnon band once the Dzyaloshinskii-Moriya spin interaction is taken into account explicitly, but fail to produce nonzero thermal Hall conductivity. Assuming accidental doping by impurities and magnon scattering off of such impurity sites fails to predict skew scattering at the level of the Born approximation. Local formation of skyrmion defects is also found incapable of generating the magnon thermal Hall effect. Turning to a spinon-based scenario, we write down a simple model by adding spin-dependent diagonal hopping to the well-known $\pi$-flux model of spinons. The resulting two-band model has a Chern number in the band structure, and generates thermal Hall conductivity whose magnetic field and temperature dependencies mimic closely the observed thermal Hall signals. In disclaimer, there is no firm microscopic basis of this model and we do not claim to have found an explanation of the data, but given the unexpected nature of the experimental observation, it is hoped this work could serve as a step towards reaching some level of understanding.

Quantum batteries are quantum-mechanical systems with many degrees of freedom which can be used to store energy and that display fast charging. The physics behind fast charging is still unclear. Is it just due to the collective behavior of the underlying interacting many-body system, or does it have its roots in the quantum-mechanical nature of the system itself? In this work we address these questions by studying three examples of quantum-mechanical many-body batteries with rigorous classical analogs. We find that the answer is model dependent and, even within the same model, depends on the value of the coupling constant that controls the interaction between the charger and the battery itself.

We demonstrate that the lead-free piezoelectric compound $\mathrm{N}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ (NBT) exhibits random lattice strain in the ferroelectric phase, and that this feature primarily dictates the way the system evolves towards the morphotropic phase boundary in the unpoled state of NBT-based piezoelectrics. Investigations on two different morphotropic phase boundary (MPB) systems, namely $\mathrm{N}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-{\mathrm{K}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ (NBT-KBT) and $\mathrm{N}{\mathrm{a}}_{0.5}\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3-\mathrm{BaTi}{\mathrm{O}}_3$ (NBT-BT), revealed that the coupled structural-polar evolution towards the MPB is primarily driven by the necessity to minimize this strain. Our study suggests that the random lattice strain originates in the random stacking of the in-phase tilt and antiphase octahedral tilted regions, and that the system is able to minimize it by adopting a sequential stacking of the two tilt types, leading to a long-period modulation in the octahedral tilt configuration over large parts of the sample volume. This hinders the development of long-range ferroelectric order as the MPB is approached. We also demonstrate that the composition showing the maximum piezoelectric coefficient corresponds to a structural state wherein considerable polar-structural disorder coexists with the field-stabilized long-range rhombohedral ferroelectric order after poling, and not coexistence of two ferroelectric phases (tetragonal and rhombohedral), generally believed.