We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of the hopping amplitude in the strong-coupling regime. We show that in this regime, accurate estimates for transition temperatures to the Néel ordered phase, in agreement with the predicted asymptotic behavior, can be deduced from the low-temperature magnetic structure factor. We also find evidence for possible instability to the magnetically ordered phase away from, but close to, half filling. Our results have important implications for parametrizing fermionic systems in optical lattice experiments and for benchmarking other numerical methods.

The influence of spin-orbit interactions on the Kondo effect has been under debate recently. Studies conducted recently on a system composed of an Anderson impurity on a two-dimensional electron gas with a Rashba spin orbit have shown that it can enhance or suppress the Kondo temperature $\left(T_{\mathrm{K}}\right)$, depending on the relative energy level position of the impurity with respect to the particle-hole symmetric point. Here, we investigate a system composed of a single Anderson impurity, side coupled to a quantum wire with spin-orbit coupling (SOC). We derive an effective Hamiltonian in which the Kondo coupling is modified by the SOC. In addition, the Hamiltonian contains two other scattering terms, the so-called Dzyaloshinskii-Moriya interaction, known to appear in these systems, and another one describing processes similar to the Elliott-Yafet scattering mechanisms. By performing a renormalization group analysis on the effective Hamiltonian, we find that the correction on the Kondo coupling due to the SOC favors the enhancement of the Kondo temperature even in the particle-hole symmetric point of the Anderson model, agreeing with the numerical renormalization group results. Moreover, away from the particle-hole symmetric point, $T_{\mathrm{K}}$ always increases with the SOC, accordingly with a previous renormalization group analysis.

We present calculations of the lattice constants, structural parameters, bulk moduli, energies of formation, and band structures of $\mathrm{Mg}-\mathrm{IV}-{\mathrm{N}}_2$ compounds with IV=Si, Ge, Sn by using the full-potential linearized muffin-tin orbital method and the quasiparticle-self-consistent $GW$ approach for the wurtzite-based $Pna{2}_1$ crystal structure. The lattice parameters calculated with the generalized gradient approximation (GGA) are found to be in good agreement (within 1%) with experiment for the cases of ${\mathrm{MgSiN}}_2$ and ${\mathrm{MgGeN}}_2$, where data are available. Similar to the Zn-IV-${\mathrm{N}}_2$ compounds, ${\mathrm{MgSiN}}_2$ is found to have an indirect gap slightly lower than the lowest direct gap, while the other materials have direct gaps. The direct gaps, calculated at the GGA lattice constant, range from 3.43 eV for ${\mathrm{MgSnN}}_2$ to 5.14 eV for ${\mathrm{MgGeN}}_2$ and 6.28 eV for ${\mathrm{MgSiN}}_2$ in the $0.8\mathrm{\Sigma }$ approximation, i.e., reducing the $\mathrm{QS}GW\mathrm{\Sigma }$ by a factor 0.8 and including an estimated zero-point-motion correction. The symmetry character of the valence-band maximum states and their splittings and effective masses are determined. The conduction-band minima are found to have slightly higher Mg $s$- than Si $s$-like character in ${\mathrm{MgSiN}}_2$ but in ${\mathrm{MgGeN}}_2$ and ${\mathrm{MgSnN}}_2$, the group-IV-$s$ character becomes increasingly dominant.

Point defects in diamond are of high interest as candidates for realizing solid state quantum bits, bioimaging agents, or ultrasensitive electric or magnetic field sensors. Various artificial diamond synthesis methods should introduce oxygen contamination in diamond, however, the incorporation of oxygen into diamond crystal and the nature of oxygen-related point defects are largely unknown. Oxygen may be potentially interesting as a source of quantum bits or it may interact with other point defects which are well established solid state qubits. Here we employ plane-wave supercell calculations within density functional theory, in order to characterize the electronic and magneto-optical properties of various oxygen-related defects. Besides the trivial single interstitial and substitutional oxygen defects we also consider their complexes with vacancies and hydrogen atoms. We find that oxygen defects are mostly electrically active and introduce highly correlated orbitals that pose a challenge for density functional theory modeling. Nevertheless, we are able to identify the fingerprints of substitutional oxygen defect, the oxygen-vacancy and oxygen-vacancy-hydrogen complexes in the electron paramagnetic resonance spectrum. We demonstrate that first principles calculations can predict the motional averaging of the electron paramagnetic resonance spectrum of defects that are subject to Jahn-Teller distortion. We show that the high-spin neutral oxygen-vacancy defect exhibits very fast nonradiative decay from its optical excited state that might hinder applying it as a qubit.

We have developed a technique for the detection of spin polarization with a quantum dot weakly coupled to an objective device. The disturbance to the object in this technique is very small since the detection is performed by sampling single electrons in the object at a very slow rate. We have applied the method to a quantum point contact (QPC) with a spin-orbit interaction. A high degree of spin polarization in the vicinity of the QPC was detected when the conductance stayed on a plateau at half of the unit conductance quantum $\left(G_{\mathrm{q}}/2\equiv e^2/h\right)$ and also on another plateau at $2e^2/h$. On the half-quantum plateau, the degree of polarization $P$ decreased with the bias source-drain voltage of the QPC, while $P$ increased on the single-quantum plateau, indicating that different mechanisms of polarization were working on these plateaus. Very long spin-relaxation times in the detector quantum dot possibly due to dynamical nuclear spin polarization were observed. An anomalous decrease of $P$ around zero bias was observed at a Kondo-like resonance peak.

We use an $s{p}^3{d}^5{s}^{*}$ tight-binding model to investigate the electronic and optical properties of realistic site-controlled (111)-oriented InGaAs/GaAs quantum dots. Special attention is paid to the impact of random alloy fluctuations on several factors that determine the fine-structure splitting in these systems. Using a pure InAs/GaAs quantum dot as a reference system, we show that the combination of spin-orbit coupling and biaxial strain effects can lead to sizable spin-splitting effects in these systems. Then, a realistic alloyed InGaAs/GaAs quantum dot with 25% InAs content is studied. Our analysis reveals that the impact of random alloy fluctuations on the electronic and optical properties of (111)-oriented InGaAs/GaAs quantum dots reduces strongly as the lateral size of the dot increases and approaches realistic sizes. For instance the optical matrix element shows an almost vanishing anisotropy in the (111)-growth plane. Furthermore, conduction and valence band mixing effects in the system under consideration are strongly reduced compared to standard (100)-oriented InGaAs/GaAs systems. All these factors indicate a reduced fine-structure splitting in site-controlled (111)-oriented InGaAs/GaAs quantum dots. Thus, we conclude that quantum dots with realistic (50–80 nm) base length represent promising candidates for polarization-entangled-photon generation, consistent with recent experimental data.

In our high mobility $p$-type AlGaAs/GaAs two-dimensional hole samples, we originally observe the $B$-periodic oscillation induced by microwave (MW) in photovoltage (PV) measurements. In the frequency range of our measurements (5–40 GHz), the period $\left(\mathrm{\Delta }B\right)$ is inversely proportional to the microwave frequency $\left(f\right)$. The distinct oscillations come from the edge magnetoplasmon (EMP) in the high quality heavy hole system. Simultaneously, we observe the giant plasmon resonance signals in our measurements on the shallow two-dimensional hole system (2DHS).

Layered structures of molybdenum disulfide $\left({\mathrm{MoS}}_2\right)$ belong to a new class of two-dimensional (2D) semiconductor materials in which monolayers exhibit a direct band gap in their electronic spectrum. This band gap has recently been shown to vanish due to the presence of metallic edge modes when ${\mathrm{MoS}}_2$ monolayers are terminated by zigzag edges on both sides. Here, we demonstrate that a zigzag nanoribbon of ${\mathrm{MoS}}_2$, when exposed to an external exchange field in combination with a transverse electric field, has the potential to exhibit a peculiar half-metallic nature and thereby allows electrons of only one spin direction to move. The peculiarity of such spin-selective conductors originates from a spin switch near the gap-closing region, so the allowed spin orientation can be controlled by means of an external gate voltage. It is shown that the induced half-metallic phase is resistant to random fluctuations of the exchange field as well as the presence of edge vacancies.

We used ab initio random structure searching (AIRSS) to investigate polymorphism in ${\mathrm{C}}_3{\mathrm{N}}_4$ carbon nitride as a function of pressure. Our calculations reveal new framework structures, including a particularly stable chiral polymorph of space group $P{4}_3{2}_{1}2$ containing mixed $s{p}^2$ and $s{p}^3$ bonding, that we have produced experimentally and recovered to ambient conditions. As pressure is increased a sequence of structures with fully $s{p}^3$-bonded C atoms and three-fold-coordinated N atoms is predicted, culminating in a dense $Pnma$ phase above 250 GPa. Beyond 650 GPa we find that ${\mathrm{C}}_3{\mathrm{N}}_4$ becomes unstable to decomposition into diamond and pyrite-structured ${\mathrm{CN}}_2$.

We report on the linear optical properties of the chiral magnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$, specifically associated with the absence of inversion symmetry, the chiral crystallographic structure, and magnetic order. Through spectroscopic ellipsometry, we observe local crystal-field excitations below the charge-transfer gap. These crystal-field excitations are optically allowed due to the lack of inversion symmetry at the Cu sites. Optical polarization rotation measurements were used to study the structural chirality and magnetic order. The temperature dependence of the natural optical rotation, originating in the chiral crystal structure, provides evidence for a finite magnetoelectric effect in the helimagnetic phase. We find a large magneto-optical susceptibility on the order of $\mathcal{V}\left(540\mathrm{nm}\right)\sim {10}^4\mathrm{rad}/\mathrm{T}\mathrm{m}$ in the helimagnetic phase and a maximum Faraday rotation of $\sim 170\mathrm{deg}/\mathrm{mm}$ in the ferrimagnetic phase. The large value of $\mathcal{V}$ can be explained by considering spin cluster formation and the relative ease of domain reorientation in this metamagnetic material. The magneto-optical activity allows us to map the magnetic phase diagram, including the skyrmion lattice phase. In addition to this, we probe and discuss the nature of the various magnetic phase transitions in ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$.

We present a diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. While a gauge-invariant electromagnetic response is well understood at the BCS level, a treatment of correlations beyond BCS theory requires extending this theoretical formalism. The challenge in such systems is to maintain gauge invariance, while simultaneously incorporating additional self-energy terms arising from strong correlation effects. Central to our approach is the application of the Ward-Takahashi identity, which introduces collective mode contributions in the response functions and guarantees that the $f$-sum rule is satisfied. We outline a powerful method, which determines these collective modes in the presence of correlation effects and in a manner compatible with gauge invariance. Since this method is based on fundamental aspects of quantum field theory, the underlying principles are broadly applicable to strongly correlated superfluids. As an illustration of the technique, we apply it to a simple class of theoretical models that contain a frequency-independent order parameter. These models include BCS-BEC crossover theories of the ultracold Fermi gases, along with models specifically associated with the high-$T_c$ cuprates. Finally, as an alternative approach, we contrast with the path integral formalism. Here, the calculation of gauge-invariant response appears more straightforward. However, the collective modes introduced are those of strict BCS theory, without any modification from additional correlations. As the path integral simultaneously addresses electrodynamics and thermodynamics, we emphasize that it should be subjected to a consistency test beyond gauge invariance, namely that of the compressibility sum rule. We show how this sum rule fails in the conventional path integral approach.

Vortex core polarity switching in NiFe disks has been evidenced using an all-electrical magnetoresistive rectification scheme. Simulation and experiments yield a consistent rectified signal loss when driving core gyration at high powers. With increasing power, the frequency range over which the loss occurs grows and the resonance downshifts in frequency, consistent with nonlinear core dynamics and periodic core polarity switching induced by the core reaching its critical velocity. Core-polarity-dependent rectification signals enable an independent verification of the switched core polarity. We also demonstrate the ability to impede core polarity switching by displacing the core towards the disk's edge where an increased core stiffness reduces the core velocity.

Multilayered Josephson junctions are modeled in the context of a field theory, and dynamics of Josephson vortices trapped inside insulators are studied. Starting from a theory consisting of complex and real scalar fields coupled to a U(1) gauge field which admit parallel $N-1$ domain-wall solutions, Josephson couplings are introduced weakly between the complex scalar fields. The $N-1$ domain walls behave as insulators separating $N$ superconductors, where one of the complex scalar fields has a gap. We construct the effective Lagrangian on the domain walls, which reduces to a coupled sine-Gordon model for well-separated walls and contains more interactions for walls at short distance. We then construct sine-Gordon solitons emerging in an effective theory in which we identify Josephson vortices carrying singly quantized magnetic fluxes. When two neighboring superconductors tend to have the same phase, the ground state does not change with the positions of domain walls (the width of superconductors). On the other hand, when two neighboring superconductors tend to have $\pi$-phase differences, the ground state has a phase transition depending on the positions of domain walls; when the two walls are close to each other (one superconductor is thin), frustration occurs because of the coupling between the two superconductors besides the thin superconductor. Focusing on the case of three superconductors separated by two insulators, we find for the former case that the interaction between two Josephson vortices on different insulators changes its nature, i.e., attractive or repulsive, depending on the positions of the domain walls. In the latter case, there emerges fractional Josephson vortices when two degenerate ground states appear due to spontaneous charge-symmetry breaking, and the number of the Josephson vortices varies with the position of the domain walls. Our predictions should be verified in multilayered Josephson junctions.

An existing conjecture states that the Shannon mutual information contained in the ground-state wave function of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the von Neumann entanglement entropy, depends on the value of the central charge of the underlying conformal field theory describing the physical properties. This conjecture applies whenever the ground-state wave function is expressed in some special basis (conformal basis). Its formulation comes mainly from numerical evidences on exactly integrable quantum chains. In this paper, the above conjecture was tested for several general nonintegrable quantum chains. We introduce new families of self-dual $Z\left(Q\right)$ symmetric quantum chains $\left(Q=2,3,...\right)$. These quantum chains contain nearest-neighbor as well next-nearest-neighbor interactions (coupling constant $p)$. In the cases $Q=2$ and $Q=3$, they are extensions of the standard quantum Ising and three-state Potts chains, respectively. For $Q=4$ and $Q\ge 5$, they are extensions of the Ashkin-Teller and $Z\left(Q\right)$ parafermionic quantum chains. Our studies indicate that these models are interesting on their own. They are critical, conformally invariant, and share the same universality class in a continuous critical line. Moreover, our numerical analysis for $Q=2–8$ indicate that the Shannon mutual information exhibits the conjectured behavior irrespective if the conformally invariant quantum chain is exactly integrable or not. For completeness we also calculated, for these new families of quantum chains, the two existing generalizations of the Shannon mutual information, which are based on the Rényi entropy and on the Rényi divergence.

An approach is proposed for evaluating dipolar and multipolar intersite interactions in strongly correlated materials. This approach is based on the single-site dynamical mean-field theory (DMFT) in conjunction with the atomic approximation for the local self-energy. Starting from the local-moment paramagnetic state described by DMFT, we derive intersite interactions by considering the response of the DMFT grand potential to small fluctuations of atomic configurations on two neighboring sites. The present method is validated by applying it to one-band and two-band $e_g$ Hubbard models on the simple-cubic $3d$ lattice. It is also applied to study the spin-orbital order in the parent cubic structure of ternary chromium fluoride ${\mathrm{KCrF}}_3$. We obtain the onset of a G-type antiferro-orbital order at a significantly lower temperature compared to that in real distorted ${\mathrm{KCrF}}_3$. In contrast, its layered A-type antiferromagnetic order and Néel temperature are rather well reproduced. The calculated full Kugel-Khomskii Hamiltonian contains spin-orbital coupling terms inducing a misalignment in the antiferro-orbital order upon the onset of antiferromagnetism.

The electronic properties of pristine and compressed bulk black phosphorus (BP) in the presence of a magnetic field perpendicular to a BP monolayer are investigated by using the tight-binding Hamiltonian model. Similar to that of graphite, the magnetic field can induce the flat, partially flat, and oscillatory Landau levels (LLs) in both kinds of BP, although there exist many distinct properties different from graphite, such as the oscillatory LL positions and the LL spacings. Also, the LLs exhibit richer dependences on the LL index, including a quadratic (linear) function of the LL index for the small (big) LL index. Furthermore, the topological node-line semimetal state in compressed BP caused by the strain is found to be sensitive to the magnetic field, indicating that even a very weak magnetic field is enough to break the node-line state. Meanwhile, it is shown that the strain can almost uniformly increase the LL spacing for the conductance band, while a different and complex LL spacing variation is observed for the valence band.

An expression is derived for angle-resolved photocurrent from a semi-infinite correlated system. Within the sudden approximation, the photocurrent is proportional to the spectral function of a one-particle two-time retarded Green's function $\mathcal{G}$ of an operator that creates an electron in a special quantum state $\chi$ localized at the surface. For a system described by a many-body single-band model, we present an analytical expression that relates the Green's function $\mathcal{G}$ with the Green's function of an infinite crystal $G_{b,\mathbf{k}}\left(\omega \right)$ in Wannier representation. The role of final states and of the crystal surface is analyzed for a model Green's function of the infinite crystal with a three-peak spectral function typical of a Mott-Hubbard metal. The momentum dependences of both the quasiparticle pole position and the spectral weight of the incoherent band manifest themselves in the shape of the photocurrent energy distribution curve.

We present detailed analytic calculations of finite-volume energy spectra, mean-field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. An emergent approximate spontaneously broken $\text{SO}\left(2\right)$ symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phononlike excitation, which is massless at the Rokhsar-Kivelson (RK) point, exists far beyond this point. The Goldstone physics is captured by a systematic low-energy effective field theory. We determine its low-energy parameters by matching the analytic effective field theory with exact diagonalization results. This confirms that the model exists in the columnar (and not in a plaquette or mixed) phase all the way to the RK point.

Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled Landau level (LL) was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CFs). One of the main consequences is the existence of anisotropic states in single-layer and bilayer systems, which was previously suggested in Jeong and Park [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We argue that in the half-filled LL in the single-layer case the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with the addition of a particle-hole symmetry-breaking mass term may evolve into rotationally symmetric states, i.e., Pfaffian states of Halperin-Lee-Read (HLR) ordinary CFs. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling factor 1, with decreasing distance between the layers, weak pairing of $p$-wave paired CFs is gradually transformed from Dirac to ordinary, HLR-like, with a concomitant decrease in the CF number. Global characterization of low-energy spectra based on the Dirac CFs agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of the Dirac formalism when applied in this context.