We develop theory models for both ballistic and disordered superconducting monolayer black phosphorus devices in the presence of magnetic exchange field and stress. The ballistic case is studied through a microscopic Bogoliubov–de Gennes formalism, while for the disordered case we formulate a quasiclassical model. Utilizing the two models, we theoretically study the response of supercurrent to an externally applied magnetic field in two-dimensional black phosphorus Josephson junctions. Our results demonstrate that the response of the supercurrent to a perpendicular magnetic field in ballistic samples can deviate from the standard Fraunhofer interference pattern when the Fermi level and mechanical stress are varied. This finding suggests the combination of chemical potential and strain is an efficient external knob to control the current response in highly sensitive strain-effect transistors and superconducting quantum interference devices. We also study the supercurrent in a superconductor-ferromagnet-ferromagnet-superconductor junction where the magnetizations of the two adjacent magnetized regions are uniform with misaligned orientations. We show that the magnetization misalignment can control the excitation of harmonics higher than the first harmonic $sin\phi$ (in which $\phi$ is the phase difference between the superconductors) in supercurrent and constitutes a full-spin-switching current element. Finally, we discuss possible experimental implementations of our findings. We foresee our models and discussions could provide guidelines to experimentalists in designing devices and future investigations.

We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion $s$-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation between $s$-wave superconductivity and incommensurate spin-density waves (SDWs). At half filling, we find an intriguing phase where the magnetic ordering of the $f$-electrons lifts the degeneracy between the charge density wave (CDW) state and the superconducting state, leading to a strong suppression of superconductivity. In addition, the system may also become a half metal in this parameter regime. Away from half filling, the CDWs vanish and are replaced by superconductivity combined with incommensurate SDWs up to moderate Kondo couplings to the $f$-electrons. We find that both CDWs as well as superconductivity enhance magnetic ordering due to the suppression of Kondo screening.

An exciton-polariton microcavity that incorporates magnetic ions can exhibit spontaneous self-trapping phenomenon which is an analog of the classical polaron effect. We investigate in detail the full model of a polariton condensate that includes pumping and losses, the spin degree of freedom, external magnetic field, and energy relaxation. In the quasi-one-dimensional case, we show that the polaron effect can give rise to a spontaneous lattice of perfectly arranged polarization domains in an antiferromagnetic configuration. We find that partial polarization of the condensate at moderate magnetic field strengths facilitates formation of such “polaron lattices,” which are qualitatively different from self-trapped polarons that appear in a fully polarized condensate. Within Bogoliubov–de Gennes approximation, we calculate an instability condition which marks the appearance of patterns. Surprisingly, we find that the stability condition displays a discontinuity at the point of partial-full polarization threshold.

CO-terminated tips currently provide the best spatial resolution obtainable in atomic force microscopy. Due to their chemical inertness, they allow us to probe interactions dominated by Pauli repulsion. The small size and inertness of the oxygen front atom yields unprecedented resolution of organic molecules, metal clusters, and surfaces. We study the capability of CO-terminated tips to laterally manipulate single iron adatoms on the Cu(111) surface with combined atomic force and scanning tunneling microscopy at 7 K. We find that even a slight asymmetry of the tip results in a distortion of the lateral force field. In addition, the influence of the tilt of the CO tip on the lateral force field is reversed compared to the use of a monoatomic metal tip which we can attribute to the inverted dipole moment of a CO tip with respect to a metal tip. Moreover, we demonstrate atom-by-atom assembly of iron clusters with CO tips while using the high-resolution capability of the CO tips in between to determine the arrangement of the individual iron atoms within the cluster. In all conducted experiments using CO tips within this study, the CO was never changed or lost from the tip's apex.

The carrier capture from a two-dimensional transition metal dichalcogenide monolayer into a quasi-zero-dimensional potential is a decisive process to exploit these remarkable materials as, e.g., single-photon sources. Here, we study theoretically the phonon-induced carrier capture in a ${\mathrm{MoSe}}_2$ monolayer using a Lindblad single-particle approach. Although one decisive control parameter of the capture efficiency is the energy selection rule, which links the energy of the incoming carriers to that of the final state via the emitted phonon, we show that additionally the spatiotemporal dynamics plays a crucial role. By varying the direction of the incoming carriers with respect to the orientation of the localized potential, we introduce a new control mechanism for the carrier capture: the spatial control.

Understanding the molecular geometry at interfaces is not only of importance for optimizing contact properties but also sets the basis in energy alignment in multilayer samples. Here we present a method to determine the tilt angle of molecular compounds by a combination of the orbital imaging technique with photoemission matrix element calculations. By simulating different tilt angles of isolated molecules and comparing the resulting photoemission intensity distribution with momentum maps measured on molecular multilayers, one is able to determine the molecules' tilt angles for each separate layer independently from one another.

The conventional $\mathit{k}·\mathit{p}$ method fails to capture the full and essential physics of many symmetry enriched multiple nodal line structures in the three-dimensional Brillouin zone. Here, we present a systematical method to construct the effective lattice model of mirror symmetry protected three-dimensional multiple nodal line semimetals, when the spin-orbit interaction is ignored. For systems with a given pair of perpendicular nodal rings, we obtain all the effective lattice models and 11 inequivalent nodal line Fermi surfaces together with their related constraints. By means of first-principles calculations, we first propose a family of real materials, the $\beta$ phase of ternary nitrides $X_2{\mathrm{GeN}}_2$ ($X=\mathrm{Ca},\mathrm{Sr},\mathrm{Ba}$), that support one kind of these Fermi surfaces. Therefore, our work deepens the understanding of the nodal line structures and promotes the experimental progress of topological nodal line semimetals.

We report ab initio density functional theory calculation and Raman scattering results to explore the electronic structure of ${\mathrm{Ba}}_5{\mathrm{CuIr}}_3{\mathrm{O}}_{12}$ single crystals. This insulating iridate, consisting of face-sharing ${\mathrm{IrO}}_6$ octahedra forming quasi-one-dimensional chains, cannot be described by the local $j_{\mathrm{eff}}=1/2$ moment picture commonly adopted for discussing the electronic and magnetic properties of iridate compounds with ${\mathrm{IrO}}_6$ octahedra. The shorter Ir-Ir distance in the face-sharing geometry, compared to corner- or edge-sharing structures, leads to strong covalency between neighboring Ir. Then, this strong covalency results in the formation of molecular orbitals (MOs) at each Ir trimer as the low-energy electronic degree of freedom. The theoretically predicted three-peak structure in the joint density of states, a distinct indication of deviation from the $j_{\mathrm{eff}}=1/2$ picture, is verified by observing the three-peak structure in the electronic excitation spectrum by Raman scattering.

We report on a theoretical study of collective electronic excitations in single-layer antimony crystals (antimonene), a novel two-dimensional semiconductor with strong spin-orbit coupling. Based on a tight-binding model, we consider electron-doped antimonene and demonstrate that the combination of spin-orbit effects with an external bias gives rise to peculiar plasmon excitations in the midinfrared spectral range. These excitations are characterized by low losses and negative dispersion at frequencies effectively tunable by doping and bias voltage. The observed behavior is attributed to the spin splitting of the conduction band, which induces interband resonances, affecting the collective excitations. Our findings open up the possibility to develop plasmonic and optoelectronic devices with high tunability, operating in a technologically relevant spectral range.

We describe the quantum phase transition in the $N$-state chiral clock model in spatial dimension $d=1$. With couplings chosen to preserve time-reversal and spatial inversion symmetries, such a model is in the universality class of recent experimental studies of the ordering of pumped Rydberg states in a one-dimensional chain of trapped ultracold alkali atoms. For such couplings and $N=3$, the clock model is expected to have a direct phase transition from a gapped phase with a broken global ${\mathbb{Z}}_N$ symmetry, to a gapped phase with the ${\mathbb{Z}}_N$ symmetry restored. The transition has dynamical critical exponent $z\ne 1$, and so cannot be described by a relativistic quantum field theory. We use a lattice duality transformation to map the transition onto that of a Bose gas in $d=1$, involving the onset of a single-boson condensate in the background of a higher-dimensional $N$-boson condensate. We present a renormalization group analysis of the strongly coupled field theory for the Bose gas transition in an expansion in $2-d$, with $4-N$ chosen to be of order $2-d$. At two-loop order, we find a regime of parameters with a renormalization group fixed point which can describe a direct phase transition. We also present numerical density-matrix renormalization group studies of lattice chiral clock and Bose gas models for $N=3$, finding good evidence for a direct phase transition, and obtain estimates for $z$ and the correlation length exponent $\nu$.

A quantum quench is a nonequilibrium dynamics governed by the unitary evolution. We propose a two-band model whose quench dynamics is characterized by an arbitrary Hopf number belonging to the homotopy group ${\pi }_3\left(S^2\right)=\mathbb{Z}$. When we quench a system from an insulator with the Chern number $C_i\in {\pi }_2\left(S^2\right)=\mathbb{Z}$ to another insulator with the Chern number $C_f$, the preimage of the Hamiltonian vector forms links having the Hopf number $C_f-C_i$. We also investigate a quantum-quench dynamics for a four-band model carrying an arbitrary second Chern number $N\in {\pi }_4\left(S^4\right)=\mathbb{Z}$, which can be realized by quenching a three-dimensional topological insulator having the three-dimensional winding number $N\in {\pi }_3\left(S^3\right)=\mathbb{Z}$.

We investigate the optical absorption and transmission of few-layer phosphorene in the framework of ab initio density functional simulations and many-body perturbation theory at the level of random-phase approximation. In bilayer phosphorene, the optical transition of the valence band to the conduction band appears along the armchair direction at about 0.72 eV, while it is absent along the zigzag direction. This phenomenon is consistent with experimental observations. The angle-resolved optical absorption in few-layer phosphorene shows that it is transparent when illuminated by near-grazing incidence of light. Also, there is a general trend of an increase in the absorption by increasing the number of layers. Our results show that the bilayer phosphorene exhibits greater absorbance compared to that of bilayer graphene in the ultraviolet region. Moreover, the maximal peak in the calculated absorption of bilayer ${\mathrm{MoS}}_2$ is in the visible region, while bilayer graphene and phosphorene are transparent. In addition, the collective electronic excitations of few-layer phosphorene are explored. An optical mode (in-phase mode) that follows a low-energy $\sqrt{q}$ dependence for all structures and another which is a damped acoustic mode (out-of-phase mode) with linear dispersion for multilayer phosphorene are obtained. The anisotropy of the band structure of few-layer phosphorene along the armchair and zigzag directions is manifested in the collective plasmon excitations.

There are several approaches to the description of van der Waals (vdW) forces within density functional theory. While they are generally found to improve the structural and energetic properties of those materials dominated by weak dispersion forces, it is not known how they behave when the material is subject to an external pressure. This could be an issue when considering the pressure-induced structural phase transitions, which are currently attracting great attention following the discovery of an ultrahard phase formed by the compression of graphite at room temperature. In order to model this transition, the functional must be capable of simultaneously describing both strong covalent bonds and weak dispersion interactions as an isotropic pressure is applied. Here, we report on the ability of several dispersion-correction functionals to describe the energetic, structural, and elastic properties of graphite and diamond, when subjected to an isotropic pressure. Almost all of the tested vdW corrections provide an improved description of both graphite and diamond compared to the local density approximation. The relative error does not change significantly as pressure is applied, and in some cases even decreases. We therefore conclude that the use of dispersion-corrected exchange-correlation functionals, which have been neglected to date, will improve the accuracy and reliability of theoretical investigations into the pressure-induced phase transition of graphite.

We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to $L=100$ spins, i.e., much larger than $L\simeq 20$ that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent $\beta$ which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent ${\beta }_{\mathrm{\Lambda }}$ which characterizes the decay of a Schmidt gap in the entanglement spectrum; and (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder $W_c$ that separates the ergodic and many-body localized regimes, compared to the values of $W_c$ in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents $\beta$ and ${\beta }_{\mathrm{\Lambda }}$ increase, with increasing $L$, for relatively small $L$ but saturate for $L\simeq 50$, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the “learning by confusion” machine-learning approach that can determine $W_c$.

Identifying the symmetry of the wave function describing the Cooper pairs is pivotal in understanding the origin of high-temperature superconductivity in iron-based superconductors. Despite nearly a decade of intense investigation, the answer to this question remains elusive. Here, we use the muon spin rotation/relaxation ($\mu \mathrm{SR}$) technique to investigate the underlying symmetry of the pairing state of the FeSe superconductor, the basic building block of all iron-chalcogenide superconductors. Contrary to earlier $\mu \mathrm{SR}$ studies on powders and crystals, we show that while the superconducting gap is most probably anisotropic but nodeless along the crystallographic $c$ axis, it is nodal in the $ab$ plane, as indicated by the linear increase of the superfluid density at low temperature. We further show that the superconducting properties of FeSe display a less pronounced anisotropy than expected.

We use density functional calculations to investigate the accommodation and migration of oxygen vacancies in bulk hexagonal ${\mathrm{YMnO}}_3$, and to study interactions between neutral ferroelectric domain walls and oxygen vacancies. Our calculations show that oxygen vacancies in bulk ${\mathrm{YMnO}}_3$ are more stable in the Mn-O layers than in the Y-O layers. Migration barriers of the planar oxygen vacancies are high compared to oxygen vacancies in perovskites, and to previously reported values for oxygen interstitials in h-${\mathrm{YMnO}}_3$. The calculated polarization decreases linearly with vacancy concentration, while the out-of-plane lattice parameter expands in agreement with previous experiments. In contrast to ferroelectric perovskites, oxygen vacancies are found to be more stable in bulk than at domain walls. The tendency of oxygen vacancies to segregate away from neutral domain walls is explained by unfavorable Y-O bond lengths caused by the local strain field at the domain walls.

Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in $\alpha \text{−}{\mathrm{RuCl}}_3$ over a wide range of frequencies, magnetic fields, and temperatures, covering in particular the vicinity of the field-driven quantum phase transition where long-range magnetic order disappears. In addition to conventional gapped magnon modes we find a highly unusual broad continuum characteristic of fractionalization which—most remarkably—extends to energies below the lowest sharp mode and to temperatures significantly higher than the ordering temperature and develops a gap of a nontrivial origin in strong magnetic fields. Our results unravel the signatures of fractionalized excitations in $\alpha \text{−}{\mathrm{RuCl}}_3$ and pave the way to a more complete understanding of the Kitaev spin liquid and its instabilities.

Abelian and non-Abelian topological phases exhibiting protected chiral edge modes are ubiquitous in the realm of the fractional quantum Hall (FQH) effect. Here, we investigate a spin-1 Hamiltonian on the square lattice which could, potentially, host the spin liquid analog of the (bosonic) non-Abelian Moore-Read FQH state, as suggested by exact diagonalization of small clusters. Using families of fully SU(2)-spin symmetric and translationally invariant chiral projected entangled pair states (PEPS), variational energy optimization is performed using infinite-PEPS methods, providing good agreement with density matrix renormalization group (DMRG) results. A careful analysis of the bulk spin-spin and dimer-dimer correlation functions in the optimized spin liquid suggests that they exhibit long-range “gossamer tails”. From the investigation of the entanglement spectrum, we observe sharply defined chiral edge modes following the prediction of the SU(2)${}_2$ Wess-Zumino-Witten theory and exhibiting a conformal field theory (CFT) central charge $c=3/2$, as expected for a Moore-Read chiral spin liquid. Using the PEPS bulk-edge correspondence, we argue the “weak” criticality of the bulk is in fact a finite-$D$ artifact of the chiral PEPS, which quickly becomes (practically) irrelevant as the PEPS bond dimension $D$ is increased. We conclude that the PEPS formalism offers an unbiased and efficient method to investigate non-Abelian chiral spin liquids in quantum antiferromagnets.

The complete set of diagrams for conventional fluctuation corrections to the normal state of an ultraclean superconductor is derived using the functional-integral approach. The standard diagrams which characterize the fluctuation phase of a superconductor, namely, Aslamazov-Larkin, Maki-Thompson, and Density of States, are obtained and proved to be insufficient to produce a gauge-invariant electromagnetic response. An additional diagram is derived, and it is found to be essential for resolving a problematic and underappreciated aspect of the conventional fluctuation formalism. It is only with the inclusion of this additional diagram that the theory is now rendered gauge invariant and does not display a normal-state Meissner effect. It is shown that not only the Aslamazov-Larkin term but all of the microscopic diagrams are encapsulated within a Gaussian-level treatment of the effective action.

Rare-earth ion-doped crystals are promising systems for quantum communication and quantum information processing. In particular, paramagnetic rare-earth centers can be utilized to realize quantum coherent interfaces simultaneously for optical and microwave photons. In this paper, we study hyperfine and magnetic properties of a ${\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal doped with ${}^{171}\mathrm{Yb}^{3+}$ ions. This isotope is particularly interesting since it is the only rare–earth ion having electronic spin $S=\frac{1}{2}$ and nuclear spin $I=\frac{1}{2}$, which results in the simplest possible hyperfine level structure. In this work, we determine the hyperfine tensors for the ground and excited states on the optical ${}^2\mathrm{F}_{7/2}\left(0\right)⟷{}^2\mathrm{F}_{5/2}\left(0\right)$ transition by combining spectral hole burning and optically detected magnetic resonance techniques. The resulting spin Hamiltonians correctly predict the magnetic-field dependence of all observed optical-hyperfine transitions, from zero applied field up to fields where the Zeeman interaction is dominating the hyperfine interaction. Using the optical absorption spectrum, we can also determine the order of the hyperfine levels in both states. These results pave the way for realizing solid-state optical and microwave quantum memories based on a ${}^{171}\mathrm{Yb}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal.