We study a periodic arrangement of magnetic regions in a quasi-one-dimensional superconducting wire. Due to the local exchange field, each region supports Andreev bound states that hybridize, forming Bloch bands in the subgap spectrum of what we call the Andreev crystal (AC). As an illustration, ACs with ferromagnetic and antiferromagnetic alignment of the magnetic regions are considered. We relate the spectral asymmetry index of a spin-resolved Hamiltonian to the spin polarization and identify it as the observable that quantifies the closing and reopening of the excitation gap. In particular, antiferromagnetic ACs exhibit a sequence of gapped phases separated by gapless Dirac phase boundaries. Heterojunctions between antiferromagnetic ACs in neighboring phases support spin-polarized bound states at the interface. In close analogy to the charge fractionalization in Dirac systems with a mass inversion, we find a fractionalization of the interface spin.

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend on a choice of unitary transform known as a gauge transformation. Over the past few decades, there have been many works that have focused on optimizing the choice of the gauge so that the corresponding Wannier functions are maximally localized or reflect some symmetry of the underlying system. In this work, we consider fully nonperiodic materials where the usual Wannier functions are not well defined and gauge optimization is impractical. To tackle the problem of calculating exponentially localized generalized Wannier functions in both periodic and nonperiodic systems, we discuss the ‘iterated projected position (IPP)” algorithm. The IPP algorithm is based on matrix diagonalization and therefore unlike optimization-based approaches, it does not require initialization and cannot get stuck at a local minimum. Furthermore, the IPP algorithm is guaranteed by a rigorous analysis to produce exponentially localized functions under certain mild assumptions. We numerically demonstrate that the IPP algorithm can be used to calculate exponentially localized bases for the Haldane model, the Kane-Mele model (in both ${\mathbb{Z}}_2$ invariant even and ${\mathbb{Z}}_2$ invariant odd phases), and the $p_x+i{p}_y$ model on a quasicrystal lattice.

Bulk-boundary correspondence, connecting the bulk topology and the edge states, is an essential principle of the topological phases. However, the conventional bulk-boundary correspondence is broken down in general non-Hermitian systems. In this paper, we construct a one-dimensional non-Hermitian Su-Schrieffer-Heeger model with periodic driving that exhibits the non-Hermitian skin effect: all the eigenstates are localized at the boundary of the systems, whether they are the bulk states or the zero and the $\pi$ modes. To capture the topological properties, the non-Bloch winding numbers are defined by the non-Bloch periodized evolution operators based on the generalized Brillouin zone. Furthermore, the non-Hermitian bulk-boundary correspondence is established: the non-Bloch winding numbers $\left(W_{0,\pi }\right)$ characterize the edge states with quasienergies $\epsilon =0,\pi$. In our non-Hermitian system, a novel phenomenon can emerge: the robust edge states can appear even when the Floquet bands are topological trivial with zero non-Bloch band invariant, which is defined in terms of the non-Bloch effective Hamiltonian. We also show the relation between the non-Bloch winding numbers $\left(W_{0,\pi }\right)$ and the non-Bloch band invariant $\left(\mathcal{W}\right)$: $\mathcal{W}=W_0-W_{\pi }$.

We study the two-dimensional $t\text{−}J$ model on a square lattice using infinite projected entangled pair states (iPEPS). At small doping, multiple orders, such as antiferromagnetic order, stripe order and superconducting order, are intertwined or compete with each other. We demonstrate the role of spin symmetry at small doping by either imposing SU(2) spin symmetry or its U(1) subgroup in the iPEPS ansatz, thereby excluding or allowing spontaneous spin-symmetry breaking, respectively, in the thermodynamic limit. From a detailed comparison of our simulations, we provide evidence that stripe order is pinned by long-range antiferromagnetic order. We also find SU(2) iPEPS, enforcing a spin-singlet state, yields a uniform charge distribution and favors d-wave singlet pairing.

We study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase (strong tension). We analyze the behavior of all Wegner-Wilson loops in both limiting cases for an arbitrary input theory of the string-net model. Using a fluxon picture, we compute perturbatively the first contributions to a perimeter law in the topological phase as a function of the quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops obey a modified area law, in agreement with a recent mean-field approach.

We develop the theory of collective modes supported by a Fermi liquid of electrons in pristine graphene. Under reasonable assumptions regarding the electron-electron interaction, all the modes but the plasmon are overdamped. In addition to the $SU\left(2\right)$-symmetric spin mode, these include also the valley imbalance modes obeying a $U\left(1\right)$ symmetry, and a $U\left(2\right)$-symmetric valley spin imbalance mode. We derive the interactions and diffusion constants characterizing the overdamped modes. The corresponding relaxation rates set fundamental constraints on graphene valley- and spintronics applications.

Spontaneous orbital magnetism observed in twisted bilayer graphene (tBG) on nearly aligned hexagonal boron nitride (BN) substrate builds on top of the electronic structure resulting from combined G/G and G/BN double moiré interfaces. Here we show that tBG/BN commensurate double moiré patterns can be classified into two types, each favoring the narrowing of either the conduction or the valence bands on average, and obtain the evolution of the bands as a function of the interlayer sliding vectors and electric fields. Finite valley Chern numbers $\pm 1$ are found in a wide range of parameter space when the moiré bands are isolated through gaps, whereas the local density of states associated with the flatbands are weakly affected by the BN substrate invariably concentrating around the AA-stacked regions of tBG. We illustrate the impact of the BN substrate for a particularly pronounced electron-hole asymmetric band structure by calculating the optical conductivities of twisted bilayer graphene near the magic angle as a function of carrier density. The band structures corresponding to other $N$-multiple commensurate moiré period ratios indicate it is possible to achieve a narrow width of $W\lesssim 30\text{−}\mathrm{meV}$ isolated folded band bundles for tBG angles $\theta \lesssim 1^{\circ }$.

We analyze the thermoelectric response of Dirac and Weyl semimetals using the semiclassical approach, focusing on the extrinsic contributions due to skew-scattering and side jump. Our results apply to the linear response Nernst effect in ferromagnetic Dirac materials such as ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ and Weyl semimetals like ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. In the case of ${\mathrm{Fe}}_3{\mathrm{Sn}}_2$ we obtain a very good agreement with known experimental anomalous Hall effect measurements, and based on that we predict a large Nernst effect in this material. We also extend the investigation to second-order response, focusing on monolayer graphene on hBN with trigonal warping as an example. Our analysis indicates that the extrinsic contributions can be a significant component of anomalous Nernst response and may be used to explain an enhanced thermoelectric response.

The observation of a metallic interface between band insulators $\mathrm{La}\mathrm{Al}{\mathrm{O}}_3$ and $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ has led to massive efforts to understand the origin of the phenomenon as well as to search for other systems hosting such two-dimensional electron gases (2-DEGs). However, the understanding of the origin of the 2-DEG is very often hindered as several possible mechanisms such as polar catastrophe, cationic intermixing, and oxygen vacancy (OV) can be operative simultaneously. The presence of a heavy element makes the $\mathrm{K}\mathrm{Ta}{\mathrm{O}}_3$ (KTO) based 2-DEG a potential platform to investigate spin-orbit coupling driven novel electronic and magnetic phenomena. In this work, we investigate the sole effect of OV in KTO, which makes KTO metallic. O $K$-edge x-ray absorption spectroscopy measurements find that OV dopes electrons in Ta $t_{2g}^{*}$ antibonding states. Photoluminescence measurements reveal the existence of a highly localized deep midgap state in oxygen-deficient KTO. Our detailed ab initio calculations demonstrate that such deep midgap state arises due to the linear clustering of OVs around Ta. Our present work emphasizes that we must pay attention to the possible presence of OVs in interpreting emergent behavior of KTO-based heterostructures.

Controlling electronic band structure is an important step toward harnessing quantum materials for practical uses. This is exemplified in the spin-polarized bands near the Fermi level of a ferromagnet where small variation to the Berry curvature can be used to control the intrinsic anomalous Hall effect (AHE). Since these pathways are highly sensitive to crystal structure, iterative post-synthesis manipulation of the underlying lattice can act as a fundamental probe and provide new opportunities for functionalization. In this work, depth-dependent magnetic inhomogeneity in a $4d$ itinerant ferromagnet ${\mathrm{SrRuO}}_3$ film is controlled by applying low energy He ion irradiation. Combined magnetometry, polarized neutron reflectometry, and magnetotransport experiments demonstrate that the Berry phase and associated AHE can be continuously and iteratively modified post-synthesis. The findings of this work should be widely applicable to other quantum materials where crystal distortions and symmetry are tightly bound to band structure and resulting Berry phase effects.

We study the phase transitions of bosonic $\nu =1/2$ fractional quantum Hall (FQH) effect in different topological lattice models under the interplay of onsite periodic potential and Hubbard repulsion. Through exact diagonalization and density matrix renormalization group methods, we demonstrate that the many-body ground state undergoes a continuous phase transition between bosonic FQH liquid and a trivial (Mott) insulator induced by the periodic potential, characterized by the smooth crossover of energy and entanglement entropy. When the Hubbard repulsion decreases, we claim that this bosonic FQH liquid would turn into a superfluid state with a direct energy level crossing and a discontinuous leap of off-diagonal long-range order.

We present a density-functional theory analysis of nitrogen-vacancy (NV) centers in diamond, which are located in the vicinity of extended defects, namely, intrinsic stacking faults, extrinsic stacking faults, and coherent twin boundaries on {111} planes in diamond crystals. Several sites for NV centers close to the extended defects are energetically preferred with respect to the bulk crystal. This indicates that NV centers may be enriched at extended defects. We report the hyperfine structure and zero-field splitting parameters of the NV centers at the extended defects, which typically deviate by about 10% but in some cases up to 90% from their bulk values. Furthermore, we find that the influence of the extended defects on the NV centers is of short range: NV centers that are about three double layers (corresponding to $\approx 6\text{Å}$) away from defect planes already show bulklike behavior.

Exact solutions to diffraction problems in wave optics are scarce though strongly demanded for accurate knowledge of electromagnetic fields in the immediate vicinity of scatterers. Here, we obtain and analyze an exact analytical solution for plane-wave diffraction at a lateral junction of two-dimensional (2D) conductors with dissimilar surface conductivities. We find that the junction near fields possesses a dipolelike radiative component and 2D surface-plasmon polaritons launched by the edge. We show that a junction between a perfect metal and an ohmic 2D conductor enhances the local absorbance, which is the ratio of absorbed power density and light intensity. It reaches a universal value of 200% near the 2D edge at normal incidence, independent of absorbance in the bulk. A junction between metal and a 2D conductor also acts as an efficient coupler between photons and 2D plasmons. Its amplitude conversion efficiency demonstrates an unbounded growth with increase in 2D impedance. Our results set the fundamental limits for field enhancement by edges and should change the strategies for design of subwavelength radiation detectors.

Materials that integrate magnetism, miniaturization, and valley properties hold potential for spintronic and valleytronic nanodevices. Recently, ferromagnetism was reported to be able to exist in the $\mathrm{V}{\mathrm{Si}}_2{\mathrm{N}}_4$ monolayer which is half-metallic and belongs to a new kind of two-dimensional material [Hong et al., Science 369, 670 (2020)]. Using first-principles calculations and model analysis, we find that $\mathrm{V}{\mathrm{Si}}_2{\mathrm{N}}_4$ is a ferromagnetic semiconductor harboring valley-contrasting physics and a magnetic critical temperature over room temperature. By tuning magnetization orientation from in plane to out of plane, valley polarization can be generated, resulting in the anomalous valley Hall effect in $\mathrm{V}{\mathrm{Si}}_2{\mathrm{N}}_4$. Furthermore, we obtain the formula for energy splitting of valleys and adopt a tight-binding model for $\mathrm{V}{\mathrm{Si}}_2{\mathrm{N}}_4$, which elucidates the physical mechanism of spin-valley coupling. More interestingly, under 4% tensile strain, the intrinsic magnetic anisotropy of $\mathrm{V}{\mathrm{Si}}_2{\mathrm{N}}_4$ becomes out of plane, and spontaneous valley polarization is achieved. Our results highlight that $\mathrm{V}{\mathrm{Si}}_2{\mathrm{N}}_4$ is a good candidate for spintronic and valleytronic applications.

The breaking of the vertical symmetry in Janus monochalcogenides gave rise to many properties that were not present in the original monochalcogenide monolayers. However, recent papers have often focused only on Janus monochalcogenides containing S, Se, and Te elements despite that O is also one of the group VI chalcogen elements. In this paper, we systematically investigate the electronic, transport, optical, and thermoelectric properties of Janus monolayers ${\mathrm{In}}_{2}X\mathrm{O}$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$) using first-principles calculations. Based on phonon spectrum analysis and ab initio molecular dynamics simulations at room temperature, ${\mathrm{In}}_{2}X\mathrm{O}$ monolayers were reported to be stable. Our calculations reveal that, while ${\mathrm{In}}_2\mathrm{SO}$ is an indirect semiconductor, ${\mathrm{In}}_2\mathrm{SeO}$ exhibits a direct semiconducting characteristic, and biaxial strain can lead to the semiconductor-metal phase transition in ${\mathrm{In}}_2\mathrm{SeO}$. Monolayer ${\mathrm{In}}_2\mathrm{TeO}$ is metal at equilibrium, and its metallic characteristics are prevented under biaxial strains. Calculations for transport properties show that the carrier mobilities of ${\mathrm{In}}_2\mathrm{SO}$ and ${\mathrm{In}}_2\mathrm{SeO}$ monolayers are highly anisotropic, and electron mobility of ${\mathrm{In}}_2\mathrm{SO}$ exceeds $3\times {10}^3{\mathrm{cm}}^2/\mathrm{Vs}$. In this paper, the optical and thermoelectric properties of ${\mathrm{In}}_2\mathrm{SO}$ and ${\mathrm{In}}_2\mathrm{SeO}$ monolayers are also investigated and discussed in detail. Finally, the electronic properties of all four possible stacking configurations of the Janus bilayers are briefly calculated. Our findings not only contribute to a more general view of the physical properties of the Janus group III monochalcogenides but also recommend them as potential nanomaterials for applications in optoelectronic and thermal devices.

We report that the occurrence of a Kondo effect in magnetic molecules crucially depends on the point symmetry and oxidation state of the adsorbed species. Two different transition metal acetylacetonate (acac) compounds [$M{\left(\mathrm{acac}\right)}_3$, with $M=\mathrm{Cr}\left(\mathrm{III}\right)$ or Co(III)] adsorbed on a Cu(111) single crystal were investigated to demonstrate the interplay. After deposition, $\mathrm{Cr}{\left(\mathrm{acac}\right)}_3$ molecules formed threefold symmetric $\mathrm{Cr}{\left(\mathrm{acac}\right)}_3$ and twofold symmetric $\mathrm{Cr}{\left(\mathrm{acac}\right)}_2$ by releasing a ligand, while $\mathrm{Co}{\left(\mathrm{acac}\right)}_3$ molecules only formed twofold symmetric $\mathrm{Co}{\left(\mathrm{acac}\right)}_2$. Threefold symmetric $\mathrm{Cr}{\left(\mathrm{acac}\right)}_3$ molecules with a total electron spin $S=\frac{3}{2}$ exhibited no Kondo effect, while a clear Kondo resonance was observed in twofold $\mathrm{Cr}{\left(\mathrm{acac}\right)}_2$ molecules. $\mathrm{Co}{\left(\mathrm{acac}\right)}_2$ molecules surprisingly showed no Kondo resonance, even in the case of twofold symmetry, which is explained by a low-spin state of $S$ = 0. To analyze the results, a simple model is proposed based on the total electron spin and the symmetry of magnetic molecule. The present approach provides a feasible design strategy for single molecule magnets on metallic surfaces.

The surface of a glassy material exhibits enhanced mobility compared to the bulk counterpart, however the underlying mechanism for this remains elusive. Herein, we present studies of the dynamical properties of a prototypical glass-forming metallic liquid ${\mathrm{Zr}}_{50}{\mathrm{Cu}}_{50}$ as a function of the distance from both the free surface and pinned surface using molecular dynamics simulations. We found that the surface mobility increases gradually on approaching the free surface, with a concomitant increase of the non-Gaussianity. The phonon density of states at the free surface exhibits lower characteristic frequencies than in the bulk and pinned surface. These results suggest phonon softening caused by anisotropic fluctuations at free surfaces as an alternative physical mechanism leading to the enhanced dynamics at free glassy surfaces from the perspective of collective excitations.

First-principles calculations are conducted to compute linear magnetoelectric coupling coefficients in epitaxial (001) ${\mathrm{Sr}}_{0.5}{\mathrm{Ba}}_{0.5}{\mathrm{MnO}}_3$ films. A large enhancement of different linear magnetoelectric elements is found in a strained-induced morphotropic phase boundary region. Such enhancement is demonstrated to originate from the behavior of the dielectric susceptibility, thanks to a simple phenomenological model that is presently shown to be relevant and accurate. This work can thus provide a promising approach towards designing highly desired single-phase multiferroic with a colossal magnetoelectric conversion.

We find that a flat-band fermion system with interactions and without disorders exhibits nonthermalized ergodicity-breaking dynamics, an analog of many-body localization (MBL). In the previous works we observed flat-band many-body localization (FMBL) in the Creutz ladder model. The origin of FMBL is a compact localized state governed by local integrals of motion (LIOMs), which are to be obtained explicitly. In this work we clarify the dynamical aspects of FMBL. We first study dynamics of two particles, and find that the states are not substantially modified by weak interactions, but the periodic time evolution of entanglement entropy emerges as a result of a specific mechanism inherent in the system. On the other hand, as the strength of the interactions is increased, the modification of the states takes place with inducing instability of the LIOMs. Furthermore, many-body dynamics of the system at finite fillings is numerically investigated by the time-evolving block decimation (TEBD) method. For a suitable choice of the filling, nonthermal and low entangled dynamics appears. This behavior is a typical example of the disorder-free FMBL.

We report the results of muon-spin spectroscopy $\left({\mu }^{+}\mathrm{SR}\right)$ measurements on the staggered molecular spin chain [pym-$\mathrm{Cu}{\left({\mathrm{NO}}_3\right)}_2{\left({\mathrm{H}}_2\mathrm{O}\right)}_2]$ (pym = pyrimidine), a material previously described using sine-Gordon field theory. Zero-field ${\mu }^{+}\mathrm{SR}$ reveals a long range magnetically ordered ground state below a transition temperature $T_{\mathrm{N}}=0.23\left(1\right)$ K. Using longitudinal-field (LF) ${\mu }^{+}\mathrm{SR}$ we investigate the dynamic response in applied magnetic fields $0<B<500$ mT and find evidence for ballistic spin transport. Our LF ${\mu }^{+}\mathrm{SR}$ measurements on the chiral spin chain $\mathrm{[}\mathrm{Cu}\left(\mathrm{pym}\right){\left({\mathrm{H}}_2\mathrm{O}\right)}_4]{\mathrm{SiF}}_6·{\mathrm{H}}_2\mathrm{O}$ instead demonstrate one-dimensional spin diffusion, and the distinct spin transport in these two systems suggests that additional anisotropic interactions play an important role in determining the nature of spin transport in $S=1/2$ antiferromagnetic chains.