We determine which translationally invariant matrix product states have a continuum limit, that is, which can be considered as discretized versions of states defined in the continuum. To do this, we analyze a fine-graining renormalization procedure in real space, characterize the set of limiting states of its flow, and find that it strictly contains the set of continuous matrix product states. We also analyze which states have a continuum limit after a finite number of coarse-graining renormalization steps. We give several examples of states with and without the different kinds of continuum limits.

Theory of spin-charge conversion effects in spintronics are presented in terms of correlation functions of physical observables, spin and electric current. Direct and inverse spin Hall effects and spin pumping effect are studied considering metallic systems with random spin-orbit interaction and spatially nonuniform Rashba interaction. The theory is free from ambiguity associated with spin current, and provides a clear physical picture of the spin-charge conversion effects. In the present approach, the spin current transmission efficiency turns out essentially to be the nonuniform component of magnetic susceptibility.

An approach to directly measure the nonlinear foldover effect for cavity magnon polaritons is demonstrated by placing a nonlinear medium (yttrium iron garnet) into a Fabry-Perot-like microwave cavity. The resulting bistability features can exhibit clockwise, counterclockwise, and butterflylike hysteresis loops and are solely dependent on the relative weight of the magnonlike and photonlike components. In addition to accurately describing our experimental observations, our model also allows us to calculate the crucial system conditions required to produce photonlike foldover effects. Though the photon subsystem has no nonlinear components of its own, these photonlike foldover effects are produced through light-matter interactions with a nonlinear magnetic subsystem. Our model's description of these nonlinear light-matter interactions and their effects is not limited to ferromagnetic systems and should be generally applicable to other coherent coupled systems.

We investigated the anisotropy of the magnetic and magnetocaloric properties of single-crystalline double-perovskite $\mathrm{T}{\mathrm{b}}_2\mathrm{CoMn}{\mathrm{O}}_6$, which crystallizes in a monoclinic $P{2}_1/n$ structure. Due to dissimilar magnetic anisotropy, the ferromagnetic order of the $\mathrm{C}{\mathrm{o}}^{2+}$ and $\mathrm{M}{\mathrm{n}}^{4+}$ moments emerges along the $c$ axis at $T_{\mathrm{C}}=100\mathrm{K}$, and the larger $\mathrm{T}{\mathrm{b}}^{3+}$ moments align perpendicular to the $c$ axis, below $T_{\mathrm{Tb}}=15\mathrm{K}$. The intricate temperature development of the metamagnetism along the $c$ axis results in a large negative change in the magnetic entropy at low temperature. On the other hand, the larger but almost reversible magnetization, perpendicular to the $c$ axis, results in a small and positive entropy change. This highly anisotropic magnetocaloric effect (MCE) leads to a giant rotational MCE, estimated to be $20.8\mathrm{J}/\mathrm{kg}\mathrm{K}$. Our findings, based on the magnetic anisotropy in $\mathrm{T}{\mathrm{b}}_2\mathrm{CoMn}{\mathrm{O}}_6$, enrich fundamental and applied research on magnetic materials, considering the distinct magnetic characteristics of double perovskites.

We study the system of attractively interacting fermions hopping in a square lattice with any linear combinations of Rashba or Dresselhaus spin-orbit coupling in a normal Zeeman field. By imposing self-consistence equations at half filling with zero chemical potential, we find that there are three phases: band insulator (BI), superfluid (SF), and topological superfluid (TSF) with a Chern number $C=2$. The $C=2$ TSF happens in small Zeeman fields and weak interactions which is in the experimentally most easily accessible regime. The transition from the BI to the SF is a first-order one due to the multiminima structure of the ground state energy landscape. There is a class of topological phase transitions (TPTs) from the SF to the $C=2$ TSF at the low critical field $h_{c1}$, then another one from the $C=2$ TSF to the BI at the upper critical field $h_{c2}$. We derive effective actions to describe these two classes of topological phase transitions, then use them to study the Majorana edge modes and the zero modes inside the vortex core of the $C=2$ TSF near both $h_{c1}$ and $h_{c2}$, especially exploring their spatial and spin structures. We find that the edge modes decay into the bulk with oscillating behaviors and determine both the decay and oscillating lengths. We compute the bulk spectra and map out the Berry curvature distribution in momentum space near both $h_{c1}$ and $h_{c2}$. We elaborate some intriguing bulk-Berry curvature-edge-vortex correspondences. We also discuss the competitions between SFs and charge density wave states in more general cases. A possible classification scheme of all the TPTs in a square lattice is outlined. Comparisons with previous works on related systems are discussed. Possible experimental implications in cold atoms in an optical lattice are given.

We apply a result from graph theory to prove exact results about itinerant ferromagnetism. Nagaoka's theorem is extended to all nonseparable graphs except single polygons with more than four vertices by applying the solution to the generalized 15-puzzle problem, which studies whether the hole's motion can connect all possible tile configurations. This proves that the ground state of a $U\to \infty$ Hubbard model with one hole away from the half filling on a two-dimensional honeycomb lattice or a three-dimensional diamond lattice is fully spin polarized. Furthermore, the condition of connectivity for $N$-component fermions is presented, and Nagaoka's theorem is also generalized to $\text{SU}\left(N\right)$-symmetric fermion systems on nonseparable graphs.

The noncentrosymmetric superconductor ${\mathrm{Mo}}_3{\mathrm{Rh}}_2\mathrm{N}$, with $T_c=4.6$ K, adopts a $\beta$-Mn-type structure (space group $P{4}_{1}32)$, similar to that of ${\mathrm{Mo}}_3{\mathrm{Al}}_2\mathrm{C}$. Its bulk superconductivity was characterized by magnetization and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation and relaxation $\left(\mu \mathrm{SR}\right)$. The low-temperature superfluid density, measured via transverse-field (TF)-$\mu \mathrm{SR}$, evidences a fully gapped superconducting state with ${\mathrm{\Delta }}_0=1.73k_{\mathrm{B}}{T}_c$, very close to $1.76k_{\mathrm{B}}{T}_c$, the BCS gap value for the weak-coupling case, and a magnetic penetration depth ${\lambda }_0=586$ nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined by zero-field (ZF)-$\mu \mathrm{SR}$ measurements, hints at a preserved time-reversal symmetry in the superconducting state. Both TF- and ZF-$\mu \mathrm{SR}$ results evidence a spin-singlet pairing in ${\mathrm{Mo}}_3{\mathrm{Rh}}_2\mathrm{N}$.

We study the (de)localization phenomena of one-component lattice fermions in spin backgrounds. The O(3) classical spin variables on sites fluctuate thermally through the ordinary nearest-neighbor coupling. Their complex two-component ($\mathrm{CP}{}^1$-Schwinger boson) representation forms a composite U(1) gauge field on bond, which acts on fermions as a fluctuating hopping amplitude in a gauge invariant manner. For the case of antiferromagnetic (AF) spin coupling, the model has a close relationship with the $t-J$ model of strongly correlated electron systems. We measure the unfolded level spacing distribution of fermion energy eigenvalues and the participation ratio of energy eigenstates. The results for AF spin couplings suggest a possibility that, in two dimensions, all the energy eigenstates are localized. In three dimensions, we find that there exists a mobility edge, and we estimate the critical temperature $T_{\mathrm{L}\mathrm{D}}\left(\delta \right)$ of the localization-delocalization transition at the fermion concentration $\delta$.

We revisit the inverse spin current model that has been previously used to explain the existence of magnetic cycloids in bulk multiferroic ${\mathrm{BiFeO}}_3$. Using a first-principles-based effective Hamiltonian method, and in combination with Monte Carlo simulations, we predict a magnetic phase diagram as a function of first- and second-nearest-neighbor interaction strength in the spin current model and show that, in contrast with previous understanding, both first and second nearest neighbors have to be taken into account to be in accordance with experimental findings, including the existence of type-1 and type-2 cycloids with, respectively, $\left[1\overline{1}0\right]$ and $\left[11\overline{2}\right]$ propagation directions, and the cycloid-to-antiferromagnetic transition under magnetic field. Other previously unknown magnetic arrangements are found in this phase diagram. The microscopic origins of all its magnetic phases are further explained in terms of the coexistence of single solutions of the spin current model having different weights (in magnitude and even sign).

We present a bond-operator theory (BOT) suitable for the description of both magnetically ordered phases and paramagnetic phases with singlet ground states in spin-1/2 magnets. This technique allows one to trace the evolution of quasiparticles across the transition between the phases. Some elementary excitations described in the theory by separate bosons appear in conventional approaches as bound states of well-known quasiparticles (magnons or triplons). The proposed BOT provides a regular expansion of physical quantities in powers of $1/n$, where $n$ is the maximum number of bosons that can occupy a unit cell (physical results correspond to $n=1$). Two variants of BOT are suggested: for two and for four spins in the unit cell (two-spin and four-spin BOTs, respectively). We consider spin-1/2 Heisenberg antiferromagnets (HAF) on a simple square lattice bilayer by the two-spin BOT. The ground-state energy $\mathcal{E}$, the staggered magnetization $M$, and quasiparticle spectra found within the first order in $1/n$ are in good quantitative agreement with previous results both in paramagnetic and in ordered phases not very close to the quantum critical point between the phases. By doubling the unit cell in two directions, we discuss spin-1/2 HAF on a square lattice using the suggested four-spin BOT. We identify the magnon and the amplitude (Higgs) modes among fifteen spin-2, spin-1, and spin-0 quasiparticles arising in the theory. The magnon spectrum, $\mathcal{E}$, and $M$ found in the first order in $1/n$ are in good quantitative agreement with previous numerical and experimental results. We observe a special moderately damped spin-0 quasiparticle (“singlon” for short) whose energy is smaller than the energy of the Higgs mode in the most part of the Brillouin zone. By considering HAF with Ising-type anisotropy, we find that both Higgs and singlon modes stem from two-magnon bound states, which merge with two-magnon continuum not far from the isotropic limit. We demonstrate that singlons appear explicitly in “scalar” correlators one of which describes the Raman intensity in $B_{1g}$ symmetry. The latter is expressed in the leading order in $1/n$ via the singlon Green's function at zero momentum, which shows an asymmetric peak. The position of this peak given by the singlon energy coincides with the position of the so-called “two-magnon” peak observed experimentally in, e.g., layered cuprates.

Spontaneous rotational-symmetry breaking in the superconducting state of doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal ${\mathrm{Sr}}_{0.1}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ provides unequivocal evidence of a twofold rotational symmetry in the superconducting gap by a bulk thermodynamic probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's low carrier concentration proving bulk superconductivity. The large basal-plane anisotropy of $H_{c2}$ (${\mathrm{\Gamma }}_{\exp }=3.5$) is attributed to a nematic phase of a two-component topological gap structure $\mathbf{\eta }=({\eta }_1,{\eta }_2)$ and caused by a symmetry-breaking energy term $\delta \left(\right|{\eta }_1{|}^2-|{\eta }_2{|}^2)T_c$. A quantitative analysis of our data excludes more conventional sources of this twofold anisotropy and provides an estimate for the symmetry-breaking strength $\delta \approx 0.1$, a value that points to an onset transition of the second order parameter component below 2 K.

We study two mechanisms for enhancing the superconducting mean-field transition temperature $T_c$ by nonmagnetic disorder in both conventional (sign-preserving gaps) and unconventional (sign-changing gaps) superconductors (SCs). In the first scenario, relevant to multiband systems of both conventional and unconventional SCs, we demonstrate how favorable density-of-states enhancements driven by resonant states in off-Fermi-level bands lead to significant enhancements of $T_c$ in the condensate formed by the near-Fermi-level bands. The second scenario focuses on systems close to localization where random disorder-generated local density-of-states modulations cause a boosted $T_c$ even for conventional single-band SCs. We analyze the basic physics of both mechanisms within simplified models, and we discuss the relevance to existing materials.

A two-dimensional Dirac semimetal with tilted Dirac cone has recently attracted increasing interest. The tilt of Dirac cone can be realized in a number of materials, including deformed graphene, surface state of topological crystalline insulator, and certain organic compounds. We study how Dirac cone tilting affects the low-energy properties by presenting a renormalization group analysis of the Coulomb interaction and quenched disorder. A random scalar potential or random vector potential along the tilting direction cannot exist on its own as it always dynamically generates a new type of disorder, which dominates at low energies and turns the system into a compressible diffusive metal. Consequently, the fermions acquire a finite disorder scattering rate. Moreover, the isolated band-touching point is replaced by a bulk Fermi arc in the Brillouin zone. These results are not qualitatively changed when the Coulomb interaction is incorporated. In comparison, random mass and random vector potential along the nontilting direction can exist individually, without generating other types of disorder. They both suppress tilt at low energies, and do not produce bulk Fermi arc. Upon taking the Coulomb interaction into account, the system enters into a stable quantum critical state, in which the fermion field acquires a finite anomalous dimension but the dynamical exponent $z=1$. These results indicate that Dirac cone tilt does lead to some qualitatively different low-energy properties compared to the untilted system.

We calculated the exchange energy of a pair of donor-bound electrons placed in the middle of an infinite quantum well (QW). In order to obtain this energy for any interdonor distance and for any QW thickness, we have first adapted to a QW the method developed by Gor’kov and Pitaevskii [L. P. Gor’kov and L. P. Pitaevskii, Dokl. Akad. Nauk SSSR 151, 822 (1963)] for a three-dimensional (3D) distribution of donors, and calculated the asymptotic form of the exchange energy. Second we have calculated the exchange energy of a “helium atom” in a QW; and third, inspired by the interpolation procedure proposed by Ponomarev et al. [I.V. Ponomarev et al., Phys. Rev. B 60, 5485 (1999)], we have obtained an interpolated expression for any interdonor distance. The obtained exchange energy is written in units of effective hartree, and the distance between the donors, as well as the width of the QW, are expressed in units of effective Bohr radius. We calculated the exchange energy for some commonly studied semiconductor materials, and discussed also the relationship between the exchange energy and the spin relaxation time for a donor concentration close to the insulator-metal transition.

Microwave spectroscopy within the Landau filling ($\nu$) range of the integer quantum Hall effect (IQHE) has revealed pinning mode resonances signifying Wigner solids (WSs) composed of quasiparticles or -holes. We study pinning modes of WSs in wide quantum wells (WQWs) for $0.8\le \nu \le 1.2$, varying the density, $n$, and tilting the sample by angle $\theta$ in the magnetic field. Three distinct WS phases are accessed. One phase, S1, is phenomenologically the same as the WS observed in the IQHEs of narrow QWs. The second phase, S2, exists at $\nu$ further from $\nu =1$ than S1, and requires a sufficiently large $n$ or $\theta$, implying S2 is stabilized by the Zeeman energy. The melting temperatures of S1 and S2, estimated from the disappearance of the pinning mode, show different behavior versus $\nu$. At the largest $n$ or $\theta$, S2 disappears and the third phase, S1A, replaces S1, also exhibiting a pinning mode. This occurs as the WQW $\nu =1$ IQHE becomes a two-component, Halperin-Laughlin ${\mathrm{\Psi }}_{111}$ state. We interpret S1A as a WS of the excitations of ${\mathrm{\Psi }}_{111}$, which has not been previously observed.

In this paper we investigate the structural and optical properties of few strain-unbalanced multiple Ge/GeSi quantum wells pseudomorphically grown on GeSi reverse-graded substrates. The obtained high epitaxial quality demonstrates that strain symmetrization is not a mandatory requirement for few quantum-well repetitions. Photoluminescence data, supported by a thorough theoretical modeling, allow us to unambiguously disentangle the spectral features of the quantum wells from those originating in the virtual substrate and to evaluate the impact on the optical properties of key parameters, such as quantum confinement, layer compositions, excess carrier density, and lattice strain. This detailed understanding of the radiative recombination processes is of paramount importance for the development of Ge/GeSi-based optical devices.

The electronic structure of $1T-\mathrm{Ta}{\mathrm{S}}_2$ showing a metal-insulator transition and a sequence of different charge density wave (CDW) transformations was discussed in the frame of variable temperature angle-resolved photoelectron spectroscopy (ARPES), scanning tunneling spectroscopy (STS), and density functional theory (DFT) calculations. For the commensurate charge density wave phase (CCDW) the Mott gap was estimated to be 0.4 eV and energy gaps ${\mathrm{\Delta }}_{\text{CCDW},1},{\mathrm{\Delta }}_{\text{CCDW},2},{\mathrm{\Delta }}_{B3-\mathit{HHB}},{\mathrm{\Delta }}_{B4-B3}$ were observed. For the nearly commensurate charge density wave phase (NCCDW), the reminiscent of higher and lower Hubbard bands and a very pronounced electronic state associated with the parabolic band at the $\overline{\mathrm{\Gamma }}$ point in the Brillouin zone were identified. The incommensurate charge density wave phase (ICCDW) showed a high value of local density of states at the Fermi level and a very pronounced edge of the metallic surface state located in the range of 0.15–0.20 eV above the Fermi level. The obtained STS and ARPES results were consistent with our theoretical calculations performed within DFT formalism including spin-orbit coupling.

We study localized electronic states at the interface between two semi-infinite Weyl semimetals by using a two-band model Hamiltonian. Specifically, we consider cases in which the surface projections of the Weyl nodes of the left system do not coincide with those on the right. We demonstrate that, depending on the position and chirality of the Weyl nodes of both semimetals, the Fermi arcs of the localized interface states can be formed between the surface projection of a Weyl node of the left crystal and the corresponding one of the right crystal, instead of connecting two surface-projected Weyl nodes of the same crystal. Because the resultant interface band disperses toward bulk states of both crystals, this mechanism may provide an efficient transport channel between the two Weyl semimetals comprising the interface.

We present here a combined experimental Raman spectroscopy and ab initio theoretical study of the vibrational modes of the $\left(\sqrt{3}\times \sqrt{3}\right)$ reconstructed SIC phase of Pb on Si(111) and discuss their relation to the atomic surface structure. The Raman response of the surface localized vibrational modes, in particular, is identified in the low-frequency spectral range (down to $15{\mathrm{cm}}^{-1})$. We demonstrate that Raman spectroscopy is a very powerful approach to test atomic structures of surfaces and a valuable complement to standard surface analytics. While the calculated spectra of H3 and T4 are too similar to allow a discrimination of these phases, the good overall agreement to the measured Raman spectra enables a classification of the observed vibrational modes.

A method based on atomic force microscopy, which allows mapping the residual stress at nanoscale on the surface of crystalline solids [Polop et al., Nanoscale 9, 13938 (2017)], sheds light on the controversial origin of the intrinsic compression that arises in continuous polycrystalline films under high atomic mobility conditions. The maps of residual stress reveal that the compression is concentrated in narrow strips adjacent and parallel to the grain-boundary triple junctions, but not inside the grain boundary as usually assumed. We explain these findings in the light of Mullins's theory for surface diffusion of adatoms towards grain boundaries. As the surface slope at the grain-boundary triple junctions is constrained by the balance between interfacial tensions, the kinetic surface profile is different from the mechanical equilibrium profile predicted by the Laplace-Young equation. Where the curvatures of both profiles differ, an intrinsic stress is generated in the form of Laplace pressure. The average value of the stress profile is compressive. In turn, the resulting stress induces a Srolovitz-type surface diffusion, which counters the Mullins-type diffusion. The competition between both diffusion mechanisms addresses the main fingerprints of the intrinsic stress behavior in polycrystalline films, namely, the stabilization of the stress profile during growth, its reversibility with the flux, and the kinetics of the stress relaxation and recovery.