We report small-angle neutron scattering (SANS) measurements of the skyrmion lattice in ${\left({\mathrm{Cu}}_{0.976}{\mathrm{Zn}}_{0.024}\right)}_2{\mathrm{OSeO}}_3$ under the application of electric and magnetic fields. These measurements show an expansion of the skyrmion lattice stability region with electric field. Furthermore, using time-resolved SANS, we observe the slow formation of skyrmions after an electric or magnetic field is applied, which has not been observed in pristine ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$ crystals. The measured formation times are dramatically longer than the corresponding skyrmion annihilation times after the external field is removed, and increase exponentially from 100 s at 52.5 K to 10 000 s at 51.5 K. This thermally activated behavior indicates an energy barrier for skyrmion formation of 1.57(2) eV, the size of which demonstrates the huge cost for creating these complex chiral objects.

A minimally invasive technique is proposed for detecting spin current noise across a junction between two quantum magnets using a high-quality microwave resonator coupled to a transmission line which is impedance matched to a photon detector downstream. Photons in the microwave resonator couple inductively to the spins in the spin subsystem, and the noise in the junction spin current imprints itself into the output photons propagating along the transmission line. The technique is capable of extracting both the dc and finite frequency noise via the output photon flux and also opens doors to the studies of photon counting statistics and to the possible generation of nonclassical radiation produced by spin current fluctuations at a quantum magnet junction.

We study the antiferromagnetic kagome Heisenberg model with an additional scalar-chiral interaction by using the infinite projected entangled-pair state (iPEPS) ansatz. We discuss in detail the implementation of the optimization algorithm in the framework of the single-layer tensor network based on the corner transfer matrix technique. Our benchmark based on the full-update algorithm shows that the single-layer algorithm is stable, which leads to the same level of accuracy as the double-layer ansatz but with much less computation time. We further apply this algorithm to study the nature of the kagome Heisenberg model with a scalar-chiral interaction by computing the bond dimension scaling of magnetization, bond energy difference, chiral order parameter, and correlation length. In particular, we find that for strong chiral coupling the correlation length, which is extracted from the transfer matrix, saturates to a finite value for large bond dimension, representing a gapped spin-liquid state. Further comparison with density matrix renormalization group results supports that our iPEPS faithfully represents the time-reversal symmetry breaking chiral state. Our iPEPS simulation results shed new light on constructing PEPS for describing gapped chiral topological states.

We report on an electron spin resonance study of H and D atoms stabilized in solid mixtures of neon, molecular deuterium, and hydrogen deuteride. We observed that H and D atoms can be stabilized in pure HD and ${\mathrm{D}}_2$ clusters formed in pores of solid Ne as well as in a Ne environment. Raising temperature from 0.1 to $1.3\mathrm{K}$ results in a rapid recombination of a significant fraction of both H and D atoms in HD and ${\mathrm{D}}_2$ clusters. The recombination rate appears to be five and seven orders of magnitude faster than in solid bulk samples of HD and ${\mathrm{D}}_2$, respectively. We explain this recombination rate enhancement by melting of clusters of molecular hydrogen isotopes, similar to what has been observed for atomic hydrogen in ${\mathrm{H}}_2$ clusters [Sheludiakov et al., Phys. Rev. B 97, 104108 (2018)]. Our observations do not provide evidence for a superfluid behavior of these clusters at temperatures of $0.1–1.3\mathrm{K}$.

We report inelastic neutron scattering on single crystals of the bilayer cuprate family ${\mathrm{La}}_{2-x}{\mathrm{Ca}}_{1+x}{\mathrm{Cu}}_2{\mathrm{O}}_{6+\delta }$, including two crystals made superconducting (transitions at 45 and 55 K) by high-pressure annealing in an oxygen-containing atmosphere. The magnetic excitations in the nonsuperconducting crystal have a similar temperature dependence as those in weakly hole-doped cuprates. In the superconducting crystals, there is a near-uniform suppression of the magnetic spectral weight with increasing temperature; in particular, there are no signs of a spin gap or “resonance” peak. This is different from the temperature dependence seen in many optimally doped cuprates but similar to the behavior seen in certain underdoped cuprates. We discuss the possible connection with pair-density-wave superconductivity.

We systematically investigate the perpendicular magnetocrystalline anisotropy (MCA) in $\mathrm{Co}-\mathrm{Pt}/\mathrm{Pd}$-based multilayers. Our magnetic measurement data show that the asymmetric Co/Pd/Pt multilayer has a significantly larger perpendicular magnetic anisotropy (PMA) energy compared to the symmetric Co/Pt and Co/Pd multilayer samples. We further support this experiment by first-principles calculations on ${\mathrm{CoPt}}_2, {\mathrm{CoPd}}_2$, and CoPtPd, which are composite bulk materials that consist of three atomic layers in a unit cell, Pt/Co/Pt, Pd/Co/Pd, and Pt/Co/Pd, respectively. By estimating the contribution of bulk spin-momentum coupling to the MCA energy, we show that the CoPtPd multilayer with symmetry breaking has a significantly larger PMA energy than the other multilayers that are otherwise similar but lack symmetry breaking. This observation thus provides evidence of the PMA enhancement due to the structural inversion symmetry breaking and highlights the asymmetric CoPtPd as an artificial magnetic material with bulk spin-momentum coupling, which opens a pathway toward the design of materials with strong PMA.

We present results of first-principles calculations of the magnetic properties of Fe chains deposited on the Re(0001) surface. By increasing the length of the chain, a transition is found from an almost collinear antiferromagnetic state for a five-atom-long chain to a spin spiral state with the rotational plane slightly tilted from the surface of the substrate for the 15-atom-long chain. It is shown that a classical spin model derived from the ab initio calculations containing only two-spin interactions supports opposite chirality of the spin spiral compared to a direct optimization of the spin configuration within the ab initio method. The differences between the results of the two methods can be understood by introducing chiral four-spin interactions in the spin model.

Surfaces of $d$-wave superconductors may host a substantial density of zero-energy Andreev states. The zero-energy flat band appears due to a topological constraint, but comes with a cost in free energy. We have recently found that an adjustment of the surface states can drive a phase transition into a phase with finite superflow that breaks time-reversal symmetry and translational symmetry along the surface. The associated Doppler shifts of Andreev states to finite energies lower the free energy. Direct experimental verification of such a phase is still technically difficult and controversial, however. To aid further experimental efforts, we use the quasiclassical theory of superconductivity to investigate how the realization and the observability of such a phase are influenced by sample geometry and surface ruggedness. Phase diagrams are produced for relevant geometric parameters. In particular, critical sizes and shapes are identified, providing quantitative guidelines for sample fabrication in the experimental hunt for symmetry-breaking phases.

Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of topological superconductors are a useful physical quantity for characterizing the topological properties of these materials. In this work, we show that the odd-frequency Cooper pair amplitudes can be expressed by a winding number extended to a nonzero frequency, which is called a “spectral bulk-boundary correspondence,” and can be evaluated from the spectral features of the bulk. The odd-frequency Cooper pair amplitudes are classified into two categories: the amplitudes in the first category have the singular functional form $\sim 1/z$ (where $z$ is a complex frequency) that reflects the presence of a topological surface Andreev bound state, whereas the amplitudes in the second category have the regular form $\sim z$ and are regarded as nontopological. We discuss the topological phase transition by using the coefficient in the latter category, which undergoes a power-law divergence at the topological phase transition point and is used to indicate the distance to the critical point. These concepts are established based on several concrete models, including a Rashba nanowire system that is promising for realizing Majorana fermions.

We show that if a quantum dot or Majorana zero mode couples to the chiral Majorana fermions, a resonant exchange of chiral Majorana fermions can occur and leads to a non-Abelian braidinglike operation analogous to the braiding of Majorana zero modes. Remarkably, any operation in the braid group can be achieved by this scheme. We further propose electrical transport experiments to observe the braidinglike operation on four chiral Majorana fermions and demonstrate the non-Abelian character in four-terminal devices of the quantum anomalous Hall insulator/topological superconductor hybrid junctions. Both a conductance peak due to the operation and the operation-order-dependent conductance are predicted. These findings pave the way to perform any non-Abelian operation on chiral Majorana fermions by electrically controllable quantum dots.

Influence of epitaxial strain and oxygen octahedra rotations on electronic structure of ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$ ultrathin films was systematically studied. The investigated films were grown by pulsed laser deposition on four different substrates: cubic (001)-oriented ${\mathrm{LaAlO}}_3$, (001) ${\left({\mathrm{LaAlO}}_3\right)}_{1/3}{\left({\mathrm{Sr}}_2{\mathrm{AlTaO}}_6\right)}_{2/3}$, (001) ${\mathrm{SrTiO}}_3$, and orthorhombic (110) ${\mathrm{DyScO}}_3$, providing a broad range of induced epitaxial strains. Magnetic properties were found to deteriorate with increasing value of the epitaxial strain, as expected due to unit cell distortion increasingly deviating from the bulk and effect of the magnetically inert layer. A combination of spectroscopic ellipsometry and magneto-optical Kerr effect spectroscopy was used to determine spectra of the diagonal and off-diagonal elements of permittivity tensor. The off-diagonal elements at room temperature confirmed the presence of two previously reported electronic transitions in the spectra of all films. Moreover they revealed another electronic transition around 4.3 eV only in the spectra of films grown under compressive strain. We proposed classification of this transition as a crystal field paramagnetic Mn $t_{2g}\to e_g$ transition. Ab initio calculations were employed to distinguish between the potential influence of oxygen octahedra rotations and distortions. The ab initio calculations indicated a negligible influence of oxygen octahedra rotations on magneto-optical properties of ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$. They further supported the proposed classification of the additional electronic transition, showing a key role of strain in controlling the electronic structure of ultrathin perovskite films.

It is well known that the matrix product state (MPS) description of a gapped ground state with a global on-site symmetry can exhibit “symmetry fractionalization.” Namely, even though the symmetry acts as a linear representation on the physical degrees of freedom, the MPS matrices—which act on some virtual degrees of freedom—can transform under a projective representation. This was instrumental in classifying gapped symmetry-protected phases that manifest in one-dimensional (1D) quantum many-body systems. Here we consider the multiscale entanglement renormalization ansatz (MERA) description of 1D ground states that have global on-site symmetries. We show that, in contrast to the MPS, the symmetry does not fractionalize in the MERA description if the ground state is gapped, assuming that the MERA preserves the symmetry at all length scales. However, it is still possible that the symmetry can fractionalize in the MERA if the ground state is critical, which may be relevant for characterizing critical symmetry-protected phases. Our results also motivate the presumed use of symmetric tensors to implement global on-site symmetries in MERA algorithms.

The response of semiconductor materials to external magnetic fields is a reliable approach to probe intrinsic electronic and spin-dependent properties. In this study, we investigate the common Zeeman splitting features of novel wurtzite materials, namely, InP, InAs, and GaAs. We present values for the effective $g$ factors of different energy bands and show that spin-orbit coupling effects, responsible for the spin splittings, also have noticeable contributions to the $g$ factors. Within the Landau level picture, we show that the nonlinear Zeeman splitting recently explained in magnetophotoluminescence experiments for InP nanowires by D. Tedeschi et al. [Phys. Rev. B 99, 161204 (2019)] is also present in InAs, GaAs, and even the conventional GaN. Such nonlinear features stem from the peculiar coupling of the A and B valence bands as a consequence of the interplay between the wurtzite crystal symmetry and the breaking of time-reversal symmetry by the external magnetic field. Moreover, we develop an analytical model to describe the experimental nonlinear Zeeman splitting and apply it to InP and GaAs data. Extrapolating our fitted results, we found that the Zeeman splitting of InP reaches a maximum value, which is a prediction that could be probed at higher magnetic fields.

Spin-orbit coupling in graphene is able to induce various topological phases and is also crucial for potential application in graphene-based spintronics. However, graphene itself exhibits extremely weak spin-orbit coupling, and it is rather challenging to enhance the spin-orbit coupling without drastically affecting its fundamental physical property in graphene via external means. In this paper, we show that the charge-compensated $n\text{−}p$ codoping approach not only can overcome the main shortcomings arising from single-element adsorption in graphene but can also result in a large Rashba spin-orbit splitting. As an example, we codope heavy adatoms with outer-shell $p$ electrons (e.g., Tl atoms acting as $n$-type dopants) on $p$-type doped graphene (e.g., by substituting carbon atoms with B atoms). We find the following: (1) Electrostatic attraction between $n$- and $p$-type dopants effectively enhances the adsorption and diffusion barrier of metallic adatoms and suppresses the undesirable formation of clustering. (2) Large Rashba spin-orbit splitting ($\sim 130\mathrm{meV}$ for 6.25% B-Tl-codoped graphene) is produced due to the electrostatic interaction. (3) The charge-compensated nature and mutual screening of $n\text{−}p$ codopants preserve the Dirac dispersion of charge carriers to some extent.

Scanning transmission electron microscopy (STEM) has enabled mapping of atomic structures of solids with sub-picometer precision, providing insight to the physics of ferroic phenomena and chemical expansion. However, only a subset of information is available, due to projective nature of imaging in the beam direction. Correspondingly, the analysis often relies on the postulated form of macroscopic Landau-Ginzburg energy for the ferroic long-range order parameter, and some predefined relationship between experimentally determined atomic coordinates and the order-parameter field. Here, we propose an approach for exploring the structure of ferroics using reduced order-parameter models constructed based on experimental data only. We develop a four-sublattice model (FSM) for the analytical description of A-cation displacement in (anti)ferroelectric-antiferrodistortive perovskites of $AB{\mathrm{O}}_3$ type. The model describes the displacements of cation A in four neighboring unit cells and determines the conditions of different structural phases’ appearance and stability in $AB{\mathrm{O}}_3$. We show that FSM explains the coexistence of rhombohedral, orthorhombic, and spatially modulated phases, observed by atomic-resolution STEM in La-doped $\mathrm{BiFe}{\mathrm{O}}_3$. Using this approach, we atomically resolve and theoretically model the sublattice asymmetry inherent to the case of the A-site La/Bi cation sublattice in $\mathrm{L}{\mathrm{a}}_x\mathrm{B}{\mathrm{i}}_{1-x}\mathrm{Fe}{\mathrm{O}}_3$ polymorphs. This approach allows the exploration of ferroic behaviors from experimental data only, without additional assumptions on the nature of the order parameter.

We investigate theoretically the existence at low temperature of a commensurate (4/7) crystalline phase of a layer of either He isotope on top of a ${}^4\mathrm{He}$ layer adsorbed on graphite. We make use of a recently developed, systematically improvable variational approach which allows us to treat both isotopes on an equal footing. We confirm that no commensurate crystalline second layer of ${}^4\mathrm{He}$ forms, in agreement with all recent calculations. Interestingly and more significantly, we find that even for ${}^3\mathrm{He}$ there is no evidence of such a phase, as the system freezes into an incommensurate crystal at a coverage lower than that (4/7) at which a commensurate one has been predicted and for which experimental claims have been made. Implications for the interpretation of recent experiments with helium on graphite are discussed.

Here we study negative differential resistance effect in hybrid carbon nanostructures composed of graphene nanoribbons and carbon nanotubes. In the coupled structure, the finite flakes of nanotubes allow the formation of resonant states in the system tuning the conductance and generating Fano antiresonances. A single-band tight-binding approximation is adopted, and the density of states and conductance of the hybrid systems are calculated within the Green's function formalism and recursive numerical approaches. Armchair and zigzag edge geometries are chosen to investigate the topology effects on the electronic and transport properties for different configurations of the hybrid systems. For nanoribbons with armchair edges we derive a multiple-mode approach to analytically calculate the transmission function for the hybrid coupled system. Large and robust negative differential resistance effects are observed in the nanotube-nanoribbon zigzag hybrids that may be used in switching electronic transport responses.

Surface acoustic waves (SAWs) are elastic waves localized on a surface of an elastic body. We theoretically study topological edge modes of SAWs for a corrugated surface. We introduce a corrugation forming a triangular lattice on the surface of an elastic body. We treat the corrugation as a perturbation, and construct eigenmodes on a corrugated surface by superposing those for the flat surface at wave vectors which are mutually different by reciprocal-lattice vectors. We thereby show emergence of Dirac cones at the $K$ and $K^{\prime }$ points analytically. Moreover, by breaking the time-reversal symmetry, we show that the Dirac cones open a gap, and that the Chern number for the lowest band has a nonzero value. This indicates the existence of topological chiral edge modes of SAWs in the gap.

We show that Ce- and Yb-based Kondo-lattice ferromagnets order mainly along the magnetically hard direction of the ground-state Kramers doublet determined by crystalline electric field. Here, we argue that this peculiar phenomenon, that was believed to be rare, is instead the standard case. Moreover, it seems to be independent on the Curie temperature $T_C$, crystalline structure, size of the ordered moment, and type of ground-state wave function. On the other hand, all these systems show the Kondo coherence maximum in the temperature dependence of the resistivity just above $T_C$, which indicates a Kondo temperature of a few degrees Kelvin. An important role of fluctuations is indicated by the non-mean-field-like transition in specific heat measurements as well as by the suppression of this effect by a strong Ising-like anisotropy. We discuss possible theoretical scenarios.

We study the correspondence between boundary excitation distribution spectrum of nonchiral topological orders on an open surface $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed surface. The closed surface is bipartitioned into two subsystems, one of which has the same topology as $\mathcal{M}$. Specifically, we focus on the case of generalized string-net models and discuss the cases where $\mathcal{M}$ is a disk or a cylinder. When $\mathcal{M}$ has the topology of a cylinder, different combinations of boundary conditions of the cylinder will correspond to different entanglement cuts on the torus. When both boundaries are charge (smooth) boundaries, the entanglement spectrum can be identified with the boundary excitation distribution spectrum at infinite temperature and constant fugacities. Examples of toric code, ${\mathbb{Z}}_N$ theories, and the simple non-Abelian case of doubled Fibonacci are demonstrated.