Magnet-superconductor hybrid (MSH) structures represent one of the most promising platforms to realize, control, and manipulate Majorana modes using scanning tunneling methods. By depositing either chains or islands of magnetic atoms on the surface of a conventional, elemental superconductor such as Pb or Re, topological superconducting phases can emerge. They feature either localized Majorana bound states at the chain ends or dispersing chiral Majorana modes at the island's boundary. Yet some of these experiments have not reached the spectral resolution to clearly distinguish between topological Majorana and trivial Shiba states due to very small superconducting gap sizes and experiments performed at sub-Kelvin temperatures. Here we consider superconducting substrates with unconventional spin-singlet pairing, including high-temperature $d$-wave and extended $s$-wave superconductors. We derive topological phase diagrams and compute edge states for cylinder and island geometries and discuss their properties. Several time-reversal invariant topological superconducting phases of the Zhang-Kane-Mele type are found and discussed. Moreover, we study one-dimensional MSH structures and show that parameters to realize topologically nontrivial magnetic chains embedded into a larger, two-dimensional substrate differ from the purely one-dimensional case. Quite generally we find that unconventional superconducting substrates work as well as the conventional $s$-wave substrates to realize topological phases. In particular, iron-based pnictide and chalcogenide superconductors are the most promising class of substrates for future high-temperature MSH systems.

The off-diagonal (electric, thermal, and thermoelectric) transport coefficients of a solid can acquire an anomalous component due to the nontrivial topology of the Bloch waves. We present a study of the anomalous Hall effect (AHE), anomalous Nernst effect (ANE), and thermal Hall effect in the Heusler-Weyl ferromagnet ${\mathrm{Co}}_2\mathrm{MnGa}$. The anomalous Wiedemann-Franz law, linking electric and thermal responses, was found to be valid over the whole temperature window. This indicates that the AHE has an intrinsic origin and the Berry spectrum is smooth in the immediate vicinity of the Fermi level. We extract ${\alpha }_{ij}^A$ from our ANE data and find that the ${\alpha }_{ij}^A/{\sigma }_{ij}^A$ ratio approaches $k_B/e$ at room temperature. Scrutinizing all topological magnets previously explored, we observe that this ratio is a sizable fraction of $k_B/e$ at room temperature. We provide a rough explanation for this feature by arguing that the two anomalous transverse coefficients depend on universal constants, the Berry curvature averaged over a window set by either the Fermi wavelength (for Hall) or the de Broglie thermal length (for Nernst). The universal scaling indicates that the widths of the two windows approaches each other at room temperature.

Angular resolved scanning transmission electron microscopy is an important tool for investigating the properties of materials. However, several recent studies have observed appreciable discrepancies in the angular scattering distribution between experiment and theory. In this paper we discuss a general approach to low-loss inelastic scattering which, when incorporated in the simulations, resolves this problem and also closely reproduces experimental data taken over an extended angular range. We also explore the role of ionic bonding, temperature factors, amorphous layers on the surfaces of the specimen, and static displacements of atoms on the angular scattering distribution. The incorporation of low-loss inelastic scattering in simulations will improve the quantitative usefulness of techniques such as low-angle annular dark-field imaging and position-averaged convergent beam electron diffraction, especially for thicker specimens.

We theoretically and numerically show that longitudinal orbital currents in ferromagnets depend on the magnetization direction, which contribute to the anisotropic magnetoresistance (AMR). This orbital contribution to AMR arises from the momentum-dependent orbital splitting, which is generally present in multiorbital systems through the orbital anisotropy and the orbital hybridization. We highlight the latter orbital hybridization as an unrecognized origin of AMR and also as a common origin of AMR and orbital Hall effect.

We propose an algorithm which combines the beneficial aspects of two different methods for studying finite-temperature quantum systems with tensor networks. One approach is the ancilla method, which gives high-precision results but scales poorly at low temperatures. The other method is the minimally entangled typical thermal state (METTS) sampling algorithm which scales better than the ancilla method at low temperatures and can be parallelized, but requires many samples to converge to a precise result. Our proposed hybrid of these two methods purifies physical sites in a small central spatial region with partner ancilla sites, sampling the remaining sites using the METTS algorithm. Observables measured within the purified cluster have much lower sample variance than in the METTS approach, while sampling the sites outside the cluster reduces their entanglement and the computational cost of the algorithm. The sampling steps of the algorithm remain straightforwardly parallelizable. The hybrid approach also solves an important technical issue with METTS that makes it difficult to benefit from quantum number conservation. By studying $S=1$ Heisenberg ladder systems, we find the hybrid method converges more quickly than both the ancilla and METTS algorithms at intermediate temperatures and for systems with higher entanglement.

The low-energy sector of 2D and 3D topological insulators (TIs) exhibits propagating edge states, which has speculated the existence of equilibrium edge currents or edge spin currents. We demonstrate that if the low-energy sector of TIs is regularized in a straightforward manner into a square or cubic lattice, then the current from the edge states is in fact canceled out exactly by that from the valence bands, rendering no edge current. This result serves as a warning that for any equilibrium property of topological insulators, the contribution from the valence bands should not be overlooked. In these regularized lattice models, there is a finite edge current only if the Dirac point of the edge states is shifted away from the chemical potential, for instance, by doping, impurities, edge-confining potential, surface band bending, or gate voltage. The edge current in small quantum dots as a function of the gate voltage is quantized, and the edge current can flow out of the gated region up to the decay length of the edge state.

Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by the projective $\mathrm{SU}\left(N\right)$ group (or its subgroup ${\mathbb{Z}}_N\times {\mathbb{Z}}_N)$ with $N>2$. The unique feature of these symmetry-protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transform, for instance, respectively in the fundamental $\left(\mathit{N}\right)$ and antifundamental $\left(\overline{\mathit{N}}\right)$ representations of $\mathrm{SU}\left(N\right)$. We show, by means of complementary analytical and numerical approaches, that these chiral SPT phases as well as the nonchiral ones are realized as the ground states of a generalized two-leg $\mathrm{SU}\left(N\right)$ spin ladder in which the spins in the first chain transform in $\mathit{N}$ and the second in $\overline{\mathit{N}}$. In particular, we map out the phase diagram for $N=3$ and 4 to show that all the possible symmetry-protected topological phases with projective $\mathrm{SU}\left(N\right)$ symmetry appear in this simple ladder model.

We consider the Ruderman-Kittel-Kasuya-Yosida (RKKY) type coupling between two magnetic impurities on metallic armchair graphene nanoribbons (AGNR). Our key findings are that the lowest-order RKKY (LO-RKKY) coupling does not describe the coupling physics, and a full implementation of electron multiple scattering in RKKY coupling leads to orders of magnitude enhancement in the coupling magnitude. Key physics of our findings are revealed in our analysis of the LO-RKKY coupling. Within the Born approximation for the electron-magnetic-impurity scattering, the LO-RKKY coupling has inherited the singular density of states feature so that incident electrons at AGNR-subband band edges give finite contributions. Our other finding, that contribution from a gapped subband to LO-RKKY coupling is very small, implies then that severe cancellations must have occurred between states at its subband band edges and states not at its subband band edges. Magnitudes of the cancellation terms are each of the same order as the LO-RKKY coupling. This cancellation no longer occurs when full multiple scattering is reinstated. Contributions to the RKKY coupling from states at subband band edges are entirely suppressed, due to the restoring of the finiteness in the wave functions of these states. Contributions from states not from the subband band edges, though modified, retain their orders of magnitude. Analytic expressions have been obtained to further illustrate the physics.

We report the nanoscale imaging of Ti-doped bilayer calcium ruthenates during the Mott metal-insulator transition by microwave impedance microscopy. Different from a typical first-order phase transition where coexistence of the two terminal phases takes place, a new metallic stripe phase oriented along the in-plane crystalline axes emerges inside both the $G$-type antiferromagnetic insulating state and the paramagnetic metallic state. The effect of this electronic state can be observed in macroscopic measurements, allowing us to construct a phase diagram that takes into account the energetically competing phases. Our work provides a model approach to correlate the macroscopic properties and mesoscopic phase separation in complex oxide materials.

We investigate the Cu $L_3$ edge resonant inelastic x-ray scattering (RIXS) spectra of a quasi-1D antiferromagnet ${\mathrm{Ca}}_2{\mathrm{CuO}}_3$. In addition to the magnetic excitations, which are well-described by the two-spinon continuum, we observe two dispersive orbital excitations, the $3d_{xy}$ and the $3d_{yz}$ orbitons. We carry out a quantitative comparison of the RIXS spectra, obtained with two distinct incident polarizations, with a theoretical model. We show that any realistic spin-orbital model needs to include a finite, but realistic, Hund's exchange $J_H\approx 0.5\mathrm{eV}$. Its main effect is an increase in orbiton velocities, so that their theoretically calculated values match those observed experimentally. Even though Hund's exchange also mediates some interaction between spinon and orbiton, the picture of spin-orbit separation remains intact and describes orbiton motion in this compound.

Phonon-phonon anharmonic effects have a strong influence on the phonon spectrum; most prominent manifestation of these effects are the softening (shift in frequency) and broadening (change in FWHM) of the phonon modes at finite temperature. Using Raman spectroscopy, we studied the temperature dependence of the FWHM and Raman shift of $E_{2g}^1$ and $A_{1g}$ modes for single-layer and natural bilayer ${\mathrm{MoS}}_2$ over a broad range of temperatures $\left(8<\mathrm{T}<300\mathrm{K}\right)$. Both the Raman shift and FWHM of these modes show linear temperature dependence for $T>100\mathrm{K}$, whereas they become independent of temperature for $T<100\mathrm{K}$. Using first-principles calculations, we show that three-phonon anharmonic effects intrinsic to the material can account for the observed temperature dependence of the linewidth of both the modes. It also plays an important role in determining the temperature dependence of the frequency of the Raman modes. The observed evolution of the linewidth of the $A_{1g}$ mode suggests that electron-phonon processes are additionally involved. From the analysis of the temperature-dependent Raman spectra of ${\mathrm{MoS}}_2$ on two different substrates—${\mathrm{SiO}}_2$ and hexagonal boron nitride—we disentangle the contributions of external stress and internal impurities to these phonon-related processes. We find that the renormalization of the phonon mode frequencies on different substrates is governed by strain and intrinsic doping. Our work establishes the role of intrinsic phonon anharmonic effects in deciding the Raman shift in ${\mathrm{MoS}}_2$ irrespective of substrate and layer number.

A Kubo formalism is used to calculate the electronic and optical conductivity of a graphene superlattice with Y-shaped Kekulé bond texture, similar to that visualized in recent experiments. We show that new conduction channels between the valleys in graphene are opened by the Kekulé distortion. This intervalley contribution to the electronic transport is not present in pristine graphene and here appears due to the folding of the Dirac cones $K,K^{\prime }$ on top of each other. The contribution of intervalley transport to the conductivity of graphene, as well as the modification of the intravalley transport, are analyzed in detail for different frequency, temperature, chemical potential, and scattering rate limits. We obtain analytical expressions for the conductivity that reproduce previous expressions used to fit experimental measurements in graphene and compare with direct numerical evaluations of the Kubo formula, finding great agreement. The optical absorption arising from intervalley transitions displays a maximum at a special frequency that can be tuned by doping. Our results show how the single parameter describing the valley coupling in this system could be obtained by measuring graphene's optical absorbance in the region where interband transitions are blocked due to finite doping.

Tellurium (Te) has attracted great research interest due to its unique crystal structure since the 1970s. However, the conduction band of Te is rarely studied experimentally because of the $p$-type accumulation layer at the surface of Te. By the atomic layer deposited dielectric doping technique, we are able to access the conduction-band transport properties of Te in a controlled fashion. In this paper, we report on a systematic study of the weak-anti-localization (WAL) effect in $n$-type two-dimensional (2D) Te films. We find that WAL agrees well with Iordanskii, Lyanda-Geller, and Pikus theory. The gate and temperature-dependent WAL reveal that the D’yakonov-Perel mechanism, dominant for spin relaxation and phase relaxation, is governed by electron-electron interaction. A large phase-coherence length near 600 nm at $T=1\mathrm{K}$ is obtained together with gate-tunable spin-orbit interaction (SOI). Transition from weak-localization to WAL depending on gate bias is also observed. These results demonstrate that newly developed solution-based synthesized Te films provide a new controllable strong SOI 2D semiconductor with high potential for spintronic applications.

We study the thermal conductivity in disordered $s$-wave superconductors. Expanding on previous works for normal metals, we develop a formalism that tackles particle diffusion as well as the weak localization (WL) and weak antilocalization (WAL) effects focusing on the two-dimensional case. Using a Green's functions diagrammatic technique, which takes into account the superconducting nature of the system by working in Nambu space, we identify the system's low-energy modes, the diffuson and the cooperon. The timescales that characterize the diffusive regime are energy dependent; this is in contrast to the normal state, where the relevant timescale is the impurity scattering time ${\tau }_e$, independent of energy. The energy dependence introduces a novel energy scale ${\varepsilon }_{*}$, which for dirty superconductors $({\tau }_e\mathrm{\Delta }\ll 1$, with $\mathrm{\Delta }$ the gap) is given by ${\varepsilon }_{*}=\sqrt{\mathrm{\Delta }/{\tau }_e}$. From the diffusive behavior of the low-energy modes, we obtain the WL correction to the thermal conductivity. We give explicit expressions in two dimensions. We determine the regimes in which the correction depends manifestly on ${\varepsilon }_{*}$ and propose an optimal regime to verify our results in an experiment. In particular, we find a parametrically large reduction of the weak localization correction in a dirty superconductor, in comparison with its value in the normal state, when the temperature is lowered by 10% below the transition temperature.

The previous theoretical study has shown that pulse irradiation to the Mott insulating state in the Hubbard model can induce the enhancement of superconducting correlation due to the generation of $\eta$ pairs [Kaneko et al., Phys. Rev. Lett. 122, 077002 (2019)]. Here, we show that the same mechanism can be applied to the Kondo lattice model, an effective model for heavy electron systems, by demonstrating that the pulse irradiation indeed enhances the $\eta$-pairing correlation. As in the case of the Hubbard model, the nonlinear optical process is essential to increase the number of photoinduced $\eta$ pairs and thus the enhancement of the superconducting correlation. We also find the diffusive behavior of the spin dynamics after the pulse irradiation, suggesting that the increase of the number of $\eta$ pairs leads to the decoupling between the conduction band and the localized spins in the Kondo lattice model, which is inseparably related to the photodoping effect.

The magnetism of the second antiferromagnetic phase (AF2) arising in the iron-based ${\mathrm{LaFeAsO}}_{1-x}{\mathrm{H}}_x$ superconductor for $x\gtrsim 0.4$ was investigated by muon spin rotation measurements under hydrostatic pressure up to 2.6 GPa. The Néel temperature $\left(T_{\mathrm{N}}\right)$ obtained for a sample with $x=0.51$ exhibits considerably greater sensitivity to pressure than that in the pristine antiferromagnetic phase (AF1; $x\lesssim 0.06)$. Moreover, while the AF1 phase is always accompanied by the structural transition (from tetragonal to orthorhombic) at a temperature $\left(T_{\mathrm{s}}\right)$ which is slightly higher than $T_{\mathrm{N}}$, the AF2 phase prevails at higher pressures, above $\sim 1.5$ GPa, where the structural transition is suppressed $\left(T_{\mathrm{s}}=0\right)$. These features indicate that the microscopic origin of the AF2 phase is distinct from that of AF1, suggesting that electronic correlation plays an important role in the former phase. We argue that the orbital-selective Mott transition is a plausible scenario to account for the observed pressure dependence of $T_{\mathrm{N}}$ and $T_{\mathrm{s}}$ in the AF2 phase.

The search for elemental allotropes is an active research field to get unusual structures with unique properties. The removal of metal atoms from pressure-induced stable binary compounds has become a useful method for obtaining elemental allotropes with interesting properties that otherwise would not be accessible at ambient pressure. Although three-dimensional boron allotropes have been studied extensively, none of those found so far are superconducting at ambient pressure. Here we propose that $\mathrm{Na}{\mathrm{B}}_4$ and $\mathrm{N}{\mathrm{a}}_2{\mathrm{B}}_{17}$ can be used as precursors to achieve superconducting boron allotropes at ambient pressure. First-principle swarm-intelligence structure search calculations identify several novel sodium borides (e.g., $\mathrm{N}{\mathrm{a}}_3{\mathrm{B}}_2,\mathrm{N}{\mathrm{a}}_2{\mathrm{B}}_3,\mathrm{Na}{\mathrm{B}}_4$, and $\mathrm{N}{\mathrm{a}}_2{\mathrm{B}}_{17})$ under high pressure. Interestingly, the B atoms in $I4/mmm\mathrm{Na}{\mathrm{B}}_4$ and $Pm\mathrm{N}{\mathrm{a}}_2{\mathrm{B}}_{17}$ form three-dimensional frameworks with open channels, where Na atoms are located. After the removal of Na atoms, two hitherto unknown boron allotropes, named as $I4/mmm{\mathrm{B}}_4$ and $Pm{\mathrm{B}}_{17}$, are stable at ambient pressure. They are metallic with superconducting critical temperatures of 19.8 and 15.4 K, respectively, becoming the highest ones among bulk boron allotropes. In addition, considering their predicted Vickers hardness of 27.3 and 26.8 GPa, they are also potential hard materials.