The spin-orbit torque (SOT) switching of trilayers with two heavy-metal layers on the same side of the ferromagnetic metal layer was studied, realizing tunable spin Hall angle, domain-wall motion, and Dzyaloshinskii-Moriya interaction. However, systematic research on the magnetoresistance in such structures is still lacking. In this work, we investigate the anisotropic magnetoresistance (AMR) and the spin Hall magnetoresistance (SMR) by inserting an ultrathin Ir layer ($t_{\mathrm{Ir}}\le 1.4\mathrm{nm}$) into Ta/CoFeB. The Ir layer with the thickness larger than 0.4 nm can transform the AMR from positive to negative, which is attributed to the electronic structure of Ir. This process realizes the interfacial modulation of AMR, which is generally considered as a bulk property. The SMR ratio decreases first and then increases with increasing Ir thickness, producing the minimum and maximum at $t_{\mathrm{Ir}}=0.3\mathrm{nm}$ and $t_{\mathrm{Ir}}=0.9\mathrm{nm}$, respectively, which reflects the ultrasmall spin-diffusion length (<0.5 nm) and strong spin-memory loss in Ir. Further analyses combined with the SOT switching measurements unravel the existence of the anomalous Hall magnetoresistance, implying the non-negligible spin accumulation due to the anomalous Hall effect of the ferromagnetic metal. The combination of a large negative AMR and comparatively smaller SMR results in a negative planar Hall resistance. Our findings enrich the understanding of the magnetoresistances of heavy-metal/ferromagnetic metal trilayer systems.

Braiding of anyons such as Majoranas or parafermions provides only Clifford gates which do not form a universal set of quantum gates. We propose a robust and resource-efficient scheme to perform non-Clifford gates on logical qudits encoded in parafermionic zero modes via the Aharonov-Casher effect. This gate can be implemented by moving a half-flux quantum around the pair of parafermionic zero modes. The parafermion modes can be realized in a two-dimensional setup via existing proposals, and a half-fluxon can be created as a part of half-fluxon/anti-half-fluxon pair in a spin-triplet Josephson junction. We provide evidence that the half-fluxon can be braided robustly around the parafermions and hence this is a reliable proposal for the implementation of the non-Clifford gate without magic state distillation. Supplementing this gate with the braiding of parafermions provides the avenue for universal quantum computing with parafermions.

To study the melting transition of a vortex crystal (or cluster) consisting of a small number of vortices confined in a mesoscopic-scale superconductor, $c$-axis magnetoresistance in the highly anisotropic high-$T_{\mathrm{c}}$ superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+y}$ (Bi2212) has been measured using a triangle-shaped stack of intrinsic Josephson junctions, which was trimmed out from a single-crystal flake of Bi2212 via a double-sided etching process using a focused ion beam. We observed oscillations of the melting transition line, in which the oscillating part of the melting temperature has sharp peaks when the number of vortices $N$ exactly coincides with the triangular number $n(n+1)/2$ ($n$ is an integer number), at least for $N<50$. This is in contrast to the case of square shapes where the enhancements appeared as broad peaks around $N=n^2$. Furthermore, the field ranges of the $N$-vortex state expand at the triangular numbers of $N$, suggesting that the triangular number of vortices has a more stable configuration than the others. Numerical studies on the configuration of vortices in a triangle shape show that geometrical matching with no defect structures is realized at the triangular numbers, whereas an edge dislocation often appears in the other nonmatching cases. The degree of suppression of the melting temperatures at nonmatching numbers is reasonably consistent with the value estimated from the increase in free energy with the introduction of an edge dislocation.

Majorana bound states, with their non-Abelian properties, are candidates for the realization of fault-tolerant quantum computation. Here we study the influence of long-range many-body interactions on Majorana zero modes present in Kitaev chains. We show that these interactions can suppress the lifetime of the Majorana zero mode. We also discuss the role of long-range interactions on the Majorana state's spatial structure, and the overlap of the Majorana states localized at opposite ends of the chain. We have determined that increasing the interaction strength leads to decreasing of the stability of the Majorana modes. Moreover, we found out that interaction between particles located at more distant sites plays a more destructive role than the interaction between nearest neighbors.

We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parametrizing the Hamiltonian self-adjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential, and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the Landauer-Büttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the Wiedemann-Franz law.

The recent experimental studies of extremely long-lived macroscopic ensembles of spin-cyclotron excitons (magnetoexcitons) which have to obey the Bose-Einstein statistics signal the emergence of an excitonic coherent phase. In the present paper the theory of a weakly interacting Bose gas of spin-cyclotron excitations is developed in terms of a virial correction to the single-magnetoexciton energy. The condition for coherent-incoherent phase transition is discussed. It is expected to be strongly related to the studied long-distance interexcitonic correlations. The results obtained theoretically are discussed in terms of their agreement with specific experimental data.

Light emitters in wide-band-gap semiconductors are of great fundamental interest and have potential as optically addressable qubits. Here we describe a unique color center in high-quality hexagonal boron nitride (h-BN) with a sharp emission line at 435 nm. The emitters are activated and deactivated by electron beam irradiation and have spectral and temporal characteristics consistent with atomic color centers weakly coupled to lattice vibrations. The emitters are conspicuously absent from commercially available h-BN and are present in only ultrahigh-quality h-BN grown using a high-pressure, high-temperature Ba-B-N flux/solvent, suggesting that these emitters originate from impurities or related defects specific to this unique synthetic route. Our results imply that the light emission is activated and deactivated by electron beam manipulation of the charge state of an impurity-defect complex.

We study anomalies in time-reversal-(${\mathbb{Z}}_2^T$) and $U\left(1\right)$-symmetric topological orders. In this context, an anomalous topological order is one that cannot be realized in a strictly $(2+1)$-dimensional system but can be realized on the surface of a $(3+1)$-dimensional [($3+1$)D] symmetry-protected topological (SPT) phase. To detect these anomalies we propose several anomaly indicators, functions that take as input the algebraic data of a symmetric topological order and that output a number indicating the presence or absence of an anomaly. We construct such indicators for both structures of the full symmetry group, i.e., $U\left(1\right)⋊{\mathbb{Z}}_2^T$ and $U\left(1\right)\times {\mathbb{Z}}_2^T$, and for both bosonic and fermionic topological orders. In all cases we conjecture that our indicators are complete in the sense that the anomalies they detect are in one-to-one correspondence with the known classification of $(3+1)\mathrm{D}$ SPT phases with the same symmetry. We also show that one of our indicators for bosonic topological orders has a mathematical interpretation as a partition function for the bulk $(3+1)\mathrm{D}$ SPT phase on a particular manifold and in the presence of a particular background gauge field for the $U\left(1\right)$ symmetry.

Theoretical studies on the electronic and lattice properties of the series of noncentrosymmetric superconductors $\text{Th}T\text{Si}$, where T = Co, Ni, Ir, and Pt, are presented. The electronic band-structure and crystal parameters were optimized within the density functional theory. Spin-orbit coupling leads to the splitting of the electronic bands and Fermi surfaces, with the stronger effect observed for the compounds with the heavier atoms Ir and Pt. The possible mixing of the spin-singlet and spin-triplet pairing in the superconducting state is discussed. The phonon dispersion relations and phonon density of states were obtained using the direct method. The dispersion curves in ThCoSi and ThIrSi exhibit low-energy modes along the $\mathrm{S}\text{−}\mathrm{N}\text{−}{\mathrm{S}}_0$ line with the tendency for softening and dynamic instability. Additionally, we calculate and analyze the contributions of phonon modes to lattice heat capacity.

Time-resolved spectroscopies using intense THz pulses appear as a promising tool to address collective electronic excitations in condensed matter. In particular, recent experiments showed the possibility to selectively excite collective modes emerging across a phase transition, as is the case for superconducting and charge-density-wave (CDW) systems. One possible signature of these excitations is the emergence of coherent oscillations of the differential probe field in pump-probe protocols. While the analogy with the case of phonon modes suggests that the basic underlying mechanism should be a sum-frequency stimulated Raman process, a general theoretical scheme able to describe the experiments and to define the relevant optical quantity is still lacking. Here we provide this scheme by showing that coherent oscillations as a function of the pump-probe time delay can be linked to the convolution in the frequency domain between the squared pump field and a Raman-like nonlinear optical kernel. This approach is applied and discussed in a few paradigmatic examples: ordinary phonons in an insulator, and collective charge and Higgs fluctuations across a superconducting and a CDW transition. Our results not only account very well for the existing experimental data in a wide variety of systems, but they also offer a useful perspective to design future experiments in emerging materials.

We provide a versatile analytical framework for calculating the dynamics of a spin system in contact with a fermionic bath beyond the Markov approximation. The approach is based on a second-order expansion of the Nakajima-Zwanzig master equation but systematically includes all quantum coherent memory effects leading to non-Markovian dynamics. Our results describe, for the free induction decay, the full time range from the non-Markovian dynamics at short times, to the well-known exponential thermal decay at long times. We provide full analytic results for the entire time range using a bath of itinerant electrons as an archetype for universal quantum fluctuations. Furthermore, we propose a quantum thermodynamic scheme to employ the temperature insensitivity of the non-Markovian decay to transport heat out of the electron system and thus, by repeated reinitialization of a cluster of spins, to efficiently cool the electrons at very low temperatures.

The $M_x{\text{Bi}}_2{\text{Se}}_3$ family are candidates for topological superconductors, where $M$ could be Cu, Sr, or Nb. Twofold anisotropy has been observed in various experiments, prompting the interpretation that the superconducting state is nematic. However, it has since been recognized in the literature that a twofold anisotropy in the upper critical field $H_{c2}$ is incompatible with the naive nematic hypothesis. In this paper we study the Ginzburg-Landau theory of a nematic order parameter coupled with an applied stress, and classify possible phase diagrams. Assuming that the $H_{c2}$ puzzle is explained by a preexisting “pinning field,” we indicate how a stress can be applied to probe an extended region of the phase diagram, and verify if the superconducting order parameter is indeed nematic. We also explore the Josephson tunneling between the proposed nematic superconducting state and an $s$-wave superconductor. The externally applied stress is predicted to serve as an on/off switch to the tunneling current, and in a certain regime the temperature dependence of the critical current can be markedly different from that between two conventional $s$-wave superconductors.

Iridate heterostructures are gaining interest as their magnetic properties are much more sensitive to structural distortion compared to pure spin systems due to spin-orbital entanglement. While bulk monolayer and bilayer iridates show $ab$-plane canted and $c$-axis antiferromagnetic (AFM) order, recent experiments on layered iridate superlattices (SLs) have revealed striking properties, especially in the bilayer SLs. A spin model is presented to illustrate the proclivity towards $ab$-plane canted AFM order. A realistic Hubbard model including spin-dependent hopping terms is constructed for the bilayer SL, and magnetic excitations are investigated in the self-consistently determined magnetic state. The Hubbard model analysis confirms the spin model results and shows strongly reduced magnon energy gap and an isospin reorientation transition from $c$-axis to $ab$-plane canted AFM order with increasing tilting.

Separating electron and phonon components in thermal conductivity is imperative for understanding thermal transport in metals and highly desirable in many applications. In this work, we predict the mode-dependent electron and phonon thermal conductivities of 18 different metals at room temperature from first principles. Our first-principles predictions, in general, agree well with those available experimental data. For phonon thermal conductivity, we find that it is in the range of 2–18 W/mK, which accounts for 1%–40% of the total thermal conductivity. It is also found that the phonon thermal conductivities in transition metals and transition-intermetallic compounds (TICs) are non-negligible compared to noble metals due to the high phonon group velocities of the former. We further show that the electron-phonon coupling effect on phonon thermal conductivity in transition metals and intermetallic compounds is stronger than that of nobles, which is attributed to the larger electron-phonon coupling constant with a high electron density of states within the Fermi window and high phonon frequency in the former. For electron thermal conductivity, we observe that the transition metals and TICs have lower electron thermal conductivities compared to noble metals, which is mainly due to the weak electron-phonon coupling in noble metals. It is found that the Lorenz number of transition metals and TICs hold larger deviations from the Sommerfeld value $L_0=2.44\times {10}^{-8}\mathrm{W}\mathrm{\Omega }{\mathrm{K}}^{-2}$. We also find the mean free paths extracted at 50% accumulation function for phonons (within 10 nm) are generally smaller than those of electrons (5–25 nm).

Skyrmion crystals (SkXs) are a periodic alignment of magnetic skyrmions, i.e., a type of topologically protected spin textures. Compared with ordinary crystals, they can be drastically deformed under anisotropic effects because they are composed of field patterns whose deformation does not cause any bond-breaking. This exotic ductility of SkXs brings about great tunability of its collective excitations, called emergent phonons, which are vital for magnonics application. The question is how to quantitatively determine the emergent phonons of distorted SkXs. Here we systematically study the long-wavelength emergent phonons of SkXs distorted by (a) a negative exchange anisotropy and (b) a tilted magnetic field. In both cases, deformation and structural transitions of SkXs thoroughly influence the frequency, anisotropy of vibrational pattern, dispersion relation, and coupling between the lattice vibration and in-lattice vibration for all modes. Tilted magnetic fields are very effective in tuning the emergent phonons, such that all modes except the Goldstone mode can be excited by AC magnetic fields when a tilted bias field is presented.

The helical electron states on the surface of topological insulators or elemental bismuth become unstable toward superconducting pairing formation when coupled to the charge or magnetic fluctuations. The latter gives rise to pairing instability in chiral channels $d_{xy}\pm i{d}_{x^2-y^2}$, as has been observed recently in the epitaxial Bi/Ni bilayer system at relatively high temperature, while the former favors a pairing with zero total angular momentum. Motivated by this observation we study the vortex bound states in these superconducting states. We consider a minimal model describing the superconductivity in the presence of a vortex in the superconducting order parameter. We show that zero-energy states appear in the spectrum of the vortex core for all pairing symmetries. Our findings may facilitate the observation of Majorana modes bounded to the vortices in heterostructures with no need for a proximity-induced superconductivity and relatively large value of $\mathrm{\Delta }/E_F$.

The antiferromagnetism in $\alpha -{\mathrm{Cu}}_3\mathrm{Mg}{\left(\mathrm{OH}\right)}_6{\mathrm{Br}}_2$ was studied by magnetic-susceptibility, specific-heat, and neutron-diffraction measurements. The crystal structure consists of ${\mathrm{Cu}}^{2+}$ kagome layers with ${\mathrm{Mg}}^{2+}$ ions occupying the centers of the hexagons, separated by ${\mathrm{Br}}^{1-}$ ions. The magnetic system orders antiferromagnetically at 5.4 K with the magnetic moments aligned ferromagnetically within the kagome planes. The ordered moment is $0.94{\mu }_B$, suggesting little quantum and geometrical fluctuations. By comparing the magnetic and specific-heat properties with those of the haydeeite, we suggest that $\alpha -{\mathrm{Cu}}_3\mathrm{Mg}{\left(\mathrm{OH}\right)}_6{\mathrm{Br}}_2$ may be described by the two-dimensional spin-$1/2$ Heisenberg kagome model and is in the region of the ferromagnetic-order side of the phase diagram.

Combining first-principles calculations and experiment, we investigate the atomic and electronic structure of the Si/EuO interface. We consider the thermodynamic stability of interface structures with different levels of oxidation to identify the most probable configuration. By comparing the calculated band alignment and core-level shifts with measured values, we validate the theoretically constructed interface model. We find that the band offset can be tuned by altering the relative energy positions of the Si and EuO conduction bands via interface oxidation, which can be used to tune this materials system for specific applications in spintronics.