Abstract: The authors study the phenomena of many-body localization in a random field Heisenberg chain. In this paper the authors use a shift-inverse exact diagonalization approach that allows them to study the mid-spectrum spectral properties of the model for system sizes of up to N=22. This has allow the authors to identify the many-body localization edge.

Abstract: We theoretically study three-dimensional topological semimetals (TSMs) with nodal lines protected by crystalline symmetries. Compared to TSMs with point nodes, e.g., Weyl semimetals and Dirac semimetals, where the conduction and the valence bands touch at discrete points, in these TSMs the two bands cross at closed lines in the Brillouin zone. We propose two different classes of symmetry protected nodal lines in the absence and in the presence of spin-orbital coupling (SOC), respectively. In the former, we discuss nodal lines that are protected by a combination of inversion symmetry and time-reversal symmetry, yet, unlike previously studied nodal lines in the same symmetry class, each nodal line has a ${Z}_{2}$ monopole charge and can only be created (annihilated) in pairs. In the second class, with SOC, we show that a nonsymmorphic symmetry (screw axis) protects a four-band crossing nodal line in systems having both inversion and time-reversal symmetries.

Abstract: Recently, phosphorene, a monolayer honeycomb structure of black phosphorus, was experimentally manufactured and has attracted rapidly growing interest. Motivated by phosphorene, here we investigate the stability and electronic properties of the honeycomb structure of the arsenic system based on first-principles calculations. Two types of honeycomb structures, buckled and puckered, are found to be stable. We call them arsenenes, as in the case of phosphorene. We find that both buckled and puckered arsenenes possess indirect gaps. We show that the band gap of puckered and buckled arsenenes can be tuned by applying strain. The gap closing occurs at 6% strain for puckered arsenene, where the bond angles between the nearest neighbors become nearly equal. An indirect-to-direct gap transition occurs by applying strain. Specifically, 1% strain is enough to transform puckered arsenene into a direct-gap semiconductor. We note that a bulk form of arsenic called gray arsenic exists which can be used as a precursor for buckled arsenene. Our results will pave the way for applications to light-emitting diodes and solar cells.

Abstract: Graphene, a two-dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative curvature, called Mackay-Terrones crystals (MTCs), have been proposed and experimentally explored, yet their topological properties have yet to be discovered. Based on the first-principle calculations, we report an all-carbon MTC with topologically nontrivial electronic states by exhibiting node lines in bulk. When the node lines are projected onto surfaces to form circles, ``drumhead''-like flat surface bands nestled inside of the circles are formed. The bulk node line can evolve into a 3D Dirac point in the absence of inversion symmetry, the existence of which has been shown to be plausible in recent experiments.

Abstract: We determine the effect of defects induced by ion bombardment on the Raman spectrum of single-layer molybdenum disulfide. The evolution of both the linewidths and frequency shifts of the first-order Raman bands with the density of defects is explained with a phonon confinement model, using density functional theory to calculate the phonon dispersion curves. We identify several defect-induced Raman scattering peaks arising from zone-edge phonon modes. Among these, the most prominent is the $\mathrm{LA}(M)$ peak at $\ensuremath{\sim}227\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ and its intensity, relative to the one of first-order Raman bands, is found to be proportional to the density of defects. These results provide a practical route to quantify defects in single-layer $\mathrm{Mo}{\mathrm{S}}_{2}$ using Raman spectroscopy and highlight an analogy between the $\mathrm{LA}(M)$ peak in $\mathrm{Mo}{\mathrm{S}}_{2}$ and the $D$ peak in graphene.

Abstract: We investigate the orthorhombic phase $({T}_{d})$ of the layered transition-metal dichalcogenide ${\mathrm{MoTe}}_{2}$ as a Weyl semimetal candidate. ${\mathrm{MoTe}}_{2}$ exhibits four pairs of Weyl points lying slightly above $(\ensuremath{\sim}6\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ the Fermi energy in the bulk band structure. Different from its cousin ${\mathrm{WTe}}_{2}$, which was recently predicted to be a type-II Weyl semimetal, the spacing between each pair of Weyl points is found to be as large as 4% of the reciprocal lattice in ${\mathrm{MoTe}}_{2}$ (six times larger than that of ${\mathrm{WTe}}_{2}$). When projected onto the surface, the Weyl points are connected by Fermi arcs, which can be easily accessed by angle-resolved photoemission spectroscopy due to the large Weyl point separation. In addition, we show that the correlation effect or strain can drive ${\mathrm{MoTe}}_{2}$ from a type-II to a type-I Weyl semimetal.

Abstract: The layered honeycomb magnet $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ has been proposed as a candidate to realize a Kitaev spin model with strongly frustrated, bond-dependent, anisotropic interactions between spin-orbit entangled ${j}_{\mathrm{eff}}=\frac{1}{2}\phantom{\rule{4.pt}{0ex}}{\mathrm{Ru}}^{3+}$ magnetic moments. Here, we report a detailed study of the three-dimensional crystal structure using x-ray diffraction on untwinned crystals combined with structural relaxation calculations. We consider several models for the stacking of honeycomb layers and find evidence for a parent crystal structure with a monoclinic unit cell corresponding to a stacking of layers with a unidirectional in-plane offset, with occasional in-plane sliding stacking faults, in contrast with the currently assumed trigonal three-layer stacking periodicity. We report electronic band-structure calculations for the monoclinic structure, which find support for the applicability of the ${j}_{\mathrm{eff}}=\frac{1}{2}$ picture once spin-orbit coupling and electron correlations are included. Of the three nearest-neighbor Ru-Ru bonds that comprise the honeycomb lattice, the monoclinic structure makes the bond parallel to the $b$ axis nonequivalent to the other two, and we propose that the resulting differences in the magnitude of the anisotropic exchange along these bonds could provide a natural mechanism to explain the previously reported spin gap in powder inelastic neutron scattering measurements, in contrast to spin models based on the three-fold symmetric trigonal structure, which predict a gapless spectrum within linear spin wave theory. Our susceptibility measurements on both powders and stacked crystals, as well as magnetic neutron powder diffraction, show a single magnetic transition upon cooling below ${T}_{\mathrm{N}}\ensuremath{\approx}13$ K. The analysis of our neutron powder diffraction data provides evidence for zigzag magnetic order in the honeycomb layers with an antiferromagnetic stacking between layers. Magnetization measurements on stacked single crystals in pulsed field up to 60 T show a single transition around 8 T for in-plane fields followed by a gradual, asymptotic approach to magnetization saturation, as characteristic of strongly anisotropic exchange interactions.

Abstract: The hybrid halide perovskite ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$ exhibits a complex structural behavior, with successive transitions between orthorhombic, tetragonal, and cubic polymorphs around 165 and 327 K. Herein we report first-principles lattice dynamics (phonon spectrum) for each phase of ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{\mathrm{PbI}}_{3}$. The equilibrium structures compare well to solutions of temperature-dependent powder neutron diffraction. By following the normal modes, we calculate infrared and Raman intensities of the vibrations, and compare them to the measurement of a single crystal where the Raman laser is controlled to avoid degradation of the sample. Despite a clear separation in energy between low-frequency modes associated with the inorganic (${\mathrm{PbI}}_{3}{}^{\ensuremath{-}}{)}_{n}$ network and high-frequency modes of the organic ${\mathrm{CH}}_{3}{\mathrm{NH}}_{3}{}^{+}$ cation, significant coupling between them is found, which emphasizes the interplay between molecular orientation and the corner-sharing octahedral networks in the structural transformations. Soft modes are found at the boundary of the Brillouin zone of the cubic phase, consistent with displacive instabilities and anharmonicity involving tilting of the ${\mathrm{PbI}}_{6}$ octahedra around room temperature.

Abstract: We present an extensive first-principles study of a large set of native defects in ${\mathrm{MoS}}_{2}$ in order to find out the types and concentrations of the most important defects in this system. The calculations are carried out for both bulk and monolayer forms of ${\mathrm{MoS}}_{2}$, which allows us to study how defect properties change between these two limiting cases. We consider single- and few-atom vacancies, antisites, adatoms on monolayer, and interstitials between layers in the bulk material. We calculate the formation energies of neutral and charged defects, determine the charge transition levels, and from these self-consistently assess the concentration of defects at thermal equilibrium as well as the resulting positions of the Fermi level. The chemical potential values corresponding to different growth conditions are carefully accounted for, and for all values of chemical potentials relevant to the growth of ${\mathrm{MoS}}_{2}$, the S vacancies are found to be the most abundant defects. However, they are acceptors and cannot be the cause of the often observed $n$-type doping. At the same time, Re impurities, which are often present in natural ${\mathrm{MoS}}_{2}$ samples, naturally provide good $n$-type doping behavior. We also calculate migration barriers for adatoms and interstitials and discuss how they can affect the growth process.

Abstract: A systematic study of both the harmonic response and spin torque ferromagnetic resonance demonstrates that the spin Hall torque efficiency in a Pt-ferromagnetic (FM) structure is strongly dependent on the interface properties and the choice of the ferromagnetic materials, a key point that has until now not been made in spin Hall studies.

Abstract: We report magnetic and thermodynamic properties of single crystal $\ensuremath{\alpha}\ensuremath{-}{\text{RuCl}}_{3}$, in which the ${\text{Ru}}^{3+}\phantom{\rule{0.28em}{0ex}}(4{d}^{5})$ ion is in its low spin state and forms a honeycomb lattice. Two features are observed in both magnetic susceptibility and specific heat data; a sharp peak at 7 K and a broad hump near 10--15 K. In addition, we observe a metamagnetic transition between 5 and 10 T. Our neutron diffraction study of single crystal samples confirms that the low temperature peak in the specific heat is associated with a magnetic order with unit cell doubling along the honeycomb (100) direction, which is consistent with zigzag order, one of the types of magnetic order predicted within the framework of the Kitaev-Heisenberg model.

Abstract: Using broadband spectroscopic ellipsometry, the authors determine the complex valued dielectric function of silver films from 0.05 eV (\ensuremath{\lambda}=25 \ensuremath{\mu}) to 4.14 eV (\ensuremath{\lambda} = 300 nm) with a statistical uncertainty of less than 1%. While several previous similar measurements exist, they span considerably shorter energy ranges and report partially inconsistent results. In view of the wide-ranging applications of silver in nanophotonics, plasmonics and optical metamaterials, we anticipate this paper to become a standard reference for many scientists and engineers.

Abstract: Tin selenide (SnSe) and tin sulfide (SnS) have recently attracted particular interest due to their great potential for large-scale thermoelectric applications. A complete prediction of the thermoelectric performance and the understanding of underlying heat and charge transport details are the key to further improvement of their thermoelectric efficiency. We conduct comprehensive investigations of both thermal and electrical transport properties of SnSe and SnS using first-principles calculations combined with the Boltzmann transport theory. Due to the distinct layered lattice structure, SnSe and SnS exhibit similarly anisotropic thermal and electrical behaviors. The cross-plane lattice thermal conductivity ${\ensuremath{\kappa}}_{L}$ is $40--60%$ lower than the in-plane values. Extremely low ${\ensuremath{\kappa}}_{L}$ is found for both materials because of high anharmonicity, while the average ${\ensuremath{\kappa}}_{L}$ of SnS is $\ensuremath{\sim}8%$ higher than that of SnSe from 300 to 750 K. It is suggested that nanostructuring would be difficult to further decrease ${\ensuremath{\kappa}}_{L}$ because of the short mean free paths of dominant phonon modes (1--30 nm at 300 K), while alloying would be efficient in reducing ${\ensuremath{\kappa}}_{L}$ considering that the relative ${\ensuremath{\kappa}}_{L}$ contribution $(\ensuremath{\sim}65%)$ of optical phonons is remarkably large. On the electrical side, the anisotropic electrical conductivities are mainly due to the different effective masses of holes and electrons along the $a, b$, and $c$ axes. This leads to the highest optimal $\mathit{ZT}$ values along the $b$ axis and lowest ones along the $a$ axis in both $p$-type materials. However, the $n$-type ones exhibit the highest $\mathit{ZT}\mathrm{s}$ along the $a$ axis due to the enhancement of power factor when the chemical potential gradually approaches the secondary conduction band valley that causes significant increase in electron mobility and density of states. Owing to the larger mobility and smaller ${\ensuremath{\kappa}}_{L}$ along the given direction, SnSe exhibits larger optimal ZTs compared with SnS in both $p$- and $n$-type materials. For both materials, the peak $\mathit{ZT}\mathrm{s}$ of $n$-type materials are much higher than those of $p$-type ones along the same direction. The predicted highest $\mathit{ZT}$ values at 750 K are 1.0 in SnSe and 0.6 in SnS along the $b$ axis for the $p$-type doping, while those for the $n$-type doping reach 2.7 in SnSe and 1.5 in SnS along the $a$ axis, rendering them among the best bulk thermoelectric materials for large-scale applications. Our calculations show reasonable agreements with the experimental results and quantitatively predict the great potential in further enhancing the thermoelectric performance of SnSe and SnS, especially for the $n$-type materials.

Abstract: The group-IV monochalcogenides SnS, SnSe, GeS, and GeSe form a family within the wider group of semiconductor ``phosphorene analogues.'' Here, we used first-principles calculations to investigate systematically their structural, electronic, and optical properties, analyzing the changes associated with the reduction of dimensionality, from bulk to monolayer or bilayer form. We show that all those binary phosphorene analogues are semiconducting, with band-gap energies covering part of the infrared and visible range, and in most cases higher than phosphorene. Further, we found that they have multiple valleys in the valence and conduction band, the latter with spin-orbit splitting of the order of 19--86 meV.

Abstract: Layered transition-metal trichalcogenides with the chemical formula $AB{X}_{3}$ have attracted recent interest as potential candidates for two-dimensional magnets. Using first-principles calculations within density functional theory, we investigate the magnetic ground states of monolayers of Mn- and Cr-based semiconducting trichalcogenides. We show that the second and third nearest-neighbor exchange interactions (${J}_{2}$ and ${J}_{3}$) between magnetic ions, which have been largely overlooked in previous theoretical studies, are crucial in determining the magnetic ground state. Specifically, we find that monolayer ${\mathrm{CrSiTe}}_{3}$ is an antiferromagnet with a zigzag spin texture due to significant contribution from ${J}_{3}$, whereas ${\mathrm{CrGeTe}}_{3}$ is a ferromagnet with a Curie temperature of 106 K. Monolayers of Mn compounds (${\mathrm{MnPS}}_{3}$ and ${\mathrm{MnPSe}}_{3}$) always show antiferromagnetic N\'eel order. We identify the physical origin of various exchange interactions, and demonstrate that strain can be an effective knob for tuning the magnetic properties. Possible magnetic ordering in the bulk is also discussed. Our study suggests that $AB{X}_{3}$ can be a promising platform to explore two-dimensional magnetic phenomena.

Abstract: We present an ab initio framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of ${\mathrm{SrTiO}}_{3}$ and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistortive mode depends significantly on the system size near the critical temperature of the cubic-to-tetragonal phase transition. By applying perturbation theory to the SCPH result, phonon lifetimes are calculated for cubic ${\mathrm{SrTiO}}_{3}$, which are then employed to predict lattice thermal conductivity using the Boltzmann transport equation within the relaxation-time approximation. The presented methodology is efficient and accurate, paving the way toward a reliable description of thermodynamic, dynamic, and transport properties of systems with severe anharmonicity, including thermoelectric, ferroelectric, and superconducting materials.

Abstract: Metasurfaces characterized by a transverse gradient of local impedance have recently opened exciting directions for light manipulation at the subwavelength scale. Here we add a temporal gradient to the picture, showing that spatiotemporal variations over a surface may greatly extend the degree of wave manipulation in metasurfaces, and break several of their constraints associated with symmetries. As an example, we synthesize a nonreciprocal classical analog to electromagnetically induced transparency, opening a narrow window of one-way efficient transmission in an otherwise opaque surface. These properties pave the way to magnetic-free, planarized, nonreciprocal ultrathin surfaces for free-space isolation.

Abstract: Exactly solvable models often provide valuable insights in theoretical studies of topological phases. Here the authors introduce exactly solvable models of interacting Majorana fermions each with extensive topological ground-state degeneracy and a hierarchy of pointlike, topological excitations that are only free to move within submanifolds of the full lattice. These very different models make up a new kind of topological quantum order.

Abstract: MXenes are a set of two-dimensional transition metal carbides and nitrides that offer many potential applications in energy storage and electronic devices. As an important parameter to design new electronic devices, we investigate the work functions of bare MXenes and their functionalized ones with F, OH, and O chemical groups using first-principles calculations. From our calculations, it turns out that the OH-terminated MXenes attain ultralow work functions between 1.6 and 2.8 eV. Moreover, depending on the type of the transition metal, the F or O functionalization affects increasing or decreasing the work functions. We show that the changes in the work functions upon functionalizations are linearly correlated with the changes in the surface dipole moments. It is shown that the work functions of the F- or O-terminated MXenes are controlled by two factors: the induced dipole moments by the charge transfers between F/O and the substrate, and the changes in the total surface dipole moments caused by surface relaxation upon the functionalization. However, in the cases of the OH-terminated MXenes, in addition to these two factors, the intrinsic dipole moments of the OH groups play an important role in determining the total dipole moments and consequently justify their ultralow work functions.

Abstract: Spin waves in perpendicularly magnetized ${\text{Pt/Co/AlO}}_{x}/\text{Pt}$ ultrathin films with varying Co thicknesses (06--12 nm) have been studied with Brillouin light spectroscopy in the Damon-Eshbach geometry The measurements reveal a pronounced nonreciprocal propagation, which increases with decreasing Co thickness This nonreciprocity, attributed to an interfacial Dzyaloshinskii-Moriya interaction (DMI), is significantly stronger than asymmetries resulting from surface anisotropies for such modes Results are consistent with an interfacial DMI constant ${D}_{\mathrm{s}}=\ensuremath{-}17\ifmmode\pm\else\textpm\fi{}011\phantom{\rule{028em}{0ex}}\text{pJ}$/m, which favors left-handed chiral spin structures This suggests that such films below 1 nm in thickness should support chiral states such as skyrmions at room temperature

Abstract: High harmonic generation (HHG) in solids is investigated. We find that interband emission is dominant for the midinfrared laser driver frequencies, whereas intraband emission dominates the far-infrared range. Interband HHG is similar to atomic HHG and therewith opens the possibility to apply atomic attosecond technology to the condensed matter phase. Interband emission is investigated with a quasiclassical method, by which HHG can be modeled based on the classical trajectory analysis of electron-hole pairs. This analysis yields a simple approximate cutoff law for HHG in solids. Differences between HHG in atoms and solids are identified that are important for adapting atomic attosecond technology to make it applicable to condensed matter.

Abstract: Hybrids of graphene and two-dimensional transition-metal dichalcogenides (TMDCs) have the potential to bring graphene spintronics to the next level. As we show here by performing first-principles calculations of graphene on monolayer ${\mathrm{MoS}}_{2}$, there are several advantages of such hybrids over pristine graphene. First, Dirac electrons in graphene exhibit a giant global proximity spin-orbit coupling, without compromising the semimetallic character of the whole system at zero field. Remarkably, these spin-orbit effects can be very accurately described by a simple effective Hamiltonian. Second, the Fermi level can be tuned by a transverse electric field to cross the ${\mathrm{MoS}}_{2}$ conduction band, creating a system of coupled massive and massless electron gases. Both charge and spin transport in such systems should be unique. Finally, we propose to use graphene/TMDC structures as a platform for optospintronics, in particular, for optical spin injection into graphene and for studying spin transfer between TMDCs and graphene.

Abstract: Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, both in experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin chain model. We show that the resulting LIOMs are quasi-local, and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.

Abstract: Intensive studies of the interplay between spin-orbit coupling (SOC) and electronic correlations in transition-metal compounds have recently been undertaken. In particular, ${j}_{\mathrm{eff}}=1/2$ bands on a honeycomb lattice provide a pathway to realize Kitaev's exactly solvable spin model. However, since current wisdom requires strong atomic SOC to make ${j}_{\mathrm{eff}}=1/2$ bands, studies have been limited to iridium oxides. Contrary to this expectation, we demonstrate how Kitaev interactions arise in $4d$-orbital honeycomb $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, despite having significantly weaker SOC than the iridium oxides, via assistance from electron correlations. A strong-coupling spin model for these correlation-assisted ${j}_{\mathrm{eff}}=1/2$ bands is derived, in which large antiferromagnetic Kitaev interactions emerge along with ferromagnetic Heisenberg interactions. Our analyses suggest that the ground state is a zigzag-ordered phase lying close to the antiferromagnetic Kitaev spin liquid. Experimental implications for angle-resolved photoemission spectroscopy, neutron scattering, and optical conductivities are discussed.

Abstract: We show that the spectral weights W mK (k ) used for the unfolding of two-component spinor eigenstates ∣ ∣ ψ SC mK ⟩=|α⟩|ψ SC mK ,α⟩+|β⟩|ψ SC mK ,β⟩ can be decomposed as the sum of the pa ...

Abstract: We introduce a numerical algorithm to simulate the time evolution of a matrix product state under a long-ranged Hamiltonian in moderately entangled systems. In the effectively one-dimensional representation of a system by matrix product states, long-ranged interactions are necessary to simulate not just many physical interactions but also higher-dimensional problems with short-ranged interactions. Since our method overcomes the restriction to short-ranged Hamiltonians of most existing methods, it proves particularly useful for studying the dynamics of both power-law interacting, one-dimensional systems, such as Coulombic and dipolar systems, and quasi-two-dimensional systems, such as strips or cylinders. First, we benchmark the method by verifying a long-standing theoretical prediction for the dynamical correlation functions of the Haldane-Shastry model. Second, we simulate the time evolution of an expanding cloud of particles in the two-dimensional Bose-Hubbard model, a subject of several recent experiments.

Abstract: The layered compound $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ is composed of a honeycomb lattice of magnetic ${\mathrm{Ru}}^{3+}$ ions with the $4{d}^{5}$ electronic state. We have investigated the magnetic properties of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ via magnetization and specific heat measurements using single crystals. It was observed that $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ undergoes a structural phase transition at ${T}_{t}\phantom{\rule{0.16em}{0ex}}\ensuremath{\simeq}\phantom{\rule{0.16em}{0ex}}150$ K accompanied by fairly large hysteresis. This structural phase transition is expected to be similar to that observed in closely related ${\mathrm{CrCl}}_{3}$. The magnetizations and magnetic susceptibilities are strongly anisotropic, which mainly arise from the anisotropic $g$ factors, i.e., ${g}_{ab}\phantom{\rule{0.16em}{0ex}}\ensuremath{\simeq}\phantom{\rule{0.16em}{0ex}}2.5$ and ${g}_{c}\phantom{\rule{0.16em}{0ex}}\ensuremath{\simeq}\phantom{\rule{0.16em}{0ex}}0.4$ for magnetic fields parallel and perpendicular to the $ab$ plane, respectively. These $g$ factors and the obtained entropy indicate that the effective spin of ${\mathrm{Ru}}^{3+}$ is one-half, which results from the low-spin state. Specific heat data show that magnetic ordering occurs in four steps at zero magnetic field. The successive magnetic phase transitions should be ascribed to the competition among exchange interactions. The magnetic phase diagram for $H\phantom{\rule{0.16em}{0ex}}\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}ab$ is obtained. We discuss the strongly anisotropic $g$ factors in $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ and deduce that the exchange interaction is strongly XY-like. $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ is magnetically described as a three-dimensionally coupled XY-like frustrated magnet on a honeycomb lattice.

Abstract: States of matter with a sharp Fermi surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include (i) quantum critical points associated with the onset of order in metals; (ii) spinon Fermi-surface [U(1) spin-liquid] state of a Mott insulator; (iii) Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of an ordering phase transition in a metal, and demonstrate that the attractive interaction mediated by the order-parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between (i)U(1) and Z_2 spin-liquid states; (ii) Halperin-Lee-Read and Moore-Read states.

Abstract: Valleys in monolayer transition-metal dichalcogenides seamlessly connect two basic carriers of quantum information, namely, the electron spin and photon helicity. Lifting the valley degeneracy is an attractive route to achieve further optoelectronic manipulations. However, the magnetic field only creates a very small valley splitting. We propose a strategy to create giant valley splitting by the proximity-induced Zeeman effect. Our first principles calculations of monolayer ${\mathrm{MoTe}}_{2}$ on a EuO substrate show that valley splitting over 300 meV can be generated. Interband transition energies become valley dependent, leading to selective spin-photon coupling by optical frequency tuning. The valley splitting is also continuously tunable by rotating the substrate magnetization. The giant and tunable valley splitting adds a different dimension to the exploration of unique optoelectronic devices based on magneto-optical coupling and magnetoelectric coupling.