We explore a new class of topologically stable zero-energy modes which are protected by coexisting chiral and spatial symmetries. If a chiral-symmetric Hamiltonian has an additional spatial symmetry such as reflection, inversion, and rotation, the Hamiltonian can be separated into independent chiral-symmetric subsystems by the eigenvalue of the space symmetry operator. Each subsystem supports chiral zero-energy modes when a topological index assigned to the block is nonzero. By applying the argument to Bloch electron systems, we detect band touching at symmetric points in the Brillouin zone. In particular, we show that Weyl nodes appearing in honeycomb lattice (e.g., graphene) and in half-flux square lattice are protected by threefold and twofold rotation symmetry, respectively. We also present several examples of Dirac semimetal with isolated band-touching points in three-dimensional $k$ space, which are protected by combined symmetry of rotation and reflection. The zero-mode protection by spatial symmetry is distinct from that by the conventional winding number. We demonstrate that symmetry-protected band touching points emerge even though the winding number is zero. Finally, we identify relevant topological charges assigned to the gapless points.

We experimentally demonstrate that unidirectional reversal of the magnetic vortex core polarity is possible by excitation with sub-100-ps-long orthogonal monopolar magnetic pulse sequences in a wide range of pulse lengths and amplitudes. The application of such short digital pulses is a favorable excitation scheme for technological applications. Measured phase diagrams of this unidirectional, spin-wave mediated vortex core reversal are in good qualitative agreement with phase diagrams obtained from micromagnetic simulations. The time dependence of the reversal process, observed by time-resolved scanning transmission x-ray microscopy indicates a switching time of 100 ps and fits well with our simulations. The origin of the asymmetric response to clockwise and counterclockwise excitation which is a prerequisite for reliable unidirectional switching is discussed, based on the gyromode–spin-wave coupling. Situations are found in which a three-dimensional dynamics is important, because a vortex-antivortex pair starts to form close to the core of the original vortex in the lower part of the disk without completing the formation across the whole thickness so that it dissolves later on and does not lead to switching of the original vortex core.

Time-reversal symmetry prohibits elastic backscattering of electrons propagating within a helical edge of a two-dimensional topological insulator. However, small band gaps in these systems make them sensitive to doping disorder, which may lead to the formation of electron and hole puddles. Such a puddle—a quantum dot—tunnel-coupled to the edge may significantly enhance the inelastic backscattering rate, due to the long dwelling time of an electron in the dot. The added resistance is especially strong for dots carrying an odd number of electrons, due to the Kondo effect. For the same reason, the temperature dependence of the added resistance becomes rather weak. We present a detailed theory of the quantum dot effect on the helical edge resistance. It allows us to make specific predictions for possible future experiments with artificially prepared dots in topological insulators. It also provides a qualitative explanation of the resistance fluctuations observed in short HgTe quantum wells. In addition to the single-dot theory, we develop a statistical description of the helical edge resistivity introduced by random charge puddles in a long heterostructure carrying helical edge states. The presence of charge puddles in long samples may explain the observed coexistence of a high sample resistance with the propagation of electrons along the sample edges.

Using the emission of the positively charged exciton as a probe, we analyze the dynamics of the optical pumping and the dynamics of the relaxation of a Mn spin exchange coupled with a confined hole spin in a II-VI semiconductor quantum dot. The hole-Mn spin can be efficiently initialized in a few tens of ns under optical injection of spin-polarized carriers. We show that this optical pumping process and its dynamics are controlled by electron-Mn flip-flops within the positively charged exciton-Mn complex. The pumping mechanism and its magnetic field dependence are theoretically described by a model including the dynamics of the electron-Mn complex in the excited state and the dynamics of the hole-Mn complex in the ground state of the positively charged quantum dot. We measure at zero magnetic field a spin-relaxation time of the hole-Mn spin in the $\mu \text{s}$ range or shorter. This hole-Mn spin relaxation is induced by the presence of valence-band mixing in self-assembled quantum dots.

The honeycomb iridates $A_2{\mathrm{IrO}}_3$ (A = Na, Li) constitute promising candidate materials to realize the Heisenberg-Kitaev model (HKM) in nature, hosting unconventional magnetic as well as spin-liquid phases. Recent experiments suggest, however, that ${{\mathrm{Li}}_2\mathrm{IrO}}_3$ exhibits a magnetically ordered state of incommensurate spiral type which has not been identified in the HKM. We show that these findings can be understood in the context of an extended Heisenberg-Kitaev scenario satisfying all tentative experimental evidence: (i) the maximum of the magnetic susceptibility is located inside the first Brillouin zone, (ii) the Curie-Weiss temperature is negative relating to dominant antiferromagnetic fluctuations, and (iii) significant second-neighbor spin exchange is involved.

We propose an experiment to use the magneto-optical Faraday effect to probe the dynamic Hall conductivity of spin-liquid candidates. Theory predicts that an external magnetic field will generate an internal gauge field. If the source of conductivity is in spinons with a Fermi surface, a finite Faraday rotation angle is expected. We predict the angle to scale as the square of the frequency rather than display the standard cyclotron resonance pattern. Furthermore, the Faraday effect should be able to distinguish the ground state of the spin liquid, as we predict no rotation for massless Dirac spinons. We give a semiquantitative estimate for the magnitude of the effect and find that it should be experimentally feasible to detect in both $\kappa {\text{−}\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{CN}\right)}_3$ and, if the spinons form a Fermi surface, herbertsmithite. We also comment on the magneto-optical Kerr effect and show that the imaginary part of the Kerr angle (circular dichroism) may be measurable.

Hyperbolic metamaterials (HMMs) based on metal/dielectric multilayers have garnered attention in recent years due to their extraordinary optical properties emanating from hyperbolic dispersion of isofrequency surfaces. We have developed a new class of epitaxial metal/dielectric superlattice HMMs based on transition-metal nitrides—titanium nitride (TiN) and aluminum scandium nitride (${\mathrm{Al}}_x{\mathrm{Sc}}_{1-x}\mathrm{N}$)—that could potentially lead to better HMM performance without requiring any traditional plasmonic materials such as gold (Au) and silver (Ag). Our results suggest that the TiN/(Al,Sc)N superlattices grown on (001) MgO substrates are nominally monocrystalline and pseudomorphic, exhibiting sharp interfaces with interface roughnesses of about one to two atomic layers. HMMs deposited on (0001) sapphire substrates grow in 111 orientation with local epitaxy inherent to individual grains, while on (001) Si substrates, the HMMs are polycrystalline. The HMM properties extracted with effective medium theory along with nonlocal field corrections indicate that the TiN/(Al,Sc)N superlattices grown on MgO substrates have both transverse negative (type-I) and transverse positive (type-II) hyperbolic dispersion of the isofrequency surfaces in the visible to near-IR spectral regions. The carrier concentration of TiN layers was varied deliberately by tuning the deposition conditions, thereby shifting the spectral range of both type-I and type-II HMM dispersions. The epitaxial thin-film-based HMMs developed here mark the beginning of a new generation of optical metamaterials with enhanced electromagnetic properties.

Thermoelectric transport in nanoscale conductors is analyzed in terms of the response of the system to a thermomechanical field, first introduced by Luttinger, which couples to the electronic energy density. While in this approach, the temperature remains spatially uniform, we show that a spatially varying thermomechanical field effectively simulates a temperature gradient across the system and allows us to calculate the electric and thermal currents that flow due to the thermomechanical field. In particular, we show that in the long-time limit, the currents thus calculated reduce to those that one obtains from the Landauer-Büttiker formula, suitably generalized to allow for different temperatures in the reservoirs, if the thermomechanical field is applied to prepare the system, and subsequently turned off at $t=0$. Alternatively, we can drive the system out of equilibrium by switching the thermomechanical field after the initial preparation. We compare these two scenarios, employing a model noninteracting Hamiltonian, in the linear regime, in which they coincide, and in the nonlinear regime, in which they show marked differences. We also show how an operationally defined local effective temperature can be computed within this formalism.

We analyze the dynamics of a domain wall in an easy-axis antiferromagnet driven by circularly polarized magnons. Magnons pass through a stationary domain wall without reflection and thus exert no force on it. However, they reverse their spin upon transmission, thereby transferring two quanta of angular momentum to the domain wall and causing it to precess. A precessing domain wall partially reflects magnons back to the source. The reflection of spin waves creates a previously identified reactive force. We point out a second mechanism of propulsion, which we term redshift: magnons passing through a precessing domain wall lower their frequency by twice the angular velocity of the domain wall; the concomitant reduction of the magnons' linear momentum indicates momentum transfer to the domain wall. We solve the equations of motion for spin waves in the background of a uniformly precessing domain wall with the aid of supersymmetric quantum mechanics and compute the net force and torque applied by magnons to the domain wall. Redshift is the dominant mechanism of propulsion at low spin-wave intensities; reflection dominates at higher intensities. We derive a set of coupled algebraic equations to determine the linear velocity and angular frequency of the domain wall in a steady state. The theory agrees well with numerical micromagnetic simulations.

We develop a fully analytical calculation of the sub-Poissonian statistics resulting from the temporal anticorrelation of the nucleation events in a supersaturated nanophase, such as occurs in particular during vapor-liquid-solid growth of nanowires [F. Glas, J. C. Harmand, and G. Patriarche, Phys. Rev. Lett. 104, 135501 (2010)]. The sequence of nucleation events is modeled as a stochastic Markov process. The deviation from Poisson statistics is quantified by a single parameter $\gamma$, namely the ratio of the nucleation probabilities immediately after and before nucleation. We first determine self-consistently, by using $q\text{−}\mathrm{calculus}$, the densities of probability of the nucleation probability, both when nucleation occurs and at an arbitrary instant. We then derive the probability for having a given number of nucleations in any given time interval. The distribution of these probabilities shows a marked narrowing with respect to Poisson statistics, in agreement with our previous experiments. We calculate explicitly the standard deviation of this distribution, which quickly saturates as the length of the time interval increases. Finally, we compute the distribution of the waiting times between nucleations. We discuss how the computed quantities vary with parameter $\gamma$. The results are in complete agreement with our numerical simulations. Somewhat surprisingly, a marked narrowing of the distribution of the numbers of nucleations occurring in fixed time intervals appears as fully compatible with a very broad distribution of waiting times.

We present electronic transport measurements through short and narrow $\left(30\times 30\mathrm{nm}\right)$ single-layer graphene constrictions on a hexagonal boron nitride substrate. While the general observation of Coulomb blockade is compatible with earlier work, the details are not: We show that the area on which charge is localized can be significantly larger than the area of the constriction, suggesting that the localized states responsible for the Coulomb blockade leak out into the graphene bulk. The high bulk mobility of graphene on hexagonal boron nitride, however, seems to be inconsistent with the short bulk localization length required to see Coulomb blockade. To explain these findings, charge must instead be primarily localized along the imperfect edges of the devices and extend along the edge outside of the constriction. In order to better understand the mechanisms, we compare the experimental findings with tight-binding simulations of such constrictions with disordered edges. Finally, we discuss previous experiments in the light of our findings.

Neutron scattering is used to probe magnetic interactions as superconductivity develops in optimally doped ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$. Applying the first moment sum rule to comprehensive neutron scattering data, we extract the change in magnetic exchange energy $\Delta \left[J_{\mathbf{R}-{\mathbf{R}}^{\prime }}\langle {\mathbf{S}}_{\mathbf{R}}·{\mathbf{S}}_{{\mathbf{R}}^{\prime }}\rangle \right]$ in the superconducting state referenced to the normal state. Oscillatory changes are observed for Fe-Fe displacements $\left|\Delta \mathbf{R}\right|<\xi$, where $\xi =1.3\left(1\right)$ nm is the superconducting coherence length. Dominated by a large reduction in the second nearest neighbor exchange energy [$-1.2\left(2\right)$ meV/Fe], the overall reduction in magnetic interaction energy is $\Delta \langle {\mathcal{H}}_{\text{mag}}\rangle =-0.31\left(9\right)$ meV/Fe. Comparison to the superconducting condensation energy $\Delta E_{\text{SC}}=-0.013\left(1\right)$ meV/Fe, which we extract from specific heat data, suggests the modified magnetism we probe drives superconductivity in ${\mathrm{Fe}}_{1+\delta }{\mathrm{Se}}_x{\mathrm{Te}}_{1-x}$.

Elastic and anelastic properties of single crystal samples of ${\mathrm{EuTiO}}_3$ have been measured between 10 and 300 K by resonant ultrasound spectroscopy at frequencies in the vicinity of 1 MHz. Softening of the shear elastic constants $C_{44}$ and $\frac{1}{2}\left(C_{11}-C_{12}\right)$ by $\sim 20–30\%$ occurs with falling temperature in a narrow interval through the transition point, $T_{\mathrm{c}}=284$ K, for the cubic-tetragonal transition. This is accounted for by classical coupling of macroscopic spontaneous strains with the tilt order parameter in the same manner as occurs in ${\mathrm{SrTiO}}_3$. A peak in the acoustic loss occurs a few degrees below $T_{\mathrm{c}}$ and is interpreted in terms of initially mobile ferroelastic twin walls, which rapidly become pinned with further lowering of temperature. This contrasts with the properties of twin walls in ${\mathrm{SrTiO}}_3$, which remain mobile down to at least 15 K. No further anomalies were observed that might be indicative of strain coupling to any additional phase transitions above 10 K. A slight anomaly in the shear elastic constants, independent of frequency and without any associated acoustic loss, was found at $\sim 140$ K. It marks a change from elastic stiffening to softening with falling temperature and perhaps provides evidence for coupling between strain and local fluctuations of dipoles related to the incipient ferroelectric transition. An increase in acoustic loss below $\sim 80$ K is attributed to the development of dynamical magnetic clustering ahead of the known antiferromagnetic ordering transition at $\sim 5.5$ K. Detection of these elastic anomalies serves to emphasize that coupling of strain with tilting, ferroelectric, and magnetic order parameters is likely to be a permeating influence in determining the structure, stability, properties, and behavior of ${\mathrm{EuTiO}}_3$.

The synthesis and characterization of a Yb-based material ${\mathrm{Ba}}_3{\mathrm{Yb}}_2{\mathrm{Zn}}_5{\mathrm{O}}_{11}$ are reported. This material is identified as a model system of a pseudospin-1/2 quantum antiferromagnet on “breathing” pyrochlore lattice characterized by an alternating array of small and large Yb tetrahedra. Despite dominant antiferromagnetic interactions $J\sim 7$ K, a large amount of magnetic entropy (25%) remains at 0.38 K, indicating that each small Yb tetrahedron forms a unique doubly degenerate singlet state. These results are well described by the Heisenberg pseudospin-1/2 single tetrahedron model.

We study the origin of a photocurrent generated in doped multilayer black phosphorus (BP) phototransistors, and find that it is dominated by thermally driven thermoelectric and bolometric processes. The experimentally observed photocurrent polarities are consistent with photothermal processes. The photothermoelectric current can be generated up to a micrometer away from the contacts, indicating a long thermal decay length. With an applied source-drain bias, a photobolometric current is generated across the whole device, overwhelming the photothermoelectric contribution at a moderate bias. The photoresponsivity in the multilayer BP device is two orders of magnitude larger than that observed in graphene.

The nonlocal correlation energy in the van der Waals density functional (vdW-DF) method can be interpreted in terms of a coupling of zero-point energies of characteristic modes of semilocal exchange-correlation (xc) holes. These xc holes reflect the internal functional in the framework of the vdW-DF method. We explore the internal xc hole components, showing that they share properties with those of the generalized-gradient approximation. We use these results to illustrate the nonlocality in the vdW-DF description and analyze the vdW-DF formulation of nonlocal correlation.

We determine the phase diagram of the Kane-Mele model with a long-range Coulomb interaction using an exact quantum Monte Carlo method. Long-range interactions are expected to play a role in honeycomb materials because the vanishing density of states in the semimetallic weak-coupling phase suppresses screening. According to our results, the Kane-Mele-Coulomb model supports the same phases as the Kane-Mele-Hubbard model. The nonlocal part of the interaction promotes short-range sublattice charge fluctuations, which compete with antiferromagnetic order driven by the onsite repulsion. Consequently, the critical interaction for the magnetic transition is significantly larger than for the purely local Hubbard repulsion. Our numerical data are consistent with $\mathrm{SU}\left(2\right)$ Gross-Neveu universality for the semimetal to antiferromagnet transition, and with 3D XY universality for the quantum spin Hall to antiferromagnet transition.

Twisted metamaterials, or arrays of identical planar metasurfaces stacked with a sequential rotation, have been recently introduced to realize broadband circular dichroism. Here we develop a generalized Floquet analysis to obtain the exact modal solutions for eigenwaves supported by these structures. The dispersion relation and wave propagation in twisted metamaterials are discussed in detail. Our analysis shows how the modal dispersion in these metamaterials becomes inherently different from the one of conventional periodic structures and how the eigenmodes support specific circular polarization properties based on a lattice effect, even when achiral inclusions are considered. These wave properties are ideal to realize optical devices that manipulate the polarization state of light over broad bandwidths. By analyzing the physical nature of these modes, including complex modes, we also extend the application of twisted metamaterials to realize passband and stop-band nanophotonic structures with strong polarization manipulation properties.

We introduce a new method, based on alternating optimization, for compact representation of spin Hamiltonians and solution of linear systems of algebraic equations in the tensor train format. We demonstrate the method's utility by simulating, without approximations, a ${}^{15}\mathrm{N}$ NMR spectrum of ubiquitin—a protein containing several hundred interacting nuclear spins. Existing simulation algorithms for the spin system and the NMR experiment in question either require significant approximations or scale exponentially with the spin system size. We compare the proposed method to the Spinach package that uses heuristic restricted state space techniques to achieve polynomial complexity scaling. When the spin system topology is close to a linear chain (e.g., for the backbone of a protein), the tensor train representation is more compact and can be computed faster than the sparse representation using restricted state spaces.

Structural and transport properties of thin Nb layers in Si/Nb/Si trilayers with Nb layer thickness $d$ from 1.1 nm to 50 nm have been studied. With decreasing thickness, the structure of the Nb layer changes from polycrystalline to amorphous at $d\simeq 3.3$ nm, while the superconducting temperature $T_c$ monotonically decreases. The Hall coefficient varies with $d$ systematically but changes sign into negative in ultrathin films with $d<1.6$ nm. The influence of boundary scattering on the relaxation rate of carriers, and band broadening in the amorphous films, may contribute to this effect.