The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of “transport equivalent effective mass” to the $\mathbf{k}·\widehat{\mathbf{p}}$ framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust, and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the abinit software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.

Plasmonic phenomena are exhibited in light-matter interaction involving materials whose real parts of permittivity functions attain negative values at operating wavelengths. However, such materials usually suffer from dissipative losses, thus limiting the performance of plasmon-based optical devices. Here, we utilize an alternative methodology that mimics a variety of plasmonic phenomena by exploiting the well-known structural dispersion of electromagnetic modes in bounded guided-wave structures filled with only materials with positive permittivity. A key issue in the design of such structures is prevention of mode coupling, which can be achieved by implementing thin metallic wires at proper interfaces. This method, which is more suitable for lower frequencies, allows designers to employ conventional dielectrics and highly conductive metals for which the loss is low at these frequencies, while achieving plasmonic features. We demonstrate, numerically and analytically, that this platform can provide surface plasmon polaritons, local plasmonic resonance, plasmonic cloaking, and epsilon-near-zero-based tunneling using conventional positive-dielectric materials.

We investigate a model of hard-core bosons with correlated hopping on the honeycomb lattice in an external magnetic field by means of a coupled-wire approach. It has been numerically shown that this model exhibits at half filling the bosonic integer quantum Hall (BIQH) state, which is a symmetry-protected topological phase protected by the $U\left(1\right)$ particle conservation [Y.-C. He et al., Phys. Rev. Lett. 115, 116803 (2015)]. By combining the bosonization approach and a coupled-wire construction, we analytically confirm this finding and show that it even holds in the strongly anisotropic (quasi-one-dimensional) limit. We discuss the stability of the BIQH phase against tunnelings that break the separate particle conservations on different sublattices down to a global particle conservation. We further argue that a phase transition between two different BIQH phases is in a deconfined quantum critical point described by two copies of the $(2+1)$-dimensional $O\left(4\right)$ nonlinear sigma model with the topological $\theta$ term at $\theta =\pi$. Finally, we predict a possible fractional quantum Hall state, the Halperin $\left(221\right)$ state, at $1/6$ filling.

In multiferroic materials, luminescence intensities can be direction dependent, i.e., different between the opposite propagating directions of emitted light. However, the effect has not been thought to be used for technological applications, since only small directional asymmetry has been reported so far. Here we show that the effect is robust in multiferroic ${\mathrm{CuB}}_2{\mathrm{O}}_4$. The luminescence intensity changes by about $70\%$ between the opposite directions of the emission, which is about 100 times larger than the previously reported values. We demonstrate that such a gigantic directional asymmetry of luminescence can be applied to the imaging of canted antiferromagnetic domains. The observation of the effect and its application to magnetic domain imaging are important for a deeper understanding of light-matter interactions as well as technological applications such as optical reading techniques for magnetic memory devices.

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the nonlinear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore two-dimensional systems that would be Anderson insulators in the absence of interaction and two- or three-dimensional systems that undergo an Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature $T_c$) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions, especially, in the regime when $T_c$ is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approach the SIT.

We compute analytically the weak (anti)localization correction to the Drude conductivity for electrons in tubular semiconductor systems of zinc-blende type. We include linear Rashba and Dresselhaus spin-orbit coupling (SOC) and compare wires of standard growth directions $\langle 100\rangle ,\langle 111\rangle$, and $\langle 110\rangle$. The motion on the quasi-two-dimensional surface is considered diffusive in both directions: transversal as well as along the cylinder axis. It is shown that Dresselhaus and Rashba SOC similarly affect the spin relaxation rates. For the $\langle 110\rangle$ growth direction, the long-lived spin states are of helical nature. We detect a crossover from weak localization to weak antilocalization depending on spin-orbit coupling strength as well as dephasing and scattering rate. The theory is fitted to experimental data of an undoped $\langle 111\rangle$ InAs nanowire device which exhibits a top-gate-controlled crossover from positive to negative magnetoconductivity. Thereby, we extract transport parameters where we quantify the distinct types of SOC individually.

We study the entanglement spectrum in the many-body localizing and thermalizing phases of one- and two-dimensional Hamiltonian systems and periodically driven “Floquet” systems. We focus on the level statistics of the entanglement spectrum as obtained through numerical diagonalization, finding structure beyond that revealed by more limited measures such as entanglement entropy. In the thermalizing phase the entanglement spectrum obeys level statistics governed by an appropriate random matrix ensemble. For Hamiltonian systems this can be viewed as evidence in favor of a strong version of the eigenstate thermalization hypothesis (ETH). Similar results are also obtained for Floquet systems, where they constitute a result “beyond ETH” and show that the corrections to ETH governing the Floquet entanglement spectrum have statistical properties governed by a random matrix ensemble. The particular random matrix ensemble governing the Floquet entanglement spectrum depends on the symmetries of the Floquet drive and therefore can depend on the choice of origin of time. In the many-body localized phase the entanglement spectrum is also found to show level repulsion, following a semi-Poisson distribution (in contrast to the energy spectrum, which follows a Poisson distribution). This semi-Poisson distribution is found to come mainly from states at high entanglement energies. The observed level repulsion occurs only for interacting localized phases. We also demonstrate that equivalent results can be obtained by calculating with a single typical eigenstate or by averaging over a microcanonical energy window, a surprising result in the localized phase. This discovery of new structure in the pattern of entanglement of localized and thermalizing phases may open up new lines of attack on many-body localization, thermalization, and the localization transition.

Protected chiral edge modes are a well-known signature of topologically ordered phases like the fractional quantum Hall states. Recently, using the framework of projected entangled pair states (PEPS) on the square lattice, we constructed a family of chiral resonating valence bond states with ${\mathbb{Z}}_2$ gauge symmetry. Here we revisit and analyze in full details the properties of the edge modes as given by their entanglement spectra on a cylinder. Surprisingly, we show that the latter can be well described by a chiral $\mathrm{SU}(2{)}_1$ conformal field theory, as for the $\nu =1/2$ (bosonic) gapped Laughlin state, although our numerical data suggest a critical bulk compatible with an emergent $\text{U}\left(1\right)$ gauge symmetry. We propose that our family of PEPS may physically describe a boundary between a chiral topological phase and a trivial phase.

We report electric polarization and magnetization measurements in single crystals of double perovskite ${\mathrm{Lu}}_2\mathrm{Mn}\mathrm{Co}{\mathrm{O}}_6$ using pulsed magnetic fields and optical second harmonic generation in dc magnetic fields. We observe well-resolved magnetic field-induced changes in the electric polarization in single crystals and thereby resolve the question about whether multiferroic behavior is intrinsic to these materials or is an extrinsic feature of polycrystals. We find electric polarization along the crystalline $\mathbf{b}$ axis, that is suppressed by applying a magnetic fields along the $\mathbf{c}$ axis, and advance a model for the origin of magnetoelectric coupling. We furthermore map the phase diagram using both capacitance and electric polarization to identify regions of ordering and regions of magnetoelectric hysteresis. This compound is a rare example of coupled hysteretic behavior in the magnetic and electric properties. The ferromagneticlike magnetic hysteresis loop that couples to hysteretic electric polarization can be attributed not to ordinary ferromagnetic domains, but to the rich physics of magnetic frustration of Ising-like spins in the axial next-nearest-neighbor interaction model.

As opposed to ordinary metals, whose Fermi surfaces are two dimensional, topological (semi)metals can exhibit protected one-dimensional Fermi lines or zero-dimensional Fermi points, which arise due to an intricate interplay between symmetry and topology of the electronic wave functions. Here, we study how reflection symmetry, time-reversal symmetry, SU(2) spin-rotation symmetry, and inversion symmetry lead to the topological protection of line nodes in three-dimensional semimetals. We obtain the crystalline invariants that guarantee the stability of the line nodes in the bulk and show that a quantized Berry phase leads to the appearance of protected surfaces states, which take the shape of a drumhead. By deriving a relation between the crystalline invariants and the Berry phase, we establish a direct connection between the stability of the line nodes and the drumhead surface states. Furthermore, we show that the dispersion minimum of the drumhead state leads to a Van Hove singularity in the surface density of states, which can serve as an experimental fingerprint of the topological surface state. As a representative example of a topological semimetal, we consider ${\mathrm{Ca}}_3{\mathrm{P}}_2$, which has a line of Dirac nodes near the Fermi energy. The topological properties of ${\mathrm{Ca}}_3{\mathrm{P}}_2$ are discussed in terms of a low-energy effective theory and a tight-binding model, derived from ab initio DFT calculations. Our microscopic model for ${\mathrm{Ca}}_3{\mathrm{P}}_2$ shows that the drumhead surface states have a rather weak dispersion, which implies that correlation effects are enhanced at the surface of ${\mathrm{Ca}}_3{\mathrm{P}}_2$.

The calculation of the equilibrium optical properties of bulk silicon by using the Bethe-Salpeter equation solved in the Kohn-Sham basis represents a cornerstone in the development of an ab-initio approach to the optical and electronic properties of materials. Nevertheless, calculations of the transient optical spectrum using the same efficient and successful scheme are scarce. We report, here, a joint theoretical and experimental study of the transient reflectivity spectrum of bulk silicon. Femtosecond transient reflectivity is compared to a parameter-free calculation based on the nonequilibrium Bethe-Salpeter equation. By providing an accurate description of the experimental results we disclose the different phenomena that determine the transient optical response of a semiconductor. We give a parameter-free interpretation of concepts such as bleaching, photoinduced absorption, and stimulated emission, beyond the Fermi golden rule. We also introduce the concept of optical gap renormalization, as a generalization of the known mechanism of band gap renormalization. The present scheme successfully describes the case of bulk silicon, showing its universality and accuracy.

We construct two-dimensional non-Abelian topologically ordered states by strongly coupling arrays of one-dimensional quantum wires via interactions. In our scheme, all charge degrees of freedom are gapped, so the construction can use either quantum wires or quantum spin chains as building blocks, with the same end result. The construction gaps the degrees of freedom in the bulk, while leaving decoupled states at the edges that are described by conformal field theories (CFT) in $(1+1)$-dimensional space and time. We consider both the cases where time-reversal symmetry (TRS) is present or absent. When TRS is absent, the edge states are chiral and stable. We prescribe, in particular, how to arrive at all the edge states described by the unitary CFT minimal models with central charges $c<1$. These non-Abelian spin liquid states have vanishing quantum Hall conductivities, but nonzero thermal ones. When TRS is present, we describe scenarios where the bulk state can be a non-Abelian, nonchiral, and gapped quantum spin liquid, or a gapless one. In the former case, we find that the edge states are also gapped. The paper provides a brief review of non-Abelian bosonization and affine current algebras, with the purpose of being self-contained. To illustrate the methods in a warm-up exercise, we recover the tenfold way classification of two-dimensional noninteracting topological insulators using the Majorana representation that naturally arises within non-Abelian bosonization. Within this scheme, the classification reduces to counting the number of null singular values of a mass matrix, with gapless edge modes present when left and right null eigenvectors exist.

We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar ${\mathrm{SiO}}_2$ and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.

Unveiling new topological phases of matter is one of the current objectives in condensed matter physics. Recent experimental discoveries of Dirac and Weyl semimetals prompt the search for other exotic phases of matter. Here we present a systematic angle-resolved photoemission spectroscopy study of ZrSiS, a prime topological nodal semimetal candidate. Our wider Brillouin zone (BZ) mapping shows multiple Fermi surface pockets such as the diamond-shaped Fermi surface, elliptical-shaped Fermi surface, and a small electron pocket encircling at the zone center $\left(\mathrm{\Gamma }\right)$ point, the $M$ point, and the $X$ point of the BZ, respectively. We experimentally establish the spinless nodal fermion semimetal phase in ZrSiS, which is supported by our first-principles calculations. Our findings evidence that the ZrSiS-type of material family is a new platform on which to explore exotic states of quantum matter; these materials are expected to provide an avenue for engineering two-dimensional topological insulator systems.

Materials which possess a high local density of states varying at a subwavelength scale theoretically permit the focusing of waves onto focal spots much smaller than the free space wavelength. To do so, metamaterials—manmade composite media exhibiting properties not available in nature—are usually considered. However, this approach is limited to narrow bandwidths due to their resonant nature. Here, we prove that it is possible to use a fractal resonator alongside time reversal to focus microwaves onto $\lambda /15$ subwavelength focal spots from the far field, on extremely wide bandwidths. We first numerically prove that this approach can be realized using a multiple-channel time reversal mirror that utilizes all the degrees of freedom offered by the fractal resonator. Then, we experimentally demonstrate that this approach can be drastically simplified by coupling the fractal resonator to a complex medium, here a cavity, that efficiently converts its spatial degrees of freedom into temporal ones. This makes it possible to achieve deep subwavelength focusing of microwave radiation by time reversing a single channel. Our method can be generalized to other systems coupling complex media and fractal resonators.

In monolayer transition-metal dichalcogenides (TMDs), electrons in opposite $K$ valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originating from in-plane mirror symmetry breaking, pins the electron spins to the out-of-plane directions, and results in Ising superconducting states with strongly enhanced upper critical fields. Here, we show that the Ising SOC generates equal-spin-triplet Cooper pairs with spin polarized in the in-plane directions. Importantly, the spin-triplet Cooper pairs can induce superconducting pairings in a half-metal wire placed on top of the TMD and result in a topological superconductor with Majorana end states. Direct ways to detect equal-spin triplet Cooper pairs and the differences between Ising superconductors and Rashba superconductors are discussed.

Motivated by an apparent paradox in [X.-L. Qi, E. Witten, and S.-C. Zhang, Phys. Rev. B 87, 134519 (2013)], we use the method of gauged Wess-Zumino-Witten functionals to construct an effective action for a Weyl fermion with a Majorana mass that arises from coupling to a charged condensate. We obtain expressions for the current induced by an external gauge field and observe that the topological part of the current is only one-third of that that might have been expected from the gauge anomaly. The anomaly is not changed by the induced mass gap, however. The topological current is supplemented by a conventional supercurrent that provides the remaining two-thirds of the anomaly once the equation of motion for the Goldstone mode is satisfied. We apply our formula for the current to resolve the apparent paradox and also to the chiral magnetic effect (CME), where it predicts a reduction of the CME current to one-third of its value for a free Weyl gas in thermal equilibrium. We attribute this reduction to a partial cancellation of the CME by a chiral vortical effect current arising from the persistent rotation of the fluid induced by the external magnetic field.

We characterize the three-orbital Hubbard model using state-of-the-art determinant quantum Monte Carlo (DQMC) simulations with parameters relevant to the cuprate high-temperature superconductors. The simulations find that doped holes preferentially reside on oxygen orbitals and that the $(\pi ,\pi )$ antiferromagnetic ordering vector dominates in the vicinity of the undoped system, as known from experiments. The orbitally-resolved spectral functions agree well with photoemission spectroscopy studies and enable identification of orbital content in the bands. A comparison of DQMC results with exact diagonalization and cluster perturbation theory studies elucidates how these different numerical techniques complement one another to produce a more complete understanding of the model and the cuprates. Interestingly, our DQMC simulations predict a charge-transfer gap that is significantly smaller than the direct (optical) gap measured in experiment. Most likely, it corresponds to the indirect gap that has recently been suggested to be on the order of 0.8 eV, and demonstrates the subtlety in identifying charge gaps.

The Josephson effect provides a direct method to probe the strength of the pairing interaction in superconductors. By measuring the phase fluctuating Josephson current between a superconducting tip of a scanning tunneling microscope and a BCS superconductor with isolated magnetic adatoms on its surface, we demonstrate that the spatial variation of the pairing order parameter can be characterized on the atomic scale. This system provides an example where the local pairing potential suppression is not directly reflected in the spectra measured via quasiparticle tunneling. Spectroscopy with such superconducting tips also shows signatures of previously unexplored Andreev processes through individual impurity-bound Shiba states. The atomic resolution achieved here establishes scanning Josephson spectroscopy as a promising technique for the study of novel superconducting phases.

Temperature influences the performance of two-dimensional (2D) materials in optoelectronic devices. Indeed, the optical characterization of these materials is usually realized at room temperature. Nevertheless, most ab initio studies are still performed without including any temperature effect. As a consequence, important features are thus overlooked, such as the relative height of the excitonic peaks and their broadening, directly related to the temperature and to the nonradiative exciton relaxation time. We present ab initio calculations of the optical response of single-layer ${\mathrm{MoS}}_2$, a prototype 2D material, as a function of temperature using density functional theory and many-body perturbation theory. We compute the electron-phonon interaction using the full spinorial wave functions, i.e., fully taking into account the effects of spin-orbit interaction. We find that bound excitons ($A$ and $B$ peaks) and resonant excitons ($C$ peak) exhibit different behavior with temperature, displaying different nonradiative linewidths. We conclude that the inhomogeneous broadening of the absorption spectra is mainly due to electron-phonon scattering mechanisms. Our calculations explain the shortcomings of previous (zero-temperature) theoretical spectra and match well with the experimental spectra acquired at room temperature. Moreover, we disentangle the contributions of acoustic and optical phonon modes to the quasiparticles and exciton linewidths. Our model also allows us to identify which phonon modes couple to each exciton state, which is useful for the interpretation of resonant Raman-scattering experiments.