Showing papers in "Physical Review B in 2011"

Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates

Abstract: We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of a magnetic solid, and argue that it may be realized in a class of pyrochlore iridates (such as ${\mathrm{Y}}_{2}$Ir${}_{2}$O${}_{7}$) based on calculations using the $\text{LDA}+U$ method. This state is a three-dimensional analog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. For intermediate correlation strengths, we find this to be the ground state of the pyrochlore iridates, coexisting with noncollinear magnetic order. A narrow window of magnetic ``axion'' insulator may also be present. An applied magnetic field is found to induce a metallic ground state.

Van der Waals density functionals applied to solids

Abstract: The van der Waals density functional (vdW-DF) of M. Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)] is a promising approach for including dispersion in approximate density functional theory exchange-correlation functionals. Indeed, an improved description of systems held by dispersion forces has been demonstrated in the literature. However, despite many applications, standard general tests on a broad range of materials including traditional ``hard'' matter such as metals, ionic compounds, and insulators are lacking. Such tests are important not least because many of the applications of the vdW-DF method focus on the adsorption of atoms and molecules on the surfaces of solids. Here we calculate the lattice constants, bulk moduli, and atomization energies for a range of solids using the original vdW-DF and several of its offspring. We find that the original vdW-DF overestimates lattice constants in a similar manner to how it overestimates binding distances for gas-phase dimers. However, some of the modified vdW functionals lead to average errors which are similar to those of PBE or better. Likewise, atomization energies that are slightly better than from PBE are obtained from the modified vdW-DFs. Although the tests reported here are for hard solids, not normally materials for which dispersion forces are thought to be important, we find a systematic improvement in cohesive properties for the alkali metals and alkali halides when nonlocal correlations are accounted for.

Influence of quantum confinement on the electronic structure of the transition metal sulfide T S 2

Abstract: Bulk MoS2, a prototypical layered transition-metal dichalcogenide, is an indirect band gap semiconductor. Reducing its size to a monolayer, MoS2 undergoes a transition to the direct band semiconductor. We support this experimental observation by first principles calculations and show that quantum confinement in layered d-electron dichalcogenides results in tuning the electronic structure at the nanoscale. We further studied the properties of related TmS2 nanolayers (Tm = W, Nb, Re) and show that the isotopological WS2 exhibits similar electronic properties, while NbS2 and ReS2 remain metallic independent on size.

Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors

Abstract: Fully relativistic first-principles calculations based on density functional theory are performed to study the spin-orbit-induced spin splitting in monolayer systems of the transition-metal dichalcogenides MoS${}_{2}$, MoSe${}_{2}$, WS${}_{2}$, and WSe${}_{2}$. All these systems are identified as direct-band-gap semiconductors. Giant spin splittings of 148--456 meV result from missing inversion symmetry. Full out-of-plane spin polarization is due to the two-dimensional nature of the electron motion and the potential gradient asymmetry. By suppression of the Dyakonov-Perel spin relaxation, spin lifetimes are expected to be very long. Because of the giant spin splittings, the studied materials have great potential in spintronics applications.

Topological nodal semimetals

Abstract: We present a study of ``nodal-semimetal'' phases in which nondegenerate conduction and valence bands touch at points (the ``Weyl semimetal'') or lines (the ``line-node semimetal'') in three-dimensional momentum space. We discuss a general approach to such states by perturbation of the critical point between a normal insulator (NI) and a topological insulator (TI), breaking either time-reversal (TR) or inversion symmetry. We give an explicit model realization of both types of states in a NI-TI superlattice structure with broken TR symmetry. Both the Weyl and the line-node semimetals are characterized by topologically protected surface states, although in the line-node case, some additional symmetries must be imposed to retain this topological protection. The edge states have the form of ``Fermi arcs'' in the case of the Weyl semimetal: these are chiral gapless edge states, which exist in a finite region in momentum space, determined by the momentum-space separation of the bulk Weyl nodes. The chiral character of the edge states leads to a finite Hall conductivity. In contrast, the edge states of the line-node semimetal are ``flat bands'': these states are approximately dispersionless in a subset of the two-dimensional edge Brillouin zone, given by the projection of the line node onto the plane of the edge. We discuss unusual transport properties of the nodal semimetals and, in particular, point out quantum critical-like scaling of the dc and optical conductivities of the Weyl semimetal and similarities to the conductivity of graphene in the line-node case.

Phonons in single-layer and few-layer MoS 2 and WS 2

Abstract: We report ab initio calculations of the phonon dispersion relations of the single-layer and bulk dichalcogenides MoS2 and WS2. We explore in detail the behavior of the Raman-active modes A1g and E 1 2g as a function of the number of layers. In agreement with recent Raman spectroscopy measurements [C. Lee et al., ACS Nano 4, 2695 (2010)], we find that the A1g mode increases in frequency with an increasing number of layers while the E 1g mode decreases. We explain this decrease by an enhancement of the dielectric screening of the long-range Coulomb interaction between the effective charges with a growing number of layers. This decrease in the long-range part overcompensates for the increase of the short-range interaction due to the weak interlayer interaction.

Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin

Abstract: Starting from symmetry considerations and the tight-binding method in combination with first-principles calculation, we systematically derive the low-energy effective Hamiltonian involving spin-orbit coupling (SOC) for silicene. This Hamiltonian is very general because it applies not only to silicene itself but also to the low-buckled counterparts of graphene for the other group-IVA elements Ge and Sn, as well as to graphene when the structure returns to the planar geometry. The effective Hamitonian is the analog to the graphene quantum spin Hall effect (QSHE) Hamiltonian. As in the graphene model, the effective SOC in low-buckled geometry opens a gap at the Dirac points and establishes the QSHE. The effective SOC actually contains the first order in the atomic intrinsic SOC strength ${\ensuremath{\xi}}_{0}$, while this leading-order contribution of SOC vanishes in the planar structure. Therefore, silicene, as well as the low-buckled counterparts of graphene for the other group-IVA elements Ge and Sn, has a much larger gap opened by the effective SOC at the Dirac points than graphene, due to the low-buckled geometry and larger atomic intrinsic SOC strength. Further, the more buckled is the structure, the greater is the gap. Therefore, the QSHE can be observed in low-buckled Si, Ge, and Sn systems in an experimentally accessible temperature regime. In addition, the Rashba SOC in silicene is intrinsic due to its own low-buckled geometry, which vanishes at the Dirac point $K$, while it has a nonzero value with deviation of $\stackrel{P\vec}{k}$ from the $K$ point. Therefore, the QSHE in silicene is robust against the intrinsic Rashba SOC.

Formation enthalpies by mixing GGA and GGA + U calculations

Abstract: Standard approximations to the density functional theory exchange-correlation functional have been extraordinary successful, but calculating formation enthalpies of reactions involving compounds with both localized and delocalized electronic states remains challenging. In this work we examine the shortcomings of the generalized gradient approximation (GGA) and GGA+U in accurately characterizing such difficult reactions. We then outline a methodology that mixes GGA and GGA+U total energies (using known binary formation data for calibration) to more accurately predict formation enthalpies. We demonstrate that for a test set of 49 ternary oxides, our methodology can reduce the mean absolute relative error in calculated formation enthalpies from approximately 7.7–21% in GGA+U to under 2%. As another example we show that neither GGA nor GGA+U alone accurately reproduces the Fe-P-O phase diagram; however, our mixed methodology successfully predicts all known phases as stable by naturally stitching together GGA and GGA+U results. As a final example we demonstrate how our technique can be applied to the calculation of the Li-conversion voltage of LiFeF3. Our results indicate that mixing energies of several functionals represents one avenue to improve the accuracy of total energy computations without affecting the cost of calculation.

Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels

Abstract: In this paper, we study transport properties of nonequilibrium systems under the application of light in many-terminal measurements, using the Floquet picture. We propose and demonstrate that the quantum transport properties can be controlled in materials such as graphene and topological insulators, via the application of light. Remarkably, under the application of off-resonant light, topological transport properties can be induced; these systems exhibit quantum Hall effects in the absence of a magnetic field with a near quantization of the Hall conductance, realizing so-called quantum Hall systems without Landau levels first proposed by Haldane.

Classification of gapped symmetric phases in one-dimensional spin systems

Abstract: Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for strongly interacting systems. Here we make an attempt to answer these questions for gapped interacting quantum spin systems whose ground states are short-range correlated. Based on the local unitary equivalence relation between short-range-correlated states in the same phase, we classify possible quantum phases for one-dimensional (1D) matrix product states, which represent well the class of 1D gapped ground states. We find that in the absence of any symmetry all states are equivalent to trivial product states, which means that there is no topological order in 1D. However, if a certain symmetry is required, many phases exist with different symmetry-protected topological orders. The symmetric local unitary equivalence relation also allows us to obtain some simple results for quantum phases in higher dimensions when some symmetries are present.

Merits and limits of the modified Becke-Johnson exchange potential

Abstract: The modified Becke-Johnson exchange potential [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)] (TB-mBJ) is tested on various types of solids which are difficult to describe theoretically: nonmagnetic semiconducting transition-metal oxides and sulfides, metals (Fe, Co, Ni, and Cu), and (anti)ferromagnetic insulators (e.g., YBa${}_{2}$Cu${}_{3}$O${}_{6}$). The results for the band gap and other quantities such as the magnetic moment or electric field gradient are analyzed in detail, in particular to have a better understanding of the mechanism which leads to improved (or sometimes worse) results with the TB-mBJ potential compared to the standard local density and generalized gradient approximations.

Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates

Abstract: There has been much interest in pyrochlore iridates A${}_{2}$Ir${}_{2}$O${}_{7}$ where both strong spin-orbital coupling and strong correlation are present. A recent local density approximation calculation [X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Phys. Rev. B 83, 205101 (2011)] suggests that the system is likely in a three-dimensional topological semimetallic phase: a Weyl semimetal. Such a system has zero carrier density and arrives at the quantum limit even in a weak magnetic field. In this paper, we discuss two quantum effects of this system in a magnetic field: a pressure-induced anomalous Hall effect and a magnetic-field-induced charge density wave at the pinned wave vector connecting Weyl nodes with opposite chiralities. A general formula of the anomalous Hall coefficients in a Weyl semimetal is also given. Both proposed effects can be probed by experiments in the near future and can be used to detect the Weyl semimetal phase.

Heat transport in silicon from first-principles calculations

Abstract: Using harmonic and anharmonic force constants extracted from density functional calculations within a supercell, we have developed a relatively simple but general method to compute thermodynamic and thermal properties of any crystal. First, from the harmonic, cubic, and quartic force constants, we construct a force field for molecular dynamics. It is exact in the limit of small atomic displacements and thus does not suffer from inaccuracies inherent in semiempirical potentials such as Stillinger-Weber's. By using the Green-Kubo formula and molecular dynamics simulations, we extract the bulk thermal conductivity. This method is accurate at high temperatures where three-phonon processes need to be included to higher orders, but may suffer from size scaling issues. Next, we use perturbation theory (Fermi golden rule) to extract the phonon lifetimes and compute the thermal conductivity $\ensuremath{\kappa}$ from the relaxation-time approximation. This method is valid at most temperatures, but will overestimate $\ensuremath{\kappa}$ at very high temperatures, where higher-order processes neglected in our calculations also contribute. As a test, these methods are applied to bulk crystalline silicon, and the results are compared and differences are discussed in more detail. The presented methodology paves the way for a systematic approach to model heat transport in solids using multiscale modeling, in which the relaxation time due to anharmonic three-phonon processes is calculated quantitatively, in addition to the usual harmonic properties such as phonon frequencies and group velocities. It also allows the construction of an accurate bulk interatomic potentials database.

Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection

Abstract: We introduce an expression for the ${\mathbb{Z}}_{2}$ topological invariant of band insulators using the non-Abelian Berry connection. Our expression can identify the topological nature of a general band insulator without any of the gauge-fixing problems that plague the concrete implementation of previous invariants. This expression can be derived from the ``partner switching'' of the Wannier function center during time-reversal pumping and is thus equivalent to the ${Z}_{2}$ topological invariant proposed by Kane and Mele. Using our expression, we have recalculated the ${Z}_{2}$ topological index for several topological insulator material systems and obtained consistent results with the previous studies.

Topological phases of fermions in one dimension

Abstract: In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the time-reversal-invariant Majorana chain (BDI symmetry class).While the band classification yields an integer topological index k, it is known that phases characterized by values of k in the same equivalence class modulo 8 can be adiabatically transformed one to another by adding suitable interaction terms. Here we show that the eight equivalence classes are distinct and exhaustive, and provide a physical interpretation for the interacting invariant modulo 8. The different phases realize different Altland-Zirnbauer classes of the reduced density matrix for an entanglement bipartition into two half chains. We generalize these results to the classification of all one-dimensional gapped phases of fermionic systems with possible antiunitary symmetries, utilizing the algebraic framework of central extensions. We use matrix product state methods to prove our results.

Manipulating light polarization with ultrathin plasmonic metasurfaces

Abstract: We analyze the design of ultrathin quarter-wave plates based on plasmonic metasurfaces. After exploring the general theoretical possibilities offered by thin surfaces to manipulate the impinging polarization, we propose optimal designs to realize quarter-wave metasurface plates, analyzing their frequency and angular response. Our designs may provide a large degree of linear polarization output for circularly polarized input over a broad bandwidth in the optical regime. The geometry may be implemented within currently available lithographic techniques and easily integrated with other optical devices for polarization manipulation, detection, and sensing at the nanoscale.

Classifying quantum phases using matrix product states and projected entangled pair states

Abstract: We give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states (MPS) and their associated parent Hamiltonians, for systems with unique as well as degenerate ground states and in both the absence and the presence of symmetries. We find that without symmetries, all systems are in the same phase, up to accidental ground-state degeneracies. If symmetries are imposed, phases without symmetry breaking (i.e., with unique ground states) are classified by the cohomology classes of the symmetry group, that is, the equivalence classes of its projective representations, a result first derived by Chen, Gu, and Wen [Phys. Rev. B 83, 035107 (2011)]. For phases with symmetry breaking (i.e., degenerate ground states), we find that the symmetry consists of two parts, one of which acts by permuting the ground states, while the other acts on individual ground states, and phases are labeled by both the permutation action of the former and the cohomology class of the latter. Using projected entangled pair states (PEPS), we subsequently extend our framework to the classification of two-dimensional phases in the neighborhood of a number of important cases, in particular, systems with unique ground states, degenerate ground states with a local order parameter, and topological order. We also show that in two dimensions, imposing symmetries does not constrain the phase diagram in the same way it does in one dimension. As a central tool, we introduce the isometric form, a normal form for MPS and PEPS, which is a renormalization fixed point. Transforming a state to its isometric form does not change the phase, and thus we can focus on to the classification of isometric forms.

First-principles investigation of the very large perpendicular magnetic anisotropy at Fe|MgO and Co|MgO interfaces

Abstract: The perpendicular magnetic anisotropy (PMA) arising at the interface between ferromagnetic transition metals and metallic oxides was investigated via first-principles calculations. In this work very large values of PMA, up to 3 erg/cm${}^{2}$, at Fe$|$MgO interfaces are reported, in agreement with recent experiments. The origin of PMA is attributed to overlap between O-${p}_{z}$ and transition metal ${d}_{{z}^{2}}$ orbitals hybridized with ${d}_{xz(yz)}$ orbitals with stronger spin-orbit coupling-induced splitting around the Fermi level for perpendicular magnetization orientation. Furthermore, it is shown that the PMA value weakens in the case of over- or underoxidation due to the fact that oxygen ${p}_{z}$ and transition metal ${d}_{{z}^{2}}$ orbital overlap is strongly affected by disorder, in agreement with experimental observations in magnetic tunnel junctions.

Tunable band gaps in bilayer transition-metal dichalcogenides

Abstract: We investigate band-gap tuning in bilayer transition-metal dichalcogenides by external electric fields applied perpendicular to the layers. Using density functional theory, we show that the fundamental band gap of MoS${}_{2}$, MoSe${}_{2}$, MoTe${}_{2}$, and WS${}_{2}$ bilayer structures continuously decreases with increasing applied electric fields, eventually rendering them metallic. We interpret our results in the light of the giant Stark effect and obtain a robust relationship, which is essentially characterized by the interlayer spacing, for the rate of change of band gap with applied external field. Our study expands the known space of layered materials with widely tunable band gaps beyond the classic example of bilayer graphene and suggests potential directions for fabrication of novel electronic and photonic devices.

Dielectric screening in two-dimensional insulators: Implications for excitonic and impurity states in graphane

Abstract: For atomic thin layer insulating materials we provide an exact analytic form of the two-dimensional (2D) screened potential. In contrast to three-dimensional systems where the macroscopic screening can be described by a static dielectric constant, in 2D systems the macroscopic screening is nonlocal ($q$ dependent) showing a logarithmic divergence for small distances and reaching the unscreened Coulomb potential for large distances. The crossover of these two regimes is dictated by 2D layer polarizability that can be easily computed by standard first-principles techniques. The present results have strong implications for describing gap-impurity levels and also exciton binding energies. The simple model derived here captures the main physical effects and reproduces well, for the case of graphane, the full many-body $\mathrm{GW}$ plus Bethe-Salpeter calculations. As an additional outcome we show that the impurity hole-doping in graphane leads to strongly localized states, which hampers applications in electronic devices. In spite of the inefficient and nonlocal two-dimensional macroscopic screening we demonstrate that a simple $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ approach is capable to describe the electronic and transport properties of confined 2D systems.

Edge and waveguide terahertz surface plasmon modes in graphene microribbons

Abstract: The authors acknowledge support from the Spanish MECD under Contract No. MAT2009-06609-C02 and Consolider Project “Nanolight.es.” A.Y.N. acknowledges the Juan de la Cierva Grant No. JCI-2008-3123

Nearly total absorption of light and heat generation by plasmonic metamaterials

Abstract: We theoretically and numerically study the absorption effect and the heat generation in plasmonic metamaterials under light radiation at their plasmonic resonance. Three different types of structures, all possessing high-performance absorption for visible lights, are investigated. The main aim of this work is to present an intuitive and original understanding of the high-performance absorption effects. From the macroscopic electromagnetic point of view, the effective-medium approach is used to describe the absorption effects of the plasmonic metamaterials. On the other hand, the field distributions and heat generation effects in such plasmonic nanostructures are investigated, which also provides a satisfactory qualitative description of such absorption behavior based upon the microscopic perspective.

Theory of double-resonant Raman spectra in graphene: Intensity and line shape of defect-induced and two-phonon bands

Abstract: We calculate the double resonant (DR) Raman spectrum of graphene, and determine the lines associated to both phonon-defect processes, and two-phonons ones. Phonon and electronic dispersions reproduce calculations based on density functional theory corrected with GW. Electron-light, -phonon, and -defect scattering matrix elements and the electronic linewidth are explicitly calculated. Defect-induced processes are simulated by considering different kind of idealized defects. For an excitation energy of $\epsilon_L=2.4$ eV, the agreement with measurements is very good and calculations reproduce: the relative intensities among phonon-defect or among two-phonon lines; the measured small widths of the D, $D'$, 2D and $2D'$ lines; the line shapes; the presence of small intensity lines in the 1800, 2000 cm$^{-1}$ range. We determine how the spectra depend on the excitation energy, on the light polarization, on the electronic linewidth, on the kind of defects and on their concentration. According to the present findings, the intensity ratio between the $2D'$ and 2D lines can be used to determine experimentally the electronic linewidth. The intensity ratio between the $D$ and $D'$ lines depends on the kind of model defect, suggesting that this ratio could possibly be used to identify the kind of defects present in actual samples. Charged impurities outside the graphene plane provide an almost undetectable contribution to the Raman signal.

Edge states and topological phases in non-Hermitian systems

Abstract: Topological stability of the edge states is investigated for non-Hermitian systems. We examine two classes of non-Hermitian Hamiltonians supporting real bulk eigenenergies in weak non-Hermiticity: SU$(1,1)$ and SO$(3,2)$ Hamiltonians. As an SU$(1,1)$ Hamiltonian, the tight-binding model on the honeycomb lattice with imaginary onsite potentials is examined. Edge states with Re$E=0$ and their topological stability are discussed by the winding number and the index theorem based on the pseudo-anti-Hermiticity of the system. As a higher-symmetric generalization of SU$(1,1)$ Hamiltonians, we also consider SO$(3,2)$ models. We investigate non-Hermitian generalization of the Luttinger Hamiltonian on the square lattice and that of the Kane-Mele model on the honeycomb lattice, respectively. Using the generalized Kramers theorem for the time-reversal operator $\ensuremath{\Theta}$ with ${\ensuremath{\Theta}}^{2}=+1$ [M. Sato et al., e-print arXiv:1106.1806], we introduce a time-reversal-invariant Chern number from which topological stability of gapless edge modes is argued.

Zak phase and the existence of edge states in graphene

Abstract: We develop a method to predict the existence of edge states in graphene ribbons for a large class of boundaries. This approach is based on the bulk-edge correspondence between the quantized value of the Zak phase $\mathcal{Z}({k}_{\ensuremath{\parallel}})$, which is a Berry phase across an appropriately chosen one-dimensional Brillouin zone, and the existence of a localized state of momentum ${k}_{\ensuremath{\parallel}}$ at the boundary of the ribbon. This bulk-edge correspondence is rigorously demonstrated for a one-dimensional toy model as well as for graphene ribbons with zigzag edges. The range of ${k}_{\ensuremath{\parallel}}$ for which edge states exist in a graphene ribbon is then calculated for arbitrary orientations of the edges. Finally, we show that the introduction of an anisotropy leads to a topological transition in terms of the Zak phase, which modifies the localization properties at the edges. Our approach gives a new geometrical understanding of edge states, and it confirms and generalizes the results of several previous works.

Highly optimized embedded-atom-method potentials for fourteen fcc metals

Abstract: Highly optimized embedded-atom-method (EAM) potentials have been developed for 14 face-centered-cubic (fcc) elements across the periodic table. The potentials were developed by fitting the potential-energy surface (PES) of each element derived from high-precision first-principles calculations. The as-derived potential-energy surfaces were shifted and scaled to match experimental reference data. In constructing the PES, a variety of properties of the elements were considered, including lattice dynamics, mechanical properties, thermal behavior, energetics of competing crystal structures, defects, deformation paths, liquid structures, and so forth. For each element, the constructed EAM potentials were tested against the experiment data pertaining to thermal expansion, melting, and liquid dynamics via molecular dynamics computer simulation. The as-developed potentials demonstrate high fidelity and robustness. Owing to their improved accuracy and wide applicability, the potentials are suitable for high-quality atomistic computer simulation of practical applications.

Compositional dependence of structural and electronic properties of Cu 2 ZnSn(S,Se) 4 alloys for thin film solar cells

Abstract: A thin-film solar cell based on Cu${}_{2}$ZnSn(S,Se)${}_{4}$ (CZTSSe) alloy was recently found to exhibit a light to electricity conversion efficiency of $10%$, making it competitive with the more mature Cu(In,Ga)Se${}_{2}$ based technologies. We study the compositional dependence of the physical properties of CZTSSe alloys through first-principles calculations and find that these mixed-anion alloys are highly miscible with low enthalpies of formation, and the cations maintain the same ordering preferences as the parent compounds Cu${}_{2}$ZnSnS${}_{4}$ and Cu${}_{2}$ZnSnSe${}_{4}$. The band gap of the CZTSSe alloy decreases with the Se content almost linearly, and the band alignment between Cu${}_{2}$ZnSnS${}_{4}$ and Cu${}_{2}$ZnSnSe${}_{4}$ is of type I, which allows for more facile $n$-type and $p$-type doping for alloys with high Se content. Based on these results we analyze the influence of composition on the efficiency of CZTSSe solar cells and explain the high efficiency of the cells with high Se content.

Avoiding power broadening in optically detected magnetic resonance of single NV defects for enhanced dc magnetic field sensitivity

Abstract: We report a systematic study of the magnetic field sensitivity of a magnetic sensor consisting of a single nitrogen-vacancy (NV) defect in diamond, by using continuous optically detected electron spin resonance (ESR) spectroscopy. We first investigate the behavior of the ESR contrast and linewidth as a function of the microwave and optical pumping power. The experimental results are in good agreement with a simplified model of the NV defect spin dynamics, leading to an optimized sensitivity around $2\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}$T$/\sqrt{\mathrm{Hz}}$ for a single NV defect in a high-purity diamond crystal grown by chemical vapor deposition. We then demonstrate an enhancement of the magnetic sensitivity by one order of magnitude by using a simple pulsed-ESR scheme. This technique is based on repetitive excitation of the NV defect with a resonant microwave $\ensuremath{\pi}$ pulse followed by an optimized readout laser pulse, allowing to fully eliminate power broadening of the ESR linewidth. The achieved sensitivity is similar to that obtained by using Ramsey-type sequences, which is the optimal magnetic field sensitivity for the detection of a dc magnetic field.

Inversion-symmetric topological insulators

Abstract: We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer $\mathcal{N}$, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is ``topological.'' We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion symmetric points and charge polarization. In two dimensions, we prove a link between the product of the inversion eigenvalues and the parity of the Chern number of the occupied bands. In three dimensions, we find a topological constraint on the product of the inversion eigenvalues thereby showing that some $3$D materials are protected topological metals; we show the link between the inversion eigenvalues and the $3$D Quantum Hall Effect, and analyze the magnetoelectric polarization ($\ensuremath{\theta}$ vacuum) in the absence of time-reversal symmetry.

Lattice dynamics of anharmonic solids from first principles

Abstract: In the search of clean and efficient energy sources intermediate temperature solid oxide fuel cells are among the prime candidates. What sets the limit of their efficiency is the solid electrolyte. A promising material for the electrolyte is ceria. This thesis aims to improve the characteristics of these electrolytes and help provide thorough physical understanding of the processes involved. This is realised using first principles calculations. The class of methods based on density functional theory generally ignores temperature effects. To accurately describe the intermediate temperature characteristics I have made adjustments to existing frameworks and developed a qualitatively new method. The new technique, the high temperature effective potential method, is a general theory. The validity is proven on a number of model systems. Other subprojects include low-dimensional segregation effects, adjustments to defect concentration formalism and optimisations of ionic conductivity.