Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap of such systems are protected by time-reversal symmetry. The study of such states was originally inspired by the robustness to scattering of conducting edge states in quantum Hall systems. Recently, such analogies have resulted in the discovery of topologically protected states in two-dimensional and three-dimensional band insulators with large spin–orbit coupling. So far, the only known three-dimensional topological insulator is BixSb1−x, which is an alloy with complex surface states. Here, we present the results of first-principles electronic structure calculations of the layered, stoichiometric crystals Sb2Te3, Sb2Se3, Bi2Te3 and Bi2Se3. Our calculations predict that Sb2Te3, Bi2Te3 and Bi2Se3 are topological insulators, whereas Sb2Se3 is not. These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. In addition, we predict that Bi2Se3 has a topologically non-trivial energy gap of 0.3 eV, which is larger than the energy scale of room temperature. We further present a simple and unified continuum model that captures the salient topological features of this class of materials. First-principles calculations predict that Bi2Se3, Bi2Te3 and Sb2Te3 are topological insulators—three-dimensional semiconductors with unusual surface states generated by spin–orbit coupling—whose surface states are described by a single gapless Dirac cone. The calculations further predict that Bi2Se3 has a non-trivial energy gap larger than the energy scale kBT at room temperature.

http://english.iop.cas.cn/rh/rp/200907/U020090713606192151652.pdf

Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface

Herein we cover the key concepts in the field of thermoelectric materials research, present the current understanding, and show the latest developments. Current research is aimed at increasing the thermoelectric figure of merit (ZT) by maximizing the power factor and/or minimizing the thermal conductivity. Attempts at maximizing the power factor include the development of new materials, optimization of existing materials by doping, and the exploration of nanoscale materials. The minimization of the thermal conductivity can come through solid-solution alloying, use of materials with intrinsically low thermal conductivity, and nanostructuring. Herein we describe the most promising bulk materials with emphasis on results from the last decade. Single-phase bulk materials are discussed in terms of chemistry, crystal structure, physical properties, and optimization of thermoelectric performance. The new opportunities for enhanced performance bulk nanostructured composite materials are examined and a look into the not so distant future is attempted.

New and Old Concepts in Thermoelectric Materials

The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

http://absimage.aps.org/image/MAR06/MWS_MAR06-2005-007233.pdf

First-principles calculations of electronic structure and spectra of strongly correlated systems: the LDA+U method

There has been a renaissance of interest in exploring highly efficient thermoelectric materials as a possible route to address the worldwide energy generation, utilization, and management. This review describes the recent advances in designing high-performance bulk thermoelectric materials. We begin with the fundamental stratagem of achieving the greatest thermoelectric figure of merit ZT of a given material by carrier concentration engineering, including Fermi level regulation and optimum carrier density stabilization. We proceed to discuss ways of maximizing ZT at a constant doping level, such as increase of band degeneracy (crystal structure symmetry, band convergence), enhancement of band effective mass (resonant levels, band flattening), improvement of carrier mobility (modulation doping, texturing), and decrease of lattice thermal conductivity (synergistic alloying, second-phase nanostructuring, mesostructuring, and all-length-scale hierarchical architectures). We then highlight the decoupling of th...

Rationally Designing High-Performance Bulk Thermoelectric Materials

Axions are weakly interacting particles of low mass, and were postulated more than 30 years ago in the framework of the Standard Model of particle physics. Their existence could explain the missing dark matter of the Universe. However, despite intensive searches, axions have yet to be observed. Here we show that magnetic fluctuations of topological insulators couple to the electromagnetic fields exactly like the axions, and propose several experiments to detect this dynamical axion field. In particular, we show that the axion coupling enables a nonlinear modulation of the electromagnetic field, leading to attenuated total reflection. We propose a new optical-modulator device based on this principle. Axions are hypothetical particles that might play an important part in particle physics, astrophysics and cosmology. So far they have eluded observation, but theoretical work now predicts that axion physics might be explored in condensed-matter systems known as topological insulators.

Dynamical axion field in topological magnetic insulators

Electronic structure calculations were performed for the rare-earth (RE) nitrides in the rocksalt structure using density functional theory calculations within the $\mathrm{LSDA}+U$ approach (local spin density approximation with Hubbard-$U$ corrections). The $\mathrm{LSDA}+U$ method is implemented in the full-potential linearized muffin-tin orbital method and applied to the $4f$ as well as $5d$ states. Parameters $U$ and $J$ were determined from atomic calculations complemented with experimental photoemission and inverse photoemission data and optical absorption data for Gd pnictides. The solution for the density matrix of $f$ electrons is not unique and thus several configurations need to be investigated to determine the lowest energy state. A trivalent solution is found to have the lowest energy in all cases except $\mathrm{CeN}$, which was found to be tetravalent. Hund's second rule requires maximizing the orbital momentum component ${L}_{z}$, which breaks the cubic symmetry and lowers the total energy. We find Hund's second rule to be obeyed in all cases except $\mathrm{EuN}$ and $\mathrm{YbN}$, where a cubic symmetry solution has lower energy. In these cases, the divalent solution is also in competition with the trivalent solution. The symmetry breaking in most cases lowers the total energy and in some cases, those with two electrons or holes away from a closed or half-filled shell, is essential to remove $f$ states from the Fermi level. The spin magnetic moments are nearly integer, defined by the number of filled $4f$ states. The orbital magnetic moment is of comparable magnitude to the spin moment. Hund's third rule, according to which the orbital and spin moment are opposite to each other in the first half of the series but parallel to each other in the second half, is also found to be obeyed. Interestingly, this leads to zero net magnetic moment for $\mathrm{SmN}$.Apart from the few cases where $f$ states remain close to the Fermi level, the band structure is borderline semiconductor to semimetallic in most cases, a RE $5d$ conduction band minimum at $X$, and a $\mathrm{N}\phantom{\rule{0.2em}{0ex}}2p$ valence band maximum at $\ensuremath{\Gamma}$. The early members of the series before $\mathrm{GdN}$ (with the exception of $\mathrm{NdN}$) are slightly semimetallic in the majority spin channel only and are thus half-metals, while the later members after Gd have a small indirect gap. In $\mathrm{EuN}$ a complicated hybridization occurs between an $f$ level pinned at ${E}_{F}$ and the $\mathrm{N}\phantom{\rule{0.2em}{0ex}}2p$ states, leading to a metallic band structure. Above the Curie temperature of these ferromagnets, in the paramagnetic state, one expects an average of majority and minority spin gaps and thus an increase in the gap.

Electronic structure of rare-earth nitrides using the LSDA + U approach: Importance of allowing 4 f orbitals to break the cubic crystal symmetry

Effects of uniaxial and hydrostatic pressure on the valence band maximum in Sb 2 Te 3 : An electronic structure study

Electronic structure of K_2Bi_8Se_13

Electronic structure of the ternary Zintl-phase compounds Zr 3 Ni 3 Sb 4 , Hf 3 Ni 3 Sb 4 , and Zr 3 Pt 3 Sb 4 and their similarity to half-Heusler compounds such as ZrNiSn

K 2Bi8 Se13 belongs to a class of complex Bi-Te-Se systems which show great potential for thermoelectric performance. This compound forms in two distinct phases α-K 2Bi8 Se13 (triclinic with space group P-1) and β-K 2Bi8 Se13 (monoclinic with space group P 21/m). In the β-phase, there is substantial disorder at four sites in the unit cell, occupied by two K and two Bi atoms. To understand the electronic properties of these two different phases we have carried out band structure calculations within ab initio density functional theory (DFT) using full potential linearized augmented plane wave (LAPW) method. The generalized gradient approximation (GGA) was used to treat the exchange and correlation potential. Spin-orbit interaction (SOI) was incorporated using a second variational procedure. The α− phase is found to be a semiconductor with an indirect band gap of 0.47eV. For the β-phase we have chosen two different ordered structures. The system is a semi-metal for one of the structures whereas for the other, it is a narrow gap semiconductor with a gap of 0.38eV in the absence of SOI, but the gap collapses and the system becomes a semimetal with low density of states at the Fermi energy when SOI is included.

Electronic structure of K2Bi8Se13

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