Zero-gap Semiconductor Research Articles

First-principles calculations of electronic structure and optical properties of strained Mg2Si

A detailed theoretical study on structural, electronic and optical properties of Mg2Si under the isotropic lattice deformation was performed based on the first-principles pseudopotential method. The results show that the isotropic lattice deformation results in a linear decrease in the energy gap for the direct Γ15-Γ1 and indirect Γ15-L1 transitions from 93% to 113%, while the indirect band gap Γ15-X1 increases from 93% to 104% and then reduces over 104%. When the crystal lattice is 93% compressed and 113% stretched, the magnesium silicide is a zero-gap semiconductor. Furthermore, the isotropic lattice deformation makes the dielectric function shift and the static dielectric constant change.

Tunable multifunctional topological insulators in ternary Heusler compounds

Recently the quantum spin Hall effect was theoretically predicted and experimentally realized in quantum wells based on the binary semiconductor HgTe (refs 1-3). The quantum spin Hall state and topological insulators are new states of quantum matter interesting for both fundamental condensed-matter physics and material science. Many Heusler compounds with C1(b) structure are ternary semiconductors that are structurally and electronically related to the binary semiconductors. The diversity of Heusler materials opens wide possibilities for tuning the bandgap and setting the desired band inversion by choosing compounds with appropriate hybridization strength (by the lattice parameter) and magnitude of spin-orbit coupling (by the atomic charge). Based on first-principle calculations we demonstrate that around 50 Heusler compounds show band inversion similar to that of HgTe. The topological state in these zero-gap semiconductors can be created by applying strain or by designing an appropriate quantum-well structure, similar to the case of HgTe. Many of these ternary zero-gap semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the rare-earth element Ln, which can realize additional properties ranging from superconductivity (for example LaPtBi; ref. 12) to magnetism (for example GdPtBi; ref. 13) and heavy fermion behaviour (for example YbPtBi; ref. 14). These properties can open new research directions in realizing the quantized anomalous Hall effect and topological superconductors.

Theoretical study of superconducting proximity effect in single and multi-layered graphene

Theoretical analysis of superconducting current in graphite thin films (or graphene) in proximity to superconductors is presented, especially paying attention to the band structure. We derive the general formula to calculate the free energy of the superconductor–graphite film–superconductor junction, which enable us to calculate the critical current of the junction. We introduce two models for the band structures: (1) Fermi point type (characteristic to monolayer case) and (2) zero-gap semiconductor type (characteristic to bilayer case). Then we calculate the superconducting critical current as a function of junction length and temperature.

Strain and electric field modulation of the electronic structure of bilayer graphene

We study how the electronic structure of the bilayer graphene (BLG) is changed by electric field and strain from ab initio density-functional calculations using the linear muffin-tin orbital and the linear augmented plane wave methods. Both hexagonal and Bernal stacked structures are considered. We only consider interplanar strain where only the interlayer spacing is changed. The BLG is a zero-gap semiconductor like the isolated layer of graphene. We find that while strain alone does not produce a gap in the BLG, an electric field does so in the Bernal structure but not in the hexagonal structure. The topology of the bands leads to Dirac circles with linear dispersion in the case of the hexagonally stacked BLG due to the interpenetration of the Dirac cones, while for the Bernal stacking, the dispersion is quadratic. The size of the Dirac circle increases with the applied electric field, leading to an interesting way of controlling the Fermi surface. The external electric field is screened due to polarization charges between the layers, leading to a reduced size of the band gap and the Dirac circle. The screening is substantial in both cases and diverges for the Bernal structure for small fields as has been noted by earlier authors. As a biproduct of this work, we present the tight-binding parameters for the free-standing single layer graphene as obtained by fitting to the density-functional bands, both with and without the slope constraint for the Dirac cone and keeping the hopping integral up to four near neighbors.

The electronic properties of graphene and carbon nanotubes

A brief review is given on the characteristic features of electronic states and transport in graphene consisting of a single sheet of graphite, and its cylinder form called a carbon nanotube. Electron motion in graphene is equivalent to that of a neutrino or a relativistic Dirac electron with vanishing rest mass. This causes the appearance of a nontrivial Berry’s phase under 2π rotation in wave-vector space, leading to the absence of backscattering and in the metallic carbon nanotube resulting in perfect conduction even in the presence of scatterers. The energy bands in carbon nanotubes are determined by periodic boundary conditions with a fictitious Aharonov-Bohm flux determined uniquely by the circumferential chiral vector. A nanotube becomes metallic when the flux vanishes and semiconducting when the flux is nonzero. The conductivity of graphene is essentially independent of the Fermi energy and the electron concentration as long as variations in effective scattering strength are neglected, and therefore graphene should be regarded as a metal rather than a zero-gap semiconductor. Various schemes are now being proposed and tested for the purpose of opening the band gap in graphene.

Heyd-Scuseria-Ernzerhof hybrid functional for calculating the lattice dynamics of semiconductors

We present an ab initio study of the lattice dynamics of group-IV elemental semiconductors and insulators using a finite differences approach. The investigated solids include cubic diamond (C), silicon (Si), germanium (Ge), and the zero-gap semiconductor gray tin $(\ensuremath{\alpha}\text{-Sn})$. The main objective of this work is to examine the performance of the screened hybrid functional (HSE) proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003); J. Chem. Phys. 124, 219906(E) (2006)] for calculating phonon-dispersion relations. We find that all local and semilocal functionals tend to underestimate the phonon frequencies, with the errors increasing with increasing atomic mass. For $\ensuremath{\alpha}\text{-Sn}$, semilocal functionals even qualitatively fail to describe the dispersion of the highest optical phonon mode. We show that this is related to semilocal functionals predicting $\ensuremath{\alpha}\text{-Sn}$ to be a metal, whereas experimentally it is a zero-gap semiconductor. The HSE functional yields the correct electronic band structure resulting in qualitatively correct phonon-dispersion relations for all four solids. Quantitatively, the phonon frequencies are slightly overestimated using HSE, in particular for the lighter elements C and Si. Our results are compared to previously reported theoretical findings.

Graphene zigzag ribbons, square lattice models and quantum spin chains

We present an extended study of finite-width zigzag graphene ribbons (ZGRs) based on a tight-binding model with hard-wall boundary conditions. We provide an exact analytic solution that clarifies the origin of the predicted width dependence on the conductance through junctions of ribbons with different widths. An analysis of the obtained solutions suggests a new description of ZGRs in terms of coupled chains. We pursue these ideas further by introducing a mapping between the ZGR model and the Hamiltonian for N-coupled quantum chains as described in terms of 2N Majorana fermions. The proposed mapping preserves the dependence of ribbon properties on its width thus rendering metallic ribbons for N odd and zero-gap semiconductor ribbons for N even. Furthermore, it reveals a close connection between the low-energy properties of the ZGR model and a continuous family of square lattice model Hamiltonians with similar width-dependent properties that includes the π flux and the trivial square lattice models. As a further extension, we show that this new description makes it possible to identify various aspects of the physics of graphene ribbons with those predicted by models of quantum spin chains (QSCs).

Tight-Binding Modeling and Low-Energy Behavior of the Semi-Dirac Point

We develop a tight-binding model description of semi-Dirac electronic spectra, with highly anisotropic dispersion around point Fermi surfaces, recently discovered in electronic structure calculations of VO2-TiO2 nanoheterostructures. We contrast their spectral properties with the well-known Dirac points on the honeycomb lattice relevant to graphene layers and the spectra of bands touching each other in zero-gap semiconductors. We also consider the lowest order dispersion around one of the semi-Dirac points and calculate the resulting electronic energy levels in an external magnetic field. In spite of apparently similar electronic structures, Dirac and semi-Dirac systems support diverse low-energy physics.

Construction Method for an AB Bipartite Network with the π Electronic Properties of Graphene: Generalization of the Edge States

We propose a method for constructing an AB bipartite lattice network class, termed a “hypergraphene network”. Edge states are defined as evanescent wave solutions with a dumping factor for the hypergraphene network. Bulk electronic states of some hypergraphene networks based on the single tight binding model are similar to the π-electronic states of graphene, i.e., they display a linear dispersion relation, a massless Dirac spectrum, and zerogap semiconductor behavior. Our approach suggests a new method to design possible network structures having the character of graphene in not only two-dimensions, but also in systems with three- or more dimensions.

The nature of “heavy” electrons in the p-HgTe zero-gap semiconductor

To interpret the low-temperature features of the electron transport in the p-HgTe zero-gap semiconductor, the model is suggested, according to which, the “heavy” electrons are the electrons for the conduction band localized in the wells of the fluctuation potential. The experimental data on the temperature, magnetic field, and baric dependences of the Hall coefficient R(T, H, P) and electrical conductivity ρ0(T, P) in lightly doped, moderately compensated, and heavily doped p-HgTe samples are analyzed.

Electron delocalization in bilayer graphene induced by an electric field

Electronic localization is numerically studied in disordered bilayer graphene with an electric-field-induced energy gap. Bilayer graphene is a zero-gap semiconductor, in which an energy gap can be opened and controlled by an external electric field perpendicular to the layer plane. We found that, in the smooth disorder potential not mixing the states in different valleys ($K$ and ${K}^{\ensuremath{'}}$ points), the gap opening causes a phase transition at which the electronic localization length diverges. We show that this can be interpreted as the integer quantum Hall transition at each single valley, even though the magnetic field is absent.

Ground state energy of current carriers in graphene

The ground state energy of current carriers in graphene considered as a zero-gap semiconductor was calculated in the two-band approximation. The condition of the electronic (hole) system stability in graphene was obtained. The possibility of the zero-gap semiconductor—semimetal transition was discussed.

Electronic band-edge properties of rock salt PbY and SnY (Y= S, Se, and Te)

The electronic band-edges of lead chalcogenides PbY and tin chalcogenides SnY (where Y = S, Se, and Te) are investigated by the means of a full-potential linearized augmented plane wave (FPLAPW) method and the local density approximation (LDA). All six chalcogenide binaries have similar electronic structures and density-of-states, but there are differences in the symmetry of the band-edge states at and near the Brillouin zone L-point. These differences give the characteristic composition, pressure, and temperature dependences of the energy gap in Pb 1− x Sn x Y alloys. We find that: (1) SnY are zero-gap semiconductors E g = 0 if the spin–orbit (SO) interaction is excluded. The reason for this is that the conduction band (CB) and the valence band (VB) cross along the Q ≡ LW line. (2) Including the SO interaction splits this crossing and creates a direct gap along the Q-line, thus away from the L symmetry point. Hence, the fundamental band gap E g in SnY is induced by the SO interaction and the energy gap is rather small E g ≈ 0.2–0.3 eV. At the L-point, the CB state has symmetric L 4 + and the VB state is antisymmetric L 4 - thereby the L-point pressure coefficient ∂ E g ( L ) / ∂ p is a positive quantity. (3) PbY have a direct band gap at the L-point both when SO coupling is excluded and included. In contrast to SnY, the SO interaction decreases the gap energy in PbY. (4) Including the SO interaction, the LDA yields incorrect symmetries of the band-edge states at the L-point; the CB state has L 4 + and the VB state has L 4 - symmetry. However, a small increase of the cell volume corrects this LDA failure, producing an antisymmetric CB state and a symmetric VB state, and thereby also yields the characteristic negative pressure coefficient ∂ E g ( L ) / ∂ p in agreement with experimental findings. (5) Although PbY and SnY have different band-edge physics at their respective equilibrium lattice constants, the change of the band-edges with respect to cell volume is qualitatively the same for all six chalcogenides. (6) Finally, in the discussion of the symmetry of the band edges, it is important to clearly state the chosen unit cell origin; a shift by ( a/2,0,0) changes the labeling L 4 + ⇔ L 4 - of the irreducible representations.

Electronic structure of silicon-based nanostructures

We have developed an unifying tight-binding Hamiltonian that can account for the electronic properties of recently proposed Si-based nanostructures, namely, Si graphene-like sheets and Si nanotubes. We considered the $sp^3s^*$ and $sp^{3}$ models up to first- and second-nearest neighbors, respectively. Our results show that the Si graphene-like sheets considered here are metals or zero-gap semiconductors, and that the corresponding Si nanotubes follow the so-called Hamada's rule [Phys. Rev. Lett. {\bf 68}, 1579 1992]. Comparison to a recent {\it ab initio} calculation is made.

The band structure and the double metal-insulator-metal phase transition in the conductivity of elastically strained zero-gap Cd x Hg1−x Te

In the zero-gap CdxHg1−xTe semiconductor subjected to an axial elastic strain, a band gap is formed between the bottom of the conduction band and the top of the valence band. In the new state, the band structure is found to depend on the initial arrangement of the valence subbands, i.e., on the composition defined by the parameter x. At x < 0.135–0.140, the material becomes a semiconductor with an indirect band gap. If 0.140 < x < 160, the band of light holes at k = 0, Γ6, is found to be above the Γ8 band. As a result, the material becomes a direct-gap semiconductor, and a double “metal-semiconductor-metal” phase transition in conductivity occurs. In this case, as the strain is increased, the type of conductivity of the zero-gap semiconductor at low temperatures changes according to the sequence as follows: electron metallic conductivity-electron activation conductivity-hopping conductivity-hole metallic conductivity.

Gold as intermolecular glue: a theoretical study of nanostrips based on quinoline-type monomers

A family of infinite nanostrips is computationally predicted. In it monomers of single, double or triple aromatic rings are linked to each other by strong C-Au-C, C-Au <-- N or N --> Au <-- N bonds. Depending on the geometry of the system and saturation of the bonds, these 1-D nanostrips are found to be insulators, narrow- or zero-gap semiconductors, or metals. The calculated dimerization and polymerization energies suggest clear exothermicity of formation. Varying the nitrogen content in the aromatic ring is found to little affect the geometry, and the 1-D band structure of the strips can be interpreted in a rigid-band picture. The orbital character of the states at the Fermi level has been analyzed. One of the new structures is found to be closely similar to graphene with respect to its band structure properties.

From graphene to graphite: Electronic structure around theKpoint

Within a tight-binding approach we investigate how the electronic structure evolves from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of graphene. It is well known that a single graphene layer is a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy, while graphite shows a semimetallic behavior with a band overlap of about $41\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. In contrast to a single graphene layer, we show that two graphene layers have a parabolic spectrum around the Fermi energy and are a semimetal like graphite; however, the band overlap of $0.16\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ is extremely small. Three and more graphene layers show a clear semimetallic behavior. For 11 and more layers the difference in band overlap with graphite is smaller than 10%.

Electronic structure and optical properties of binary skutterudite antimonides

The electronic structure near the Fermi level of binary skutterudite antimonides and optical properties are studied by the ab initio density functional calculation method. Lattice parameters of their compounds are determined by the calculation of the total energy by taking into account the spin-orbit interaction. The calculated band structure shows that lattice parameters strongly affect the band gap and the ordering of electronic states at $\ensuremath{\Gamma}$. ${\mathrm{CoSb}}_{3}$ is a narrow gap semiconductor with the band gap ${E}_{g}=118\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. Both ${\mathrm{RhSb}}_{3}$ and ${\mathrm{IrSb}}_{3}$ are zero-gap semiconductors, where in ${\mathrm{RhSb}}_{3}$ a conduction band and a valence band overlap slightly near $\ensuremath{\Gamma}$. Band structures near the gap on binary skutterudite antimonides can be represented by the four band model consisting of the two-band nonparabolic Kane model plus two parabolic bands. By using the band model the thermoelectric power for ${\mathrm{CoSb}}_{3}$ is calculated. The obtained electronic structure and the wave function are used to calculate and discuss interband optical absorption spectra and the x-ray absorption and emission near edge structure spectra. The calculated x-ray absorption (emission) near edge structure spectra are in good agreement with recent experimental data. Also the valence band density of states is shown to describe the experimental x-ray photoelectron spectra well.

Spin-Hall Insulator

Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin-Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum-Hall effect in that all the states below the gap contribute and there occurs no dissipation. However, the spin-Hall conductance is not quantized even in two dimensions. This is the first example of a nontrivial topological structure in a band insulator without any magnetic field.

Systematic study of electronic band structures for binary skutterudite compounds

The electronic band structures are calculated for TX 3 (T=Co, Rh, Ir and X=P, As, Sb) and NiP 3 by using an FLAPW method. CoSb 3, IrP 3, IrAs 3 and IrSb 3 are narrow gap semiconductors while CoAs 3 and RhAs 3 are zero-gap semiconductors. CoP 3, RhP 3 and RhSb 3 are typical semimetals and NiP 3 is a metal.