Degenerate Semiconductors Research Articles

The impact of atomic defects on high-temperature stability and electron transport properties in Sr2Mg1−xNixMoO6–δ solid solutions

The computational modeling within a density functional theory was applied for simulations of electronic spectra and calculations of structural and energy characteristics of the cubic double perovskite oxides Sr2Mg1−xNixMoO6–δ, where x = 0, 0.5, and 1. The oxygen stoichiometric molybdates are antiferromagnetic semiconductors with an energy gap near 2 eV. The energy-based arguments show that anti-site cation disorder may contribute to the structural stability of the molybdates. It is found that nickel doping is favorable for mitigated chemical expansion. The replacement of magnesium by nickel is accompanied by the contribution of Ni3d states to the valence band while leaving hybrid Mo4d-O2p states in the conduction band virtually unchanged. It is shown that the compounds under study are thermodynamically unstable in heavily reducing conditions which is confirmed by experimental results. The appearance of oxygen deficiency in Sr2Mg1−xNixMoO6–δ results in the formation of oxygen vacancy associated donor states near the bottom of the conduction band and the transition from the intrinsic to degenerate semiconductor. It is suggested that the influence of nickel dopants on the energy and density of the donor states may help to explain variations of the conducting properties with doping level.

Effects of Ge Doping on the Charge Transport and Thermoelectric Properties of Permingeatites Cu3Sb1−yGeySe4

Permingeatites Cu3Sb1−yGeySe4 (0 ≤ y ≤ 0.14) were synthesized by mechanical alloying and hot pressing. The charge-transport parameters (Hall coefficient, carrier concentration, mobility, and Lorenz number) and thermoelectric properties (electrical conductivity, Seebeck coefficient, power factor, thermal conductivity, and figure of merit) were examined with respect to the Ge doping level. A single permingeatite phase with a tetragonal structure was obtained without subsequent heat treatment, but a small amount of the secondary phase Cu2GeSe3 was found for the specimens with y ≥ 0.08. All hot-pressed compacts exhibited a relative density of 97.5%–98.3%. The lattice constants of the a-axis and c-axis were decreased by the substitution of Ge at the Sb sites. As the Ge content increased, the carrier concentration increased from 5.2 × 10<sup>18</sup> to 1.1 × 10<sup>20</sup> cm<sup>−3</sup>, but the mobility decreased from 92 to 25 cm<sup>2</sup>·V<sup>−1</sup>·s<sup>−1</sup>. The Lorenz number of the undoped Cu3SbSe4 implied a non-degenerate semiconductor behavior, ranging from (1.57–1.56) × 10<sup>−8</sup> V<sup>2</sup>·K<sup>−2</sup> at 323–623 K. The thermoelectric figure of merit was 0.39 at 623 K, resulting from a power factor of 0.49 mW·m<sup>−1</sup>·K<sup>−2</sup> and a thermal conductivity of 0.76 W·m<sup>−1</sup>·K<sup>−1</sup>. However, the Lorenz numbers of the Gedoped specimens indicated degenerate semiconductor characteristics, increasing to (1.63–1.94) × 10<sup>−8</sup> V<sup>2</sup>·K<sup>−2</sup> at 323–623 K. The highest thermoelectric figure of merit of 0.65 was at 623 K for Cu3Sb0.86Ge0.14Se4, resulting from the significantly improved power factor of 0.93 mW·m<sup>−1</sup>·K<sup>−2</sup> and the thermal conductivity of 0.89W·m<sup>−1</sup>·K<sup>−1</sup>. As a result, the thermoelectric properties were remarkably enhanced by doping Ge into the Sb sites of the permingeatite.

Magnetotransport and thermal properties of microwave synthesized nanostructured Bi2Te3

Magnetotransport and thermal properties of microwave-synthesized nanostructured Bi2Te3, a well-known material of topological interest, have been studied in detail. Temperature-dependent resistivity shows a disordered metal-like behavior at high temperature with unsaturated ln(T)-dependent upturns at low temperature manifesting localization tendency. The slopes (κ) of the normalized conductivity (Δσ) vs ln(T) curves change sharply with magnetic fields upto 1 T and then saturate at a certain higher field (Bϕ), which is an indication of a combined electron–electron interaction and quantum interference effect (QIE) dominated transport. A noteworthy result is a crossover from positive to negative Coulomb screening factor (F) in Bi2Te3. Low-field (H ≤ 1 T) magnetoconductivity at low temperature follows a 2D Hikami–Larkin–Nagaoka equation, thereby revealing the QIE and associated dephasing nature of the electronic states at high temperatures. High-field (14 T) magnetoresistance (MR) at 2 K shows interesting features like low-field weak antilocalization, possibly a defect-induced negative MR that vanishes after post-annealing treatment, and a high field parabolic character in place. The Seebeck coefficient (S) is negative and varies quasilinearly with a slight but notable slope change at intermediate temperatures. Heat capacity measurements are in line with a narrow gap degenerate semiconductor with a low θD of 140 K. A combined analysis of heat capacity and thermopower reveals the localization of carriers at low temperatures and is in line with transport data.

Disorder-Induced Anderson-Like Localization for Bidimensional Thermoelectrics Optimization

Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, couldplay an important role in global sustainable energy. However, improving thermoelectric efficiency has proven difficult, largelydue to the complex interdependence of electronic properties of solids. Early work by Ioffe has developed into the standardthermoelectric optimization paradigm of tuning the electronic carrier concentration in semiconductors. Although the localizationtheory of electrons by Anderson and Mott has developed in parallel, its potential for thermoelectrics optimization has notbeen explored. Here, we show that electron localization induced by structural disorder also provides an effective optimizationstrategy for thermoelectric materials. By using a transport model that includes the relevant physics of localization it is shownthat the maximum thermoelectric figure-of-merit can be increased ~20% by tuning both carrier concentration and disorder.This approach is demonstrated in two model Ge-Sb-Te material systems and confirms that the peak figure-of-merit occursin slightly disordered materials. Particularly for highly degenerate semiconductors this bidimensional optimization strategyprovides a new methodology to attain high thermoelectric performance.

High Entropy Semiconductor AgMnGeSbTe4 with Desirable Thermoelectric Performance

AbstractA new p‐type high entropy semiconductor AgMnGeSbTe4 with a band gap of ≈0.28 eV is reported as a promising thermoelectric material. AgMnGeSbTe4 crystallizes in the rock‐salt NaCl structure with cations Ag, Mn, Ge, and Sb randomly disordered over the Na site. Thus, a strong lattice distortion forms from the large difference in the atomic radii of Ag, Mn, Ge, and Sb, resulting in a low lattice thermal conductivity of 0.54 W m−1 K−1 at 600 K. In addition, the AgMnGeSbTe4 exhibits a degenerate semiconductor behavior and a large average power factor of 10.36 µW cm−1 K−2 in the temperature range of 400–773 K. As a consequence, the AgMnGeSbTe4 has a peak figure of merit (ZT) of 1.05 at 773 K and a desirable average ZT value of 0.84 in the temperature range of 400–773 K. Moreover, the thermoelectric performance of AgMnGeSbTe4 can be further enhanced by precipitating of Ag8GeTe6, which acts as extra scatting centers for holes with low energy and phonons with medium wavelength. The simultaneous optimization in power factor and lattice thermal conductivity yields a peak ZT of 1.27 at 773 K and an average ZT of 0.92 (400–773 K) in AgMnGeSbTe4‐1 mol% Ag8GeTe6.

Emergence of magnetic anisotropy by surface adsorption of transition metal dimers on γ-graphyne framework

In this paper a systematic study is carried out to demonstrate the structural stability and magnetic novelty of adsorbing transition metal (TM) dimers (A-B) on graphyne (GY) surface, GY@A-B. Our research points out that the dimers are strongly adsorbed onto GY due to their large natural pores and the electron affinity of the sp-hybridized carbon atoms. Electronic properties of these dimer-graphyne composite systems are of particular importance as they behave as degenerate semiconductors with partial occupation of states at E F. Furthermore, their remarkable spin polarization (>80%) at Fermi energy (E F) can be of paramount importance in spintronics applications. Most of the GY@A-B structures exhibit large magnetic anisotropies as well as magnetic moments along the out-of-plane direction with respect to the GY surface. Particularly, GY@Co–Ir, GY@Ir–Ir and GY@Ir–Os structures possess positive magnetic anisotropic energies (MAE) of 121 meV, 81 meV and 137 meV, respectively, which are comparable to other well-known TM dimer doped systems. The emergence of high MAE can be understood using the second-order perturbation theory on the basis of the strong spin–orbit coupling (SOC) between the two TMs and the degeneracy of their d-orbitals near E F. A close correspondence between the simulated and the analytical results has been established through our work. Further, a simple estimation shows that, GY@A-B structures have the potential to store data up to 64 PB m−2. These intriguing electronic characteristics along with magnetism suggest GY@A-B to be a promising material for future magnetic storage devices.

Effects of Charge Compensation on the Thermoelectric Properties of (La1-zCez)0.8Fe4-xCoxSb12 Skutterudites

La/Ce-partially double-filled and Co-charge-compensated (La1−zCez)0.8Fe4−xCoxSb12 skutterudites were synthesized, and their thermoelectric properties were studied by varying the filling ratio and charge compensation. X-ray diffraction analysis revealed that the matrix phase was skutterudite and a secondary phase was determined to the marcasite FeSb2. However, the formation of marcasite could be inhibited by increasing the Co content. Rare-earth antimonides, including LaSb2 and CeSb2, which were formed in fully filled La1−zCezFe4−xCoxSb12, were not found after La/Ce partial filling. La/Ce filling and Co substitution were confirmed by the decrease in lattice constants, from 0.9137 to 0.9099 nm, with increasing Ce and Co contents. Electrical conductivity showed negative temperature dependence, indicating metallic or degenerate semiconductor characteristics. Intrinsic conduction resulted in the maximum Seebeck coefficient at temperatures between 723 and 823 K. As the Co-substitution and Ce-filling contents increased, the Seebeck coefficient increased, while electrical and thermal conductivities decreased. This was considered to be due to difference in the valences of La<sup>3+</sup> and Ce<sup>3+/4+</sup> and the increase in carrier concentration caused by Co charge compensation. However, because they had similar atomic masses and ionic radii, the effects of the La/Ce filling ratio were not significant. Instead, Co charge compensation had the dominant effect on thermoelectric properties. The maximum Seebeck coefficient of 165.4 µVK<sup>-1</sup> was obtained for (La0.25Ce0.75)0.8Fe3CoSb12 at 823 K, and the highest electrical conductivity of 2.27 × 10<sup>5</sup> S m<sup>-1</sup> was achieved for (La0.75Ce0.25)0.8Fe4Sb12. (La0.25Ce0.75)0.8Fe3CoSb12 exhibited the lowest thermal conductivity of 2.15 W m<sup>-1</sup>K<sup>-1</sup> at 523 K and (La0.75Ce0.25)0.8Fe3.5Co0.5Sb12 showed the highest power factor of 2.53 mW m<sup>-1</sup> K<sup>-2</sup> at 723 K. The maximum dimensionless figure of merit, ZTmax = 0.71, was achieved at 723 K for (La0.75Ce0.25)0.8Fe3CoSb12.

Semiconductor to metal transition in the solids/melts of Te and pseudo-binary of Hg1−xCdxTe for x = 0, 0.1, and 0.2

This paper reports the experimentally measured thermal and electrical conductivities from which the Lorenz numbers as functions of temperature were derived for the solids and melts of elemental Te and samples of Hg1−xCdxTe of x = 0, 0.1, and 0.2. The structural changes in the vicinity of the solid–liquid phase transition of elemental Te and various Hg1−xCdxTe solid solutions were assessed by closely examining these experimental properties and the derived Lorenz numbers. The values of Lorenz numbers for the solids of these samples were higher than the value of L0, i.e., the Lorenz number for the free-electron gas derived by Sommerfeld [Naturwissenschaften 15, 825 (1927)], implying the characteristics of a non-degenerate semiconductor. With the increasing value of x, or the larger bandgap, the materials become more non-degenerate with larger deviation from L0. As the solids started to melt, the measured values of the Lorenz number for all samples started to decrease and eventually reached and maintained at values close to L0 at higher temperatures. The trend of the Lorenz number indicates the transition from a non-degenerate semiconductor of the solid samples to a metal or degenerate semiconductor when the temperatures of the samples reached above their liquidus temperatures.

Hybrid functional analysis of planar metal-organic frameworks

The electronic energy band structure and optical properties of the planar metal-organic frameworks, namely M-HAB and M3[HITP] (M = Ni, Cu; HAB = hexaaminobenzene; HITP = hexaiminotriphenylene) were investigated in this work using two hybrid exchange-correlation functionals. The materials studied here contain nickel and copper, 3d electrons of which should be considered as strongly correlated subsystem. These semi-core electrons are treated here by means of the hybrid HSE06 and PBE0 functionals. We have found that Ni-HAB and Cu-HAB are metals, whereas Ni3[HITP]2 and Cu3[HITP]2 are degenerate p-type semiconductors.

Quantum magnetoconductivity characterization of interface disorder in indium-tin-oxide films on fused silica

Disorder arising from random locations of charged donors and acceptors introduces localization and diffusive motion that can lead to constructive electron interference and positive magnetoconductivity. At very low temperatures, 3D theory predicts that the magnetoconductivity is independent of temperature or material properties, as verified for many combinations of thin-films and substrates. Here, we find that this prediction is apparently violated if the film thickness d is less than about 300 nm. To investigate the origin of this apparent violation, the magnetoconductivity was measured at temperatures T = 15 – 150 K in ten, Sn-doped In2O3 films with d = 13 – 292 nm, grown by pulsed laser deposition on fused silica. We observe a very strong thickness dependence which we explain by introducing a theory that postulates a second source of disorder, namely, non-uniform interface-induced defects whose number decreases exponentially with the interface distance. This theory obeys the 3D limit for the thickest samples and yields a natural figure of merit for interface disorder. It can be applied to any degenerate semiconductor film on any semi-insulating substrate.

Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation

The van Roosbroeck system models current flows in (non-)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another state-of-the-art Scharfetter–Gummel scheme, namely the diffusion-enhanced scheme. Physically, the diffusion-enhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized Scharfetter–Gummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non-)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, drift-diffusion simulations of a p–i–n device are performed.

FT-IR, Molecular Structure and Nonlinear Optical Properties of 2-(pyranoquinolin-4-yl)malononitrile (PQMN): A DFT Approach

A combined experimental and theoretical study for Fourier transform infrared spectra for 2-(pyranoquinolin-4-yl)malononitrile (PQMN) compound has been made. In advance, we investigate many physical characteristics based on DFT/B3LYP using 6-311G(d,p) basis set such as optimum structure, vibrational frequencies, thermo-chemistry, overall dipole moment, HOMO/LUMO Bandgap, nuclear repulsive energy and ionization energies, electronic affinity and chemical potential, global electrophilicity index, global hardness and finally softness (ζ). Also, we studied the non-linear optical (NLO) properties of PQMN. Results emphasize both degeneracy and diamagnetic properties of PQMN. PQMN Frontiers’ molecular orbitals (FMOs) split into two distinguished alpha (spin ↑) and beta (spin ↓) states with the same energy 3.7 eV, although its singlet spins state. Moreover, the calculated dipole moment (DM) value (13.3 Debye) for PQMN explains the mystery behind its reactive tendency with the nearby media. PQMN is a unique model for a degenerate diamagnetic semiconductor that can be easily used for optoelectronic manufactured devices such as solar cells and spintronic devices.

Ruthenium-based half Heusler alloys RuTiX (X = Si, Ge, Sn): An FP-LAPW-based analytical study of structural, electronic, elastic, mechanical and transport properties

An full potential linearized augmented plane wave (FP-LAPW)-based analytical study of structural, electronic, mechanical and thermoelectric properties has been done for the Ruthenium-based half heusler RuTiX (X = Si, Ge and Sn) compounds. An efficient method to develop Half Heusler (HH) alloys is by examining their stability of structure in various phases, by plotting electronic band structures, computing elastic constants and also by studying the presence of magnetic moments. In this study, we have used DFT-based calculations to scrutinise the paramagnetic/ferromagnetic (FM) as well as metallic/semiconducting behavior of these HH compounds. The predicted phase stability using the energy versus volume curves reveals that they are stable in Type C phase. RuTiSi and RuTiGe are found to be stable in the paramagnetic phase whereas RuTiSn is stable in the FM phase with a finite value of magnetic moment. The electronic band structures and density of states (DOS) plots predict that the studied compounds belong to [Formula: see text]-type degenerate semiconductors as the Fermi Level lies within the valence band. Due to the existence of finite DOS at the Fermi level, they show an enhanced metallic behavior. A small value indirect gap is found between valence band maximum (VBM) and conduction band minimum (CBM) in all these studied RuTiX HH alloys depicting their semiconducting nature. The elastic constants of cubic phase are computed for the first time and they obey the mechanical stability criteria. The positive value of [Formula: see text] and value of [Formula: see text]/[Formula: see text] ratio of these HH compounds exhibit their ductile nature. The thermoelectric properties of these compounds are investigated, and a comparatively higher figure of merit reveals their scope of application in thermoelectric devices.

Epsilon‐Negative Carbon Aerogels with State Transition from Dielectric to Degenerate Semiconductor

AbstractAerogels with negative parameters have become a research hotspot since the discovery of negative Poisson's ratio and negative thermal expansion coefficient in aerogels. The negative parameters are originally brought up and studied in electromagnetic metamaterials, leaving a question that whether aerogels can be used to construct metamaterials with negative electromagnetic parameters. Here, the authors show that negative permittivity (epsilon‐negative) property can be achieved in carbon aerogels, and its value is adjusted continuously by changing the composition of carbon aerogels but keeping their microstructure unchanged. This is a novel strategy different from the typical array‐structure‐containing metamaterials. Moreover, a physical state transition is found when increasing the carbonization temperature, where the initial low‐loss dielectric state evolves into a high‐loss one upon increasing the temperature from 400 to 700 °C followed by a final degenerate semiconductor state when increasing the temperature to 800 °C and above. This work can provide a new method toward the design of electromagnetic metamaterials, starting by choosing the component materials with optimal composition.

Single crystal growth and characterization of new Zintl phase Ca9Zn3.1In0.9Sb9

Complex Zintl phases have yielded a large variety of promising new thermoelectric materials. In this study we report the discovery of the new Zintl phase Ca9(Zn1–xInx)4Sb9 (x ​~ ​0.9), needle-like crystals of which were serendipitously obtained from an In- and Sb-rich flux. Although its composition is reminiscent of Ca9Zn4+xSb9, an excellent thermoelectric material with zT ​> ​1, the substitution of In on the Zn site leads to the formation of an entirely new structure type. Single crystal X-ray diffraction revealed a structure characterized by TSb4 tetrahedra (T ​= ​statistically disordered Zn and In atoms) and ZnSb3 triangular units, which share common corners to form [T4Sb9]18− polyanions. The average structure was found to have hexagonal symmetry. The valence electron count in this heavily-disordered structure appears to follows the Zintl-Klemm rules, suggesting semiconducting behavior. Single crystal electrical conductivity and Seebeck coefficient measurements support this conclusion, suggesting that the as-grown crystals are degenerate p-type semiconductors.

An electronic phase diagram of hole-doped BiCuSeO crystals determined by transport characterization under various growth conditions

Temperature-hole-concentration dependent electronic phase-diagram of BiCuSeO.

Metastable Ta2N3 with highly tunable electrical conductivity via oxygen incorporation.

The binary Ta–N chemical system includes several compounds with notable prospects in microelectronics, solar energy harvesting, and catalysis. Among these, metallic TaN and semiconducting Ta3N5 have garnered significant interest, in part due to their synthetic accessibility. However, tantalum sesquinitride (Ta2N3) possesses an intermediate composition and largely unknown physical properties owing to its metastable nature. Herein, Ta2N3 is directly deposited by reactive magnetron sputtering and its optoelectronic properties are characterized. Combining these results with density functional theory provides insights into the critical role of oxygen in both synthesis and electronic structure. While the inclusion of oxygen in the process gas is critical to Ta2N3 formation, the resulting oxygen incorporation in structural vacancies drastically modifies the free electron concentration in the as-grown material, thus leading to a semiconducting character with a 1.9 eV bandgap. Reducing the oxygen impurity concentration via post-synthetic ammonia annealing increases the conductivity by seven orders of magnitude and yields the metallic characteristics of a degenerate semiconductor, consistent with theoretical predictions. Thus, this inverse oxygen doping approach – by which the carrier concentration is reduced by the oxygen impurity – offers a unique opportunity to tailor the optoelectronic properties of Ta2N3 for applications ranging from photochemical energy conversion to advanced photonics.

Measurement of Piezoelectric Characteristics of Diode Structures Using the «Obzor-103» Vector Analyzer

The results of the study of semiconductor film heterostructures CdS-Cu2S and CdS-ZnS-Cu2S by the resonance-antiresonance method are presented. The semiconductor heterostructures CdS-Cu2S and CdS-ZnS-Cu2S applied on a molybdenum basis were used as samples. The molybdenum base was used as the first current contact. A degenerate p-type Cu2S semiconductor was used as the second current contact. Piezoelectric devices include piezoelectric transducers, based on piezoelectric elements made of the material having a direct or reverse piezoelectric effect.The advantages and disadvantages of resonance antiresonance have been demonstrated. Measurements of the amplitude-frequency characteristics were performed using the vector analyzer "Obzor - 103". The methods of sample research and the procedure of measurements of complex reflection and transmission coefficients with the help of measuring complex "Obzor - 103" are presented. The scheme of measurement of the complex reflection coefficient S11 and the complex transmission coefficient S21 of the four-pole in the 50 Ohm path is presented. Appropriate definitions of complex display and transmission coefficients are given. Using the "Obzor - 103" vector analyzer, the complex reflection coefficients of the S11 samples were measured and the resonance bands from 883 to 1273 MHz were recorded.Based on the determined values of the resonance and anti-resonance frequencies, the figure of merit of the investigated heterostructures and capacitance values were calculated. The calculation was performed using additional data obtained from the study of the samples using the emitter meter "E7-20" under conditions close to the resonance. Comparison of the calculated values shows a significant difference in the behavior of the samples based on CdS and ZnS. Compared to the capacity and figure of merit for the piezoceramic elements presented in OST II 0444-78.The structures studied by us showed significantly lower values of quality and capacity. The much lower values of the figure of merit are explained by the fact that in our work we investigated thin-film structures rather than the volumetric piezo-ceramic elements, the values of which are given in OST II 0444-78.The highest Q-values (~ 62) were obtained for the CdS-ZnS-Cu2S heterostructure. For structures with CdS films, the Q-values is less than 27.94. The Q-value of 62.65 for the CdS-ZnS-Cu2S structure is quite large, even compared to the value for a well-known piezoceramic such as CTS-19, whose Q-value is 60 and which is a bulk material. Thus, studies conducted to evaluate the piezoelectric properties of heterostructures with CdS-Cu2S and CdS-ZnS-Cu2S semiconductor films demonstrate the presence of the piezoelectric properties of these structures and the prospects for their developmentThe results obtained are new and show the prospect of research on semiconductor heterostructures for the development of new piezoelectric devices.

Low field magnetization in Pb1-x-ySnyMnxTe semimagnetic semiconductors

Abstract We report and analyse the results of our calculation of low field magnetization of the degenerate dilute magnetic semiconductor Pb1-x-ySnyMnxTe for × = 0.03 and y = 0.72, for a carrier density of holes p = 1.4 × 1020 cm−3. The contribution comes from two different mechanisms namely localized magnetic impurities of Mn+2 , and band effects. For the calculation of magnetic impurity contribution we assume that the these impurities are distributed in random fashion over the host system and we use three spin cluster model which includes single, pair and triple spin clusters. Moreover, we consider two types of three spin clusters like open and closed triplets. The band effect includes lattice diamagnetism as well as spin polarization of carriers. The former has been calculated using a two band model of the host system and the effects of the impurities are incorporated through the modification of its band gap. The variation of the energy band gap as a function of Sn and Mn concentrations and temperature is considered through an empirical expression and value of the energy gap so obtained for Pb1-x-ySnyMnxTe ( × = 0.03 and y = 0.72) is about 125 meV at 5 K. The spin density of carriers is evaluated using the second order k → . π → perturbation theory. The major contribution to local moment magnetization comes from single spin clusters and then from pair and triads. The diamagnetic contribution arises from the diamagnetic susceptibility and hence it is negative. The contribution from spin density of carriers, as expected, is very small in the range of carrier density considered for present study. Good agreement between our theory with experiment is another important feature of our calculation.

Band engineering of non-hexagonal 2D tetragonal-silicene sheet and nanoribbons: A theoretical approach

We report combined first-principle and tight-binding (TB) calculation to investigate the mechanical and electronic properties of non-hexagonal two-dimensional (2D) tetragonal-silicene (TS) sheet and nanoribbons (NRs). The results obtained by the TB method are consistent with the density functional theory (DFT) results. The elastic constants of the TS sheet are comparable to silicene. The existence of two Dirac cones is observed at different k→ points in the irreducible Brillouin Zone. A spin-orbit bandgap larger than silicene is observed in TS. The criteria for the stability and robustness of the Dirac Cones on the TB parameters are extensively investigated. Both the Dirac points are robust and stable under a wide range of hopping parameters. The degeneracy of the Dirac cones can be removed by introducing asymmetry in the on-site energy. Comparing the DFT and TB band structures, the values of the TB hopping parameters are estimated. The electronic properties of the TSNRs show a strong dependence on the width and the edge states. The symmetric armchair TSNRs show a width dependent multiple Dirac cones in the Brillouin zone. The number of Dirac cones of the NR is found to be dependent on the TB hopping parameters as well. On the other hand, asymmetric armchair TSNRs are semiconducting. The tuning of the bandgap for asymmetric armchair TSNRs by modulating the TB hopping parameters is also explored. Zigzag TSNR behaves as a degenerate semiconductor with the presence of Dirac cones just below and above EF. We subsequently expect that these theoretical findings will give a better comprehension of Dirac materials and their NRs with its potential application in nano-electronics.