A comparative spin orbit coupling DFT study of opto-electronic properties of Bi2Se3 and Bi2Te3 bulk crystal

doi:10.1016/j.cocom.2024.e00951

Computational Condensed Matter

Volume 40, September 2024, e00951

https://doi.org/10.1016/j.cocom.2024.e00951 Get rights and content

Abstract

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

are the ideal candidate for spintronics and many other novel applications due to their strong opto-electronic properties. These materials are regarded as topological insulator as they portray band inversion which is considered to be a key signature of topology. Moreover, because of their superior opto-electronic qualities,

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

are intriguing in the realm of optical and electronic applications. This paper compares the optical and electronic characteristics of

{Bi}_{2} {Te}_{3}

and

{Bi}_{2} {Se}_{3}

in the framework of density functional theory taking PBE-GGA and mBJ-GGA as exchange correlation potential. The analysis of band structure and density of states (DOS) confirms the gapped nature without and with SOC calculation. The introduction of SOC gives the accurate result which matches with the experimental figure. Optical properties including reflectivity, absorption coefficient, energy loss function, refractive index, extinction coefficient, and optical conductivity are analyzed without and with SOC. We have also calculated birefringence, dichroism, and the optical skin depth which has not been reported yet for those compounds. The spectroscopic limited maximum efficiency (SLME), which theoretically determines the power conversion efficiency (PCE) of solar cells is also calculated. Based on the optical and electronic properties, possible uses of

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

are discussed without and with SOC effect.

Introduction

In condensed matter physics, the idea of the quantum Hall effect [1], in which electrons are trapped in two dimensions and exposed to a strong magnetic field, is the most promising finding of the 1980s. This effect investigates the recently discovered materials that are thought to be the first topological insulators (TIs) and are defined by the quantum hall system. Better TI results are obtained by continuing the progress that was preceded by the fractional quantum hall effect [2] and the quantum spin hall effect [3]. In quantum spin hall effect, the materials were first considered as quantum spin hall insulators, but a later study [4] revealed that quantum spin hall insulators cannot generate spin current in the absence of any electrons in the Fermi level. Scientists were inspired by this notion, and as a result, additional models were developed to verify whether a material is a TI, such as those based on z2 topology, Chern number, etc. [5]. In their bulk state, topological insulators exhibit an open band gap, while at their surfaces or edge states, they display a gapless band. Bulk band gaps of TIs are generally found to be smaller than those of 2D semiconductors. TIs are an excellent insulator for use in electronic and opto-electronic devices due to their resilient surface states and high mobility ratio [6], [7], [8], [9], [10].

Among the classified 2D and 3D TIs, 3D TIs show reasonably good response in thermoelectric and electronic properties due to their narrow band gap, and are designed by taking group V and VI elements. The TIs are the emerging Van der Waals compound characterized by their special spin–orbit interaction, which inverts the orbital band character of the valence band (VB) and conduction band (CB). The key applications of TIs are optical recording, broadband photodetectors, laser photonics and high-speed optoelectronics [11], [12], [13]. Compared with the other TIs,

{Bi}_{2} {Te}_{3}

has dominating applications in thermoelectric generators and Peltier cooling devices as it is more thermoelectric material at nearly room temperature.

{Bi}_{2} {Se}_{3}

as one of the alloys of

{Bi}_{2} {Te}_{3}

has been studied for its potential use in spintronics and quantum computing due to its robustness against decoherence and its ability to host non-Abelian anyons. In addition

Bi

based double peroxide material (magnetic) has potential applications in magnetic memories and tunnel junctions [14]. The bulk band gap of

{Bi}_{2} {Se}_{3}

is comparatively large and one can see the technological relevance of the material at room temperature. There exists a difference in the band structures of both the TIs characterized by the constant-energy contour of the Dirac cone.

{Bi}_{2} {Se}_{3}

has an almost spherical nature of the Dirac cone while

{Bi}_{2} {Te}_{3}

is signified by hexagonal wrapping in the Dirac cone [15]. The complex band structure can be understood easily with the help of spin–orbit coupling (SOC). The SOC plays an important role in exploring the band structure by positioning the band extrema away from the high symmetry points in the Brillouin zone [16]. The inclusion of SOC in heavy material leads to some decrease in band gap due to unfilled d-states that moves towards Fermi level [17], [18]. Without SOC,

{Bi}_{2} {Te}_{3}

shows a direct gap at high symmetry

Γ

point, while SOC results in a reduced indirect band gap instead of the direct gap.

Currently, there are literatures available for computing the electronic structures of

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

using experimental methods. The TB-mBJ potential in combination with SOC has not been studied, yet there are known computational outcomes utilizing the PBE potential. Moreover, some computational work on the optical properties of these materials in the absence of SOC has been done. The primary objective of this work is to compare the electronic and optical properties of

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

without and with SOC due to the limited work done with SOC. SOC is included in order to ensure that our calculated results match the experimental results; otherwise, the results differ from the experimental data. This is due to the fact that heavier atoms have stronger atomic magnetic fields, and an atom’s SOC strength grows almost to the fourth power of its atomic number. In addition, the compound’s optical and electronic results are analyzed to various uses in photovoltaic cells, LED technology, etc. [19], [20], [21], [22], [23], [24], [25]. For a better understanding of the result, we have calculated the spectroscopic limited maximum efficiency (SLME) to see the level of theoretical PCEs of solar cells.

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Section snippets

Computational precursor

The computational method to carry out this work is based on the first principles method to calculate the electronic structure and optical properties in the light of DFT. The DFT is powerful tool that provides a good balance between accuracy and computational cost. DFT often provides accurate estimation of electronic band gap. DFT is also applicable in wide range of materials like insulators, semiconductors, conductors, polymers and biological molecules [26], [27], [28]. The calculations are

Electronic properties

The electronic properties have been calculated by optimizing the crystal structure into their stable form. The TB-mBJ calculation is carried out by following a PBE calculation first. The energy band diagrams of bulk

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

without and with spin–orbit coupling are shown in (Figs. 3, 4). The band structures for both the crystals are calculated along the high symmetry points

Γ \to Z \to F \to Γ \to L

which comprise the Brillouin zone. Both the band diagrams depict the open band gap at the Fermi level.

Conclusions

The summary of this work comprises an investigation of the electronic and optical properties of

{Bi}_{2} {Se}_{3}

and

{Bi}_{2} {Te}_{3}

in comparison without and with SOC. The comprehensive study shows that since the crystals include heavy atoms, their electrical band gaps rely on SOC. It is found that when the PBE potential is employed, the band gaps deviate from the experimental works, but when the TB-mBJ calculation is utilized, the band gaps agree well with both the experimental and available theoretical works.

CRediT authorship contribution statement

Burhan Ahmed: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. B. Indrajit Sharma: Writing – review & editing, Conceptualization. Bikram Baruah: Formal analysis. Subhasis Panda: Conceptualization. Asim Roy: Formal analysis.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors thank to the Physics department of National Institute of Technology, Silchar for providing the computational facility at the Paramshavak compact cluster. The authors also thanks the Assam University, SIlchar for providing the access to the journals for smooth progress of the work.

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Tuning the electrical and optical properties of topological insulator Bi2Se3 by Ar+ ion irradiation
2025, Materials Letters
We employed X-ray diffraction analysis, electron transport measurements, and optical ellipsometry to investigate the topological insulator Bi₂Se₃ before and after argon ion irradiation with an energy of 15 keV and a fluence of 5⋅10¹⁵ cm⁻². The electrical resistivity in the temperature range of 2–300 K and optical properties in the spectral range of 1250–40000 cm⁻¹ at room temperature were measured. After irradiation, the rocking curve exhibited five local maxima, suggesting the crystal had fragmented into five mosaic blocks. The temperature-dependent electrical resistivity was modeled using a phenomenological approach accounting for electron–phonon and electron–electron scattering mechanisms. Irradiation led to enhancements in both scattering processes and an increase in electrical resistivity. Notable alterations were observed in the optical properties after irradiation: a more than twofold decrease in maximum optical conductivity, emergence of additional features in the infrared region of the imaginary part of dielectric permittivity, and reduction in reflectivity magnitude across the entire spectral range. We assume that such changes are associated with a change in the electronic structure of the irradiated layer.
Surface State Electronic Characteristics and Z2 Topological Invariant of Bi2Te3 Topological Insulator Through PBE and LmBJ Potential
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