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<p>A topological insulator (TI) is characterized by its band inversion (in its bulk) which is caused by the strong spin-orbit interaction and an exotic metallic state in its surface. In this work, using a DFT study, we prove that <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1910_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(Bi_2Te_3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <msub> <mi>i</mi> <mn>2</mn> </msub> <mi>T</mi> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> has a band inversion in its bulk form and becomes conducting in its surface. The existence of single band inversion is analyzed with PBE and TB-mBJ potential taking spin-orbit interaction into consideration. The metallic surface state is confirmed with the PBE and LmBJ potential. The LmBJ potential enables the study of heterogeneous, finite, and low-dimensional systems and has not been studied yet for <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1910_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(Bi_2Te_3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <msub> <mi>i</mi> <mn>2</mn> </msub> <mi>T</mi> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>. We also prove that <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1910_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(Bi_2Te_3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>B</mi> <msub> <mi>i</mi> <mn>2</mn> </msub> <mi>T</mi> <msub> <mi>e</mi> <mn>3</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> is a <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1910_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mathbb {Z}_2 \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> topological insulator from the <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13538_2025_1910_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\( \mathbb {Z}_2 \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> invariant calculation by computing an evolution of hybrid Wannier charge centers.</p>

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Surface State Electronic Characteristics and \(\mathbb {Z}_2\) Topological Invariant of \(Bi_2Te_3\) Topological Insulator Through PBE and LmBJ Potential

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Burhan Ahmed,
  • B. Indrajit Sharma

摘要

A topological insulator (TI) is characterized by its band inversion (in its bulk) which is caused by the strong spin-orbit interaction and an exotic metallic state in its surface. In this work, using a DFT study, we prove that \(Bi_2Te_3\) B i 2 T e 3 has a band inversion in its bulk form and becomes conducting in its surface. The existence of single band inversion is analyzed with PBE and TB-mBJ potential taking spin-orbit interaction into consideration. The metallic surface state is confirmed with the PBE and LmBJ potential. The LmBJ potential enables the study of heterogeneous, finite, and low-dimensional systems and has not been studied yet for \(Bi_2Te_3\) B i 2 T e 3 . We also prove that \(Bi_2Te_3\) B i 2 T e 3 is a \( \mathbb {Z}_2 \) Z 2 topological insulator from the \( \mathbb {Z}_2 \) Z 2 invariant calculation by computing an evolution of hybrid Wannier charge centers.