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<p>In electronic models on lattices with strong geometric frustration (flat band models), the band dispersion of electrons can vanish, resulting in what is known as a flat band. Flat bands are known to serve as a platform for the emergence of various intriguing physical properties. Realizing flat bands in actual materials, however, remains a challenging task. In this paper, we report that the flat band model approximately holds in the pyrochlore oxide Pb<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6903_Article_IEq7.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>Bi<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6903_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>O<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6903_Article_IEq9.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_7\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>7</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>, as demonstrated by first-principles calculations. Furthermore, we propose that, among the two key parameters in flat band systems—the flat band width and the carrier density—the latter can be selectively controlled, approximately, by utilizing the solid solution Pb<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6903_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>(Sb,Bi)<InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6903_Article_IEq11.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_2\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>O<InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10948_2025_6903_Article_IEq12.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(_7\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>7</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>. This finding represents a new step toward “flatronics,” a field focused on controlling flat band systems.</p>

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Flat Bands in Pb\(_2\)Bi\(_2\)O\(_7\): A New Step Towards the Realization of “Flatronics”

  • 期刊论文

  • 发表日期：

    2025年1月15日

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  • Izumi Hase

摘要

In electronic models on lattices with strong geometric frustration (flat band models), the band dispersion of electrons can vanish, resulting in what is known as a flat band. Flat bands are known to serve as a platform for the emergence of various intriguing physical properties. Realizing flat bands in actual materials, however, remains a challenging task. In this paper, we report that the flat band model approximately holds in the pyrochlore oxide Pb \(_2\) 2 Bi \(_2\) 2 O \(_7\) 7 , as demonstrated by first-principles calculations. Furthermore, we propose that, among the two key parameters in flat band systems—the flat band width and the carrier density—the latter can be selectively controlled, approximately, by utilizing the solid solution Pb \(_2\) 2 (Sb,Bi) \(_2\) 2 O \(_7\) 7 . This finding represents a new step toward “flatronics,” a field focused on controlling flat band systems.