<p>Multilayer flakes of two-dimensional materials were recently shown to be tunable by twisting monolayers on their surface. This raises the question whether qualitatively new phenomena can occur in such finite-thickness moiré systems. Here we demonstrate the emergence of distinct topological phases and transitions in N-layered flakes of nodal superconductors with a single monolayer twisted on top of it. We show that a c-axis current transforms the whole system into a chiral topological superconductor. Increasing the current drives a sequence of topological transitions between states characterized by a Chern number increasing from <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41535_2024_719_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="62" /> </InlineMediaObject> <EquationSource Format="TEX">$\sim {\mathcal{O}}(N)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>~</mo> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> <mrow> <mo>(</mo> <mrow> <mi>N</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> up to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41535_2024_719_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">$\sim {\mathcal{O}}({N}^{2})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>~</mo> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> <mrow> <mo>(</mo> <mrow> <msup> <mrow> <mi>N</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, well beyond the additive effect of stacking <i>N</i> layers. We predict thickness-independent signatures of these states in the thermal Hall and tunneling microscopy measurements. Twisted superconductor flakes thus provide an example of a “2.5-dimensional” material where the synergy of two-dimensional layers extended in a third dimension realize states inaccessible in either monolayer or bulk materials.</p>

2.5-dimensional topological superconductivity in twisted superconducting flakes

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2025年1月27日

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Kevin P. Lucht,
J. H. Pixley,
Pavel A. Volkov

摘要

Multilayer flakes of two-dimensional materials were recently shown to be tunable by twisting monolayers on their surface. This raises the question whether qualitatively new phenomena can occur in such finite-thickness moiré systems. Here we demonstrate the emergence of distinct topological phases and transitions in N-layered flakes of nodal superconductors with a single monolayer twisted on top of it. We show that a c-axis current transforms the whole system into a chiral topological superconductor. Increasing the current drives a sequence of topological transitions between states characterized by a Chern number increasing from $\sim {\mathcal{O}}(N)$ $~ O (N)$ up to $\sim {\mathcal{O}}({N}^{2})$ $~ O (N^{2})$ , well beyond the additive effect of stacking N layers. We predict thickness-independent signatures of these states in the thermal Hall and tunneling microscopy measurements. Twisted superconductor flakes thus provide an example of a “2.5-dimensional” material where the synergy of two-dimensional layers extended in a third dimension realize states inaccessible in either monolayer or bulk materials.