Theory of Intervalley-Coherent AFM Order and Topological Superconductivity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>tWSe</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math>
Ammon Fischer, Lennart Klebl, Valentin Crépel, Siheon Ryee, Angel Rubio, Lede Xian, Tim O. Wehling, Antoine Georges, Dante M. Kennes, Andrew J. Millis
Abstract
The recent observation of superconductivity in the vicinity of Fermi surface reconstructed insulating or metallic states has established twisted bilayers of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>WSe</a:mi> </a:mrow> <a:mn>2</a:mn> </a:msub> </a:mrow> </a:math> as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries, and topology. In this work, we use a first-principles, material-specific theoretical treatment that is unbiased with respect to electronic instabilities to study the emergence of electronic ordering in twisted <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>WSe</c:mi> </c:mrow> <c:mn>2</c:mn> </c:msub> </c:mrow> </c:math> driven by gate-screened Coulomb interactions. We construct exponentially localized moiré Wannier orbitals that faithfully capture the band structure and topology of the system, project the gate-screened Coulomb interaction onto them, and use unbiased functional renormalization group techniques to resolve the momentum and orbital structure of the leading instabilities and the relevant energy scales. We find an interplay between intervalley-coherent antiferromagnetic (IVC-AFM) order and chiral, mixed-parity <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>d</e:mi> <e:mo>/</e:mo> <e:mi>p</e:mi> </e:math> -wave superconductivity for carrier concentrations near a displacement field and twist-angle-tunable van Hove singularity. Our microscopic approach establishes incommensurate IVC-AFM spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>θ</g:mi> <g:mo>=</g:mo> <g:mn>5.08</g:mn> <g:mo>°</g:mo> </g:mrow> </g:math> twisted <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:msub> <i:mrow> <i:mi>WSe</i:mi> </i:mrow> <i:mn>2</i:mn> </i:msub> </i:mrow> </i:math> and explains key aspects of recent experiments including the asymmetric density dependence of the spin ordering with respect to the van Hove line, the single- and double-peak structure of the DOS in the ordered (hole-doped) IVC-AFM phase, the emergence of superconductivity as the density is varied across the van Hove line, and the evolution of the displacement field-density phase diagram with twist angles between <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mn>3.7</k:mn> <k:mo>°</k:mo> <k:mo>…</k:mo> <k:mn>5</k:mn> <k:mo>°</k:mo> </k:math> . We show that the interplay of electronic correlations and nontrivial quantum geometry in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>tWSe</m:mi> </m:mrow> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:mrow> </m:math> manifests in orbital-selective order parameters associated to the IVC-AFM and SC states that are detectable by local spectroscopy measurements.