Summary: | FeSe is classed as a Hund’s metal, with a multiplicity of <i>d</i> bands near the Fermi level. Correlations in Hund’s metals mostly originate from the exchange parameter <i>J</i>, which can drive a strong orbital selectivity in the correlations. The Fe-chalcogens are the most strongly correlated of the Fe-based superconductors, with <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mrow><mi>x</mi><mi>y</mi></mrow></msub></semantics></math></inline-formula> the most correlated orbital. Yet little is understood whether and how such correlations directly affect the superconducting instability in Hund’s systems. By applying a recently developed ab initio theory, we show explicitly the connections between correlations in <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mrow><mi>x</mi><mi>y</mi></mrow></msub></semantics></math></inline-formula> and the superconducting critical temperature <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>. Starting from the ab initio results as a reference, we consider various kinds of excursions in parameter space around the reference to determine what controls <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>. We show small excursions in <i>J</i> can cause colossal changes in <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>. Additionally we consider changes in hopping by varying the Fe-Se bond length in bulk, in the free standing monolayer M-FeSe, and M-FeSe on a SrTiO<inline-formula><math display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula> substrate (M-FeSe/STO). The twin conditions of proximity of the <inline-formula><math display="inline"><semantics><msub><mi>d</mi><mrow><mi>x</mi><mi>y</mi></mrow></msub></semantics></math></inline-formula> state to the Fermi energy, and the strength of <i>J</i> emerge as the primary criteria for incoherent spectral response and enhanced single- and two-particle scattering that in turn controls <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>. Using constrained RPA, we show further that FeSe in monolayer form (M-FeSe) provides a natural mechanism to enhance <i>J</i>. We explain why M-FeSe/STO has a high <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula>, whereas M-FeSe in isolation should not. Our study opens a paradigm for a unified understanding what controls <inline-formula><math display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> in bulk, layers, and interfaces of Hund’s metals by hole pocket and electron screening cloud engineering.
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