Shiro Sakai

<jats:p>Motivated by recent advances in the realization of Truchet-tiling structures in molecular networks and metal-organic frameworks, we investigate the wave localization issue in this kind of structure. We introduce an electron model based on random Truchet tilings, square lattices with randomly oriented diagonal links, and uncover a rich interplay between spectral and localization phenomena. By varying the strength of diagonal couplings, we explore successive transitions from an extended phase, through a regime with a mobility edge, to a fully localized phase. The energy-resolved fractal dimension analysis captures the emergence and disappearance of mobility edges, while an anomalous shift and asymmetry in the Van Hove singularity are identified as key signatures of the underlying disordered Truchet-tiling structure. Notably, by using the finite-size scaling of level spacing statistics, we clarify that the transition occurs at a finite level of disorder even in the two-dimensional system. Our findings position Truchet-tiled electron systems as a versatile platform for engineering disorder-driven localization and interaction effects in amorphous quantum materials and photonic architectures.</jats:p>

<jats:p>We explore the superconducting properties of the bilayer Hubbard model, which exhibits a high transition temperature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mo>(</a:mo><a:msub><a:mi>T</a:mi><a:mi>c</a:mi></a:msub><a:mo>)</a:mo></a:math> for an <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>s</b:mi><b:mo>±</b:mo></b:msub></b:math> pairing, using a cluster extension of the dynamical mean-field theory. Unlike the single-layer Hubbard model, where the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>d</c:mi></c:math>-wave superconductivity emerges by doping the Mott insulator, the parent state of the bilayer system is a correlated band insulator. Above <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>T</d:mi><d:mi>c</d:mi></d:msub></d:math>, slight hole (electron) doping introduces a striking dichotomy between electron and hole pockets: The electron (hole) pocket develops a pseudogap while the other becomes a nearly incipient band. We reveal that the superconductivity is driven by kinetic (potential) energy gain in the underdoped (overdoped) region. We also find a very short coherence length, for which we argue the relevance to multiorbital physics. Our Letter offers crucial insights into the superconductivity in the bilayer Hubbard model potentially relevant to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:msub><e:mi>La</e:mi><e:mn>3</e:mn></e:msub><e:msub><e:mi>Ni</e:mi><e:mn>2</e:mn></e:msub><e:msub><e:mi mathvariant="normal">O</e:mi><e:mn>7</e:mn></e:msub></e:mrow></e:math>.</jats:p>