K. C. Lam | Searcharxiv

arXiv2026

Exotic Pressure-Driven Band Gap Widening in Carbon Chain-Filled KFI Zeolite and Its Pathway to High-Pressure Semiconducting Electronics and High-Temperature Superconductivity

Semiconducting devices face persistent challenges in operating at high pressure, as the band theory predicts that materials transition to a more metallic state under compression. However, our findings with carbon chains in KFI substrates reveal a conditional deviation from this norm. We not only witness the transition from polyyne (semiconductor) to cumulene (metal) at medium pressure, but we also observe an unexpected re-entrance of the polyyne at high pressures, where the band gap in the polyyne increases with pressure. In addition, the synthesis of long cumulene chains has posed a longstanding challenge in the quest for high-temperature organic superconductivity. We have identified critical conditions for synthesizing extended cumulene chains within zeolite frameworks, highlighting the interplay between unconventional charge density waves and significant torsions. The KFI zeolite facilitates the formation of carbon chains exceeding 5,000 atoms, in stark contrast to around 100 other zeolites that are limited to ~10 atoms. The cumulene@KFI system demonstrates a superconducting transition temperature reaching ~62 K, surpassing the highest reported values for bulk iron-based superconductors. This interplay between carbon structures and superconductivity not only advances our understanding of charge density waves but also heralds a new era in the study of novel applications

cond-mat.supr-con↗

arXiv2017

An adaptive fast solver for a general class of positive definite matrices via energy decomposition

In this paper, we propose an adaptive fast solver for a general class of symmetric positive definite (SPD) matrices which include the well-known graph Laplacian. We achieve this by developing an adaptive operator compression scheme and a multiresolution matrix factorization algorithm which achieve nearly optimal performance on both complexity and well-posedness. To develop our adaptive operator compression and multiresolution matrix factorization methods, we first introduce a novel notion of energy decomposition for SPD matrix $A$ using the representation of energy elements. The interaction between these energy elements depicts the underlying topological structure of the operator. This concept of decomposition naturally reflects the hidden geometric structure of the operator which inherits the localities of the structure. By utilizing the intrinsic geometric information under this Energy framework, we propose a systematic operator compression scheme for the inverse operator $A^{-1}$. In particular, with an appropriate partition of the underlying geometric structure, we can construct localized basis by using the concept of interior and closed energy. Meanwhile, two important localized quantities are introduced, namely the error factor and the condition factor. Our error analysis results show that these two factors will be the guidelines for finding the appropriate partition of the basis functions such that prescribed compression error and acceptable condition number can be achieved. By virtue of this insight, we propose the Patch Pairing algorithm to realize our energy partition framework for operator compression with controllable compression error and condition number.

math.NA↗