{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T04:22:21Z","timestamp":1787458941543,"version":"build-2736575974"},"reference-count":75,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T00:00:00Z","timestamp":1787270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012216","name":"Jiangsu University of Science and Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012216","id-type":"DOI","asserted-by":"crossref"}]},{"id":[{"id":"https:\/\/ror.org\/00tyjp878","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Biorthogonal quantum geometry is often read through scalar tensor components. In non-Hermitian bands, however, the biorthogonal contraction can lose the ordering of the left-right interband matrix elements from which a scalar component is formed. We study this information loss for spectrally separated, diagonalizable two-band Bloch Hamiltonians. For a specified control parameter, the Hamiltonian variation defines a local response vertex. In the instantaneous biorthogonal eigenbasis, the interband part of this vertex is completely specified by two ordered matrix elements, whereas the corresponding equal-parameter scalar QGT component retains only their product. This separation leads to a local classification of interband vertices into no-interband, Hermitian-locked, generic complex-transverse, and complex-null cases. On a complex-null branch, the scalar component can vanish even though one ordered interband matrix element remains nonzero. We identify this as a local chiral-vertex mechanism in a vertex-resolved geometric response kernel, distinct from generic non-Hermiticity or exceptional-point proximity. Nonreciprocal SSH, a two-dimensional complex-spin\u2013orbit lattice, and a kz-only chiral ladder stack realize the same mechanism in one, two, and three dimensions, while diagonal and gain\u2013loss-like vertices provide nonselective comparisons.<\/jats:p>","DOI":"10.3390\/e28080936","type":"journal-article","created":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T09:31:59Z","timestamp":1787304719000},"page":"936","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Directed Interband Response at Null Biorthogonal Quantum-Geometric Components"],"prefix":"10.3390","volume":"28","author":[{"given":"Xinyi","family":"Xie","sequence":"first","affiliation":[{"name":"School of Science, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia-Ning","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Science, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-1440-4686","authenticated-orcid":false,"given":"Bo","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Science, Jiangsu University of Science and Technology, Zhenjiang 212100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/00018732.2021.1876991","article-title":"Non-Hermitian physics","volume":"69","author":"Ashida","year":"2020","journal-title":"Adv. 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