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(i)\u00a0As mentioned in the introduction, a weakening or screening of the e\u2212e interaction would be required to realize TSC\u2014for example nearby screening layers [73]. (ii)\u00a0It avoids complications arising from the bare Coulomb potential. For V(r)=1\/r, a positive background ensuring charge neutrality is normally required to remove the singular behavior of the Fourier component at k=0. However, this treatment fails when working in the full Fock space: if k=0 component is simply removed, states with larger electron number spuriously acquire lower energy due to the background contribution. This issue is absent for a screened interaction, which does not require introducing a positive background. For simplicity, we set the screening length to be the magnetic length.","type":"other"},{"key":"gpyx-z281Cc75R1","unstructured":"\u03c6jLLL(r) is the unnormalized wave function of the lowest LL in the Landau gauge: \u03c6jLLL(r)=\u2211s=\u2212\u221e\u221ee\u2212i(kj+sLx\/l\u00afB2)y\u2212(kjl\u00afB2+sLx\u2212x)2\/2l\u00afB2, where kj=2\u03c0j\/a with a the intervortex separation, l\u00afB is the magnetic length for charge-2e Cooper pairs, and the summation comes from the torus geometry of our system. Although the definition of kj can in principle be shifted by 2\u03c0\/Ly, we adopt the above convention so that the nodes of \u0394k are included in the allowed momenta for finite systems.","type":"other"},{"key":"gpyx-z281Cc76R1","unstructured":"The flux quantum for electrons is \u03d50\u2261h\/e while that for charge-2e Cooper pairs is \u03d5\u00af0\u2261h\/2e=\u03d50\/2. Therefore, the system with N\u03d5 magnetic unit cells (i.e., the total magnetic flux is N\u03d5\u03d50) contains 2N\u03d5 vortices.","type":"other"},{"key":"gpyx-z281Cc77R1","unstructured":"See Supplemental Material at http:\/\/link.aps.org\/supplemental\/10.1103\/gpyx-z281 for details of additional information and results, which includes Refs.\u00a0[78\u201386].","type":"other"},{"key":"gpyx-z281Cc78R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.50.1219","type":"journal-article"},{"key":"gpyx-z281Cc79R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.29.6833","type":"journal-article"},{"key":"gpyx-z281Cc80R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.48.7383","type":"journal-article"},{"key":"gpyx-z281Cc81R1","first-page":"1109","type":"journal-article","volume":"2","author":"E. Rashba","year":"1960","journal-title":"Sov. Phys. Solid State","ISSN":"https:\/\/id.crossref.org\/issn\/0038-5654","issn-type":"print"},{"key":"gpyx-z281Cc82R1","doi-asserted-by":"publisher","DOI":"10.1088\/0022-3719\/17\/33\/015","type":"journal-article"},{"key":"gpyx-z281Cc83R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.67.085302","type":"journal-article"},{"key":"gpyx-z281Cc84R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.256603","type":"journal-article"},{"key":"gpyx-z281Cc85R1","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.81.034713","type":"journal-article"},{"key":"gpyx-z281Cc86R1","volume-title":"Introduction to Superconductivity","author":"M. Tinkham","year":"1996","type":"book"},{"key":"gpyx-z281Cc87R1","unstructured":"The pairing matrix \u0394k in Eq.\u00a0(3) becomes independent of the Rashba-coupling strength gR by rescaling \u03940\u2192\u03940\/\u03b2(gR) [66], where \u03b2(gR) is a monotonically increasing function with \u03b2(0)=0 and \u03b2(\u221e)=1\/2. We hence absorb this scaling into \u03940. When evaluating the interaction matrix elements Vk1k2k1\u2032k2\u2032 in Eq.\u00a0(2), we take the gR\u2192\u221e limit for simplicity.","type":"other"},{"key":"gpyx-z281Cc88R1","unstructured":"When computing the lowest N eigenvalues using the Lanczos algorithm, the iteration is terminated once all targeted eigenvalues satisfy |E(i)\u2212E(i\u22123)|&lt;10\u22128, where E(i) denotes the eigenvalue obtained at the i th step. Gram-Schmidt orthonormalization is used at each iteration step to maintain orthogonality.","type":"other"},{"key":"gpyx-z281Cc89R1","unstructured":"Our target LL is identical to the n=1 LL of graphene with full spin and valley polarization. According to Refs.\u00a0[90, 91, 92], the fully spin- and valley-polarized composite Fermi liquid is favored over the Pfaffian state in the n=1 LL of graphene for the Coulomb interaction. Although we consider the screened Coulomb interaction, the qualitative conclusion is not expected to change.","type":"other"},{"key":"gpyx-z281Cc90R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.76.081403","type":"journal-article"},{"key":"gpyx-z281Cc91R1","doi-asserted-by":"publisher","DOI":"10.12693\/APhysPolA.119.592","type":"journal-article"},{"key":"gpyx-z281Cc92R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.92.205120","type":"journal-article"},{"key":"gpyx-z281Cc93R1","unstructured":"The largest accessible size, (nx,ny)=(4,8), has the Hilbert space dimension of 6.7\u00d7107 within a given (K,P) sector (the dimensions are comparable across sectors). The next larger size, (nx,ny)=(10,4), has the dimension of 1.4\u00d71010, which exceeds the practical limits of exact diagonalization.","type":"other"},{"key":"gpyx-z281Cc94R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2006.08.001","type":"journal-article"},{"key":"gpyx-z281Cc95R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.4.011036","type":"journal-article"},{"key":"gpyx-z281Cc96R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.86.195126","type":"journal-article"},{"key":"gpyx-z281Cc97R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.2.041002","type":"journal-article"},{"key":"gpyx-z281Cc98R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.195422","type":"journal-article"},{"key":"gpyx-z281Cc99R1","doi-asserted-by":"publisher","DOI":"10.1038\/ncomms2340","type":"journal-article"},{"key":"gpyx-z281Cc100R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.87.035132","type":"journal-article"},{"key":"gpyx-z281Cc101R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.90.195101","type":"journal-article"},{"key":"gpyx-z281Cc102R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.90.155447","type":"journal-article"},{"key":"gpyx-z281Cc103R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.4.031009","type":"journal-article"},{"key":"gpyx-z281Cc104R1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev-conmatphys-031115-011336","type":"journal-article"},{"key":"gpyx-z281Cc105R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.96.235144","type":"journal-article"},{"key":"gpyx-z281Cc106R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.066801","type":"journal-article"},{"key":"gpyx-z281Cc107R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41535-018-0085-4","type":"journal-article"},{"key":"gpyx-z281Cc108R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.085116","type":"journal-article"},{"key":"gpyx-z281Cc109R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.100.075155","type":"journal-article"},{"key":"gpyx-z281Cc110R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.037703","type":"journal-article"},{"key":"gpyx-z281Cc111R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.107.L161105","type":"journal-article"},{"key":"gpyx-z281Cc112R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-025-09169-7","type":"journal-article"},{"key":"gpyx-z281Cc114R1","doi-asserted-by":"publisher","DOI":"10.1038\/s41586-023-07010-7","type":"journal-article"},{"key":"gpyx-z281Cc115R1","doi-asserted-by":"publisher","DOI":"10.1103\/kcm5-hx56","type":"journal-article"},{"key":"gpyx-z281Cc116R1","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2426680122","type":"journal-article"},{"key":"gpyx-z281Cc118R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.111.014508","type":"journal-article"},{"key":"gpyx-z281Cc120R1","doi-asserted-by":"publisher","DOI":"10.1103\/6bgj-bfdn","type":"journal-article"},{"key":"gpyx-z281Cc121R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.newton.2025.100340","type":"journal-article"},{"key":"gpyx-z281Cc125R1","doi-asserted-by":"publisher","DOI":"10.1103\/txjx-s4zx","type":"journal-article"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/accepted\/10.1103\/gpyx-z281","content-type":"application\/pdf","content-version":"am","intended-application":"unspecified"},{"URL":"https:\/\/link.aps.org\/article\/10.1103\/gpyx-z281","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/gpyx-z281\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T17:51:25Z","timestamp":1790877085000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/gpyx-z281"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,16]]},"references-count":118,"journal-issue":{"issue":"24","published-print":{"date-parts":[[2026,6]]}},"URL":"https:\/\/doi.org\/10.1103\/gpyx-z281","relation":{},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,16]]},"assertion":[{"value":"2025-10-19","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a9 2026 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"246601"}}