{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4b117b9f956bfef733e2dfa710a46d99d196b664f248d452a733a97a83245b36","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["17e2ac3c6f82b5d11f06e0b22b7195d4110dab64c3c9f3eba623838791e0a04a","5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5c8e32dad6f60e1397b6fc5c8b377b57992e75ccd5d45bf9895e3383f27a1b60","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.mit-2d-electrons.parallel-field-suppression","kind":"phenomenon","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"17e2ac3c6f82b5d11f06e0b22b7195d4110dab64c3c9f3eba623838791e0a04a","relation":"special_case"}],"plain":"A magnetic field along the sheet, which aligns electron spins but does not bend their paths, raises the resistance many times and in silicon transistors removes the metal-like behavior. Why spin alignment has such a large effect, and why some ultra-clean samples stay metallic even with all spins aligned, is not understood.","posed_since":"","precise":"In Si-MOSFETs near $n_c$ an in-plane field $B_{\\mathrm{parallel}}$ raises $\\rho$ by one to two orders of magnitude and saturates at $B_c(n)$, where the electrons become fully spin polarized; above $B_c$ the metallic $\\mathrm{d}\\rho/\\mathrm{d}T > 0$ is lost in Si-MOSFETs, while in ultra-clean SiGe/Si/SiGe wells a metallic state and a metal-insulator transition survive in the fully polarized (spinless, two-valley) system (Melnikov et al. 2020). Explain the magnitude of the positive magnetoresistance and its saturation at B_c, explain why the spinless two-valley system stays metallic while the Si-MOSFET does not, and give the ratio $n_c(B > B_c)/n_c(0)$.","problem_ref":null,"references":"","settled_by":"A theory that predicts $\\rho(B_{\\mathrm{parallel}}, T, n)$ including $B_{c}(n)$ with parameters fixed independently, plus transport at $B > B_{c}$ down to $T << 0.01 E_{F}$ in both Si-MOSFETs and SiGe/Si/SiGe wells.","status_note":"A metallic state of fully spin-polarized electrons was reported in ultra-clean SiGe/Si/SiGe wells (Melnikov et al., Physical Review B 101, 045302, 2020); no theory accounts for the material dependence.","title":"Why does an in-plane field suppress the 2D metallic 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