{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"fa774e7756210e949436705b6016c24e6d217c10d7af145cdc2d5093036277d7","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"125be2c11fbd507f0819585a8e1a55ef55cdc67b8b145a0a4eb0f5f9cd18b27c","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"mechanism","assisted_by":[],"external_id":"cm.anderson-transitions.exponent-puzzle","kind":"phenomenon","literature_status":"contested","n":"1","parents":[],"plain":"Adding phosphorus to silicon switches it from insulator to metal at a critical concentration, and the conductivity then rises as a power of the distance from that point. Measured powers differ between kinds of samples and from theory for non-interacting electrons, and the reason is disputed.","posed_since":"","precise":"In uncompensated Si:P, Si:B and Ge:Ga, $\\sigma(T = 0) \\sim (n/n_c - 1)^{s}$ with $s \\sim 0.5$ reported in several studies, while compensated samples give $s \\sim 1$. The non-interacting 3D orthogonal-class value is $s = \\nu \\sim 1.57$ (Wegner scaling $s = \\nu(d - 2)$), and the Chayes-Chayes-Fisher-Spencer bound (rigorous form of the Harris criterion) requires $\\nu \\ge 2/d$, which $s \\sim 0.5 = \\nu$ would violate. Explain the discrepancy (extrapolation of $\\sigma(T)$ to $T = 0$, Coulomb interaction, local magnetic moments, hybridization of impurity and conduction bands, or dopant inhomogeneity) and give the true s for uncompensated material.","problem_ref":null,"references":"","settled_by":"Measurements on dopant-controlled samples down to $T << 10\\,\\mathrm{mK}$ with a scaling analysis that includes finite-temperature corrections, compared with a controlled theory of the interacting transition.","status_note":"Claimed resolutions (Stupp et al., Physical Review Letters 71, 2634, 1993; Carnio, Hine and Romer, Physical Review B 99, 081201, 2019, linking the puzzle to hybridization of conduction and impurity bands) are not generally accepted.","title":"Conductivity exponent puzzle in doped semiconductors","topic_ref":"e7c62ae37eee99d87e4dd2b7fcb626097b84c27b343145bcc79a7fe68ba3dbb1"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"46913c55716dab0d9e6ed0e981038b302eef554a48070c53a7b06049fd9d3a99","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"94b585ae14575526343ebdd04f2410a3484bd0af604e47514ebd3a97694d4c9a","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"itndXfqU0Mp_uvRM-Di-OpLfDN2ajLqagPF9R8EcMO5igWN-9CT6Z8LTZcLlvLS66S6hZiP9VFlsOzkcm9aGCg"},"schema":"pubphys.envelope/1"},"record_hash":"46913c55716dab0d9e6ed0e981038b302eef554a48070c53a7b06049fd9d3a99","leaf_index":909}