{"product_id":"little-parks-effect-physics-t-shirt","title":"Little–Parks Effect – Superconducting Flux Quantum Physics T-Shirt","description":"\u003cp\u003eA superconducting loop with a repeating temperature story: one flux quantum at a time.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn 1962 William Little and Roland Parks threaded a magnetic field through a hollow superconducting cylinder and watched its transition temperature oscillate. A circulating supercurrent costs kinetic energy and depresses the transition temperature between peaks. The peaks occur at integer multiples of the superconducting flux quantum; the h\/2e period identifies paired charge carriers.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eT_c(Φ) = T_c(Φ + Φ₀), Φ₀ = h\/(2e) ≈ 2.067 833 848 × 10⁻¹⁵ Wb.\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eT_c: superconducting transition temperature (K).\u003c\/li\u003e\n\u003cli\u003eΦ: axial magnetic flux through the cylinder’s hole (Wb).\u003c\/li\u003e\n\u003cli\u003eΦ₀: superconducting flux quantum (Wb).\u003c\/li\u003e\n\u003cli\u003eh: Planck constant, 6.626 070 15 × 10⁻³⁴ J s.\u003c\/li\u003e\n\u003cli\u003ee: elementary charge, 1.602 176 634 × 10⁻¹⁹ C.\u003c\/li\u003e\n\u003cli\u003en in Φ = nΦ₀: integer winding number (dimensionless).\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e This description is for a thin-walled superconducting cylinder, with wall thickness smaller than the penetration depth. T_c is maximal at Φ = nΦ₀; the suppression vanishes there. The thin-cylinder curve consists of parabolic arcs, not a sine wave. The period is h\/2e, not h\/e.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eW. A. Little \u0026amp; R. D. Parks, “Observation of Quantum Periodicity in the Transition Temperature of a Superconducting Cylinder,” Phys. Rev. Lett. 9, 9–12 (1962), doi:10.1103\/PhysRevLett.9.9.\u003c\/li\u003e\n\u003cli\u003eR. D. Parks \u0026amp; W. A. Little, “Fluxoid Quantization in a Multiply-Connected Superconductor,” Phys. Rev. 133, A97–A103 (1964), doi:10.1103\/PhysRev.133.A97.\u003c\/li\u003e\n\u003cli\u003eNIST: SI 2019 definitions of h and e.\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eApproved physics print block:\u003c\/p\u003e\u003cp\u003e“LITTLE–PARKS EFFECT”\u003c\/p\u003e\u003cp\u003e“T_c(Φ) = T_c(Φ + Φ₀),  Φ₀ = h\/2e”\u003c\/p\u003e\u003cp\u003e“Φ₀ ≈ 2.07 × 10⁻¹⁵ Wb”\u003c\/p\u003e\u003cp\u003e“Thread magnetic flux through a tiny superconducting ring and its critical temperature rises and falls, repeating every flux quantum h\/2e.”\u003c\/p\u003e\u003cp\u003ePrinted front and back. Physics. Personified.\u003c\/p\u003e","brand":"Pixelated Physics","offers":[{"title":"S \/ White","offer_id":51242841899111,"sku":"24942259681587738907","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":51242841931879,"sku":"62480907765326860081","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":51242841964647,"sku":"34220259474410345474","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":51242841997415,"sku":"12175587788193579685","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":51242842030183,"sku":"27863499507986948575","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":51242842062951,"sku":"47570271162323391172","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":51242842095719,"sku":"71650723513836969593","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":51242842128487,"sku":"33313954311533703685","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":51242842161255,"sku":"13815080500774849006","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":51242842194023,"sku":"26105678102628528463","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":51242842226791,"sku":"32686714902413323107","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":51242842259559,"sku":"15612675627291283848","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":51242842292327,"sku":"23942726581706081432","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":51242842325095,"sku":"27195158561391856488","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":51242842357863,"sku":"52574016874394996035","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":51242842390631,"sku":"24316704588771773457","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/little-parks-effect-physics-t-shirt_front_mc17_black.png?v=1793975474","url":"https:\/\/pixelatedphysics.com\/pt\/products\/little-parks-effect-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}