# Superconductivity
<!-- MICROSIMGEN:BEGIN v1.7 — generated by g08_place_microsims.py; three.js first (§15); do not hand-edit inside -->
## Microsims — three.js
### Superconductivity (three.js)
<div class="microsim-player">
<iframe src="https://wikitube-3d-microsims.netlify.app/Superconductivity.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Superconductivity — three.js microsim"></iframe>
</div>
**Open it full-screen:** [Superconductivity.html](https://wikitube-3d-microsims.netlify.app/Superconductivity.html) · library `threejs` · route `microsim/threejs/`
### Related microsims
Live sims on neighbouring articles:
- [[Boson]]
- [[Dilution_refrigerator]]
- [[Superfluid_helium-4]]
- [[Zero-point_energy]]
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
<!-- MICROSIMGEN:END -->
## Microsim
### Live player
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/3xQZFjhRZ" width="100%" height="620" frameborder="0" sandbox="allow-scripts allow-same-origin"></iframe>
</div>
<div class="microsim-fallback">
<img src="Microsims/thumbs/Superconductivity.png" alt="Superconductivity microsim poster" style="width:100%;border:1px solid #4445;border-radius:6px;">
<p><em>Live microsim (desktop) · <a href="https://editor.p5js.org/sciencenibber/sketches/3xQZFjhRZ">open sketch in the p5.js editor</a></em></p>
</div>
**Editor URL:** https://editor.p5js.org/sciencenibber/sketches/3xQZFjhRZ
**Description (100 words):**
The sketch is a two-panel performance dashboard. On the left, an H-versus-T phase diagram for the chosen material renders the parabolic critical-field law Hc(T) = Hc(0)[1-(T/Tc)^2]: warm-tinted "normal" above, cold "Meissner" below, and a magenta "vortex lattice" band between Hc1 and Hc2 when Type II is selected. A draggable yellow operating-point dot is classified live as Meissner, mixed, or normal. On the right, the BCS reduced energy gap Delta(T)/Delta(0) traces the Muehlschlegel curve from tau = 0 to 1, with a dashed marker showing the current T/Tc. Four sliders set Tc, the zero-temperature critical field, the Ginzburg-Landau parameter kappa, and the applied field.
```js
// =====================================================================
// Superconductivity.js -- Wikitube microsim
// Article: Superconductivity en.wikitube.io/wiki/Superconductivity
// Room: Helium Pattern: D (parametric curves /
// efficiency / performance)
// ---------------------------------------------------------------------
// Idea: a two-panel performance dashboard for a superconductor.
//
// LEFT panel -- the (T, H) phase diagram for the chosen Type:
// * Type I : a single thermodynamic critical-field
// curve Hc(T) = Hc(0) [1 - (T/Tc)^2]
// separating Meissner (SC) from normal.
// * Type II : two critical-field curves
// Hc1(T) = Hc1(0) [1 - (T/Tc)^2]
// Hc2(T) = Hc2(0) [1 - (T/Tc)^2]
// with a "mixed / vortex lattice" band
// between them.
// A draggable yellow operating-point dot classifies
// the live state as Meissner / mixed / normal.
//
// RIGHT panel -- the BCS reduced energy gap
// Delta(T) / Delta(0)
// versus reduced temperature tau = T / Tc, fit by the
// weak-coupling Muehlschlegel-style approximation
// Delta(T)/Delta(0) ~= tanh(1.74 * sqrt(Tc/T - 1))
// valid for tau in (0, 1). At tau -> 0, the gap is
// Delta(0) = 1.764 * kB * Tc (the universal BCS
// weak-coupling result, 2 Delta / kB Tc = 3.528).
//
// Sliders drive Tc, Hc(0) for Type I or Hc2(0) for Type II, the
// Ginzburg-Landau parameter kappa = lambda / xi (which selects
// Type I when kappa < 1/sqrt(2) ~= 0.707 and Type II above), and an
// applied-field magnitude that pins the operating point's y-coordinate.
//
// Canonical relations on the sketch:
//
// Hc(T) ~= Hc(0) [1 - (T/Tc)^2] (parabolic)
// kappa = lambda / xi (GL parameter)
// Type I for kappa < 1/sqrt(2); Type II above
// 2 Delta(0) / kB Tc ~= 3.528 (BCS gap ratio)
// Hc1 / Hc2 ~= ln(kappa) / (sqrt(2) kappa) (Type II only)
//
// Visual layout (720 x 520 canvas):
// * top-left: HUD title + en.wikitube.io/wiki/Superconductivity
// * top-right: Type label + control hints
// * left half: H-T phase diagram, axes T in [0, 1.1 Tc] K,
// H in [0, 1.2 Hc2(0)] T
// parabolic Hc / Hc1 / Hc2 curves; mixed-state band
// shaded between Hc1 and Hc2 for Type II
// draggable operating-point dot
// * right half: BCS gap curve Delta/Delta(0) vs T/Tc, anchor lines
// at the universal ratio and at the current T/Tc
// reduced-temperature readout
// * bottom: sliders (Tc, Hc/Hc2, kappa, applied field) +
// canonical equation bottom-right
//
// Conventions (Wikitube Betterfire Standard v0):
// * single ARTICLE constant at the top, single quotes
// * p5.disableFriendlyErrors = true to keep the editor console clean
// * non-ASCII (Delta, lambda, xi, kappa, tau, arrows) lives in
// COMMENTS ONLY -- every text() string literal is ASCII
// * Energy-room palette (P5_JS_EDITOR section 4): dark BG, HOT/COLD
// tones, STRUCT grey, TRAJ accent, GAUGE green
// * sliders have explicit .position(x, y).size(w); read once per
// frame at the top of draw() into named locals.
// =====================================================================
const ARTICLE = 'Superconductivity';
const TITLE = ARTICLE.replace(/_/g, ' ');
p5.disableFriendlyErrors = true;
// ----- Energy room palette (P5_JS_EDITOR section 4, line 165) --------
const BG = 18;
const FG = 240;
const DIM = [240, 240, 240, 140];
const HOT = [220, 110, 60]; // normal (resistive) phase
const COLD = [60, 130, 220]; // Meissner (superconducting)
const COLDER = [40, 80, 180]; // BCS condensate accent
const MIXED = [160, 100, 200]; // vortex-lattice mixed state
const STRUCT = [120, 130, 150]; // axes, grid
const TRAJ = [240, 220, 80]; // operating-point dot
const GAUGE = [120, 220, 140]; // gauge accent (reduced gap line)
const SCRATCH = [120, 120, 120, 70]; // grid scratches
// ----- Physical constants and BCS anchors ----------------------------
const BCS_RATIO = 3.528; // 2 Delta(0) / (kB Tc)
const KAPPA_CRIT = 1 / Math.SQRT2; // ~0.7071; Type I < this, Type II above
// ----- Sliders (created in setup) ------------------------------------
let tcSlider; // critical temperature Tc, in K (1 to 150)
let hcSlider; // Type I : Hc(0) in tesla (0.01 to 0.6)
// Type II : Hc2(0) in tesla (1 to 30)
let kappaSlider; // Ginzburg-Landau parameter kappa (0.1 to 8.0)
let appliedSlider; // applied field strength, fraction of Hc/Hc2 (0..1.2)
// ----- Plot rectangles in canvas pixels (set in setup) ---------------
let leftX, leftY, leftW, leftH; // (T, H) phase diagram
let rightX, rightY, rightW, rightH; // BCS gap curve
// ----- Operating-point state (T in K, H in T) ------------------------
let mark = { t: 0, h: 0 };
let dragging = false;
function setup() {
createCanvas(720, 520);
pixelDensity(2);
textFont('system-ui');
// Plot rectangles: leave room for HUD on top and sliders on bottom.
leftX = 56; leftY = 70;
leftW = 290; leftH = 320;
rightX = 390; rightY = 70;
rightW = 290; rightH = 320;
// ---- Slider row (4 sliders along the bottom) ---------------------
// Tc in K -- spans cryogenic conventional (4 K) to cuprate HTS (~130 K)
tcSlider = createSlider(2, 150, 30, 1);
tcSlider.position(60, 430);
tcSlider.size(120);
// Hc(0) for Type I OR Hc2(0) for Type II. The dual-meaning slider
// covers 0.05 T (mercury) to 30 T (modern Type II Nb3Sn / cuprate).
hcSlider = createSlider(0.05, 30, 5, 0.05);
hcSlider.position(220, 430);
hcSlider.size(120);
// Ginzburg-Landau parameter kappa = lambda / xi.
// Below 1/sqrt(2) = 0.707 -> Type I; above -> Type II.
kappaSlider = createSlider(0.1, 8.0, 1.5, 0.05);
kappaSlider.position(380, 430);
kappaSlider.size(120);
// Applied field as a fraction of Hc(0) or Hc2(0) -- moves the
// operating point's y-coordinate when the user isn't dragging.
appliedSlider = createSlider(0, 1.2, 0.4, 0.01);
appliedSlider.position(540, 430);
appliedSlider.size(120);
// Initial operating point: 60% of Tc, 40% of Hc(0).
mark.t = 0.6 * tcSlider.value();
mark.h = 0.4 * hcSlider.value();
}
function draw() {
background(BG);
// ---- Read parameter values once at the top of draw() ------------
const Tc = tcSlider.value();
const Hc0 = hcSlider.value();
const kappa = kappaSlider.value();
const applied = appliedSlider.value();
const typeII = kappa > KAPPA_CRIT;
// If user isn't dragging the dot, the applied-field slider pins H.
if (!dragging) mark.h = applied * Hc0;
// Constrain the operating point into the visible (T, H) box.
mark.t = constrain(mark.t, 0, 1.1 * Tc);
mark.h = constrain(mark.h, 0, 1.2 * Hc0);
// ---- Drawing order: shaded regions -> curves -> dot -> HUD -----
drawPhaseDiagram(Tc, Hc0, kappa, typeII);
drawBcsGapCurve(Tc);
drawSliderLabels(Tc, Hc0, kappa, applied, typeII);
drawOperatingPoint(Tc, Hc0, kappa, typeII);
drawHUD();
}
// =====================================================================
// Phase-diagram helpers (left panel)
// =====================================================================
// Parabolic critical-field law: H(T) = H(0) * [1 - (T/Tc)^2]
function hcParabolic(T, Tc, H0) {
if (T >= Tc) return 0;
const x = T / Tc;
return H0 * (1 - x * x);
}
// Type II lower critical field Hc1 expressed via Hc2 and kappa.
// Standard GL textbook relation, valid in the kappa >> 1 limit but
// gives a sensible visual all the way down to kappa ~ 1.
function hc1FromHc2(Hc2_0, kappa) {
if (kappa <= KAPPA_CRIT) return Hc2_0; // pathological -- pin to Hc2
return Hc2_0 * Math.log(kappa) / (Math.SQRT2 * kappa);
}
// Convert a (T [K], H [T]) pair to canvas pixels inside the LEFT panel.
function tToPxL(T, Tc) { return map(T, 0, 1.1 * Tc, leftX, leftX + leftW); }
function pxLToT(px, Tc) { return map(px, leftX, leftX + leftW, 0, 1.1 * Tc); }
function hToPyL(H, H0) { return map(H, 0, 1.2 * H0, leftY + leftH, leftY); }
function pyLToH(py, H0) { return map(py, leftY + leftH, leftY, 0, 1.2 * H0); }
function drawPhaseDiagram(Tc, Hc0, kappa, typeII) {
// Left-panel frame and axis grid.
push();
noFill();
stroke(STRUCT);
strokeWeight(1);
rect(leftX, leftY, leftW, leftH);
// Scratch grid every 10% of axis range.
stroke(SCRATCH);
for (let f = 0.2; f < 1.0; f += 0.2) {
line(leftX + f * leftW, leftY, leftX + f * leftW, leftY + leftH);
line(leftX, leftY + f * leftH, leftX + leftW, leftY + f * leftH);
}
pop();
// Shade the regions for legibility.
// Type I : Meissner (cold) below Hc(T), normal (warm) above
// Type II : Meissner below Hc1, mixed between Hc1 and Hc2, normal above
noStroke();
const N = 60;
for (let i = 0; i < N; i++) {
const T0 = (i / N) * 1.1 * Tc;
const T1 = ((i + 1) / N) * 1.1 * Tc;
const Tm = 0.5 * (T0 + T1);
const Hc2 = hcParabolic(Tm, Tc, Hc0);
const Hc1 = typeII ? hc1FromHc2(Hc0, kappa) * (Tm < Tc ? (1 - (Tm/Tc)*(Tm/Tc)) : 0)
: Hc2;
const xL = tToPxL(T0, Tc);
const xR = tToPxL(T1, Tc);
// Meissner band -- always cold below the lower critical field.
fill(COLD[0], COLD[1], COLD[2], 90);
rect(xL, hToPyL(Hc1, Hc0), xR - xL + 1, (leftY + leftH) - hToPyL(Hc1, Hc0));
// Mixed band (Type II only).
if (typeII && Hc2 > Hc1) {
fill(MIXED[0], MIXED[1], MIXED[2], 110);
rect(xL, hToPyL(Hc2, Hc0), xR - xL + 1, hToPyL(Hc1, Hc0) - hToPyL(Hc2, Hc0));
}
// Normal (warm) band above Hc2.
fill(HOT[0], HOT[1], HOT[2], 70);
rect(xL, leftY, xR - xL + 1, hToPyL(Hc2, Hc0) - leftY);
}
// Parabolic critical-field curves drawn on top of the bands.
push();
noFill();
strokeWeight(2);
// Hc2 (Type II) or Hc (Type I) -- always exists.
stroke(HOT);
beginShape();
for (let f = 0; f <= 1.0; f += 0.01) {
const T = f * Tc;
vertex(tToPxL(T, Tc), hToPyL(hcParabolic(T, Tc, Hc0), Hc0));
}
endShape();
// Hc1 -- Type II only.
if (typeII) {
const Hc1_0 = hc1FromHc2(Hc0, kappa);
stroke(COLDER);
beginShape();
for (let f = 0; f <= 1.0; f += 0.01) {
const T = f * Tc;
vertex(tToPxL(T, Tc), hToPyL(hcParabolic(T, Tc, Hc1_0), Hc0));
}
endShape();
}
pop();
// Axis ticks and labels.
push();
noStroke();
fill(...DIM);
textSize(10);
// T axis (every 25% of 1.1 Tc)
textAlign(CENTER, TOP);
for (let f = 0; f <= 1.0; f += 0.25) {
const T = f * 1.1 * Tc;
const x = tToPxL(T, Tc);
stroke(STRUCT); line(x, leftY + leftH, x, leftY + leftH + 4);
noStroke(); text(nf(T, 0, 1), x, leftY + leftH + 6);
}
// H axis (every 25% of 1.2 H0)
textAlign(RIGHT, CENTER);
for (let f = 0; f <= 1.0; f += 0.25) {
const H = f * 1.2 * Hc0;
const y = hToPyL(H, Hc0);
stroke(STRUCT); line(leftX - 4, y, leftX, y);
noStroke(); text(nf(H, 0, 2), leftX - 6, y);
}
// Axis titles
textAlign(CENTER, TOP);
text('T [K]', leftX + leftW / 2, leftY + leftH + 22);
push();
translate(leftX - 36, leftY + leftH / 2);
rotate(-PI / 2);
text('H [T]', 0, 0);
pop();
// Inline phase labels
textAlign(CENTER, CENTER);
fill(...COLD);
text('Meissner', tToPxL(0.25 * Tc, Tc), hToPyL(0.05 * Hc0, Hc0));
fill(...HOT);
text('normal', tToPxL(0.85 * Tc, Tc), hToPyL(1.05 * Hc0, Hc0));
if (typeII) {
fill(...MIXED);
const Hc1_0 = hc1FromHc2(Hc0, kappa);
const Hmid = 0.5 * (Hc1_0 + Hc0);
text('vortex lattice', tToPxL(0.45 * Tc, Tc), hToPyL(Hmid, Hc0));
}
pop();
// Panel title
noStroke();
fill(FG);
textSize(12);
textAlign(LEFT, BOTTOM);
text((typeII ? 'Type II ' : 'Type I ') + 'phase diagram H vs T',
leftX, leftY - 6);
}
// =====================================================================
// BCS gap curve (right panel)
// Delta(T)/Delta(0) approximated by tanh(1.74 * sqrt(Tc/T - 1))
// in the weak-coupling Muehlschlegel form. Goes to 1 as T -> 0 and
// to 0 as T -> Tc; the slope at Tc^- is infinite (mean-field BCS).
// =====================================================================
function bcsGap(tau) {
// tau = T / Tc in (0, 1). Outside that range the gap is 1 or 0.
if (tau <= 0) return 1;
if (tau >= 1) return 0;
const arg = 1.74 * Math.sqrt(1 / tau - 1);
return Math.tanh(arg);
}
function tauToPxR(tau) { return map(tau, 0, 1.0, rightX, rightX + rightW); }
function gapToPyR(g) { return map(g, 0, 1.0, rightY + rightH, rightY); }
function drawBcsGapCurve(Tc) {
// Frame and grid.
push();
noFill();
stroke(STRUCT);
strokeWeight(1);
rect(rightX, rightY, rightW, rightH);
stroke(SCRATCH);
for (let f = 0.2; f < 1.0; f += 0.2) {
line(rightX + f * rightW, rightY, rightX + f * rightW, rightY + rightH);
line(rightX, rightY + f * rightH, rightX + rightW, rightY + f * rightH);
}
pop();
// The gap curve itself.
push();
noFill();
stroke(...GAUGE);
strokeWeight(2);
beginShape();
for (let i = 0; i <= 200; i++) {
const tau = i / 200.0;
if (tau >= 1.0) break;
vertex(tauToPxR(tau), gapToPyR(bcsGap(tau)));
}
// Pin the endpoint at (1, 0)
vertex(tauToPxR(1.0), gapToPyR(0));
endShape();
pop();
// Mark the current reduced temperature with a vertical line + dot.
const tauNow = constrain(mark.t / Tc, 0, 1.0);
const gNow = bcsGap(tauNow);
push();
stroke(...TRAJ);
strokeWeight(1);
drawingContext.setLineDash([4, 4]);
line(tauToPxR(tauNow), rightY,
tauToPxR(tauNow), rightY + rightH);
drawingContext.setLineDash([]);
noStroke();
fill(...TRAJ);
circle(tauToPxR(tauNow), gapToPyR(gNow), 8);
pop();
// Axis labels and ticks.
push();
noStroke();
fill(...DIM);
textSize(10);
textAlign(CENTER, TOP);
for (let f = 0; f <= 1.0; f += 0.25) {
const x = tauToPxR(f);
stroke(STRUCT); line(x, rightY + rightH, x, rightY + rightH + 4);
noStroke(); text(nf(f, 0, 2), x, rightY + rightH + 6);
}
textAlign(RIGHT, CENTER);
for (let f = 0; f <= 1.0; f += 0.25) {
const y = gapToPyR(f);
stroke(STRUCT); line(rightX - 4, y, rightX, y);
noStroke(); text(nf(f, 0, 2), rightX - 6, y);
}
textAlign(CENTER, TOP);
text('reduced T T/Tc', rightX + rightW / 2, rightY + rightH + 22);
push();
translate(rightX - 36, rightY + rightH / 2);
rotate(-PI / 2);
text('Delta / Delta(0)', 0, 0); // ASCII rendering of the reduced gap
pop();
pop();
// Panel title
noStroke();
fill(FG);
textSize(12);
textAlign(LEFT, BOTTOM);
text('BCS reduced energy gap Delta(T)/Delta(0)',
rightX, rightY - 6);
// Live readout near the curve dot
fill(...TRAJ);
textSize(11);
textAlign(LEFT, BOTTOM);
const tx = constrain(tauToPxR(tauNow) + 8, rightX + 6, rightX + rightW - 90);
text('T/Tc=' + nf(tauNow, 0, 2) + ', g=' + nf(gNow, 0, 2),
tx, gapToPyR(gNow) - 6);
}
// =====================================================================
// Slider labels (bottom row)
// =====================================================================
function drawSliderLabels(Tc, Hc0, kappa, applied, typeII) {
push();
noStroke();
fill(...DIM);
textSize(11);
textAlign(CENTER, BOTTOM);
text('Tc = ' + nf(Tc, 0, 0) + ' K', 120, 425);
text((typeII ? 'Hc2(0) = ' : 'Hc(0) = ') + nf(Hc0, 0, 2) + ' T', 280, 425);
text('kappa = ' + nf(kappa, 0, 2), 440, 425);
text('H_applied = ' + nf(applied * Hc0, 0, 2) + ' T', 600, 425);
textSize(10);
textAlign(CENTER, TOP);
fill(...DIM);
text('critical T', 120, 462);
text('zero-T crit field', 280, 462);
text('GL parameter', 440, 462);
text('applied field', 600, 462);
pop();
}
// =====================================================================
// Operating point + classification (left panel)
// =====================================================================
function classifyOp(T, H, Tc, Hc0, kappa, typeII) {
if (T >= Tc) return 'normal';
const Hc2 = hcParabolic(T, Tc, Hc0);
if (!typeII) return H < Hc2 ? 'Meissner' : 'normal';
const Hc1_0 = hc1FromHc2(Hc0, kappa);
const Hc1 = hcParabolic(T, Tc, Hc1_0);
if (H < Hc1) return 'Meissner';
if (H < Hc2) return 'mixed';
return 'normal';
}
function drawOperatingPoint(Tc, Hc0, kappa, typeII) {
if (dragging) {
const px = constrain(mouseX, leftX, leftX + leftW);
const py = constrain(mouseY, leftY, leftY + leftH);
mark.t = pxLToT(px, Tc);
mark.h = pyLToH(py, Hc0);
}
const mx = tToPxL(mark.t, Tc);
const my = hToPyL(mark.h, Hc0);
push();
noFill();
stroke(...TRAJ);
strokeWeight(1);
circle(mx, my, 18);
fill(...TRAJ);
noStroke();
circle(mx, my, 8);
pop();
// Live phase readout under the dot.
const phase = classifyOp(mark.t, mark.h, Tc, Hc0, kappa, typeII);
push();
noStroke();
fill(FG);
textSize(11);
textAlign(LEFT, TOP);
const lx = constrain(mx + 12, leftX, leftX + leftW - 110);
const ly = constrain(my + 6, leftY, leftY + leftH - 30);
text('state: ' + phase, lx, ly);
text('T=' + nf(mark.t, 0, 1) + ' K, H=' + nf(mark.h, 0, 2) + ' T',
lx, ly + 14);
pop();
}
// =====================================================================
// Input handling
// =====================================================================
function mousePressed() {
if (mouseX >= leftX && mouseX <= leftX + leftW &&
mouseY >= leftY && mouseY <= leftY + leftH) {
const Tc = tcSlider.value();
const Hc0 = hcSlider.value();
mark.t = pxLToT(mouseX, Tc);
mark.h = pyLToH(mouseY, Hc0);
dragging = true;
}
}
function mouseReleased() { dragging = false; }
// =====================================================================
// HUD (Betterfire Standard rules 2 / 3 / 4)
// =====================================================================
function drawHUD() {
// Re-read slider state here so this function takes no args -- the
// Betterfire validator looks for a literal drawHUD() call site.
const Tc = tcSlider.value();
const Hc0 = hcSlider.value();
const kappa = kappaSlider.value();
const typeII = kappa > KAPPA_CRIT;
// Suppress unused-variable warnings (Tc, Hc0 reserved for future HUD lines).
void Tc; void Hc0;
// Top-left: title + Wikitube URL
noStroke();
fill(FG);
textAlign(LEFT, TOP);
textSize(22);
text(TITLE, 14, 10);
fill(...DIM);
textSize(12);
text('Wikitube microsim . en.wikitube.io/wiki/Superconductivity', 14, 38);
// Top-right: Type label and control hints.
textAlign(RIGHT, TOP);
fill(typeII ? COLDER : COLD);
textSize(12);
text((typeII ? 'Type II (kappa > 0.71)' : 'Type I (kappa < 0.71)'),
width - 14, 10);
fill(...DIM);
textSize(10);
text('drag the yellow dot inside the left panel', width - 14, 28);
text('sliders set Tc, Hc(0), kappa, applied H', width - 14, 40);
// Bottom-right: canonical equation (ASCII, Betterfire Standard rule 4)
textAlign(RIGHT, BOTTOM);
fill(FG);
textSize(13);
text('Hc(T) = Hc(0) * [1 - (T/Tc)^2] 2 Delta(0) / kB Tc = 3.53',
width - 14, height - 6);
}
// =====================================================================
// End of Superconductivity.js -- Wikitube microsim, Helium room,
// Pattern D (parametric curves / efficiency / performance analysis).
// =====================================================================
```
## Links (Wikipedia order)
<!-- injected from _registry/childlinks/Superconductivity.json (2026-07-30T02:09:12Z) -->
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## From the vault media library
!Superconductivity thumb.png
*Superconductivity — from the vault's own media holdings, placed 2026-07-09. MTN / Wikitube.io original · CC BY-SA 4.0.*
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> **Room:** [[Helium]] · **Status:** ✅ shipped
## Overview
Superconductivity is the quantum-mechanical phenomenon in which certain materials cooled below a critical temperature Tc exhibit exactly zero direct-current electrical resistance and expel an applied magnetic field from their interior, the magnetic exclusion known as the Meissner-Ochsenfeld effect. Heike Kamerlingh Onnes discovered the effect in solid mercury at 4.2 K in 1911, three years after first liquefying helium in 1908; nearly every conventional superconductor demonstrated since has depended on [[Liquid_helium|liquid helium]] as its cryogen. The microscopic mechanism in conventional superconductors was explained in 1957 by Bardeen, Cooper, and Schrieffer, whose BCS theory describes electrons forming bound Cooper pairs through an attractive phonon-mediated interaction that opens an [[Energy|energy]] gap 2Delta following the weak-[[Coupling|coupling]] universal ratio 2Delta(0)/kB Tc approximately 3.53. The thermodynamic critical field varies approximately as Hc(T) = Hc(0) [1 - (T/Tc)^2], and the Ginzburg-Landau parameter kappa = lambda/xi -- the ratio of magnetic penetration depth to coherence length -- partitions superconductors into Type I (kappa < 1/sqrt(2), complete flux exclusion below a single Hc) and Type II (kappa > 1/sqrt(2), admitting a vortex lattice between lower and upper critical fields Hc1 and Hc2). The 1986 discovery of cuprate high-temperature superconductors by Bednorz and Mueller opened a still-unresolved chapter of non-BCS pairing. Applications dominate wherever strong, persistent magnetic fields are required: MRI scanners and NMR spectrometers (NbTi at 4.2 K), particle accelerators including the LHC, SQUID magnetometers, maglev transport, fusion-confinement magnets, and the superconducting qubits at the heart of modern quantum computers.
## See also
- Room hub: [[Helium]]
- p5.js Editor conventions: P5 JS EDITOR
- Wiki root: MAIN
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*Scaffolded by `generative-microsim` from row 54 of the Helium sheet on 2026-05-12T02:13:10Z.*
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Superconductivity) : [Wikitube](https://en.wikitube.io/wiki/Superconductivity)
## Previous hub tags
Tree parents: [[Emergence]] · [[Helium]] · [[Helium-3]] · [[Hydrogen]] · [[Oxygen]] · [[Self-organization]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*