Experiment 9Bench 9MZU-PE / CRY-9Normal

Superconductivity: BCS Theory and the Meissner Effect

Cryostat & Levitation Stage

Cool a sample through its transition, watch the magnet lift off, and follow the four-probe resistance to zero.

Duration: 3 hours
Kittel: Chapter 10
Topics: Meissner effectBCS theoryType I/II

Cryostat — levitation stage

YBa₂Cu₃O₇ disc · Liquid nitrogen · 300.00 K

MeissnerVortex

Standby

NormalLevitation 0.00 mm

Drag to orbit the dewar

Four-probe resistance

R against T at the applied field

R(T)Present working pointTransitionCoolant base temperature

BCS energy gap

Δ(T)/Δ(0) against T/T_c

Δ(0)

13.985meV

Δ(T)

0.0000meV

2Δ(0)/k_BT_c

3.53

Critical field

H_c1 and H_c2(T) — type II

H_c2H_c1Applied field

Bench readings

Thermometry, four-probe bridge and Hall gaussmeter

Sample thermometer

Sample temperature

KBASE

Four-probe resistance

mΩ

Applied field

T / T_c

λ(T)/λ(0)

∞

Levitation height

Specimen

Type

Type II

T_c

92K

H_c2(T)

0.0000T

H_c1(T)

0.0000T

λ(0)

150nm

The first superconductor found above the boiling point of nitrogen, which is why this one can be demonstrated with LN₂ in an ordinary lecture theatre.

Cryostat control

MZU-PE / CRY-9

Ready

Cryogenic liquids. Asphyxiation and cold-burn risk — never seal the dewar and never touch the transfer line.

Specimen

Dewar

Coolant

Cheap, safe and available anywhere — but it stops at 77 K, so it can only be used on high-temperature superconductors.

Temperature

Setpoint300 K

Applied field

Magnet field5.0 mT

MeissnerVortexNormal

Key Equations

BCS gap and its zero-temperature value:

2\Delta(0) = 3.53\,k_BT_c

London screening of the field:

B(x) = B_0e^{-x/\lambda_L},\quad \frac{\lambda(T)}{\lambda(0)}=\frac{1}{\sqrt{1-(T/T_c)^4}}

Critical field:

H_c(T) = H_c(0)\left[1-\left(\tfrac{T}{T_c}\right)^{2}\right]

Type I and type II

A type I superconductor expels the field completely until

H_c

, then goes normal all at once. A type II lets flux in above

H_{c1}

as quantised vortices and stays superconducting all the way to

H_{c2}

— which is why every high-field magnet is wound from a type II material.

Procedure

0/4

AThe Meissner effectLoad YBCO with liquid nitrogen in the dewar and a small field applied. Cool from 300 K down to 77 K and watch the field lines, the magnet and the four-probe resistance. Record the temperature at which the resistance reaches zero.
BThe energy gapStep T/T_c from 0.1 to 1.0 and record Δ(T)/Δ(0) and λ(T)/λ(0) at each point. Note how sharply the gap collapses close to T_c and what happens to the penetration depth there.
CType I against type IILoad lead (type I) with liquid helium and raise the field until superconductivity is destroyed — record H_c. Then load niobium (type II) and find both H_c1, where vortices first appear, and H_c2.
DWhy liquid nitrogen is not enoughKeeping LN₂ in the dewar, try in turn to superconduct YBCO, BSCCO, Nb₃Sn, Nb, Pb and Al. Record which ones work and explain the pattern.

Table 9 — superconducting state

0 entries

Note the coolant as well as the temperature: it decides what you can reach.

#	Specimen	Type	T_c/ K	Coolant	T/ K	T/T_c	B applied/ T	H_c(T)/ T	R/ mΩ	Δ(T)/ meV	Levitation/ mm	State
No readings yet — set the controls, then press “Record reading”.

Analysis & Reflection

Analysis questions

Why does the BCS energy gap close at the critical temperature? What happens to the Cooper pairs there?
From your Task B data, plot $\lambda(T)/\lambda(0)$ against $T/T_c$ . Why does the penetration depth diverge as $T \to T_c$ , and what does that mean physically for the screening currents?
State the difference between a perfect conductor and a superconductor. Which of the two effects you observed on this bench could a perfect conductor not reproduce?
From Task D, explain exactly why liquid nitrogen works for YBCO and BSCCO but not for niobium, lead or aluminium.
The levitation height on this stage follows the superfluid density 1 − (T/T_c)⁴. Explain why the magnet sinks as the disc is warmed even before the resistance returns.

Physics problems

Using $2\Delta(0)=3.53k_BT_c$ , calculate the zero-temperature gap of niobium in meV and compare with the panel.
Explain how the isotope effect, T_c ∝ M^(−1/2), points to phonons as the pairing mechanism in a conventional superconductor.
A lead sample is at 4.2 K. Using $H_c(T)=H_c(0)[1-(T/T_c)^2]$ with $H_c(0)=80.3$ mT, calculate the field that would drive it normal, then check it on the bench.
Why can a type II superconductor carry current in a very high field while a type I cannot? Refer to flux vortices and to pinning.