--- title: "Meissner effect and hard superconductors" subject: "Electrical Engineering Material" chapter: 5 key: "semester_3/electrical_engineering_material:meissner-hard-superconductor" source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/meissner-hard-superconductor site: BCT Engineering --- # Meissner effect and hard superconductors Electrical Engineering Material · Chapter 5: Superconductivity - Asked in: 2074 Chaitra, 2+4+2 marks - Video: [What is Superconductivity | Meissner effect | Types of Superconductors SAHAPADI VLOG](https://www.youtube.com/watch?v=-9GzrOd0goo) — SAHAPADI - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/meissner-hard-superconductor - Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-5 ## Question What is Meissner effect? Explain the difference between type I and type II superconductors. Type II superconductor is also called hard superconductor, why? ## Short answer The Meissner effect is the complete expulsion of magnetic flux from a superconductor below T_c, making it a perfect diamagnet (B=0). Type-I have a single low H_c, sharp transition; type-II have two critical fields (H_c1, H_c2) and a mixed vortex state. Type-II is hard because flux vortices get pinned at defects, causing hysteresis and enabling high critical current densities in strong fields. ## Answer #### Meissner effect **Meissner effect** is the complete expulsion of magnetic flux from the interior of a material when it is cooled below its critical temperature $T_c$ in a weak magnetic field ($H < H_c$). The superconductor becomes a **perfect diamagnet**. Inside the superconductor: $$ \begin{aligned} B &= \mu_0 (H + M) = 0 \\ \Rightarrow M &= -H, \quad \chi_m = \frac{M}{H} = -1 \end{aligned} $$ Screening currents flow in a thin surface layer (the London penetration depth, $\lambda_L \approx 10$ to $100$ nm) and create a field that exactly cancels the applied field inside. ```text T > Tc (normal) T < Tc (superconducting) | | | | | | | \ \ / / | |+-----+| | \ \ +---+ / / | || || | cool ) )| |( ( | || || | ----> / / +---+ \ \ | |+-----+| | / / \ \ | | | | | | | flux lines bend around it ``` The effect is independent of history: whether the field is applied before or after cooling, the flux is expelled. This shows a superconductor is not just a perfect conductor (a perfect conductor would trap the flux present at cooling). #### Type-I vs type-II superconductors ```text -M -M | /| | /\ | / | | / \ | / | | / \_ | / | |/ \__ |/ |____ H +----|------|--- H 0 Hc 0 Hc1 Hc2 Type-I Type-II ``` | Point | Type-I | Type-II | |---|---|---| | Critical fields | One, $H_c$ | $H_{c1}$ and $H_{c2}$ | | Meissner effect | Complete up to $H_c$ | Complete only below $H_{c1}$ | | Transition | Sharp | Gradual, via mixed (vortex) state | | Field values | Low (below about 0.2 T) | $H_{c2}$ up to tens of tesla | | Examples | Pb, Hg, Sn, Al | NbTi, Nb$_3$Sn, YBCO | #### Why type-II is called a hard superconductor - It stays superconducting up to a very high field $H_{c2}$, so superconductivity is **hard to destroy**. - In the mixed state, flux vortices get **pinned** at defects, dislocations and impurities. This makes the magnetization irreversible with a large **hysteresis loop**, just like a hard magnetic material. - Because of pinning, it can carry a **large critical current density** in strong fields. - Most are alloys or compounds that are mechanically hard and brittle (e.g. Nb$_3$Sn). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the Meissner effect? A. Complete expulsion of magnetic flux from a material cooled below Tc in a weak field B. Drop of resistance to zero when a current flows C. Trapping of the existing flux when a perfect conductor is cooled D. Increase of Tc with applied field Answer: A. Below Tc and for H < Hc the interior has B = 0, so the superconductor is a perfect diamagnet. (Key point: Meissner effect definition) 2. Why does the Meissner effect show a superconductor is more than a perfect conductor? A. A superconductor has a higher conductivity than any perfect conductor B. Flux is expelled whether the field is applied before or after cooling, while a perfect conductor would trap flux present at cooling C. A perfect conductor expels flux but a superconductor traps it D. A superconductor needs no cooling to expel flux Answer: B. The expelled state is independent of history, so it is a true thermodynamic state, not just zero resistance. (Key point: History independence) 3. How do the two types respond as the field rises? A. Type-I has a mixed state between Hc1 and Hc2; type-II turns normal suddenly at Hc B. Both turn normal suddenly, but type-II at a higher field C. Type-I stays fully diamagnetic up to Hc then turns normal suddenly; type-II has a mixed state between Hc1 and Hc2 D. Type-I has two critical fields and type-II has one Answer: C. Type-I has a single Hc with a sharp transition. Type-II has Hc1 and Hc2 with vortices in between. (Key point: Type-I vs type-II transition) 4. Why is type-II called a hard superconductor? A. It is made of pure soft metals like Pb and Hg B. It has a lower critical field than type-I C. It shows completely reversible magnetization D. Vortices are pinned at defects, giving irreversible magnetization, hysteresis and high Jc, and it survives very high fields Answer: D. Flux pinning gives hysteresis like a hard magnet, large Jc and a very high Hc2. 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