⚡Superconducting Devices Unit 1 – Introduction to Superconductivity

Key Concepts and Definitions

• Superconductivity phenomenon where certain materials exhibit zero electrical resistance and expel magnetic fields below a characteristic critical temperature $T_c$
• Critical temperature $T_c$ transition temperature below which a material becomes superconducting, varies for different materials
• Critical current density $J_c$ maximum current density a superconductor can carry without losing its superconducting properties
• Critical magnetic field $H_c$ maximum magnetic field a superconductor can withstand before reverting to its normal state
  • Type I superconductors have a single critical field $H_c$
  • Type II superconductors have a lower critical field $H_{c1}$ and an upper critical field $H_{c2}$
• Meissner effect expulsion of magnetic fields from the interior of a superconductor, resulting in perfect diamagnetism
• Cooper pairs two electrons with opposite spins and momenta that pair up in a superconductor, enabling the flow of electrical current without resistance
• Coherence length characteristic distance over which the superconducting order parameter varies, determines the size of Cooper pairs
• Penetration depth distance to which a magnetic field can penetrate into a superconductor before being expelled by the Meissner effect

Historical Background

• 1911 discovery of superconductivity in mercury by Heike Kamerlingh Onnes
  • Observed a sudden drop in electrical resistance to zero at 4.2 K
• 1933 Meissner effect discovered by Walther Meissner and Robert Ochsenfeld
  • Demonstrated the expulsion of magnetic fields from superconductors
• 1950s development of the Ginzburg-Landau theory and the BCS theory
  • Ginzburg-Landau theory phenomenological approach to describe superconductivity using an order parameter
  • BCS theory microscopic theory explaining the formation of Cooper pairs through electron-phonon interactions
• 1962 Josephson effect predicted by Brian Josephson
  • Described the tunneling of Cooper pairs between two superconductors separated by a thin insulating barrier
• 1986 discovery of high-temperature superconductivity in cuprates by Georg Bednorz and Karl Müller
  • Opened up new possibilities for practical applications of superconductivity
• 21st century ongoing research into novel superconducting materials and mechanisms
  • Iron-based superconductors, topological superconductors, and room-temperature superconductivity

Physics of Superconductivity

• Electron-phonon interactions formation of Cooper pairs through the exchange of virtual phonons, leading to an attractive interaction between electrons
• BCS theory microscopic theory explaining the formation of Cooper pairs and the origin of the superconducting energy gap
  • Electrons with opposite spins and momenta form Cooper pairs
  • Energy gap opens up around the Fermi level, preventing the scattering of electrons and resulting in zero electrical resistance
• Ginzburg-Landau theory phenomenological approach to describe superconductivity using an order parameter $\psi$
  • Order parameter $\psi$ complex quantity representing the density and phase of the superconducting electrons
  • Minimization of the Ginzburg-Landau free energy functional leads to the Ginzburg-Landau equations
• London equations describe the electrodynamics of superconductors
  • Relate the current density and the magnetic field in a superconductor
  • Explain the Meissner effect and the existence of a penetration depth
• Josephson effect tunneling of Cooper pairs between two superconductors separated by a thin insulating barrier
  • Josephson current flow of supercurrent through the barrier without any applied voltage
  • Josephson junction two superconductors coupled by a weak link, enabling the Josephson effect
• Flux quantization magnetic flux through a superconducting loop is quantized in units of the magnetic flux quantum $\Phi_0 = h/2e$

Types of Superconductors

• Type I superconductors exhibit a complete Meissner effect and have a single critical field $H_c$
  • Examples include pure metals like lead, mercury, and aluminum
  • Abrupt transition from the superconducting state to the normal state at $H_c$
• Type II superconductors have a lower critical field $H_{c1}$ and an upper critical field $H_{c2}$
  • Partial Meissner effect between $H_{c1}$ and $H_{c2}$, allowing magnetic flux to penetrate the superconductor in the form of vortices
  • Examples include alloys and compounds like niobium-tin and yttrium barium copper oxide (YBCO)
• Conventional superconductors materials that can be explained by the BCS theory, typically with low $T_c$ values
  • Electron-phonon interactions are responsible for the formation of Cooper pairs
• Unconventional superconductors materials that cannot be fully explained by the BCS theory, often with high $T_c$ values
  • Examples include cuprates, iron-based superconductors, and heavy fermion superconductors
  • May involve alternative pairing mechanisms, such as spin fluctuations or electronic correlations
• Low-temperature superconductors materials with $T_c$ values typically below 30 K, requiring cooling with liquid helium
• High-temperature superconductors materials with $T_c$ values above 30 K, enabling cooling with liquid nitrogen
  • Discovered in 1986 with the cuprate superconductors
  • Expanded the potential for practical applications of superconductivity

Superconducting Materials

• Elemental superconductors pure metals that exhibit superconductivity
  • Examples include mercury (Hg), lead (Pb), and niobium (Nb)
  • Generally have low $T_c$ values and are Type I superconductors
• Alloy superconductors materials composed of two or more elements that display superconductivity
  • Examples include niobium-tin (Nb3Sn) and niobium-titanium (NbTi)
  • Often have higher $T_c$ values and are Type II superconductors
• Cuprate superconductors family of high-temperature superconductors containing copper oxide planes
  • Examples include yttrium barium copper oxide (YBCO) and bismuth strontium calcium copper oxide (BSCCO)
  • Exhibit $T_c$ values above 77 K, enabling cooling with liquid nitrogen
• Iron-based superconductors family of high-temperature superconductors containing iron-pnictide or iron-chalcogenide layers
  • Examples include LaFeAsO and FeSe
  • Exhibit $T_c$ values up to 55 K and unconventional pairing mechanisms
• Organic superconductors carbon-based materials that display superconductivity
  • Examples include fullerenes and molecular crystals like $\kappa$-(BEDT-TTF)2Cu[N(CN)2]Br
  • Typically have low $T_c$ values but provide insights into novel superconducting mechanisms
• Heavy fermion superconductors materials containing rare earth or actinide elements with strongly correlated electrons
  • Examples include CeCu2Si2 and UPt3
  • Exhibit unconventional superconductivity and complex phase diagrams

Applications and Devices

• Superconducting magnets produce strong, stable magnetic fields with minimal power consumption
  • Used in MRI machines, particle accelerators, and fusion reactors
  • Enabled by Type II superconductors like NbTi and Nb3Sn
• Superconducting power transmission efficient transmission of electrical power over long distances without resistive losses
  • Potential to reduce energy waste and improve grid stability
  • Requires high-temperature superconductors for cost-effective implementation
• Superconducting generators and motors compact, lightweight, and efficient electrical machines
  • Offer higher power densities and reduced losses compared to conventional designs
  • Applications in wind turbines, electric vehicles, and ship propulsion
• Superconducting quantum interference devices (SQUIDs) highly sensitive magnetometers based on Josephson junctions
  • Used for measuring extremely weak magnetic fields, such as those produced by the human brain or in geophysical surveys
  • Enable non-invasive medical imaging and mineral exploration
• Superconducting qubits building blocks for quantum computers, exploiting the coherence and entanglement of superconducting circuits
  • Examples include flux qubits, charge qubits, and transmon qubits
  • Offer scalability and compatibility with existing microwave technology
• Superconducting single-photon detectors (SSPDs) highly sensitive detectors for individual photons, utilizing the breakdown of superconductivity upon photon absorption
  • Applications in quantum communication, quantum cryptography, and optical quantum computing
  • Provide high detection efficiency, low dark counts, and fast response times

Challenges and Limitations

• High cost of cooling most superconductors require expensive cryogenic cooling systems to maintain their superconducting state
  • Liquid helium cooling for low-temperature superconductors is particularly costly
  • High-temperature superconductors can be cooled with liquid nitrogen, but still require significant infrastructure
• Mechanical properties superconductors are often brittle and difficult to fabricate into wires or complex shapes
  • Ceramic cuprate superconductors are particularly challenging to work with
  • Requires the development of specialized processing techniques and composite materials
• Flux pinning and AC losses Type II superconductors are subject to flux pinning and AC losses when exposed to alternating magnetic fields
  • Flux pinning can lead to reduced critical current density and magnetic field gradients
  • AC losses generate heat and reduce the efficiency of superconducting devices
• Quenching sudden loss of superconductivity due to local heating or excessive current
  • Can cause damage to superconducting devices and pose safety risks
  • Requires the implementation of quench protection systems and fault-tolerant designs
• Material complexity many high-performance superconductors are complex, multi-element compounds
  • Precise control over stoichiometry and crystal structure is essential for optimal performance
  • Reproducibility and large-scale production can be challenging
• Incomplete theoretical understanding the mechanisms behind unconventional superconductivity are not yet fully understood
  • Hinders the predictive design of new superconducting materials with desired properties
  • Requires further experimental and theoretical research to elucidate the underlying physics

Future Directions and Research

• Room-temperature superconductivity the ultimate goal of superconductivity research, enabling widespread practical applications
  • Requires the discovery of novel superconducting materials or mechanisms
  • Theoretical predictions and experimental hints suggest the possibility of achieving this milestone
• Topological superconductors materials that combine superconductivity with topological properties, such as Majorana fermions
  • Potential applications in fault-tolerant quantum computing and quantum information processing
  • Examples include proximitized semiconductor nanowires and iron-based superconductors
• Superconducting metamaterials artificial structures engineered to exhibit unique electromagnetic properties
  • Enable the control and manipulation of electromagnetic waves in unconventional ways
  • Potential applications in cloaking, sub-wavelength imaging, and novel sensors
• Superconducting spintronics integration of superconductivity with spin-based electronics
  • Exploits the interplay between superconductivity and spin-dependent transport
  • Potential applications in low-power, high-speed information processing and storage
• Hybrid superconducting devices combination of superconductors with other functional materials, such as ferromagnets or topological insulators
  • Enable the realization of novel device functionalities and quantum phenomena
  • Examples include superconducting spin valves and topological Josephson junctions
• Computational materials discovery use of advanced computational methods, such as machine learning and high-throughput screening, to identify new superconducting materials
  • Accelerates the exploration of vast chemical and structural phase spaces
  • Guides experimental efforts towards the most promising candidates for high-temperature or unconventional superconductivity