Fact-checked by Grok 2 weeks ago

Persistent current

A persistent current is a perpetual electric current that circulates indefinitely within a closed loop of superconducting material without any external power source or energy dissipation, owing to the zero electrical resistance characteristic of the superconducting state below the critical temperature.^[1] This phenomenon arises when a superconductor is cooled in the presence of a magnetic field, inducing surface currents that trap and maintain the flux (frozen-in-flux) even after the external field is removed, effectively behaving like a permanent magnet.^[1] The observation of persistent currents dates back to 1914, when Heike Kamerlingh Onnes and his team at Leiden University demonstrated their existence in superconducting mercury rings, providing definitive proof of zero resistance as a novel quantum mechanical effect distinct from ordinary conductivity. Building on the initial discovery of superconductivity in 1911, these currents were further explored in the 1930s through experiments like the Meissner effect, which revealed that superconductors expel magnetic fields, leading to the induction of persistent shielding currents on their surfaces. In type-I superconductors, such as lead, these currents flow uniformly on the surface, while in type-II materials like niobium alloys, they enable higher field tolerances through vortex pinning.^[1] Mechanistically, persistent currents stem from the pairing of electrons into Cooper pairs, which move coherently without scattering, as described by BCS theory in 1957; this coherence allows the current to persist for years or even indefinitely in ideal conditions, limited only by flux creep or thermal fluctuations in practical setups.^[2] Experimental demonstrations, such as those using hollow lead cylinders, show magnetic fields maintained over extended periods—up to a day or more—confirming the absence of decay.^[1] In mesoscopic systems, like nanoscale rings, quantum interference effects can modulate these currents, linking them to broader Aharonov-Bohm phenomena, though macroscopic applications focus on bulk superconductors.^[3] Persistent currents are foundational to numerous technologies, enabling efficient, high-field superconducting magnets operated in "persistent mode" where a one-time induction sustains the field without ongoing power input.^[4] Key applications include magnetic resonance imaging (MRI) scanners, which rely on stable fields from niobium-titanium coils for precise imaging; particle accelerators like those at CERN, where they generate intense fields for beam steering; and nuclear magnetic resonance (NMR) spectrometers for chemical analysis. High-temperature superconductors, such as yttrium barium copper oxide (YBCO; T_c ≈ 93 K),^[5] allow operation using liquid nitrogen cooling (77 K) rather than more expensive liquid helium, and as of 2025, research continues toward materials with even higher critical temperatures, potentially enabling room-temperature applications and revolutionizing energy storage in superconducting magnetic energy storage (SMES) systems.^[6]

Definition and Background

Core Definition

A persistent current is a perpetual electric current that circulates indefinitely without an external power source or energy dissipation. These currents arise in closed-loop geometries where the flow maintains equilibrium due to underlying physical mechanisms that prevent decay. Key characteristics of persistent currents include effectively zero resistance in superconductors or quantum coherence in mesoscopic normal systems, confinement to closed paths such as rings or loops, and remarkable stability over extended timescales—potentially years or longer in ideal conditions.^[1] This stability stems from the absence of dissipative processes, distinguishing them from transient currents driven by external fields or voltages. Persistence requires specific mechanisms like zero resistivity in superconducting states or quantum phase coherence in mesoscopic normal systems, with classical analogs in bound current configurations arising from magnetization in materials (see Mechanisms in Classical Systems). In contrast, such currents are impossible in ohmic conductors, where resistance leads to inevitable energy dissipation through Joule heating (I²R losses).^[1] These phenomena manifest across scales, from mesoscopic rings to macroscopic superconducting coils used in applications like stable magnetic field generation.

Historical Development

The discovery of superconductivity by Heike Kamerlingh Onnes in 1911 laid the foundational roots for understanding persistent currents, as he observed that the electrical resistance of mercury vanished at temperatures near absolute zero, allowing currents to flow without dissipation in superconducting loops.^[7] In 1914, Onnes and his team demonstrated persistent currents directly by inducing them in closed loops of superconducting mercury and lead, where the currents continued indefinitely without external power, providing conclusive evidence of zero resistance. This phenomenon implied the potential for indefinitely sustained currents, though initial interpretations focused on zero resistance rather than quantized orbital effects. In 1930, Wander Johannes de Haas and Pieter van Alphen reported the de Haas-van Alphen effect in bismuth, revealing oscillatory magnetization in metals under magnetic fields, which demonstrated the quantization of electron orbits and provided early evidence of persistent current-like behavior in normal metals at low temperatures. These observations highlighted the electromagnetic response underlying current persistence, setting the stage for theoretical advancements. In the 1930s, Fritz and Heinz London developed a phenomenological theory of superconductivity, published in 1935, which explicitly linked persistent currents to the superconducting state's electromagnetic properties, proposing that supercurrents arise to screen magnetic fields and maintain zero resistivity.^[8] Their London equations described how induced currents in superconductors persist indefinitely, influencing the Meissner effect discovered in 1933 and shaping mid-20th-century research. During the 1940s and 1950s, experimental confirmations of these ideas, including long-term persistence in lead cylinders, solidified the concept, while the 1957 BCS theory by Bardeen, Cooper, and Schrieffer provided a microscopic explanation, though it built directly on the London framework for macroscopic currents.^[1] The 1960s marked practical advancements with the development of niobium-titanium (NbTi) alloys, enabling high-field superconducting magnets operated in persistent mode, where currents up to several amperes could be trapped in closed loops without external power, achieving fields like 2.5 T at 4.2 K as demonstrated by Stan Autler in 1960.^[9] This era transitioned persistent currents from laboratory curiosities to engineering applications in particle accelerators and MRI systems. In the 1980s, theoretical predictions by Boris Altshuler and collaborators extended the concept to mesoscopic normal-metal systems, forecasting quantum-coherent persistent currents in disordered rings due to phase-coherent electron transport, on the order of the Thouless energy.^[10] Experimental realizations in the 1990s confirmed these mesoscopic effects, with V. Chandrasekhar et al. observing harmonic persistent currents in individual gold rings at millikelvin temperatures in 1991, measuring magnetic responses consistent with theoretical amplitudes around 1 nA.^[11] Post-2000 developments incorporated high-temperature superconductors discovered in 1986, allowing persistent currents in cuprates for advanced magnets, while nanoscale devices refined quantum interpretations. A key 2009 experiment by A. C. Bleszynski-Jayich et al. precisely quantified nanoampere-scale persistent currents in mesoscopic gold rings at sub-kelvin temperatures, validating disorder-averaged predictions and bridging classical and quantum regimes.^[12]

Mechanisms in Classical Systems

Bound Currents in Magnetized Materials

In magnetized materials, bound currents arise from the magnetization \mathbf{M}, which is equivalent to volume current density \mathbf{J}_b = \nabla \times \mathbf{M} and surface current density \mathbf{K}_b = \mathbf{M} \times \hat{\mathbf{n}} at the boundaries.^[13] These currents represent the microscopic circulation of charges that produce the overall magnetic field without requiring an external power source.^[14] From a classical perspective, these bound currents originate from atomic or molecular current loops, where electrons orbiting atomic nuclei or intrinsic spins generate small Amperian loops that align to form the net magnetization.^[13] In a lattice of such aligned loops, internal currents largely cancel, leaving effective surface currents that mimic a solenoid.^[15] Representative examples include natural permanent magnets like lodestone, a form of magnetite (\ce{Fe3O4}), where aligned atomic magnetic moments create surface bound currents responsible for its attraction to iron. In electromagnets, an external field induces magnetization in a ferromagnetic core, such as soft iron, generating bound currents that enhance the magnetic field while the applied current flows.^[16] These bound currents exhibit no net charge accumulation because they form closed, solenoidal loops with zero divergence, \nabla \cdot \mathbf{J}_b = 0, producing purely magnetic effects.^[13] Their stability ensures they persist indefinitely as long as the magnetization remains intact, whether through permanent alignment in hard ferromagnets or sustained induction in soft materials, providing an analogy to—but distinct from—persistent currents in superconductors, as they model steady-state effects without zero electrical resistance.^[17] The magnetization \mathbf{M}, which quantifies the magnetic moment per unit volume, gives rise to two types of bound currents: a volume current density and a surface current density.^[13] The volume bound current density is given by \mathbf{J}_m = \nabla \times \mathbf{M}, representing the effective current from the curling of magnetization within the material. On the surface, the bound surface current density is \mathbf{K}_m = \mathbf{M} \times \hat{\mathbf{n}}, where \hat{\mathbf{n}} is the outward unit normal to the surface; this arises from the discontinuity in magnetization at the boundary. These expressions derive from the microscopic picture of orbiting electrons in atoms, averaged over the material to yield macroscopic effects.^[18]^[19] A key property of these bound currents is their divergence-free nature: \nabla \cdot \mathbf{J}_m = \nabla \cdot (\nabla \times \mathbf{M}) = 0, which follows from vector calculus identities and ensures no net charge accumulation, consistent with steady-state conditions in magnetostatics. This divergence-free condition implies that the currents form closed loops entirely within the material.^[15] These bound currents contribute to the total magnetic field \mathbf{B} through a modified Ampère's law: \oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 (I_\text{free} + I_\text{bound}), where I_\text{bound} accounts for the integrated effects of \mathbf{J}_m and \mathbf{K}_m piercing an Amperian loop. Unlike free currents, which can be controlled by voltage sources in conductors, bound currents are passive responses to the material's internal structure and applied fields, such as in ferromagnets where domain alignments produce persistent magnetization.^[14] A classic example is a uniformly magnetized sphere with constant \mathbf{M} = M \hat{\mathbf{z}}. Here, the volume current density \mathbf{J}_m = 0 since \nabla \times \mathbf{M} = 0, but the surface current is \mathbf{K}_m = M \sin\theta \hat{\phi}, equivalent to azimuthal currents that mimic a uniformly magnetized dipole. This surface current distribution produces a dipole field outside the sphere, identical to that of a small current loop.^[18]

Persistent Currents in Superconducting Systems

Superconducting State and Zero Resistance

Superconductivity emerges in certain materials below a critical temperature T_c, where electrons form bound pairs known as Cooper pairs through an attractive interaction mediated by lattice vibrations (phonons). These pairs behave as bosons and condense into a single quantum state, forming a macroscopic wavefunction that enables dissipationless charge transport, resulting in zero electrical resistivity (\rho = 0). This superconducting state is characterized by a energy gap in the electronic spectrum, preventing scattering that would otherwise cause resistance in normal metals.^[20] A defining feature of the superconducting state is the Meissner effect, where the material exhibits perfect diamagnetism by completely expelling magnetic fields from its interior upon entering the superconducting phase.^[21] This expulsion occurs through the induction of persistent screening currents on the surface that generate an opposing magnetic field, maintaining zero internal magnetic induction (B = 0).^[21] The effect distinguishes superconductors from perfect conductors, as it actively excludes fields rather than merely trapping them.^[22] In the superconducting state, once induced, these screening currents—or supercurrents—circulate indefinitely in closed loops without decay due to the absence of resistance. This persistence is ideal in type-I superconductors but can be limited in type-II materials by mechanisms such as flux creep, where thermal activation allows magnetic flux lines to gradually move through the lattice, and thermal fluctuations that disrupt vortex pinning.^[23] Key parameters governing the superconducting state include the critical temperature T_c (e.g., 9.2 K for niobium), the thermodynamic critical field H_c that marks the transition to the normal state, and the coherence length \xi, which defines the spatial extent over which the superconducting order parameter varies.^[24] Superconductors are classified into type-I and type-II based on their response to magnetic fields. Type-I superconductors, typically pure elements, display a complete Meissner effect up to H_c, beyond which superconductivity is abruptly destroyed.^[25] In contrast, type-II superconductors, often alloys, allow partial magnetic field penetration between a lower critical field H_{c1} and upper critical field H_{c2}, forming quantized vortices that coexist with superconductivity; however, persistent screening currents still maintain the overall diamagnetic response outside the vortex cores.^[25] This mixed state enables type-II materials to sustain higher fields while supporting persistent currents essential for applications like magnets.^[26]

Generation and Persistence of Supercurrents

Persistent currents in superconductors are induced through methods that exploit the material's transition to the zero-resistance state below its critical temperature T_c. One common approach involves cooling the superconductor through T_c while an external current is flowing, effectively switching the system into persistent mode where the current continues indefinitely without an applied voltage.^[27] Alternatively, persistent currents can be generated via flux trapping, where an external magnetic field is applied or varied during the cooling process, inducing a screening current that persists due to flux quantization in the superconducting loop.^[28] These techniques ensure that once established, the supercurrent circulates without dissipation, leveraging the expulsion of magnetic fields known as the Meissner effect.^[1] The theoretical foundation for the persistence of these supercurrents lies in the London equations, which describe the electromagnetic response of superconductors. The first London equation relates the superconducting current density \mathbf{J}_s to the vector potential \mathbf{A} as

\mathbf{J}_s = -\frac{n_s e^2}{m} \mathbf{A},

where n_s is the density of superconducting electrons, e is the electron charge, and m is the electron mass; this relation implies that \mathbf{J}_s accelerates without resistance under an electric field, enabling indefinite current flow.^[29] From this, the magnetic field penetrates the superconductor only to a depth \lambda, the London penetration depth, given by

\lambda = \sqrt{\frac{m}{\mu_0 n_s e^2}},

beyond which the supercurrent screens the interior, maintaining the persistent state.^[30] These equations highlight how the collective motion of Cooper pairs sustains the current against ohmic losses. In theory, persistent supercurrents endure indefinitely due to the absence of resistance in the superconducting state. In practice, for niobium-titanium (NbTi) coils operating at 4 K, the decay time exceeds 100,000 years, determined by the inductance-to-resistance ratio where joint resistances are below $10^{-12} \, \Omega.^[31] This exceptional stability is exemplified in superconducting magnets for magnetic resonance imaging (MRI) systems, which operate in persistent mode to deliver ultra-stable fields with minimal power input after initial ramp-up.^[32] However, decay can occur due to quench events, where localized heating drives portions of the superconductor into the normal state, disrupting the current loop, or from radiation-induced defects that introduce scattering centers and gradual resistance.^[33]^[34]

Quantum Effects in Normal Systems

Mesoscopic Persistent Currents

Mesoscopic persistent currents arise from quantum interference effects in normal metal rings at scales comparable to the phase coherence length l_\phi, where the Aharonov-Bohm phase acquired by electrons encircling a magnetic flux leads to equilibrium currents that oscillate periodically with the applied flux \Phi. These currents, predicted in the early 1980s, manifest in resistive conductors without invoking superconductivity, relying instead on the coherent propagation of electron waves around the ring.^[35] In the theoretical framework for non-interacting electrons in a clean, ballistic ring of circumference L, the persistent current exhibits a sawtooth profile as a function of flux, approximated by its fundamental harmonic:

I(\Phi) = -\frac{e v_F}{L} \sin\left( \frac{2\pi \Phi}{\Phi_0} \right),

where v_F is the Fermi velocity, e is the elementary charge, and \Phi_0 = h/e is the magnetic flux quantum. Electron-electron interactions or many-channel effects smooth this profile, reducing the amplitude and introducing harmonic components. In diffusive rings with weak disorder, the ensemble-averaged current vanishes due to random phases, but the typical current for a single ring remains finite, scaling with the Thouless energy E_{Th} = \hbar D / L^2, where D is the diffusion constant.^[36]^[37] The magnitude of these currents is small, on the order of e E_{Th} / \Phi_0, which corresponds to nanoamperes for typical micron-sized rings (e.g., approximately 1–10 nA for L \approx 1 \, \mum and D \approx 100 \, \mathrm{cm}^2/\mathrm{s}). Temperature dependence is strong: the currents decay exponentially above T \sim E_{Th}/k_B, often vanishing for T > 1 K in such systems, as thermal smearing disrupts phase coherence. At finite temperatures, the current amplitude is further suppressed by a factor involving the thermal length l_T = \sqrt{\hbar D / k_B T}.^[38]^[37] Observing these currents requires stringent conditions, including low temperatures below 0.5 K to preserve l_\phi > L, weak disorder to avoid strong localization, and a strictly closed-loop geometry to enable full encirclement of the flux. Phase-breaking mechanisms, such as electron-phonon scattering or impurities, limit the accessible ring sizes to submicron scales in metals like gold or copper.^[37]

Experimental Realizations in Rings

Early experimental realizations of persistent currents in mesoscopic normal conductors focused on metallic rings at cryogenic temperatures to maintain phase coherence. In 1990, Lévy et al. reported the first evidence using an ensemble of approximately 10^7 isolated copper rings with diameters around 0.6–1.5 μm, fabricated via electron-beam lithography and lift-off techniques.^[39] They measured the magnetization using a SQUID magnetometer in a dilution refrigerator at temperatures down to 0.3 K, observing flux-periodic oscillations with a period equal to the flux quantum Φ₀ = h/e and an amplitude corresponding to an average persistent current of about 3 × 10^{-3} e v_F / L per ring, where v_F ≈ 1.6 × 10^6 m/s is the Fermi velocity and L is the ring circumference.^[39] This result, obtained in a low-noise cryostat to minimize thermal decoherence, provided initial confirmation of theoretical predictions but highlighted the small signal size due to ensemble averaging. Single-ring measurements addressed the averaging issue inherent in ensembles, where disorder-induced random phases cause currents to cancel out. In 1991, Chandrasekhar et al. isolated and probed a single gold ring (diameter ≈ 0.8 μm, width ≈ 0.15 μm) using integrated SQUID detection at 20 mK.^[11] The experiment revealed a diamagnetic response with h/e periodicity and a persistent current amplitude of up to ≈ 100 nA—larger than typical theoretical expectations—demonstrating clear parametric dependence on the threaded magnetic flux.^[11] Fabrication involved e-beam lithography on a Si substrate, followed by thermal evaporation of gold, ensuring minimal disorder while maintaining ballistic or diffusive transport regimes. Further advancements in semiconductor systems came in 1993 with Mailly et al., who examined a single lithographic ring (diameter ≈ 1 μm) etched into a GaAs-AlGaAs two-dimensional electron gas heterostructure. Using mutual inductance measurements in a dilution refrigerator at 40 mK, they detected persistent currents up to ≈ 10 nA with Φ₀ periodicity, confirming the effect in a clean, tunable system where electron density could be adjusted via gating. These results underscored the role of low temperatures and high-quality fabrication in preserving coherence lengths exceeding the ring size. Experiments in the mid-1990s and early 2000s revealed finer details, including harmonics from electron-electron interactions. In 2001, Bluhm et al. studied diffusive gold rings (diameter ≈ 1 μm) in an array but analyzed individual responses via SQUID at millikelvin temperatures, observing both h/e (diamagnetic) and h/2e (paramagnetic) periodicities in the persistent currents, with amplitudes around 1–10 nA.^[40] This dual periodicity, absent in non-interacting models, confirmed the enhancement from Coulomb effects in disordered samples.^[40] A significant breakthrough occurred in 2009 with Bluhm et al., who employed ultrasensitive cantilever torsional magnetometry to measure 33 individual gold rings (diameters 0.4–1.2 μm) at temperatures below 0.5 K.^[12] This technique, which detects torque from the ring's magnetic moment with reduced back-action compared to SQUIDs, yielded persistent currents up to ≈ 1 nA, consistent with interaction-enhanced theoretical predictions for clean, single-mode rings.^[12] The measurements highlighted temperature-dependent decay and flux tunability, validating the parametric form I(Φ) ≈ - (e / h) ∂F/∂Φ, where F is the free energy. Key challenges in these realizations include the exponential suppression of currents by thermal fluctuations (coherence length l_φ ∝ 1/√T) and disorder, leading to near-zero ensemble averages; thus, single-ring setups in dilution refrigerators (achieving < 50 mK) and precise flux control via superconducting coils are essential.^[11] Fabrication via e-beam lithography ensures sub-micron dimensions, while detection methods like SQUIDs or cantilevers provide the necessary picotesla sensitivity for nA-scale currents.^[12] Theoretical studies predict enhanced flux-periodic responses in graphene nanorings due to their Dirac fermions and potentially longer coherence lengths, though experimental realizations remain challenging as of 2025. Similarly, theoretical analyses suggest robust edge-state contributions to persistent currents in rings made from topological insulators like Bi₂Se₃, with h/e periodicity potentially preserved up to higher temperatures due to spin-momentum locking; however, experimental demonstrations are limited. These developments highlight the potential scalability of persistent currents in low-dimensional systems for quantum device applications.

References

[1]
[PDF] Superconductivity: The Meissner Effect, Persistent Currents and the ...
The persistence of a current induced in a superconducting cylinder of lead is demonstrated by measurements of its magnetic field over a period of a day.
[2]
[PDF] SUPERCONDUCTIVITY - Portland State University
The induced current is called the persistent current. The current persists, it does not decay because the resistance of the ring is zero. Actually no ...Missing: history | Show results with:history
[3]
Persistent Currents in Normal Metal Rings - Harris Lab | Yale
In this work, I present measurements of persistent currents in normal metal rings performed with cantilever torsional magnetometry. With this technique, the ...
[4]
[PDF] Uses of Superconductivity in Particle Accelerators
2.4 Persistent Currents Currents flow in a superconducting filament to exclude flux. These currents are called “persistent currents” because until about five ...
[5]
[PDF] Critical currents and magnet applications of high-Tc superconductors.
CRITICAL CURRENTS AND. MAGNET APPLICATIONS OF. HIGH-T SUPERCONDUCTORS ... are routinely used to construct persistent-current magnets ... temperature superconductors ...
[6]
[2410.17318] Persistent currents in ultracold gases - arXiv
Oct 22, 2024 · Persistent currents flowing in spatially closed tracks define one of the most iconic concepts in mesoscopic physics. They have been studied in ...
[7]
Heike Kamerlingh Onnes – Facts - NobelPrize.org
In 1911 Kamerlingh Onnes discovered that the electrical resistance of mercury completely disappeared at temperatures a few degrees above absolute zero. The ...
[8]
The electromagnetic equations of the supraconductor - Journals
Electric currents are commonly believed to persist in a supra-conductor without being maintained by an electromagnetic field.
[9]
Brief History | Superconductivity | Applications
Even more significantly, had applied the persistent current in a solenoid to provide the magnetic field for a solid state maser, perhaps the first application ...
[10]
Coherence and persistent currents in mesoscopic rings
Jul 16, 1990 · We calculate, to first order in the screened electron-electron interaction, the grand potential and the equilibrium current in a mesoscopic normal-metal ring.Missing: 1980s | Show results with:1980s
[11]
[PDF] Magnetization, Bound Currents, and the H Field - UT Physics
The currents (10) and (11) are called the bound currents, by analogy with the bound charges in a dielectric. Example: A uniformly magnetized cylinder, ...
[12]
[PDF] Magnetic Fields in Matter B
Materials interact with magnetic fields through diamagnetism, where the induced moment opposes the field, and paramagnetism, where it aligns with the field. ...
[13]
Chapter 6. Magnetostatic Fields in Matter
Since the material is uniformly magnetized, its bound volume current is equal to zero. The bound surface current is equal to. This current distribution is ...
[14]
Lodestone – 600 BC - Magnet Academy - National MagLab
All varieties of magnetite display signs of magnetism, but of them, only lodestone possesses distinctly north-south polarity. Lodestone and other magnetic iron ...Missing: bound currents
[15]
[PDF] Electromagnetic Fields and Energy - Chapter 9: Magnetization
May 9, 2022 · Currents in an electromagnet are used to induce the permanent magnetization, ex ploiting the hysteresis in the magnetization of certain ...
[16]
[PDF] Magnetization, Bound Currents, and the H Field - UT Physics
Such magnetic moments are usually induced by an external magnetic fields, but in permanent magnets they can remain long after the external field is switched off ...
[17]
[PDF] Section 6: Magnetostatics
ρ = -∇∙P plus a polarization surface charge P σ = ∙P n . Now, we discuss the physical picture for bound currents. Fig. 6.2 shows a thin slab of uniformly ...
[18]
5.5: Magnetization - Engineering LibreTexts
Oct 3, 2023 · If the magnetization is uniform, the net total current is zero as the current passing through the loop at one side is canceled by the current ...
[19]
<i>Landmarks</i>: Superconductivity Explained - PHYSICS - APS.org
Sep 11, 2006 · It also explained why superconductivity could only occur near absolute zero–the tenuous Cooper pairs break up in the presence of too much ...
[20]
Meissner and Ochsenfeld revisited - IOPscience
To mark the 50th anniversary of its original publication a translation of the Meissner and Ochsenfeld article describing the exclusion of magnetic field ...
[21]
Meissner effect, diamagnetism, and classical physics—a review
Feb 1, 2012 · We review the literature on what classical physics says about the Meissner effect and the London equations.
[22]
Persistence of pinning and creep beyond critical drive within the ...
Sep 12, 2018 · We challenge this perception by studying the effects of thermal fluctuations within the framework of strong vortex pinning in type II ...
[23]
Critical Temperatures of Some Pure Metals or Type 1 Superconductors
Aug 14, 2003 · ... critical temperatures (Tc), i.e. the temperature at which they become superconducting. ... Niobium, Nb, 9.288, -263.862, -442.9516. Osmium, Os ...
[24]
Flux Lattice in Superconductors and Melting | NIST
Jan 23, 2020 · Most superconductors (called type-II) allow the field to penetrate, but the magnetic flux is quantized into tubes called vortices.
[25]
[1903.09083] Strong pinning theory of thermal vortex creep in type II ...
Mar 21, 2019 · We study thermal effects on pinning and creep in type-II superconductors where vortices interact with a low density n_p of strong point-like defects.<|separator|>
[26]
(PDF) Current Inducting Techniques for Superconducting Rings
Aug 7, 2025 · A procedure has been developed to generate a persistent current in superconducting rings. The basis of the method is a magnetic circuit made ...
[27]
Persistent current in coils made out of second generation high ...
Aug 13, 2008 · The coil was immersed in liquid nitrogen. The persistent current was induced by a transformer arrangement, as shown in Fig. 1. The ...Missing: methods | Show results with:methods
[28]
[PDF] Electrodynamics of Superconductors - 1. Physikalisches Institut
London equation. Thus the superconducting current density is proportional to the vector potential A instead of being proportional to E as in the case of ...<|separator|>
[29]
[PDF] Lecture 4: London's Equations - MIT
Sep 15, 2003 · The density of conduction electrons, the number per unit volume, is n. The current density is ω. Page 6. Massachusetts Institute of Technology.
[30]
[PDF] Stabilization and control of persistent current magnets using variable ...
Mar 30, 2023 · Around eight hours after the magnet is placed into persistent current mode, an automated tuning program is started which uses magnetic field ...
[31]
Niobium-titanium (Nb-Ti) superconducting joints for persistent-mode ...
Oct 3, 2019 · Superconducting joints are essential for persistent-mode operation in a superconducting magnet system to produce an ultra-stable magnetic field.
[32]
[PDF] Superconducting Magnets Quench Propagation and Protection
Quench in a superconductor: A sudden, unexpected and unrecoverable transition to the normal state of the superconductor in the device (magnet, bus bar, ...Missing: persistent | Show results with:persistent
[33]
Experimental Study of the Decay of Persistent Currents in a Soft ...
In a previous experiment, it was observed that the persistent current in a thin Pb superconducting ring decays when the material is subjected to 𝛼 -particle ...Missing: factors quench
[34]
Josephson behavior in small normal one-dimensional rings
... 1983, Pages 365-367. Physics Letters A. Josephson behavior in small normal one-dimensional rings. Author links open overlay panel. M. Büttiker , Y. Imry 1 , R.
[35]
Persistent current in a mesoscopic ring with diffuse surface scattering
Jul 15, 1999 · The persistent current in a clean mesoscopic ring with ballistic electron motion is calculated. The particle dynamics inside a ring is ...Missing: sawtooth v_F
[36]
Normal persistent currents - Taylor & Francis Online
By ULRICH ECKERN and PETER SCHWAB ... Finally, we would like to discuss a situation which would be ideal for seeing both effects: 'normal' persistent currents as ...
[37]
[PDF] Persistent current in normal metals - Physics
Various energy scales of the disordered rings are the following: Thouless energy Ec ∼ ¯h/τD = 7.3mK, mean energy level spacing. ∆ ∼ 1/2N0V = 19µK, where ...
[38]
Magnetization of mesoscopic copper rings: Evidence for persistent ...
Magnetization of mesoscopic copper rings: Evidence for persistent currents. L. P. Lévy, G. Dolan, J. Dunsmuir, and H. Bouchiat. AT&T Bell ...
[39]
Magnetic response of a single, isolated gold loop | Phys. Rev. Lett.
Dec 16, 1991 · Magnetic response of a single, isolated gold loop. V. Chandrasekhar ... The amplitude of the oscillatory component corresponds to a persistent ...
[40]
Diamagnetic Persistent Current in Diffusive Normal-Metal Rings
Feb 19, 2001 · We have measured a diamagnetic persistent current with flux periodicities of both h ⁡ / e and h ⁡ / 2 ⁢ e in an array of thirty diffusive mesoscopic gold rings.
[41]
Persistent Currents in Normal Metal Rings - Science
We have developed a technique for detecting persistent currents that allows us to measure the persistent current in metal rings over a wide range of ...
[42]
Electrostatically Confined Quantum Rings in Bilayer Graphene
We propose a new system where electron and hole states are electrostatically confined into a quantum ring in bilayer graphene.
[43]
Bound states and persistent currents in topological insulator rings
The predicted persistent currents 4 have been experimentally measured, also on a single ring, in various experiments in metals 5–7 and semiconductors. 8