London Moment Research Articles

Measurement of the London moment

We report on the measurement of the London moment produced in a rotating spherical shell superconductor. In the process of qualifying gyroscopes for the Gravity Probe B Relativity Mission we investigated the question of how a magnetic moment develops in rotating superconductors. We have been able to perform experiments which show that the dipole moment appears independent of the initial rotational state of the superconductor.

Magnetoelastic theory of type-II superconductors in the mixed state.

This paper presents a macroscopic theory for analyzing the magnetoelastic response of elastic type-II superconductors in the mixed state. The theory includes not only the vortex-dynamic effect, the normal-current effect, and the flux-flow Hall effect, but also the effect of the London moment induced by the local motion of the deformable superconductor in the mixed state. The theory is considered to be valid within the framework of the generalized Galilean relativity at the magnetoquasistatic approximation. By this theory, a set of linearized coupled wave equations is derived to study some problems concerning magnetoelastic wave propagation in type-II superconductors in the mixed state. Attenuation and dispersion behaviors of the magnetoelastic wave are then analyzed. It is shown that the nonlocal effect on the length scale of the London penetration depth may be of importance in analyzing the propagation behavior of the magnetoelastic wave at frequencies higher than the depinning frequency. It is also shown that the effect of the London moment induced by dynamic deformation can be of significance as compared with the effect of the normal Lorentz current on the magnetoelastic coupling behavior of elastic type-II superconductors in the mixed state. Furthermore, it is found that there is a phase change between the transverse elastic wave and the magnetic wave induced in the type-II superconductor in the mixed state. This effect is found to be closely related to the vortex-dynamic properties of the superconductor.

Rotation-induced electric fields in metals and superconductors.

Recent attempts to design inertial sensors based on quantum-interference effects in high-[ital T][sub [ital c]] superconducting materials have led to a renewed interest in the origin of electric and magnetic fields in accelerated superconductors. In the case of a rotating superconductor, the formation of the London moment is well understood; however, there still exists some controversy concerning the direction and magnitude of the rotationally induced electric field. This situation is reminiscent of the old controversy concerning gravitationally induced electric fields in metals. In this paper we present a self-consistent theory of rotationally induced electric fields in both normal metals and superconductors. In the former case we treat normal carriers employing Thomas-Fermi theory; in the latter case we treat superelectrons using Ginzburg-Landau theory. In both cases we treat the lattice deformation with linear elastic theory. Self-consistent numerical solutions of these models show that the rotationally induced electric field in normal metals is given by [bold E]=[minus][ital K]([ital M]/[ital e])[omega][sup 2][bold r], where [ital M] is the mass of a lattice ion, [ital e][gt]0 is the magnitude of charge on an electron, [omega] is the angular velocity, [bold r] is the distance from the axis of rotation, and [ital K] is amore » positive-definite constant that depends on the lattice Lame coefficients in a complicated way. This result is in qualitative agreement with previous analyses [Dessler [ital et] [ital al]., Phys. Rev. 168, 737 (1968); Herring, Phys. Rev. 171, 1361 (1968)]. The results we obtain for a rotating superconductor are markedly different.« less

Observation of the London moment and trapped flux in precision gyroscopes

The London-moment readout has been observed in flight quality gyroscopes and it has been demonstrated that it is possible to reduce magnetic field trapped in these gyroscopes to levels as low as 1.5*10/sup -11/ T. A preliminary analysis shows that the horizontal component of the London-moment signal is 60% of the total expected London-moment signal and is proportional to the gyro spin speed. Experiments were carried out in a unique ground test facility which was designed to provide the conditions necessary to observe the London moment of the spinning gyroscope.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Interaction between gravity and moving superconductors

We propose a unified phenomenological theory to investigate the interaction between arbitrarily moving superconductors and gravitational fields including the Newtonian gravity, gravitational waves, vector transverse gravitoelectric fields, and vector gravitomagnetic fields. In the limit of weak field and low velocity, the expressions for the induced electromagnetic and gravitational fields in the interior of a moving superconductor are obtained. The Meissner effect, London moment, DeWitt effect, effects of gravitational wave on a superconductor, and induced electric fields in the interior of a freely vibrating superconductor are recovered from these two expressions. We demonstrate that the weak equivalence principle is valid in superconductivity, that Newtonian gravity and gravitational waves will penetrate either a moving superconductor or a superconductor at rest, and that a superconductor at rest cannot shield either vector gravitomagnetic fields or vector transverse gravitoelectric fields.

The London moment for high temperature superconductors

Inside a stationary superconductor the magnetic field is zero, as described by the London equations. These equations also describe the development of a magnetic field in a superconductor when it is set into rotation. The generated magnetic moment is called the London moment. We show that the high- T c superconductors develop a London moment of the same magnitude as the conventional superconductors and discuss the consequences of this for the interpretation of the London penetration depth.

Measurement of the London moment in two high-temperature superconductors

THE well-known London equations dictate that the magnetic field inside a stationary superconductor vanishes. The same equations, however, predict that the superconductor generates a magnetic field when it is put into uniform rotation. The associated magnetic moment is known as the London moment. Here we show that high-transition-temperature (high-Tc) superconducting oxides indeed possess this fundamental property, and when rotated, develop a London moment of the same magnitude as that of conventional superconductors, provided that the signal is scaled to the shielded volume fraction. This confirms that high-Tc superconductivity corresponds to a superfluid phase in the London sense, and that the mass of the carriers that appears in the expression of the London moment is the free-electron mass, irrespective of the nature of the carriers in the normal state.

Determination of h/m* Using a Rotating Niobium Ring

A precise measurement of the ratio of Planck's constant to the mass of a Cooper pair of electrons, h/m*, may be made using a rotating, superconducting ring. When the ring is stationary, the flux threading it is an integer multiple of the flux quantum, hc/e* (e*=2e). When the ring rotates there is an additional contribution to the flux, proportional to the rotation rate, from the London moment field, 2m*cω/e*. The rotation velocities at which the flux is zero are therefore a set of evenly spaced points, separated by Δω. If the cross sectional area of the ring is S, then h/m*=2SΔω. We have obtained new data in this experiment and are in the process of measuring the expansion coefficient of our quartz rotor in order to correct the room temperature area measurement.

Precise determination of h/me using a rotating, superconducting ring.

A precise determination of h/${m}_{e}$ (Planck's constant divided by the free-electron mass) using a rotating, superconducting ring is in progress. The measurement is based on flux quantization and the London moment---two manifestations of the macroscopic quantum nature of superconductivity. Here we report the first results from a precision, thin-film niobium ring. These data have a statistical error of 10 parts per million (ppm). A systematic error exists at the level of 2500 ppm, due to the presence of electric charge on the rotor. A model for the charge distribution is suggested and used to adjust the results and obtain a value of h/${m}_{e}$. This work has determined h/${m}_{e}$ directly to an accuracy of 100 ppm, a higher level of precision than previously reported. Recent theoretical calculations have predicted a relativistic mass increase of 150 ppm for electrons in superconducting niobium, but the uncertainty in our final results prevented the clear identification of this effect.

Relativistic thermoelectromagnetic gravitational effects in normal conductors and superconductors

The general principles needed to compute the effect of a stationary gravitational field on the thermoelectric phenomena in normal conductors and superconductors are formulated from a general relativistic point of view. These principles are then applied to a variety of devices which can, in principle, measure the gravitational field. Generalizations of the Thomson, Seebeck, Peltier and Josephson effects and the London moment are obtained.

New relativistic gravitational effects using charged-particle interferometry

A new class of gravitational effects, in the quantum interference of charged particles, are studied in electron interferometry and superconducting Josephson interferometry. These include phase shifts due to the gravitationally induced Schiff-Barnhill field, rotationally induced London moment, and the modification of the Aharonov-Bohm type of phase shifts, due to the general relativistic coupling of the electromagnetic field to the gravitational field. These effects are interesting, even from a purely theoretical point of view, because they involve an elegant interplay between gravitation, electromagnetism, and quantum mechanics. But new predictions are also made which, if confirmed, would provide the first observation of relativistic gravitational effects, involving the electric charge, at the quantum mechanical level. The possibility of using these effects to detect gravitational waves is also discussed.

Correction to the formula for the London moment of a rotating superconductor

This paper gives a full quantum mechanical analysis of the magnetic field (first discussed by London) that appears spontaneously when a sample of superconductor is set into rotation. It is shown that, for slow rotation velocities and using certain approximations, the fieldB threading a cavity within a superconductor that rotates at angular velocityω is given byeB=2(mo−W/c2)ω, where — e is the charge on the electron,mo is the free electron mass,W is the work function of the superconductor, andc is the velocity of light. In this calculation effects that are second order in the rotation velocity have been ignored, and the result is only strictly valid at the zero of temperature. The application of this result to experiments using practical, nonideal apparatus is then illustrated for a simple geometry.

Relativistic mass corrections for rotating superconductors

The relativistic Hamiltonian and Dirac current density for a charged particle in a rotating frame are derived. Simple results are obtained correct to all orders in the particle velocity and to first order in the rotation velocity. An extension is made to the many-electron current and is used for calculating the relativistic corrections to the magnetic field generated within a rotating superconductor (London moment). With the use of simple solid-state models, estimates of the corrections for common elemental superconductors are presented. The results predict several hundred ppm corrections for most superconductors and are of direct significance to high-precision measurements of h/m/sub e/ now under way at Stanford. In addition, comparison of the experimental values with the accepted value of h/m/sub e/ for the free electron at rest will provide a direct measure of the expectation value for the kinetic energy of the electron wave functions averaged over the Fermi surface, a quantity not observed directly by any other technique.

Some calculations with magnetic field dependent orbitals

Calculations with magnetic field dependent orbitals, which include usual cartesian gaussians and London's field dependent orbitals as special cases, are presented. Magnetic susceptibility and magnetic shielding of H 2 and HF molecules are calculated within the finite perturbation Hartree—Fock LCAO method.

Ultra-low magnetic field apparatus for a cryogenic gyroscope

We have completed the construction of an apparatus for continued Earth-based testing of a gyroscope system to be used in a satellite test of general relativity. The immediate goal is a readout capable of measuring the direction of the gyroscope spin axis to an angular resolution of one arcsecond over a limited range. A combination of SQUID magnetometers and persistent current loops are used to measure the London moment of the spinning superconducting rotor, which is levitated electrostatically. The apparatus makes use of a new magnetic field shielding technique for obtaining large superconductor shielded regions below 10 −7 gauss to obtain a trapped flux signal in the gyroscope sufficiently smaller than the London moment signal. A recently prepared shield provides a gyroscope environment of 2.3 × 10 −7 gauss; a factor of nearly 100 improvement over our previous ability using conventional μ-metal shielding.

Comments on the use of London's field dependent orbitals

Some arguments are given here in favour of the use of field dependent orbitals in order to ensure exact gauge invariance of calculated magnetic properties. The critisism recently raised in the literature by several authors against using London's prescription for obtaining translational independent second order magnetic properties is disccused.

A high accuracy gyroscope readout test facility for the relativity gyroscope experiment

We are building an apparatus for Earth-based testing of a gyroscope system to be used in a satellite test of general relativity. The immediate goal is a readout capable of measuring the direction of the gyroscope spin axis to an angular resolution of one arcsecond over a limited range. A combination of SQUID magnetometers and persistent current loops are used to measure the London moment of the spinning superconducting rotor levitated electrostatically. To obtain a trapped flux signal in the gyroscope sufficiently smaller than the London moment signal, the apparatus makes use of a new magnetic field shielding technique for obtaining large superconductor shielded regions below 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-7</sup> gauss.

A high accuracy all-angle gyroscope readout using quantized flux

Means are described to use SQUID magnetometer flux counting and the London moment of a spherical, superconducting gyroscope to read out the gyroscope spin axis direction to an accuracy of at least 23 bits per quadrant. The system is discussed in analogy to optical fringe counting as applied to distance measurement. Several methods of applying both analog and digital SQUID magnetometers to the readout problem are given, as well as limitations on each. Described are two methods of increasing the flux available for measurement: magnetizing the gyroscope with a trapped field, and optimizing readout circuit inductances. Finally, the same principle on which the gyroscope readout is based is applied to a description of a high accuracy, flux counting, digital angle encoder.

A SQUID readout system for a superconducting gyroscope

A design of a read out system for a superconducting gyroscope to be used in an orbiting Gyroscope Relativity Experiment is discussed. The London Moment of the superconducting rotor, which lies along the spin axis of the rotor, will be measured with a SQUID type magnetometer. The SQUID will be built around the gyro rotor, with a very close spacing to give an inductance between 10-8and 10-9Hy. A SQUID of this design should resolve 10-4φ o . The angular resolution of the gyroscope will then be \Delta\theta = 3.5 \times 10^{-3} arc-second, which is sufficient for the intended experiment.

On the London Moment in Rotating Superconducting Cylinders

A microscopic treatment, based on the BCS model of a superconductor, of the magnetic field generated inside a rotating cylindrical superconductor (London moment) is presented. The rotation of the superconductor is treated by considering the superconductor to be in an appropriate gravitational field and Bogolubov's self-consistent field method is used to calculate the current generated by the rotation. The field obtained is found to agree with that predicted by other treatments and observed experimentally.