Showing papers by "Andre K. Geim published in 1997"

Of flying frogs and levitrons

Abstract: Diamagnetic objects are repelled by magnetic fields. If the fields are strong enough, this repulsion can balance gravity, and objects levitated in this way can be held in stable equilibrium, apparently violating Earnshaw's theorem. In fact Earnshaw's theorem does not apply to induced magnetism, and it is possible for the total energy (gravitational+magnetic) to possess a minimum. General stability conditions are derived, and it is shown that stable zones always exist on the axis of a field with rotational symmetry, and include the inflection point of the magnitude of the field. For the field inside a solenoid, the zone is calculated in detail; if the solenoid is long, the zone is centred on the top end, and its vertical extent is about half the radius of the solenoid. The theory explains recent experiments by Geimet al, in which a variety of objects (one of which was a living frog) was levitated in a field of about 16 T. Similar ideas explain the stability of a spinning magnet (Levitron TM ) above a magnetized base plate. Stable levitation

Phase transitions in individual sub-micrometre superconductors

Abstract: The properties of a superconductor are expected to change radically when its size becomes comparable to that of the Cooper pairs, the quasiparticles responsible for superconductivity. The effect of such confinement is well understood for the case of thesuppression of superconductivity by magnetic fields (which gives rise to so-called Little–Parks oscillations of the phase boundary)1,2,3,4. But little is known about what happens in small superconductors in the zero-resistance state, which cannot be probed by resistance measurements. Here we apply a new technique of ballistic Hall magnetometry5 to study the magnetization of individual superconducting discs of diameters down to 100 nm. The superconducting state of these discs is found to be qualitatively different from both macroscopic and microscopic6 superconductors, with numerous phase transitions whose character changes rapidly with size and temperature. This exotic behaviour is due to size quantization of the Cooper-pair motion and resulting transitions between discrete states of the superconducting Bose condensate in a magnetic field.

Ballistic Hall micromagnetometry

Abstract: We report a magnetization measurement technique which allows quantitative studies of thermodynamic properties of individual submicron superconducting and ferromagnetic particles.

Magnetization of mesoscopic superconducting disks

Abstract: Solutions of Ginzburg-Landau equations coupled with three-dimensional Maxwell equations reveal an intriguing magnetic response of small superconducting particles, qualitatively different from the two-dimensional approximation but in agreement with recent experiments Depending on the radius and thickness, first or second order transitions are found for the normal to superconducting state For a sufficiently large radius of the disk, several transitions in the superconducting phase are obtained which correspond to different angular momentum giant vortex states The incorporation of the finite thickness in the calculation is crucial in order to obtain agreement with the position and the size of these jumps, and the line shape and magnitude of the magnetization curves

Fundamental relation between electrical and thermoelectric transport coefficients in the quantum Hall regime

Abstract: The two components S-xx and S-yx of the phonon-drag thermoelectric power in two-dimensional electron gases (2DEGs) are found to be related by S-yx = alpha B(dS(xx)/dB) in the integer and fractional quantum Hall regime. A similar relation exists for electrical resistivity, rho(xx) = alpha B(d rho(xy)/dB), and we show that experimentally the constant alpha is the same in both cases indicating the universal character of such relations for transport in 2DEGs. These results link the behavior of S-yx, which hitherto has not been understood, to that of S-xx and thus opens a new way of explaining this quantity.

The Hall effect of an inhomogeneous magnetic field in mesoscopic structures

Abstract: We present a simulation of the motion of electrons in a mesoscopic Hall bar, scattered by a local inhomogeneous magnetic field. In the low-field regime, the Hall resistance is found to be determined precisely by the average magnetic field in the cross junction, which implies a valuable device application of non-invasive access for measuring magnetic flux, like SQUIDs do, but on a rather small (submicron) scale. The bending resistance is found to depend sensitively on the local magnetic field profile, which may also imply certain device applications, such as detecting the local magnetic properties of small objects. We also discuss briefly the asymmetric effect due to non-identical leads and asymmetric location of the field profile in the cross junction.

Magnetization of mesoscopic superconducting discs

Abstract: Solutions of Ginzburg-Landau eqns. coupled with three dimensional Maxwell eqns. reveal intriguing magnetic response of small superconducting particles, qualitatively different from the two dimensional approximation but in agreement with recent experiments. Depending on the radius and thickness first or second order transitions are found for the normal to superconducting state. For a sufficient large radius of the disc several transitions in the superconducting phase are obtained which correspond to different angular momentum giant vortex states. The incorporation of the finite thickness in the calculation is crucial in order to obtain agreement with the position and the size of these jumps, and the line shape and magnitude of the magnetization curves.

Many-body blockade of resonant tunneling of two-dimensional electrons

Abstract: In high magnetic fields tunneling of two-dimensional electrons requires an extra energy to overcome an effective barrier due to electron-electron interaction. This barrier is clearly visible as a shift of the tunnel resonance to higher biases. The filling factor \ensuremath{ u}=1 marks a surprisingly rapid transition between low-field (quadratically developing shift) and high-field (saturation) regimes. At low temperatures, the many-body shift decays linearly with increasing temperature, which can be attributed to coupling of a tunneling electron to phononlike excitations in the correlated electron system.

Magneto-optical study of correlated electron-hole layers in single-barrier heterostructures

Abstract: We report the low-temperature photoluminescence investigation of a single-barrier GaAs/AlAs/ GaAs p-i-n heterostructure with applied magnetic fields of up to 17 T. Under conditions of forward bias, electrons and holes accumulate at opposite sides of the barrier to form two coupled 2D layers of tunable density. We observe an onset of polarized recombination peaks originating from these layers when the filling factor is immediately lower than two. From the properties of the onset and the shift of the peaks with applied voltage we conclude that we have to take into account the Coulomb interaction between the layers to describe properly the physical situation of the system and we propose the picture of a correlated ground state to explain the experimental findings.

Type of phase transitions in a mesoscopic superconducting disc

Abstract: The Ginzburg–Landau equations coupled with the three-dimensional Maxwell equations are solved for the disc geometry in order to explain recent magnetization experiments. In order to explain the experimental results on a 0.5 μm radius Al disc, we have to assume that the superconducting state stays in the lowest angular momentum giant-vortex state even in regions where it is not the lowest energy state.