Théorie BCS | EPFL Graph Search

La théorie BCS est une théorie de la supraconductivité qui fut proposée en 1957 par John Bardeen, Leon Neil Cooper, et John Robert Schrieffer. Elle explique la supraconductivité par la formation de paires d'électrons (paires de Cooper) sous l'effet d'une interaction attractive entre électrons résultant de l'échange de phonons. Pour leur travail, ces auteurs obtinrent le prix Nobel de physique en 1972. Origine de l'attraction entre les électrons Il est possible de comprendre l'origine de l'attraction entre les électrons grâce à un argument qualitatif simple. Dans un métal, les électrons chargés négativement exercent une attraction sur les ions positifs qui se trouvent dans leur voisinage. Ces ions étant beaucoup plus lourds que les électrons, ils ont une plus grande inertie. Pour cette raison, lorsqu'un électron est passé près d'un ensemble d'ions positifs, ces ions ne reviennent pas immédiatement à leur position d'équilibre d'origine. Il en résulte un excès de charges pos

Development of a Millikelvin Scanning Tunneling Microscope for Applications in Ultra High Vacuum and High Magnetic Fields

Maximilian Assig

In this thesis we discuss the realization of a scanning tunneling microscope (STM) operating at temperatures below 20 mK. This is accomplished by attaching the STM to a dilution refrigerator. We can apply high magnetic fields up to 14 T perpendicular and 0.5 T parallel to the sample surface. A full ultra high vacuum (UHV) preparation chamber is attached to the cryostat allowing in situ preparation of the samples to investigate. This setup allows us to investigate low temperature phase transitions in solids and offers the possibility for ultimate energy resolution tunneling spectroscopy measurements on the atomic scale. The concept of realizing the mK-STM is given. A main point of concern was the design of the STM unit. The choice of materials should be well adapted for the use at very low temperatures and in high magnetic fields. A special concern are thermal expansion coefficients and thermal conductivity. In addition, we analyzed the variation of the tip sample distance for a given external excitation for our STM design and two variations of the Besoke-STM by using a one dimensional mass spring model. This gives us the possibility to extract an optimization criterion for our design to limit the response of the tip sample distance to vibrations that are transmitted to the STM. The external damping mechanism, which ensures a low mutual vibration level of the STM as well as the grounding concept for the electronics is explained. To characterize the STM at operating temperatures of 1.5 K, 800 mK and 15 mK we measured topography images of Au(111) and Cu(111) surfaces. This allows us to extract the stability between tip and sample. A statistical analysis of the noise in the tunneling current without activated feedback loop yields a stability of 2.7±0.1 pm in a frequency range f ≈ 0.03 – 25 Hz at 800 mK. To verify if tip and sample are cooled efficiently, we measured the temperature at their positions with additional thermometers. We achieved 17 mK at the tip and 20 mK at the sample position, respectively. The energy resolution of the STM setup was verified by taking tunneling spectra between a superconductor and a normal conducting metal. These spectra could be fitted using the BCS theory of superconductivity. From those ts we can extract the upper limit of the effective temperature of the electrons which is Teff = 87 ± 3 mK for our best measurement. This corresponds to an energy resolution of 3.5 kbTeff = 26 ± 1 µeV. Further, the tunneling conductance between two superconductors was investigated. A sub-gap structure, which can be related to Andreev reflections in asymmetric tunneling junction was observed. In addition, at zero bias voltage a peak due to the Josephson effect can be measured. Side peaks with intensities that scale with this zero bias conductance peak appear most probably due to the interaction of Cooper pairs with the electromagnetical environment in which the junction is placed. Investigating the dependence of the conductance between a superconducting tip and a normal conducting sample on externally applied magnetic fields leads to the appearance of shoulders in the coherence peaks. These shoulders shift linearly with the external magnetic field. Such an effect has been measured for planar tunnel junctions and can be explained with the lifting of the spin degeneracy of the quasi-particle density of states in a superconductor. It was observed for the first time by Meservey, Tedrow and Fulde. The fact, that we are now able to prepare STM tips showing the Meservey-Tedrow-Fulde effect enables us to measure the absolute spin polarization at EF with atomic resolution.

EPFL2011

Hydraulic fracture growth in quasi-brittle materials

Dong Liu

Hydraulic fracturing is a technique often used in the oil and gas industry to enhance the production of wells in low-permeability reservoirs. It consists of fluid injection at a sufficiently large injection rate to create and propagate tensile fractures inside the rock formation. The growth of a hydraulic fracture is a highly non-linear moving boundary hydro-mechanical problem. Many physical processes get tightly involved and influence the fracture growth, such as the elastic deformation of the material, fracture surface creation, viscous fluid flow inside the propagating fracture, and fluid leak-off into the solid principally. The linear hydraulic fracture mechanics (LHFM) theory describes well this coupled process, with adequate comparisons between predictions and observations in the linear elastic medium. However, deviations from LHFM predictions have been reported at the laboratory and field scales in some cases, notably a larger fluid pressure and a shorter fracture length. These deviations are often associated with the non-linear nature of rock fracture deformation. However, the impact of these material non-linearities on the coupled problem of hydraulic fracture propagation has not been fully understood. In this context, this thesis investigates numerically and experimentally the effect of the quasi-brittle nature of rocks on hydraulic fracture growth. We first solve the propagation of a hydraulic fracture using a power-law fracture length-dependent fracture energy to model macroscopically the effect of an enlarging process zone. The use of Gauss-Chebyshev quadrature and barycentric Lagrange interpolation techniques reduces the hydraulic fracture propagation problem to a set of non-linear ordinary differential equations. We find that this increasing apparent toughness leads to a slower fracture growth compared with constant toughness LHFM solutions and a faster transition to the toughness dominated regime. We show that the solution can be approximated by the self-similar constant toughness solutions with the instantaneous toughness value. We then explore the impact of the quasi-brittle nature of rocks by using a cohesive zone model in combination with elastohydrodynamic lubrication to simulate HF growth. We notably account for fluid cavitation at the fracture tip and the effect of fracture roughness on flow. The fracture growth finally converges toward the LHFM predictions but deviate from LHFM predictions when the cohesive zone cannot be neglected. These deviations indicate an increase of energy dissipation. The additional energy dissipation compared with LHFM mainly comes from the viscous fluid flow in the rough fracture process zone and is larger for a larger ratio between the in-situ stress and the material peak cohesive stress. We finally discuss HF experiments performed on two impermeable rocks under different confinement and injection conditions. We notably develop an inversion technique to reconstruct the fracture front geometry using diffracted waves recorded via an array of 32 sources and 32 receivers. We find that transmitted waves attenuate before the arrival of the fracture front estimated from diffracted waves, indicating the existence of a fracture process zone of centimeters extent. This fracture process zone is found to be comparable with the fracture extent, thus implying an important artifact of laboratory HF experiments performed in quasi-brittle rocks on finite-size centimeter-decimeter samples.

EPFL2021

Microscopic theory for the Markovian decay of magnetization fluctuations in nanomagnets

Ioannis Rousochatzakis

We present a microscopic theory for the phonon-driven decay of the magnetization fluctuations in a wide class of nanomagnets where the dominant energy is set by isotropic exchange and/or uniaxial anisotropy. Based on the Zwanzig-Mori projection formalism, the theory reveals that the magnetization fluctuations are governed by a single decay rate omega(c), which we further identify with the zero-frequency portion of the associated self-energy. This dynamical decoupling from the remaining slow degrees of freedom is attributed to a conservation law and the discreteness of the energy spectrum and explains the omnipresent monoexponential decay of the magnetization over several decades in time, as observed experimentally. A physically transparent analytical expression for omega(c) is derived which highlights the three specific mechanisms of the slowing-down effect which are known so far in nanomagnets.