The motion of conduction electron in solids has long been a subject of interest and fascination. In a crystalline or ordered material, where the potential is periodic, the conduction electron are well described by Bloch theory which the electron wave function are specially extended throughout the system. The electrical con-duction in such a system can be described by the Boltzmann transport. The results of the theory are that at high temperatures the resistivity is dominated by phonon scattering and at low temperature the resistivity is dominated by the impurities. The Boltzmann equation predicts, in the low temperature regime, a resistivity which is given by
ρ(T ) = ρe+ AT5, (2.1)
where A is a constant, and ρe is the residual or impurity resistivity, which is caused by collision of electron with impurities. Since the impurities are treated as static, the residual resistivity is temperature independent. It is also well known that in the formalism of Boltamann transport theory the impurity concentrations are assumed to be extremely low. In the extremely disordered limit, the scattered electrons can be described by superpositions of Bloch waves.
In 1958, Anderson(1) pointed out that,when the randomness or disorder in the potential is sufficient high, i.e., in the strong disorder limit, the electron wave
functions may be altered from the Bloch forms. He showed that the electron wave would be localized in regions where the potential is particularly suitable.
Thouless(2; 3) and co-workers(4; 5) had tempted to formulate a scaling descrip-tion of the localizadescrip-tion problem. They predicted that in one dimensional system, once the residual resistance of a wire exceeded a critical value of the order of ~/e2 (∼ 4KΩ), hence the electronic states would be localized. Several experiments had been reported to check this prediction.
In 1979, Abrahams, Anderson, Licciardello, and Ramakrishnan(6) based on those arguments of Thouless and co-works(2; 3; 4), successfully constructed a scaling theory of localization. They concluded that, in the presence of any amount of impurities, there would be no extended states in two dimensional systems.
They showed that the conductance would undergo a crossover from a logarithmic decrease to an exponential decrease with increasing the linear dimension of the system. In three dimensional system, the scaling theory predicted that the metal-insulator transition would be continuous.
The localization theory is a single particle description. Considering many body effects, Al’tshuler and Aronov(7; 8) pointed out that the interaction be-tween the conduction electrons, in the presence of weak disorder, would have strong effects on the transport properties. They studied the Coulomb inter-actions between screened, two dimensional electrons whose motion is diffusive.
They found the interactions between electrons are greatly enhanced in this case, causing a logarithmic singularity in the density of states in turn results in a non-ohmic conductivity which is similar to that predicted by localization.(9;10) This theory is commonly referred to as electron-electron interaction theory. Such a singularity in the density of states led to very similar effects on the electronic transport properties as those predicted by the weak localization theory.
There have been a number of experimental studies in the past several years of various types of disordered conductors, which have been aimed at testing these predictions. The behavior of the resistance as a function of temperature agreed qualitatively with the theory. These experiments have also shown that the be-havior is strongly dependent on the system dimensionality.(11; 12;13; 14)
To differentiate between the weak localization effects and the electron-electron interaction effects, magnetoresistance measurements are extremely important.
Hikami, Larkin, and Nagaoka,(15) and Al’tshuler and co-worker(9; 10; 16) con-sidered the effects of a magnetic field on the behavior of resistivity at low tem-peratures. These studies showed that localization and interaction respond very differently to a magnetic field. It turns out that localization effects result in an anisotropic magnetoresistance in a very low magnetic field regime. Interaction ef-fects, on the contrary, result in an isotropic magnetoresistance, but the magnitude of this magnetoresistance is important only at significantly high magnetic fields.
It was also found that the effects of spin-orbit scattering and spin-spin scattering can be very important. If the spin-orbit scattering is strong enough, it can cause an effect with a sign opposite to that of localization.(17) That is, it cause the resis-tance to decrease as the temperature is lowered, rather than increase. This effect is known as anti-localization. A number of very successful measurements have been performed to test these predictions.(17; 18; 19;20;21;22;23) In particular, magnetoresistance measurements have been used to infer the electron inelastic scattering time, the spin-obit scattering time, and the spin-spin scattering time, and hence the overall contribution to the zero field behavior from localization an be determined.
It is well established that one can extract the electron-phonon scattering time, electron-electron scattering time, spin-orbit scattering time, and spin-spin scattering time from magnetoresistivity measurements. There have been many experiments done in this direction to obtain these phase breaking times which have proved that this is a very reliable method. There have been many experi-ments using this method to obtain the phase breaking times in different dimen-sional systems. Bergmann does a lot of works on spin-orbit inelastic scattering time.(24;25;26) Lin and Giordano(27;28) study the electron-electron scattering time in 1D and 2D in AuPd films. Their results are good agreement with theoreti-cal predictions and widely accepted. In experimental side, Lin and Wu(29;30;31) and many scientists study the electron-phonon inelastic scattering time, τep, in many different systems(32; 33; 34; 35). They point out that the τep ∝ T−p where p ranges from 2 to 4. In theoretic side, Sergeev and Mitin establish a phonon-drag theory which can explain experiment results well.(36; 37; 38)
Lin and Giordano perform systematic measurements of inelastic scattering times in several AuPd films. They point out the the saturated inelastic times
depend on the sheet resistance, R¤, and conclude that the observed saturation inelastic scattering time cannot be explained in terms of magnetic scattering. Af-ter that, more and more experimental works observe the same behaviors. In 1997 Mohanty(39) collects many experimental results and points out that experiment always observe a constant τφ when temperature is sufficiently low. The satu-ration of τφ occurs in both one and two dimensional metal and semiconductor mesoscopic structures. The observation of τφ saturation immediately triggered many experimental and theoretical groups asking whether the saturation might be universal in all material systems and dimensions.
The electron dephasing time τφ is one of the most important quantities gov-erning quantum interference phenomena. Recently, the behavior of the dephasing time near zero temperature, τφ0 has attracted many experimental(39; 40; 41; 42;
43; 44; 45; 46; 47) and theoretical(48; 49; 50; 51; 52; 53; 54; 55; 56) attentions.
One of the central themes of this renewed interest is concerned with whether τφ0 should reach a finite or an infinite value as temperature approach 0 K. The con-nection of the τφ0 behavior with fundamental condensed matter physic problems, such as the validity of the Fermi-liquid picture, has been intensively addressed.
Conventionally, it is accepted that τφ0should reach an infinite value in the presence of only electron-electron and electron-phonon scattering.
For a long time, the saturation behavior of τφ0 has often been ascribe to a finite spin-spin scattering time, due to the presence of a tiny amount of magnetic im-purity in the sample. Such a finite scattering rate will eventually dominate over the relevant inelastic scattering in the limit of sufficiently low temperatures. The idea of magnetic scattering induced dephasing immediately became widely ac-cepted. Hikami greatly shaped the current understanding of the effect of spin-flip scattering on the weak localization magnetoresistance. According to the descrip-tion, magnetic scattering can lead to decoherence between the two time-reversed wave traversing a closed loop, resulting in a suppression of weak localization and related quantum interference effects. Generally, the spin-spin scattering time is taken to be essentially independent of temperature, compared with the relatively strongly temperature-dependent electron-phonon and electron-electron scatter-ing times. With this Understandscatter-ing, it is natural to interpret any saturated τφ0 measured in the experiments in terms of a finite spin-spin scattering time.
The Saclay-MSU group has measured the dephasing time of quasiparticles in several noble metal narrow wires. They found that the τφ varies as T−2/3 which is the prediction of one dimension Nyquist electron electron scattering time down to 40 mK. Once, several ppm magnetic impurities are doped into the wires, measured inelastic scattering times show a weak temperature dependent at low temperature. They concluded that a saturation of τφ occurs only in wires that contain a small amount of magnetic impurity.(57; 58)
In contrast to the conclusion reached by the Saclay-MSU group discussed above, Mohanty et. al.,(45;59) have tested and argued for a non-magnetic origin for the saturation behavior of τφ0. Mohanty et. al., first study very pure Au wires (containing less than 1 ppm of magnetic impurities), finding that there is always a saturation of τφ0. From these measurements, they find realizes that both the values of τφ0 and the onset temperature of saturation could be tune by adjusting the sample parameters such as the wire length, resistance, and diffusion constant. To explore this idea, Webb et. al., repost further measurements on several carefully fabricated Au wires, whose onset temperature of saturation is indeed push down to very low temperatures. Webb et. al., argue that τφ0 should still saturate in these wires at a temperature ¿ 40 mK.
To clarify the effect of magnetic scattering on τφ, Webb et. al., ion implant several ppm of Fe impurities in their pure Au wires. They find that τφ decreases by more than an order of magnitude upon adding these impurities, but remains temperature dependent down to 40 mK. Therefore, they concludes that the sat-uration behavior of τφ0 observed in pure Au wires can not be due to magnetic scattering. In addition, they point out that saturation behavior of τφ0 is also of-ten observed in semiconductor mesoscopic structures. Since such structures are thought to contain only the smallest concentration of magnetic impurities, they conclude that the widely observed saturation must be universal and can not be simply due to magnetic scattering. It should be noted that the sample properties of the Au wires studied by Webb and co-workers were essentially similar to those studied by Saclay-MSU group.
Beside of the scattering forms discussed above, dynamic structure defeat is another source of saturation of τφ0.(60;61; 62;63;64;65;66; 67;68) The simplest realization of the dynamic structure defeat is that of an atom which may sit in a
doublet well potential, the two wells being localized along a line directed between their centers which are separated by a displacement. In the absence of coupling to a bath of excitations, the lowest two states of the atom are, approximately, the positional eigenstates associated with harmonic oscillations within either well.
The next level usually has energy above the barrier between the well minima and therefore is not localized to either well. Atoms may move between the two positions on quantum-mechanic tunneling. In the process, the atom directly tunnels through the potential barrier between the wells. Because of the thermal activated transitions, this process must dominate at sufficiently low temperatures.
The original motivation for studying such a model was the observation of log-arithmic anomalies in the resistivity of metallic glasses.(11;69) Most of the works also only focused on the resistivity, specific heat, and susceptibilty. Only a few works on electron dephasing time are reported. Lin and co-workers study the annealing effects in a lot of three-dimensional polycrystalline disordered metal films.(70) They perform systematic measurements of τϕ on several series of sput-tered and subsequently annealed AuPd and Sb thick films. Such controlled an-nealing measurements are crucial for testing theoretical models of dephasing that invoke the role of magnetic scattering and dynamical defeats.
In the first part of the thesis, I will discuss our experimental observation of temperature dependence of dephasing time in Cu93Ge4Au3films. Our results indi-cate that a very short electron dephasing time possessing very weak temperature dependence around 6 K, followed by an upturn with further decrease in temper-ature below 4 K. The low tempertemper-ature upturn is progressively more pronounced in more disordered samples. Resistance is logarithmic increase with decreasing temperature in wide temperature range and it is insensitive to magnetic field up to 15 T. In the thesis, we will discuss the temperature dependent resistance at different magnetic field and temperature dependent dephasing time in series of samples with different levels of disorder on weak localization effect, Kondo effect, and two-level system effect. Synthesizing all discussion, we can rule out all others inelastic scattering and make sure out observed low temperature dephasing time is from two-level system scattering. This is the first systematic work discussing the disorder dependence with low temperature temperature dephasing times of dynamic structure defeat effect.