Quantum diffusion of muons in metals

We consider the influence of electrons on the quantum diffusion of muons in metals. The temperature dependence of the muon-diffusion coefficient is found.     

Empirical information on quantum diffusion

The applicability of the quantum theory of diffusion to experiments on muon motion in selected metals is examined. Thereby the conventional picture of immediate self-trapping of the muon is employed. Small-polaron hopping of muons at intermediate temperatures seems to be established. There are indications for coherent diffusion in several metals at low temperatures. The quantitative behavior of the diffusion coefficient or transfer rate at low temperatures found in Al and Cu is in disgreement with the theoretical predictions.Many discussions with O. Hartmann, E. Karlsson, L.O. Norlin, T.O. Niinikoski, D. Richter, J.M. Welter, and A. Yaouanc are grateful acknowledged.     

Kinetics and dynamics of muon localisation and trapping

The physics of muons in solids involved three basic questions: Where do muons go? Through which states do they pass during their lifetime? How can we establish mechanisms for these solid state processes? This paper discusses the underlying factors of quantum diffusion, the dynamics of trapping, and the importance of metastable states. A further central factor is the random strain present in even the best crystals, and its character and influence are outlined. I shall summarise the growing evidence for the importance of transient states in semiconductors, metal hydrides and in metals like Al and Cu, and indicate some of the consequences of the non-equilibrium behaviour.     

The use of positive muons in metal physics

The present status of work in metal physics by the new method of “muon spin rotation” is reviewed. This spectroscopy is based on the spin interactions of positive or negative muons and resembles NMR as far as the interpretation of interactions in metals is concerned. The positive muon behaves in several respects as a light isotope of hydrogen in metals. Local properties like site symmetry, local magnetic field, dynamic effects from surrounding spins as well as effects from the diffusion of the particle itself can be measured with high sensitivity.A brief review of the technical aspects is given. The problems of diffusion of light positive particles in metals are discussed, with regard to specific mechanisms at low temperatures, trapping of muons by impurities, etc. The local electronic structure around this kind of impurity in normal metals as well as ferromagnets has been subject to a large nnumber of studies. Other applications include the interaction of muons with other kinds of defects, the study of metal hydrides and measurements on the dynamics of spin glasses.     

New results on diffusion in fcc metals

The Kondo model for the diffusion of light particles in metals has provided a satisfactory explanation for the low temperature diffusion rates for muons in the fcc metals Cu and Al. Explicit experiments which show the strong dependence of muon behaviour on the presence of conduction electrons have now been performed belowT=1 K in Al. Challenging new diffusion studies on fcc metals such as Pt are also presented.     

Inhomogeneous quantum diffusion of muons in solids

This article deals with the problems raised when a muon(muonium) quantum diffusion in a crystal is highly inhomogeneous. It is shown how static disorder arising from the crystal doping influence the diffusion process and drastically changes both the time decay of the polarization function and the temperature dependence of the depolarization rate. The spin depolarization of muons moving in a spatially inhomogeneous defect potential and trapping of particles by the long-ranged traps is studied in detail. Most attention is given to the particle localization and delocalization phenomena resulting in the two-component behavior of muon polarization at low temperature. Finally, the experimental data on muon depolarization in insulators KCl, GaAs, N₂ and superconducting metals Al, V are analyzed.     

The positive muon and the positron as probes of defects

Conclusions A brief but hopefully general comparison has been made between muons and positrons as probes for the study of defects in metals. Since muon experiments are not only more demanding in manpower, cost and availability than positron experiments, they should be carefully designed in light of the knowledge that the muon is extremely sensitive to both intrinsic and extrinsic defects. Initial experiments should provide estimates of the muon diffusion coefficients as a function of sample temperature. High temperature hydrogen diffusion measurements do provide quidelines, although so far most of the observations of muon trapping have been made at low sample temperatures where hydrogen diffusion data do not exist. Given that the diffusion constant is known as a function of temperature, high-purity Fe²⁶ after low temperature electron irradiation is therefore a good candidate to study with muons. Since the defect type and concentration can be controlled in electron irradiated samples, such investigations could confirm the stated values of the diffusion constants in Fe thereby providing a new method for evaluating diffusion coefficients below Stage III in different metals.All the samples should be initially characterized by other less costly techniques to obtain, where possible, the concentration and type of extrinsic and intrinsic defects. Both transverse and longitudinal measurements should be made to unravel the question of different diffusion mechanisms versus defect-, impurity- or self-trapping.Provided that the full capabilities of the muon are utilized and coupled with complementary techniques, i.e., positron annihilation, the muon will constitute a useful new probe in deepening our understanding or defects in metals.Work supported by the US Dept. of Energy under contract DE-AC02-76CH00016.     

Atomic quantum diffusion,tunnelling states and some related phenomena in condensed systems

This article presents a review of some basic problems and results in the theory of atomic quantum diffusion, atomic tunnelling states and some related phenomena in condensed systems: crystals and amorphous materials.General concepts, including the defecton concept, are reviewed in the introduction. The first part of this paper considers the principal ideas, results and problems in the quantum diffusion theory for both underbarrier and overbarrier transitions of atomic particles in solids. Much attention is given to the fundamental role of the interactions between a weakly tunnelling particle and its environment, i.e. defects, other tunnelling particles and thermal fluctuations of atomic configurations.The second part of this review deals with the theory of atomic tunnelling states, their peculiar origin and low-temperature effects and, particularly, the origin and effects of the intrinsic atomic low-energy excitations in amorphous materials. The third part of this article discusses some related low-temperature phenomena. Some experimental data associated with the phenomena under consideration are presented. Finally, some actual problems of the theory are discussed in the Concluding Remarks.The review contains a discussion of results mainly coming to our attention by the summer of 1982.     

Muon diffusion and level crossing in copper

We have studied the quantum diffusion of positive muons in pure copper over the temperature range 12 mK≤T≤150 K using weak longitudinal field μSR. Below 150 K, this technique has proved to be the most sensitive to the muon hop rate. Our final results for the behaviour of the muon hop rate are well explained within the framework of theories for the quantum diffusion of light interstitials in metals of Kondo, Yamada and others. In addition, the use of level-crossing resonance has allowed us to measure the electric quadrupole interaction strength (and sign) of the copper nuclei, ω_Q= −3.314(7) μS⁻¹. These results have enabled us to show that the muon occupies the same octahedral site at all the temperatures studied, ruling out the possibility of metastable muon sites contributing to any significant portion of the muon polarization.     

Diffusion and localization of muons at very low temperatures

Conclusion The measurements of muon diffusion below 2 K have provided many new data and ideas in the metals Cu and Al, although the understanding is far from complete. Especially intriguing are theAlMn data with their very clear temperature and concentration dependence over a wide temperature range. My feeling is that we now approach well-defined situations where the basic properties of muon diffusion and localization can be seen. Still I would hesitate to draw any definite conclusions regarding the existence of e. g. coherent motion, and I strongly hope that the existing theories of low-temperature diffusion can be further developed, hopefully yielding less extreme results for muons in the very low temperature range.     

A geminate recombination model for photoluminescence decay in plasma-deposited amorphous Si:H

We develop a model of geminate electron-hole recombination, including tunnelling and diffusion, to account for photoluminescence decay in amorphous semiconductors. The model correctly predicts the shape of the decay, the luminescence quantum efficiency, and the microscopic electron mobility.     

Quantum coherent effects in Anderson insulators

During the last two decades quantum interference effects have been extensively studied in the transport properties of diffusive systems such as metals and semiconductors. When the spatial disorder in these systems exceeds a critical value the electronic wavefunctions are localized and their ground state is insulating (the Anderson transition). At finite temperatures charge transport in this phase involves phonon-assisted tunnelling between localized states. This mode of transport is purely quantum mechanical and has no classical analogue. Anderson insulators are therefore the paradigmatic system for studying interference phenomena of electron waves in random media. In this paper we discuss the question of quantum coherence in Anderson insulators and review some of the experimental manifestations of interference phenomena in their transport properties.     

The dynamics of triple-well trapped Bose-Einstein condensates with atoms feeding and loss effects

In this paper, we consider the macroscopic quantum tunnelling and self-trapping phenomena of Bose-Einstein condensates （BECs） with three-body recombination losses and atoms feeding from thermal cloud in triple-well potential. Using the three-mode approximation, three coupled Gross-Pitaevskii equations （GPEs）, which describe the dynamics of the system, are obtained. The corresponding numerical results reveal some interesting characteristics of BECs for different scattering lengths. The self-trapping and quantum tunnelling both are found in zero-phase and ：r-phase modes. Furthermore, we observe the quantum beating phenomenon and the resonance character during the self-trapping and quantum tunnelling. It is also shown that the initial phase has a significant effect on the dynamics of the system.     

Theory of incoherent hydrogen diffusion in metals

Hydrogen migration in a one-dimensional model of the bcc lattice is examined using the double-time Green functions, for temperatures at which the migration mechanism is mainly due to the thermally activated tunnelling of a proton. In deriving the coefficient of incoherent hydrogen diffusion, allowance is made for the lattice distortion around the hydrogen and for the two-phonon scattering processes. It is shown that the observed temperature break in the activation energy of incoherent hydrogen diffusion in bcc metals is the result of the change in the mechanism responsible for an elementary diffusion process near the Debye temperature, anmely, it is the result of the transition from “passive” to “active” transport.     

The investigation of defects in metals with positive muons

It is shown that the trapping of positive muons by defects in metals attracting positively charged particles may be used to investigate such defects in considerable detail by spin relaxation of positive muons.     

Reversible Carriers Tunnelling in Asymmetric Coupled InGaN/GaN Quantum Wells

Temperature-dependent photoluminescence （PL） and time resolved photoluminescence （TRPL） are performed to study the PL characteristics and carrier transfer mechanism in asymmetric coupled InGaN/GaN multiple quantum wells （AS-QWs）. Our results reveal that abnormal carrier tunnelling from the wide quantum well （WQW） to the narrow quantum well （NQW） is observed at temperature higher than about lOOK, while a normal carrier tunnelling from the NQW to the WQW is observed at temperature lower than 100 K. The reversible carrier tunnelling between the two Q Ws makes it possible to explore new types of temperature sensitive emission devices. It is shown that PL internal quantum efficiency （IQE） of the NQW is enhanced to about 46% due to the assistant of the abnormal carrier tunnelling.     

The quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole

Applying Parikh's quantum tunnelling method, this paper has studied the quantum tunnelling radiation of Schwarzschild de Sitter black hole with a global monopole. The result shows that the tunnelling rates at the event horizon and the cosmological horizon are related to Bekenstein--Hawking entropy and the derived radiation spectrum is not precisely thermal when considering energy conservation and self-gravitation interaction.     

Measuring macroscopic diffusion of positive muons in metals

Conclusions We have discussed some schemes for measuring the diffusion coefficient for positive muons in metals, using diffusion over macroscopic distances. The method offers some promise of yielding diffusion information over wider temperature ranges and a greater variety of metals than the presently used technique. The major difficulty in applying the laminate scheme will be fabricating suitable, well-characterized targets that are thick enough to stop a significant fraction of the ⁺ beam. The use of a surface (i.e., 4 MeV) ⁺ beam appears most promising, but this brings with it formidable technical problems in heating and cooling the targets. We may hope that these problems will be attacked vigorously and effectively in the near future.Research performed under the auspices of the U.S. Department of Energy.     

Effects of electron correlations,dynamical screening and plasmon excitations on muon diffusion in metals

An investigation is made of the effects of electron-electron interaction on muon diffusion in metals. It is shown that electron-electron correlation plays an important role in the motion of muons. The equation-of-motion method is used to calculate the correlation function. It is shown that electron correlations effectively reduce the muon hopping rate at low temperatures. It is also shown that the effect of dynamic screening increases the hopping rate. We found that due to plasmon excitation, the hopping rate is reduced by a factor which can be as larger as one to two orders of magnitude.     

Exciton tunnelling in ZnCdSe quantum well/CdSe quantum dots

Exciton tunnelling through a ZnSe barrier layer of various thicknesses is investigated in a Zn_0.72Cd_0.28Se/CdSe coupled quantum well/quantum dots (QW/QDs) structure using photoluminescence (PL) spectra and near resonant pump-probe technique. Fast exciton tunnelling from quantum well to quantum dots is observed by transient differential transmission. The tunnelling time is 1.8, 4.4 and 39 ps for barrier thickness of 10, 15 and 20 nm, respectively.