Study of transport in a strongly correlated electron system

Date: 2 April 2021 1. SURNAME: ESWARAN FIRST NAME: MUKESH MIDDLE NAME(S): 2. DEPARTMENT/SCHOOL: Vancouver School of Economics 3. FACULTY: Arts 4. PRESENT RANK: Emeritus Professor SINCE: 1 July 2018 5. POST-SECONDARY EDUCATION University or Institution Degree Subject Area Dates University of British Columbia Ph.D. Economics 1978 1981 University of British Columbia M.A. Economics 1977 1978 Louisiana State University Ph.D. Physics 1971 1975 Indian Institute of Technology M.Sc. Physics 1969 1971

活動報告 University of British Columbiaでの実習報告

The potential, the density of electrons and charged donors, the charge per unit area in the channel and the subband levels are calculated for a high electron mobility transistor (HEMT) under equilibrium conditions. As a new theoretical foundation a modified local density approximation (MLDA) is used which is a convenient and sufficiently exact tool for a quantitative treatment of semiconductor heterostructures. It is shown that a proper consideration of quantum effects and of the influence of charged donors are necessary for obtaining reliable quantitative results. The channel charge is calculated in dependence of important geometrical, material and technological parameters including the temperature and the results are compared with those of other authors. Especially the influence of the thickness of the doped AlxGa1−xAs layer and of an undoped AlxGa1−xAs spacer is discussed carefully.



In der vorliegenden Arbeit werden das Potential, die Dichte der Elektronen und geladenen Donatoren, die Flachenladung im Kanal und die Subbandenergien fur einen Transistor mit hoher Elektronenbeweglichkeit (HEMT) berechnet. Als neue theoretische Grundlage hierfur wird eine modifizierte Naherung der lokalen Dichte (MLDA) verwendet, die sich als bequeme und ausreichend genaue Methode zur quantitativen Beschreibung von Halbleiter-Heterostrukturen erwiesen hat. Es wird gezeigt, das eine angemessene Berucksichtigung der Quanteneffekte und des Einflusses der geladenen Donatoren unerlaslich sind, um zuverlassige quantitative Ergebnisse zu erhalten. Die Kanalladung wird in Abhangigkeit von geometrischen, technologischen und Materialparametern einschlieslich der Temperatur berechnet, und die Ergebnisse werden mit denen anderer Autoren verglichen. Insbesondere wird der Einflus der Dicke der dotierten AlxGa1−xAs-Schichten und einer undotierten AlxGa1−xAs-Zwischenschicht eingehend diskutiert.

Calculation of the electronic properties of a high electron mobility transistor. I: Equilibrium conditions

A quantum mechanical calculation of the conductivity of a simple model of a superionic conductor which considers short range interactions betweetn the mobile ions is p’resented. This model yields results which depend strongly on the nuclear spin on the mobile ion. In principle, this isotope dependent conductivity could lead to isotope separation. In practice, ignored interactions between the mobile ions and the nonmobile ions in the lattice could mask this effect.

Isotope effects in superionic conductors

Photon-photon bound state in a magnetic medium

The dc conductivity of a system of strongly interacting electrons in narrow-band materials is calculated using the large-interaction limit of the Hubbard model with impurities. A generalized-moment method allows for the calculation of the conductivity for arbitrary electron and impurity concentrations as a function of magnetization. The conductivity vanishes for a half-filled band, and in the absence of impurities it increases approximately linearly with the number of empty or doubly occupied sites. In the absence of electron-electron scattering the impurity-limited conductivity varies linearly as the product of the hole and electron concentrations. Numerical results indicate that to within 3% a generalized Matthiessen's rule holds; the resistivities due to impurities and electron-electron interactions are additive. An upper bound on the conductivities of strongly interacting electrons in narrow-band materials is obtained. The model of a planar antiferromagnet is used to explain the anisotropic conductivity of nickel sulfide below the N\'eel temperature.

Electrical conductivity in narrow-band materials

Interactions between strongly correlated electrons (or holes) and spin waves are investigated with the aid of a simple physical model. The model is the large-interaction limit of the Hubbard model with an additional ferromagnetic Heisenberg interaction between nearest-neighbor singly occupied sites. We find that even though there is no obvious electron-magnon attraction in the model, electron-magnon bound states exist for some crystal structures.

Electron-Magnon Bound States

All the three-electron wave functions and energy levels are obtained for the one-dimensional Hubbard model. The second and third virial coefficients for the system are calculated exactly. The virial expansion is converted into an electron density expansion which appears to converge much better than the virial series. The two-particle and three-particle contributions to the specific heat, entropy, intra-atomic correlation function, and magnetic susceptibility of the system are obtained and presented graphically.

Low-density thermodynamics of the Hubbard chain

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Mukesh Eswaran

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Papers

Electrical conductivity in narrow-band materials

Electron-Magnon Bound States

Low-density thermodynamics of the Hubbard chain