Israel D. Vagner: Research Activity

1 Two-dimensional de Haas-van Alphen effect and diamagnetic phase transitions:

1.1 Theory of two-dimensional de Haas-van Alphen effect

In [12] for the first time the finite temperature quantum statistics and thermodynamics of a two-dimensional electron gas under strong magnetic field was presented in a closed analytical form. It was shown how the sharp magnetic field dependence of the free energy and magnetization is governed by the motion of the chemical potential between the adjacent Landau levels. The theory was aimed to substitute the famous Landau-Lifshits-Kosevich formula, which was extremely operative in three dimensional systems and is inapplicable to 2DEG. Experimental study of dHvA effect in 2DEG, performed in GHMFL (Wiegers et all. 1997) has shown an excellent agreement with the theory developed in [12,32].

1.2 Ideally Conducting Phases and Condon Domains

Another aspect treated in [12] is the physics of diamagnetic phase transitions in 2DEG (the Condon domains). It was discovered there that the in 2DEG the Condon domains fix thermodynamically the chemical potential between the adjacent Landau levels, thus creating a quantum Hall effect state within each domain. This discovery stimulated intense experimental activity in nonlinear de Haas van Alphen in 2DEG (see J.J. Quinn, Nature, 1985) and renewed theoretical [27,86] and experimental (Gould, PRL 1997) interest in conventional 3D Condon domains.

2 Prediction and detailed theory of quantum oscillations in Q2D Cu-O superconductors

In [20] it was conjectured, for the first time, that the dHvA effect can be operative in studying the Fermi surface of newly discovered (at that time) High-Tc superconductors. This semi-qualitative paper was followed by a series of papers (see [79] for the references), where nonlinear Gor'kov equations for quasi-two-dimensional superconductors in high magnetic field where solved for the first time. During the last decade this paper was followed by numerous publications of several theoretical groups in different countries and has stimulated a very productive experimental activity in GHMFL.

3 Integer and Fractional Quantum Hall effects

3.1 IQHE

In [18] a scaling theory is presented which explains the D. Tsui and Chang experiments of the similarity between the QHE coefficients.
In [33] the relativistic and scaling invariance of QHE medium is demonstrated and possible experimental verification of its exactness are suggested.

3.2 FQHE

An early microscopic treatment of the even-denominator problem in FQHE is presented in [16,26]. It is shown there that 2DEG is unstable towards the phase separation in the vicinity of certain filling factors. This theory is instrumental in clarifying some aspects of the optics experiments in FQHE regime in GHMFL by G. Martinez group.

3.3 Spin-excitons and Skyrmions

In [62] it is shown that, at n = 1, in a periodic potential the energy gap in the spin-exciton spectrum may vanish. This will result in new cooperative phenomena as exciton condensation in 2DEG.
In [69] a microscopic theory of spin-exciton condensation in to a skyrmion phase is constructed.

4 Prediction and detailed theory of the anomalies in Hyperfine interaction in quantum Hall effect systems

In [11] the anomalous (exponential in inverse temperature, instead of generally believed linear in temperature) dependence of the nuclear spin-lattice relaxation in two-dimensional metals under strong magnetic fields was predicted. In [21] this theory was applied to the heterojunctions and it was shown there that T₁^-1(H) is similar to r_xx(H) in quantum Hall effect regime. This paper has stimulated enormous experimental activity, starting with the confirmation by K. Von Klitzing group (1990) of this similarity. Development of the experimental technics in this field resulted in discovery of Skyrmions (Barret 1995), specific heat anomaly (Bayot et. all. 1996) etc. The review on main theoretical achievements in this subject, [71].

5 Mesoscopic and Nanoparticles physics

5.1 Nano-Electrons

In [47] the spectrum of an electron on a nanosphere under magnetic filed was obtained and used to calculate the thermodynamics of the electron gas confined to a nano-sphere. Recently this theory is generalized for nanoparticles of arbitrary shape with the axial symmetry [88] . The obtained results open the way for analytical and numerical studies of the level statistics, integrability and chaos in these systems.

5.2 Levitating Mesoscopics

In [82] a new mesoscopic system is suggested and theoretically studied: a multi-ring grating under a He film creates an electric potential in 2D electron, levitating above the He surface, which results in a mesoscopic multi-ring 2DEG structure. This system has several advantages over standard solid state multi-ring structure as one can gradually vary the main parameters (ring radius, impurity concentration etc.) It is shown that single-channel rings are feasible which will permit to study the mesoscopic phenomena in 1D Luttinger liquid limit.

5.3 Meso-Nucleo-Spinics

In [85] a new branch of nonequilibrium mesoscopic physics was theoretically developed. Namely, it was shown there that sufficiently strong nuclear spin polarization, combined with the spin-orbit interaction, may result in a new type of the Berry phase of electron wave functions, thus providing the possibility of observing the Bohm-Aharonov and week localization kind phenomena even in the absence of external magnetic field. Importance of this effect for the reading off the information in a quantum computing devices is shown in [80].

5.4 Quantum Computers

The mechanism of the indirect interaction between the nuclear spins in QHE systems developed in [67] is applied, in [80], where a model for a quantum computer is proposed. This model is considered as one of the most practically realizable in the literature on this subject, and has stimulated various developments (see e.g. B. Kane, Nature 1998).

Last updated 23-Nov-05.
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