Kaner Cyclotron Resonance Research Articles

What is what in the nanoworld: a handbook on nanoscience and nanotechnology

Preface to the Second Edition. Preface to the First Edition. Source of Information. A. From Abbe's principle to Axbel' - Kaner cyclotron resonance. B. Grom B92 protocol to Burstein-Moss Shift. C. From cage compound to cyclotron resonance. D. From D'Alembert equation to Dzyaloshinskii-Moriya interaction. E. From (e,2e) reaction to Eyring equation. F. From Fabry-Perot resonator to FWHM (full width at half maximum). G. From gain-guided lasers to gyromagnetic frequency. H. From habit plane to hyperelastic scattering. I. From ideality factor to isotropy (of matter). J. From Jahn - Teller effect to Joule's law of electric heating. K. From Kane Model to Kuhn-Thomas-Reiche sum rule. L. From lab-on-a-chip to Lyman series. M. From Mach-Zender interferometer to Murrell-Mottram potential. N. From NAA (neutron activation analysis) to Nyquist-Shannon sampling theorem. O. From octet rule to oxide. P. From PALM (photoactivable localization microscopy) to pyrrole. Q. From Q-control to qubit. R. From Rabi flopping to Rydberg gas. S. From Saha equation to synergetics. T. From Talbot's law to type II superconductors. U. From ultraviolet photoelectron spectroscopy (UPS) to Urbach rule. V. From vacancy to von Neumann machine. W. From Waidner-Burgess standard to Wyckoff notation. X. From XMCD (X-ray magnetic circular dichroism) to XRD (X-ray diffraction). Y. From Yasukawa potential to Yukawa potential. Z. From Zeeman effect to Zundel ion. A list and a presentation of Scientific Journals which contain the stem Nano in their title. Abbreviations for the scientific journals which appear as sources in the text. Appendix - main properties of intrinsic (or lightly doped). Semiconductors.

The power absorption and the penetration depth of electromagnetic radiation in lead telluride under cyclotron resonance conditions

Cyclotron resonance absorption in n- and p-type PbTe was observed by Nii and was analysed under classical skin effect conditions. When the values of DC magnetic field corresponding to peaks are plotted against the field directions, a close fit is obtained between the calculated and observed results based on the assumption of a 〈1 1 1〉 ellipsoids of revolution model for the both conduction and valance band extrema. From the best fit m t =0.024 m 0 and 0.03 m 0 for the transverse effective masses and K= m l/ m t=9.8 and 12.2 for the anisotropic mass rations are obtained for the conduction and valance band, respectively. The observed absorption curve shows weak structures at low magnetic field. They are supposed to be due to second harmonics of Azbel'–Kaner cyclotron resonance. However, it turns out to be unnecessary to introduce other bands to explain the experimental results. The applicability of the classical magneto-optical theory is examined by calculating the power absorption coefficient and penetration depth as a function of DC magnetic field.

On the 〈110〉 cylindrical fermi surface and the anisotropic cyclotron resonance peak in lead

The angular dependence of the Azbel'-Kaner cyclotron resonance peaks in lead is analyzed. All of the anisotropies in the cyclotron resonance peaks originating from the 〈110〉 arms of the Fermi surface in the third band are shown to be characterized by a set of three effective masses with one negative, corresponding to a hyperboloidal shape of the Fermi surface. The splitting of the cyclotron resonance peaks found by Khaikin and Mina [ Sov. Phys.-JETP 15, 24 (1962)] is also explained by the set of masses in terms of the approximately 3.2 degree misalignment of the (001) sample surface.

On the angular dependence of the cyclotron resonance peaks in lead

The angular dependence of the Azbel'-Kaner cyclotron resonance peaks in lead is analyzed in terms of Shockley's formula. All of the anisotropies in the cyclotron resonance peaks originating from the 〈110〉 cylindrical arms of the Fermi surface measured in the four parallel field geometries by Ônuki et al. [ J. Phys. Chem. Solids 38, 419 (1977)] are shown to be characterized by the set of the effective masses ( m 1, m 2, m 3) = (1.18, 0.244, −8.71) m along the crystal directions ([001], [110], [110]) and their equivalents. This means that the cyclotronic motion in the {110} planes is electron-like and its orbits are elliptic in k-space characterized by masses ( m 1, m 2) while the heli-axial motion is hole-like. The physical origins of this unusual behavior are discussed in direct-lattice space.

Cyclotron Resonance in Deformed Lead Crystals

The effect of dislocations on the electron relaxation time in Azbel'-Kaner cyclotron resonance has been studied in plastically bent lead crystals. The relaxation rate τ-1 in bent and annealed samples depends almost linearly on dislocation densities. It is compared with those determined from the electrical resistivity and the de Haas-van Alphen effect.

Study of the electron-phonon interaction in cadmium using high frequency Azbel'-Kaner cyclotron resonance

The frequency and temperature dependence of the effective mass, m*, and relaxation time, tau , of electrons on the lenticular orbit on the 3rd band Fermi surface sheet of cadmium have been obtained from high-frequency Azbel'-Kaner cyclotron resonance experiments. The measurements were carried out in the frequency range omega /2 pi =80-460 GHz (wavelengths of 4-0.6 mm) and in the temperature range T=1.5-7K. In agreement with theory the effective masses vary quadratically with frequency and temperature.

Electron-phonon relaxation time in mercury

Electron scattering times determined by Azbel'-Kaner cyclotron resonance in mercury are discussed in terms of the electron-phonon interaction. Anisotropy in the electron-phonon relaxation time is explained in terms of an orbital αk2(ω)Fk(ω) function which describes the electron-phonon interaction and the phonon spectrum. AT5 temperature dependence of the electron-phonon relaxation frequency is also considered.

Cyclotron resonance in mercury: Temperature dependence and the electron-phonon interaction

The temperature dependence of the effective cyclotron mass and the electronic relaxation time in mercury have been investigated by Azbel'-Kaner cyclotron resonance using a microwave frequency of 35 GHz. The measurements cover the temperature range 1.15 to 2.5 K in 0.05-K intervals. Two orbits are studied with the magnetic field in the binary-bisectrix crystallographic plane of the sample surface. For both orbits, the cyclotron mass ${m}^{*}$ is found to increase as the temperature squared, in good agreement with the prediction of the theory of the electron-phonon interaction. The relative mass increments at 2.5 K with respect to 0 K are 4.2% for one orbit and 3.6% for another. These different values indicate that the effect is dependent upon the cyclotron orbits, and are discussed in terms of a directional phonon spectrum. The experimental relaxation rate varies more rapidly than the cube of the temperature. The variation is found to be proportional to ${T}^{5.2\ifmmode\pm\else\textpm\fi{}0.3}$, which confirms previous experimental results, and indicates that the low-energy portion of the ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})F(\ensuremath{\omega})$ spectrum is nonquadratic.

Azbel'-Kaner Cyclotron Resonance at Far-Infrared Frequencies: General Theory and Experiments on Ga

Azbel'-Kaner Cyclotron Resonance at Far-Infrared Frequencies: General Theory and Experiments on Ga

Cyclotron Resonance and the Cohen Nonellipsoidal Nonparabolic Model for Bismuth. III. Experimental Results

Complete measurements of the anisotropy of the central-orbit cyclotron effective masses by Azbel'-Kaner cyclotron resonance have been taken at a frequency of 24.03 GHz and a temperature of 1.15 \ifmmode^\circ\else\textdegree\fi{}K for the magnetic field in the three crystallographic planes of Bi. Deviations of up to 10% from ellipsoidal behavior were observed for the electron-effective-mass anisotropies. Except in one instance, the various effective-mass anisotropies give a good fit to the Cohen nonellipsoidal nonparabolic (NENP) model and the fit is clearly superior to the Lax ellipsoidal nonparabolic model fit. The ratio of the Fermi energy to the $L$-point band-gap energy, $\frac{{E}_{F}}{{E}_{g}}$, was determined from fitting the NENP model and found to be 1.5\ifmmode\pm\else\textpm\fi{}0.4, in good agreement with other measurements. The fit to the NENP model also indicated that $\frac{{m}_{2}}{{m}_{2}}$ is approximately 1, implying that the $L$-point valence and conduction bands have identical parameters. The cyclotron effective masses agree within 3% with the values obtained by Edel'man and Khaikin, and disagree by as much as 30% with the values obtained by Kao. Quantum oscillations of the microwave surface impedance similar in nature to de Haas-Schubnikov oscillations have also been observed, but periods arising from the large cross-sectional areas could not be detected and no conclusions regarding the NENP model could be made. Magnetoplasma oscillations due to standing Alfv\'en waves have also been observed. The mass-density values derived from these measurements agree with the values obtained by other investigators. However, the carrier concentration derived from the Alfv\'en-wave periods differs by nearly 12% with the value derived from the Azbel'-Kaner cyclotron-resonance measurements. This difference may be due to nonellipsoidal effects.

Probing the Electron-Phonon Interaction in Potassium by Far-Infrared Cyclotron Resonance

To probe the electron-phonon interaction in potassium, Azbel'-Kaner cyclotron resonance has been observed at four frequencies in the far infrared (29.69, 32.12, 45.407, and 58.25 ${\mathrm{cm}}^{\ensuremath{-}1}$). The experiments were performed on a novel reflection cavity spectrometer with balanced homodyne detection driven by a c.w. far-infrared laser. Signals are seen for $\mathrm{E}\ensuremath{\parallel}\mathrm{H}$ and $\mathrm{E}\ensuremath{\perp}\mathrm{H}$ at 29.69 and 32.12 ${\mathrm{cm}}^{\ensuremath{-}1}$, but only for $\mathrm{E}\ensuremath{\perp}\mathrm{H}$ at 45.407 and 58.25 ${\mathrm{cm}}^{\ensuremath{-}1}$. Two effects distinguish cyclotron resonance in potassium in the infrared from that observed at microwaves. First, since the resonant electron does not escape the skin depth before the infrared field changes phase, the resonances suffer from retardation effects and are no longer amenable to the usual Azbel'-Kaner or Chambers theory of cyclotron resonance. Second, there is a strong enhancement of the electron-phonon relaxation rate due to the large density of phonon states available to scatter the excitations when the laser frequency is near the Debye frequency, $\ensuremath{\approx}75$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The line-shape analysis, used to extract the electron-phonon coupling parameter $\ensuremath{\lambda}$, does not reproduce all of the observed features. In particular, it does not reproduce absorption features on the high-field side of the subharmonic resonance which are shown to be related to the cyclotron waves that propagate across the magnetic field in the bulk. Nevertheless, by focusing attention on the breadth and position of the leading edge of the resonance, we can extract an electron-phonon $\ensuremath{\lambda}$. $\ensuremath{\lambda}$ is found to be 0.11\ifmmode\pm\else\textpm\fi{}0.02 and agrees with that determined by the temperature dependence of the phonon-limited dc resistivity.

High-Frequency Cyclotron Resonance in Lead and the Electron-Phonon Interaction

The frequency and temperature dependences of the electron-phonon interaction have been investigated in lead by the Azbel'-Kaner cyclotron-resonance technique. The experiments have been performed in the unusual millimeter and submillimeter microwave band from 70 to 500 GHz, corresponding to the wavelength 4 to 0.6 mm. In this frequency band the photon energy value, $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}2$ meV, is near the typical phonon energy in lead. The experiments were performed in the temperature range from 1.5 up to 6\ifmmode^\circ\else\textdegree\fi{}K. The effective mass ${m}^{*}$ and relaxation time $\ensuremath{\tau}$, measured on two different types of orbits, are frequency and temperature dependent. These dependences are directly related to the electron-phonon interaction. For both orbits ${m}^{*}$ is found to increase as the temperature squared and the frequency squared. The maximum relative increases are $\frac{{m}^{*}(5.4^{\ensuremath{\circ}}K)}{{m}^{*}(0^{\ensuremath{\circ}}K)}=1.03$ and $\frac{{m}^{*}(457 \mathrm{GHz})}{{m}^{*}(0 \mathrm{GHz})}=1.008$. The relaxation frequency ${\ensuremath{\tau}}^{\ensuremath{-}1}$ dependence varies as the cube of both the temperature and the frequency. The theoretical dependences on $T$ and $\ensuremath{\omega}$ are thus well confirmed, but the order of magnitude of the frequency effects is smaller than predicted.

Azbel'-Kaner cyclotron resonance in zinc

Azbel'-Kaner cyclotron resonance has been studied in the three principal crystal planes of zinc at 34 GHz and temperatures between 1.5 and 4.2 K. The results are in general agreement with those of other workers. Two new mass series have been observed which have been assigned to an orbit on the first band caps and a limiting point orbit on the inside ring of the monster. The temperature dependence of the lifetime has been determined for the central orbit on the third band lens in the plane normal to the c axis. The temperature dependent part of the lifetime was found to satisfy the relation 1/ tau th=cT3 where c=(8.70+or-0.38)*106 s-1K-3. The lineshape for this resonance was also found to be in excellent agreement with Chambers' theory of lineshapes in AKCR. A noticeable anisotropy in the mass enhancement was found for orbits on the third band lens. Anomalies in the surface impedance associated with the propagation of short wavelength cyclotron waves have also been observed.

Acoustic Geometric and Acoustic Cyclotron Resonances in Gallium

Acoustic geometric and acoustic cyclotron resonances in high-purity single crystals of gallium were investigated at 1.3 \ifmmode^\circ\else\textdegree\fi{}K and in the normal geometry where the magnetic field is perpendicular to the wave vector of the ultrasonic waves. These waves, polarized longitudinally and of frequencies in the range 60-400 MHz, were propagated along the three principal crystallographic axes $a$, $b$, and $c$ of gallium. The extremal dimensions of the Fermi surface in the ${k}_{a}{k}_{b}$, ${k}_{b}{k}_{c}$, and ${k}_{c}{k}_{a}$ planes, obtained by measuring the periodicity $\ensuremath{\Delta}(\frac{1}{H})$, of the geometric-resonance oscillations, are compared with the predictions of the augmented-planewave and pseudopotential models. The results are in good agreement with the values given by the pseudopotential model. A map of effective masses in the $\mathrm{ab}$, $\mathrm{bc}$, and $\mathrm{ca}$ planes, obtained from acoustic-cyclotron-resonance experiments, is given. These data are compared to those of Moore, who used the Azbel'-Kaner cyclotron resonance (AKCR). Some branches of effective masses were found which have not been observed by AKCR and, reciprocally, many resonances observed by AKCR were not observed in the present work.

Azbel'-Kaner Cyclotron Resonance and Magnetic Surface Levels in Beryllium

Azbel'-Kaner Cyclotron Resonance and Magnetic Surface Levels in Beryllium

Experimental Study of Retardation Effects in Cyclotron Resonance

When the electron transit time through the skin layer becomes comparable to the rf period, Azbel'-Kaner cyclotron resonance is substantially altered. As Drew has shown explicitly, the retardation effect leads to an exponentially decreasing amplitude of successive subharmonics and a progressive change of the resonance line shape. We present and analyze data on a particular non-free-electron-like orbit on the Fermi surface of Ga, which at frequencies in the range 8-54 GHz shows strong retardation. The data confirm the expected exponential decay and related line-shape changes, and give evidence for their frequency and mean-free-path dependence.

Retardation Effects in Azbel'-Kaner Cyclotron Resonance

Corrections to the Azbel'-Kaner theory of the magnetic-field-dependent surface impedance of metals have been calculated. The results illustrate the effects of the finite transit time of the electrons in their passage through the skin layer. The cyclotron-resonance line shapes are modified from the Azbel'-Kanel results for both the high-(${\ensuremath{\omega}}_{c}\ensuremath{\tau}$) and low-(${\ensuremath{\omega}}_{c}\ensuremath{\tau}$) limits. The bearing of these results on experimental determinations of carrier effective masses and relaxation times are discussed. Finally, the background signals from the nonresonant electrons are calculated for an arbitrary cutoff angle for specular reflection of the electrons at the surface.

Azbel'-Kaner Cyclotron Resonance in Mercury

Azbel'-Kaner cyclotron-resonance experiments have been carried out with two very flat mercury crystals at a microwave frequency of 34.28 GHz and a temperature of 1.2 \ifmmode^\circ\else\textdegree\fi{}K. Cyclotron effective masses of ten orbits were measured with an error of less than 2%. Five of the orbits (labeled $\ensuremath{\mu}\ensuremath{\gamma}$, ${\ensuremath{\gamma}}_{2}$, $\ensuremath{\kappa}$, ${\ensuremath{\mu}}_{2}$, and ${\ensuremath{\epsilon}}_{1}$) were observed for the first time by Azbel'-Kaner cyclotron resonance. The cyclotron masses of $\ensuremath{\alpha}$ orbits in the electron lenses were represented by an interpolation scheme which gives the mass for any field direction. This interpolation scheme showed that the second-zone electron lens is tipped 3\ifmmode^\circ\else\textdegree\fi{} out of a (100) plane of the reciprocal lattice toward the [111] direction and that there is a 9% anisotropy of the mass in the (100) plane. A similar interpolation scheme describing the frequencies of de Haas-van Alphen (dHvA) oscillations, which correspond to the $\ensuremath{\beta}$ arms of the first-zone hole surface, is also presented. The oscillations were caused by two effects which could not be separated: quantum oscillations of the microwave surface impedance and dHvA torque. Methods for accurately determining the crystal orientation within the experimental apparatus, using the symmetry of the electron-lens masses and of signal peaks arising from open-orbit induced-torque effects, are presented. Cyclotron resonance with the magnetic field inclined to the sample surface is discussed. Several effects indicate anomalous penetration of the electromagnetic field into the metal.

Azbel' - Kaner Cyclotron Resonance in Arsenic

Azbel' - Kaner cyclotron resonance has been measured in arsenic single crystals at 1.15 \ifmmode^\circ\else\textdegree\fi{}K using a microwave frequency of 24 GHz. The cyclotron effective masses are given as a function of the direction of the magnetic field for the binary-bisectrix plane and for the binarytrigonal plane. Data are also given for a third plane whose orientation is not quite the binarytrigonal plane. The high $\ensuremath{\omega}\ensuremath{\tau}$ of the crystals has permitted the measurement of several mass series which have not been detected in previous cyclotron-resonance experiments, in particular, the hole-mass series in the binary-bisectrix plane and the low-mass series ($0.03{m}_{0}$) corresponding to the necks of the hole surface. Also, as a result of the much higher sample quality, previously reported cyclotron masses have been measured more accurately for these crystal orientations. In addition, quantum oscillations in the surface impedance and cyclotron resonance were measured in the bisectrix-trigonal plane by tilting the magnetic field out of the binary-trigonal plane. Neither effect has been previously reported. One set of masses can be described by three or six nearly prolate spheroids having principal effective masses ${m}_{1}=0.134{m}_{0}$, ${m}_{2}=0.140{m}_{0}$, and ${m}_{3}=1.35{m}_{0}$, each tilted (+84.5 \ifmmode\pm\else\textpm\fi{} 1.5)\ifmmode^\circ\else\textdegree\fi{} from the trigonal axis. A second set of masses is described by three or six ellipsoids having principal effective masses ${m}_{1}=0.146{m}_{0}$, ${m}_{2}=0.068{m}_{0}$, and ${m}_{3}=0.946{m}_{0}$, each tilted (+37.3 \ifmmode\pm\else\textpm\fi{} 1.5)\ifmmode^\circ\else\textdegree\fi{} from the trigonal axis. These results are in general agreement with previous work. A comparison with de Haas---van Alphen data indicates that the first set corresponds to electrons (three ellipsoids) and the second set corresponds to holes (six ellipsoids). A new polishing solution is also given for each crystallographic plane, as well as a discussion of four methods for fitting the data.

Short-Wavelength Cyclotron Waves and Electron Correlations in Potassium

Observations of the Azbel'-Kaner cyclotron resonance spectra in thick slabs of high-purity potassium metal have revealed additional oscillations on the high-field side of the fundamental resonance. These anomalies in the surface impedance correspond to turning points of the cyclotron-wave dispersion curve at wavelengths which are short compared to orbit radii. The behavior of the signals agrees quite well with free-electron theory and confirms the extremely oscillatory character of the extraordinary mode. The absence of deviations due to Fermi-liquid effects in our experiments is investigated, and in particular we show under what circumstances the Fermi-liquid parameter ${A}_{1}$ can be determined from these signals.