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We report on experimental studies of magnetic quantum oscillations of the interlayer thermopower in the charge density wave state of the multiband organic conductor $$\upalpha $$ -(BEDT-TTF) $$_{2}\text {KHg}(\text {SCN})_4$$ . The magnetic field is along the direction perpendicular to the conducting layers. The interlayer thermopower or Seebeck effect has been measured in magnetic fields of up to 32 T and temperatures down to 0.5 K. The thermopower magnetic field dependence was measured at two temperatures 0.5 K and 4 K. Quantum oscillations observed in thermopower, at fields above 8 T and temperature 4 K, originate only from the $$\alpha $$ orbit, whereas at 0.5 K the energy spectrum consists of Landau levels of not only the $$\alpha $$ orbit but also the second harmonic as obtained from the fast Fourier transform analysis. In addition to the $$\alpha $$ and 2 $$\alpha $$ frequencies, the oscillation spectrum reveals existence of a low-frequency peak at $$F_{\lambda } = 180$$ T which was previously observed in both magnetoresistance and magnetization. The behavior of thermopower magnetic quantum oscillations amplitude is analyzed using the Lifshitz–Kosevich formula, and the influence of different damping factors such as the temperature, spin splitting, Dingle and magnetic breakdown factors is studied. In addition, we analyze how the second harmonic of fundamental $$\alpha $$ frequency observed at low temperatures in the $$\text {CDW}_0$$ state at field perpendicular to the conducting layers affects the thermopower quantum oscillations amplitude. At low temperature, we find that on entering the low-field state, the scattering rate is observed to increase dramatically. We also observe an apparent increase in the effective mass of first harmonic from $$m_{\alpha }^*=1.7 m_{\text{e}}$$ , in the low-field state to $$m_{\alpha }^*=3.3 m_{\text{e}}$$ , in the high-field state. For the second harmonic, a constant effective mass of $$m_{2\alpha }^*=3.2 m_{\text{e}}$$ is estimated above and below the kink field.

A self-consistent theory of Fermi systems hosting flat bands is developed. Compared with an original model of fermion condensation, its key point consists in proper accounting for mixing between condensate and non-condensate degrees of freedom that leads to formation of a non-BCS gap $$\Upsilon (\mathbf{p})$$ in the single-particle spectrum. The results obtained explain: (1) the two-gap structure of spectra of single-particle excitations of electron systems of copper oxides, revealed in ARPES studies, (2) the role of violation of the topological stability of the Landau state in the arrangement of the $$T-x$$ phase diagram of this family of high- $$T_\mathrm{c}$$ superconductors, (3) the topological nature of a metal–insulator transition, discovered in homogeneous two-dimensional low-density electron liquid of MOSFETs more than 20 years ago.

Any metal–insulator transition (MI transition) in a crystalline material must be a transition from a situation in which electronic bands overlap to a situation when they do not (Mott, Metal–insulator, 2nd edn. Taylor@Francis, London, 1990). For this case the self-consistent equations for the two-band conductor are formulated (cf. Dubovskii, JETP Lett. 99(1):22–26, 2014). The description of the MI phase transition is based on two order parameters. The first one is the material density distribution at the MI boundary $$\rho ({\vec {r}})$$ . The second one is a four-component complex vector in spin space $$\Upsilon ({\vec {r}})$$ . The value $$\Upsilon ({\vec {r}})$$ determines the electron density in the metallic or semimetallic phase in the presence of an external magnetic field. Two different components of the vector describe possible spin states of electrons and holes inserted in the external magnetic field. The solution gives a singular behavior of the surface tension at the MI interface in the vicinity of the MI phase transition. At low temperature quantum oscillations of the surface tension in the magnetic field take place.

The observation of significant magnetoresistance anisotropy of a two-dimensional electronic system in very clean GaAs/AlGaAs heterostructure samples in presence of moderately large perpendicular magnetic fields is a striking example of novel anisotropic behavior in the quantum Hall regime. Anisotropy appears to be the strongest at quantum Hall even-denominator filled states for filling factors ν>4 where several Landau levels are occupied. A possible explanation of these findings is due to the existence of charge density waves that are known to cause interesting phase transitions at high Landau levels. An alternative explanation of this phenomenon is to argue that the strongly correlated electronic system has stabilized in an orientationally ordered anisotropic quantum Hall liquid state. Quantum Monte Carlo calculations with a translationally invariant wave function in which rotation symmetry is broken indicate that this might be the case.

Our Hall bar shape device based on Bi2Se3 nano-plate was fabricated and studied at a dilution temperature with a tilted magnetic field up to 45 Tesla. It is found that, three types of carriers, one of three-dimensional (3D) and two of two-dimensional (2D), were identified by analyzing the angular dependence of Shubnikov-de Haas (SdH) oscillations, which confirmed the coexistence of bulk carriers and band bending induced two-dimensional electron gas in our transport experiment. The co-contributions to quantum oscillations indicated the independence of these states, without smearing out by scattering between each other, which may lay the foundations for detecting topological surface states (TSS) with residual bulk carriers in Bi2Se3.

A history is given of liquid 3He research from the time when 3He first became available following World War II through 1972 when the discovery of the superfluid phases was made. The Fermi liquid nature was established early on, and the Landau Fermi liquid theory provided a framework for understanding the interactions between the Fermions (quasiparticles). The theory’s main triumph was to predict zero sound, which was soon discovered experimentally. Experimental techniques are treated, including adiabatic demagnetization, dilution refrigerator technology, and Pomeranchuk cooling. A description of the superfluid 3He discovery experiments using the latter two of these techniques is given. While existing theories provided a basis for understanding the newly discovered superfluid phases in terms of l>0 Cooper pairs, the unexpected stability of the A phase in the high-P, high-T region of the phase diagram needed for its explanation a creative leap beyond the BCS paradigm. The use of sum rules to interpret some of the unusual magnetic resonance in liquid 3He is discussed. Eventually a complete theory of the spin dynamics of superfluid 3He was developed, which predicted many of the exciting phenomena subsequently discovered.

Shubnikov-de Haas oscillation and cyclotron resonance were studied for high mobility p-type Ge channels in strained Ge/Si1−xGex quantum wells, using pulsed high magnetic fields up to 50 T. Fine quantum oscillations were observed in ρxx. Reflecting the complex Landau level structure in the nearly degenerate valence bands, the Fourier transform of the oscillatory spectra consists of several peaks. Cyclotron resonance was measured at photon energies between 10 and 17 meV. Two well-defined resonance peaks were observed in two samples with different x, resulting in different strains. A large non-parabolicity and large strain dependence of the effective masses were observed.

We have measured the energy gaps in single-layer and bilayer graphene by means of temperature dependent transport experiments in high magnetic fields up to 33 T. They follow the expected Landau level splitting when a finite level width is taken into account. The quantum Hall effect, hitherto only observed up to 30 K, remains visible up to 200 K in bilayers and even up to room temperature in single-layer graphene. Our experiments in single-layer graphene show that the lowest Landau level, shared equally between electrons and holes at zero energy, becomes extremely narrow in high magnetic fields. It is this narrowing, together with the large Landau level splitting in graphene that leads to an extremely robust localization and makes the quantum Hall effect visible up to room temperature. In high magnetic fields (B>20 T) we observe a strongly increasing resistance with decreasing temperature. These results are explained with field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements.

Our study presents the experimental measurements of Aharonov-Bohm (AB) oscillations on single Bi nanowires with diameter d

This review addresses the quantum mechanical nature of the formation and stability of ultrathin metal films. The competition between quantum confinement, charge spilling effects, and Friedel oscillations determines whether an atomically smooth metal film will be marginally, critically, or magically stable or totally unstable against roughening. Pb(111) films represent a special case, not only because of strong quantum oscillations in the stability of two-dimensional thin films but also because of the exceptionally fast coarsening of Pb nanoclusters. The latter appears to be due to the combined effects of size quantization and the existence of a unique mass exchange medium in the form of an unusually dense and highly dynamic wetting layer. The consequences of size quantization on the physical and chemical properties of the films are profound, some of which will be highlighted in this review.

He-3 crystals start to show facets on their surface only at about 100 mK, well below the roughening transition temperature. To find out the reason for this discrepancy, we have performed the first quantitative investigation on the growth dynamics of the faceted and rough surfaces of He-3 crystals in the temperature range of 60-110 mK. We have applied an original method to obtain the variation of the overpressure on the crystal surface by measuring its curvature and height locally using a Fabry-Perot interferometer. The growth of the rough surface was found to be limited by the transport of the latent heat which elaborates in the liquid, in accordance with theoretical predictions (Puech L., et al. in J. Low Temp. Phys. 62:315, 1986; Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990) and previous measurements near the minimum of the melting curve (Graner F., et al. in J. Low Temp. Phys. 75:69, 1989 and 80:113, 1990). The mobility of an elementary step on a facet was shown to be limited by the latent heat transport as well. The values obtained for the step free energy are by two orders of magnitude smaller than at ultra low temperatures, which we show to be the result of quantum oscillations of the solid-liquid interface, which quickly become damped when temperature decreases below 100 mK.

The status of Fermi liquid behavior in weakly magnetic transition metal compounds is reviewed. Single-crystals of the weak itinerant ferromagnets ZrZn2, Ni3Al, and YNi3 display a non-Fermi liquid (NFL) temperature dependence of the resistivity consistent with an inhomogenous ferromagnetic state. But at high-magnetic fields they exhibit quantum oscillations of a Fermi liquid ground state. On the other hand, the helical magnet MnSi displays a pronounced change from a Fermi liquid to NFL resistivity under pressure, where a small regime of partial magnetic order in the NFL regime suggests unconventional textures driven by an unpinning of the helical order. But the stability of the chiral interactions under pressure and magnetic field points at a more complex origin of the NFL behavior.

Quantum oscillation experiments were performed on Θ-(BEDT-TTF)2I3 crystals. In the neat crystals used here, quantum oscillations for the α-orbit (Fα=780T) are already observed at a field of 2T and the magnetic breakdown for the β-orbit (Fβ=4200T) occurs at 3T. The warping of the Fermi-surface of the α-orbit and the β-orbit could be determined to be ΔFα=6.5T and ΔFβ=16T, respectively. Superconductivity at 3.6K was observed in about 30% of the crystals. After tempering at 70° C all crystals show bulk superconductivity at 4K. The structure of this new ΘT-(BEDT-TTF)2I3 phase could be solved.

Shubnikov-de Haas (SdH) oscillations are measured in the organic conductor, κ-(BETS)2FeBr4. In the canted antiferromagnetic (CAF) phase (μ0H

The detailed topology of the Fermi surface of the quasi-one-dimensional conductor (DMET)2I3 was investigated by the magnetooptical measurements. A pair of planar Fermi surface which has higher corrugations of Fourier components was observed. This result seems to suggest that the metallic state of this salt is stabilized by the higher corrugations of the Fermi surface.

We report on electrical transport and magnetization measurements of the quasi-two-dimensional layered superconductor β″-(ET)2SF5CH2CF2SO3. The absence of a resistive peak when a strong magnetic field is aligned along the conducting planes reflects the fact that the material is one of the most anisotropic ET-based metals with possible incoherent interlayer transport. Consequences of this feature may be the enhanced amplitude of magnetic quantum oscillations in the superconducting state and an unusual angulardependent metal-insulator transition.

A very general Hamiltonian which describes the coupling of charge carriers via a spin susceptibility is used to derive a formula for the free energy difference between the superconducting and the normal state of a d-wave superconductor. The formula is then specialized to the nearly antiferromagnetic Fermi liquid (NAFL) model and evaluated numerically. The comparison with specific heat data measured for optimally doped YBa2Cu3O6.95 reveals the necessity to include even contributions far away from the Fermi surface to the free energy. The usual restriction to a narrow shell around the Fermi surface in deriving the free energy formula is proved to be inadequate.

The derivation of the quasiclassical equations considered here depends on the structure of the Gor'kov equations. In a spatially varying situation they couple particle and hole functions with momenta only very near the Fermi surface. The equations are written in a form in which the dependence on the Fermion excitation energy can be integrated out. This produces an envelope function which describes the spatial superfluid structure, but not the oscillations of the full Green's function on the scale of the Fermi wavelength.

The collective response of superconducting thin-film arrays of 300×300 coupled YBa2Cu3O7/Ag weak-link junctions is investigated as a function of external magnetic fields. Our highT c arrays, which were fabricated using electron-beam and photolithography techniques, are based on a substrate-induced defect method. In this method, a square array of thin-film Ag lines produces a two-dimensional lattice of junctions in an overlaying thin-film array of highT c lines. We find that the zero-field resistive transition of the array is governed by a Kosterlitz-Thouless-type transition. Below the super-conducting transition, we observe quantum oscillations in magnetoresistance curves at both integer and half-integer multiples of the flux quantum. These results suggest that long-range phase coherence may be established in large highT c arrays.

Landau quantum oscillations of the magnetization, commonly referred to as the dHvA effect, appear to be a general property of superconductors in the mixed state. This is both intriguing from a fundamental point of view, and fortunate in that it provides a microscopic probe with which to explore the many-body environment of a superconductor. The results of experiments to date can be understood rather well in terms of a general theory of the dHvA effect for an interacting system. We indicate the nature of this and comment on the implications for molecular and oxide superconductors.

Quasiparticle excitations of Landau-Fermi liquids can be described by a Boltzmann-Landau transport equation. We use this property to characterize the Fermi-liquid state of correlated metals, and discuss leading corrections to standard results of Fermi-liquid theory. Our non-Fermi liquid corrections are smaller than the standard results by a factor small(D−1), where D is the dimension of the metal and small represents the expansion parameters of Fermi-liquid theory. We present, as an instructive example, results for the first-order non-Fermi liquid corrections to Korringa's law.

This is the second in a series of papers on a consistent microscopic theory of transverse dynamics in spin-polarized or binary Fermi liquids. We demonstrate when and how the exact theory of Ref. 1 reduces to the conventional theory of highly polarized degenerate low-density Fermi liquids and gases. In the lowest approximations, i.e. for an ideal polarized Fermi gas and in the first (Born) order, our theory assumes the standard form. In the next order in density and/or interaction, the main equations still have a fairly conventional form, though they already contain the peculiar zero-temperature attenuation which is missing in the standard theory. This attenuation can be incorporated into the standard Fermi liquid formalism by adding an imaginary part to a mixed spin component of the Landau interaction function. The source of this imaginary contribution atT = 0 is a pole in the integral expression for the Landau interaction function (the situation is very similar to the case of collisionless Landau damping). In the next order, the standard theory fails completely, and even the form of the equations of transverse dynamics becomes very unconventional. We calculated explicitly the parameters of transverse spin dynamics and the spectrum of spin waves, including the zero-temperature attenuation, and, as a by-product, the polarization dependencies of thermodynamic parameters. The calculation includes a possible non-locality of the interaction. An application of the results to3He↑-4He mixtures covers the non-locality in the direct interaction channel as well as the non-locality and retardation associated with a phonon-mediated part of particles' interaction.

Results of measurements of the low temperature magnetic susceptibility of normal liquid3He have been performed as a function of pressure from which we have calculated the Fermi Liquid parameter F o a .

We have measured the g-shift in superfluid3He-B as a function of temperature above 0.5 mK at a pressure of 1.03 bar, and a frequency of 3.87 MHz. We compare our results with predictions of the quasi-classical and Ginzburg-Landau theories, and present values of the Fermi-liquid parameter F 2 a and the β-parameter β345.

The transverse spin susceptibility for a Fermi liquid in a uniform magnetic field is calculated in the collisionless regime using the Landau theory of Fermi liquids. The singularities corresponding to the l=0 and l=1 spin waves are investigated in pure and dilute3He as a function of the wave vector q up to the threshold of the Landau damping.

The Einstein relation is studied for the diffusivity-mobility ratio of the carriers in ultrathin films of bismuth in the presence of crossed electric and magnetic fields at very low temperatures, and the numerical results are presented for McClure and Choi, hybrid, Cohen, Lax, and ellipsoidal parabolic energy bands by formulating the respective modified carrier energy spectra. It is found that this ratio increases with decreasing film thickness, increasing electron concentration, and decreasing magnetic field. The quantum oscillations of the ratio show up much more significantly in the McClure than in the other models.

Forced flow of a Fermi liquid is studied for a cell geometry consisting of two planes with a separation on the order of mean free path. An approximate transport equation is used to derive an integral equation for the velocity profile, which is solved numerically. Results for the total flux through the cell, which determines the dissipation, are given as a function of the Knudsen number N (ratio of cell thickness to mean free path). Effects of specular reflection at the boundaries are considered. It is found that the dissipation has a minimum at N approximately equal to 1/2, and behaves linearly for N greater than or equal to 3. Implications for present experimentation are discussed.

Using time-independent perturbation theory, we solve the energy eigenvalue equation for a free-electron gas in bismuth with the McClure-Choi modified nonellipsoidal nonparabolic (MNENP) model in the presence of a uniform dc magnetic fieldB. We investigate the effect of the dc magnetic field on the electron density at very low temperatures and compare the numerical results for this new band model with those for the Cohen nonellipsoidal nonparabolic (NENP), Lax ellipsoidal nonparabolic (ENP), and ellipsoidal parabolic (EP) models. The results show that the quantum oscillations of the electron density for the MNENP model show up much more notably than in the NENP, ENP, and EP models. The MNENP model seems better suited than the other models for describing physical phenomena associated with the magnetic field effect in bismuth at very low temperatures.

Stistical mechanics of submonolayer helium films on graphite substrates is conventionally described by site localization models. However, there is evidence from dynamical experiments that the atoms are highly mobile, which leads the authors to believe that a solid state band model might be a more appropriate description. Here Landau Fermi liquid theory for finite temperatures is applied as a test case. It is shown to give the correct asymptotic behavior in both high- and low-temperature limits. By an appropriate quasiparticle interaction simplification, Landau Fermi liquid theory gives good agreement with magnetic susceptibility data for 3He films on Grafoil for all temperatures. The possible inclusion of the substrate is also discussed.

We calculate the effect of pressure on the annular area between the cap and monster of the Fermi surface of cadmium, using an isotropic parallel band model based on the free-electron model and the Stark-Falicov model. The latter gives good agreement with experiment.

The microwave resonance of the magnetic surface states in antimony has been observed at 23 and 70 GHz and the orientation dependences of the resonance fields have been studied in detail in the trigonal-bisectrix and binary-bisectrix planes. Two dominant series and two less prominent series of the resonances have been observed and interpreted in terms of the Fermi surface of antimony. The two dominant series are attributed to the approximately cylindrical portions of the electron and hole Fermi surfaces. The other two are discussed in connection with the nonellipsoidal shape of the Fermi surface of holes. The Fermi velocities of a few representative points of the Fermi surfaces are evaluated. The results are compatible with the velocities estimated from other properties.

Effects of parabolic and nonparabolic band structures on ultrasonic waves propagating at an angle θ relative to the direction of a dc magnetic fieldB in a degenerate semiconductor such as n-type InSb are investigated by using a quantum treatment which is valid at high frequencies and in strong magnetic fields. The interaction of conduction electrons with ultrasonic waves is via deformation-potential and piezoelectric couplings. It is found that the absorption coefficient and change in sound velocity oscillate with the dc magnetic field when ultrasonic waves propagate along the dc magnetic field for both parabolic and nonparabolic band structures. However, when the angle θ is different from zero, the absorption coefficient and change in sound velocity for the parabolic band structure do not oscillate with the magnetic field, due to the reduction of the component of the sound wave vector along the magnetic field, and those for the nonparabolic band structure will still oscillate with the magnetic field, due to the nonlinear effect of the energy eigenvalue equation.

We have solved numerically the induced interaction equations for the magnetic field dependence of the Landau parameters in a strongly correlated Fermi system. The system we studied consists of a single component Fermi liquid with parabolic energy bands and a large on-site repulsive interaction. In the limit of full polarization, the equations have been solved analytically.

Recent experimental studies of the electronic properties of the 3d ferromagnets iron, cobalt, and nickel are reviewed in relation to models for the majority-spin and minority-spin band structures and Fermi surfaces. Attention is focussed on the experimentally observed consequences of spin-orbit coupling; this interaction causes the band structures and Fermi surfaces of these metals to depend on the orientation of the magnetization vector, and it can result in the formation of “spin-hybridized” sheets of the Fermi surface. A discussion is also given of the use of the de Haas-van Alphen effect to search for changes in the ferromagnetic band splitting as a function of temperature.

An attempt is made to investigate theoretically the effective electron mass in ultrathin films of ternary chalcopyrate semiconductors in the presence of crossed electric and magnetic fields on the basis of a newly derivedE-k dispersion relation of the conduction electrons, which includes various types of anisotropies in the energy spectrum. It is found, takingn-CdGeAs2 as an example, that the effective electron mass at the Fermi level depends on the Fermi energy and the magnetic and size quantum numbers, respectively, which is a characteristic feature of cross-fields. It is also observed that the crystal field parameter effectively enhances the numerical magnitude of the effective Fermi level mass. The corresponding results for isotropic parabolic energy bands are also obtained from the expressions derived.

Simultaneous measurement of the cross-sectional areaS of the Bi electron Fermi surface by means of ultrasound giant quantum oscillations and of the cyclotron massm c by means of diamagnetic resonances are presented. The experimental quantity γ(ϑ)=S/(m c/m0) measured in the binary plane shows that neither the ellipsoidal, nonparabolic model nor the restricted nonellipsoidal, nonparabolic model is a good band model for electrons in Bi.

We report measurements on the auperconducting transition temperature T/sub c/ and the normal resistance R/sub n/ of quench-condensed pure and granular aluminum films. The changes of the superconducting transition temperature are characteristically dependent on the coating film thickness and are inversely dependent on the Al film thickness. The observed oscillations of the transition temperature are interpreted in the framework of the theory of quantum oscillations developed by Kagan and Dubovskii.

We develop a systematic procedure for the computation of ground-state properties of dense Fermi liquids, which is based on a Jastrow trial wave function and forms a systematic extension of the hypernetted-chain technique to Fermi statistics. The derivation of the Fermi hypernetted-chain equations is described in detail, and preliminary numerical results are reported.

A simple relationship is derived between the amplitudes of the oscillations in the magnetothermopower and the transverse magnetoresistivity. The relationship is found to be in reasonably good agreement with the available experimental data.

The effect of the parabolic and nonparabolic band structures on the longitudinal and transverse resistivities in a semiconductor such as n-type InSb in the presence of a dc magnetic field directed along the propagation of ultrasound is investigated using a quantum mechanical treatment which is valid at high frequencies and in strong magnetic fields. We discuss this effect in the limiting cases of nondegenerate and degenerate statistics. It is found that the longitudinal and transverse resistivities in nondegenerate materials change with the dc magnetic field for the nonparabolic band structure. For the parabolic model, the longitudinal resistivity does not depend upon the dc magnetic field. In degenerate materials, however, the longitudinal and transverse resistivities for both parabolic and nonparabolic band structures will oscillate with the dc magnetic field. These oscillations are interpreted as the so-called “giant quantum oscillations” which occur in a degenerate electron gas. The dependence on the dc magnetic field arises from the nonlinear effect of the energy bands due to the nonparabolicity of the energy-band structure, and from the resonant interaction between the ultrasound and conduction electrons in degenerate materials.

The longitudinal magnetoacoustic effects on energy bands in the bismuth structure are investigated by using the quantum mechanical treatment which is valid at high frequencies and in strong magnetic fields. It is found that the absorption coefficient and change in sound velocity oscillate with the dc magnetic field for the Cohen nonellipsoidal nonparabolic (NENP) model. However, no oscillations in the absorption coefficient can be observed in strong magnetic fields for both elliposidal nonparabolic (ENP) and ellipsoidal parabolic (EP) models. These oscillations can be interpreted as the so-called “giant quantum oscillations” which arise from the resonant absorption of the sound wave by electrons. It is also found that the absorption coefficient and change in sound velocity increase with the sound frequency for NENP, ENP, and EP models. There exists a large, discontinuous cusp in the high-frequency region for both ENP and EP models. However, no large, discontinuous cusp can be observed for the NENP model. Therefore, from the numerical analysis presented here, it seems that the NENP model will give a much better description of the energy band structure in bismuth than do the ENP and EP models.

Both the real and imaginary parts of the transverse acoustic impedance of normal liquid3He have been measured at excitation frequencies of 10 and 30 MHz, fluid pressures from 0.7 to 27 bar, and temperatures from 3 mK to 1 K. The impedance is obtained from the changes in resonance frequency and Q of a quartz crystal, which is electrically driven to oscillate in a thickness shear mode while immersed in liquid3He. These results are compared with the predictions of Fermi liquid theory, which takes into account two contributions to the impedance: (1) incoherent single-quasiparticle excitations, and (2) the excitation of the collective transverse sound mode. At 0.7 bar, our measurements of the impedance are in agreement with the predictions of Fermi liquid theory and imply that the symmetric Fermi liquid parameterF 2=1.25±0.4 ifF 1=6.3. At higher pressures, we also observe agreement in the region ωτ

Using a sensitive mutual inductance method, measurements of first- and second-order phase transitions in indium microcylinders (2.8–7.6 µm in diameter) have been made. Quantum oscillations in the supercooling field have been observed. The values of κ SC (T/T c )=κ1(T/T c ) derived fromH SC =H C3 have been corrected for both the temperature and the size dependence in the relationship betweenH c2 andH c3 . The results for κ1(T/T c ) from the 7.6-µm sample then agree reasonably well with the temperature dependence of κ1 observed for niobium. However, for the smallest cylinders anomalously low values of κ SC (T/T c ) were obtained nearT c . Very close to the transition temperature second-order (nonhysteretic) phase transitions have been observed and are interpreted in terms of the Ginzburg-Landau theory.

Using the quantum statistical method, a study is made of the effect of a dc magnetic field on the longitudinal and transverse magnetoresistance in the very low-temperature limit, and numerical results are presented for the MNENP, NENP, ENP, and EP models. The results show that the larger the magnetic field, the greater is the amplitude of the oscillations. The amplitude of oscillations in the transverse magnetoresistance is much larger than that in the longitudinal magnetoresistance. There are spikelike discontinuities in the transverse magnetoresistance. The quantum oscillations of both magnetoresistances for the MNENP model show up much more clearly than those for the NENP, ENP, and EP models.

It was found that very carefully prepared Na crystals gave quite large-amplitude de Haas-van Alphen oscillations, as if little or none of the metal had undergone the martensitic transformation in cooling to liquid helium temperatures. Detailed study of the absolute amplitude and the harmonic content of the oscillations gave the ratio of the spin susceptibility to that of a free electron gas as χ/χ0=1.632±0.007, the spin-splitting factor as g=2.636±0.024, and the parameterB0in Fermi liquid theory asB0=−0.241±0.007. These determinations are appreciably more accurate than earlier ones, and are consistent with them and agree well with recent theoretical estimates. In the analysis of the observed oscillations it was necessary to take account of strong magnetic interaction effects, particularly at 0.6 K, and the results provide some evidence for a modified from of the theory of magnetic interaction in the presence of significant phase smearing.

Quantum oscillations in the transverse magnetoresistance of aluminum single crystals were measured at 4.2 K in fields near the [001] direction of up to 50 kOe. The rotation diagrams around two axes, the current axis (θ-rotation) and normal to it (Φ-rotation), were investigated by directly measuring the amplitude of oscillations in steps of about 0.1†. As the field was tilted from [001] by about 2.5† in the Φ plane, the separation of double maxima in the θ rotation diagram changed from 0.8† to 5.0† for the [010] current samples, and from 2.8° to 5.6° for the [110]current samples, and the amplitude of oscillation decreased. A fast oscillation, which had not been observed in conventional dc magnetoresistance measurements, was simultaneously detected near the field direction where the β-orbit oscillations have a maximum amplitude.

An investigation has been carried out of the quantum oscillations of the magnetic susceptibility of an isotropic metal at constant pressure and at low temperatures in strong magnetic fields, when the amplitude of the density of electron states is of the order of the classical value. It is shown that quantum magnetostriction gives rise to a dependence of susceptibility on the ratio of the contributions to the moduli of elasticity due to electrons and to the lattice. The shape of susceptibility oscillations depends substantially on the Fermi-liquid interaction parameters. Conditions are discussed under which the thermo-dynamic stability at the oscillation peaks may be broken. The low-temperature oscillations of the derivative of volume with respect to the magnetic field are also considered. It is shown that at points of magnetic instability, jumps in volume are possible.

The scattering of quasiparticles in a normal Fermi fluid is analyzed within the framework of Landau's kinetic theory, and a generalized Bethe-Salpeter equation for the scattering amplitude is derived. This integral equation accounts for both large and small momentum and energy transfers ; in the forward-scattering limit it reduces to Landau's well-known equation. An explicit expression for the scattering probability is also derived. An off-diagonal generalization of the quasiparticle interaction function f is introduced and its calculation from microscopic theory is discussed. The results are applied to an explicit calculation of the scattering amplitude in a dilute hard-sphere Fermi gas, to second order in the scattering-length parameter kFas, and the calculation is shown to be consistent with symmetry requirements for the scattering of fermions.

A chain model incorporating the periodicity of the incommensurate spin density wave is used to describe the Fermi surface of antiferromagnetic chromium, and is found to give excellent semiquantitative agreement with much of the de Haas-van Alphen data obtained by other investigators. New experimental data are presented which confirm the anomalous features of the transverse magnetoresistance oscillations observed in antiferromagnetic chromium with the spin density wave vector Q∥[001], the current J∥[010], and the magnetic field H in the (010) plane near [100]. These anomalous features are explained with the help of the chain model as arising from a quantum interference effect in the transport of charge along open orbits in the direction of Q. Estimates are obtained from our experimental data for the size of the magnetic breakdown fields that characterize the interferometer trajectories, and hence for the energy gaps on the Fermi surface associated with the spin density wave. Previous theoretical estimates of the magnetic breakdown fields obtained by a perturbation calculation for a model of tight-binding s electrons are in poor agreement with our values.