Quantum oscillations in confined and degenerate Fermi gases. I. Half-vicinity model

We propose an analytical model for the prediction and accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate Fermi gases. Our model considers only half-vicinity states of Fermi level. We show that the half-vicinity model quite accurately estimates quantum oscillations depending on confinement and degeneracy. Periods of quantum oscillations are even analytically expressed for one-dimensional case. Furthermore, similarities between functional behaviors of total occupancy variance and conventional density of states functions at Fermi level are discussed.     

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula,this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container.The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed.It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy.It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects,such as the nonextensivity of the system,the anisotropy of the pressure,and so on.     

Electrons as harmonic oscillators in degenerate semiconducting quantum dots

We show that for a generic sample of a semiconductor inside a parabolic quantum dot, this sample is degenerate so that a typical case relative to an n-type semiconductor is considered. In our study, by using a quantum-box approach, Fermi velocity is calculated for evaluating later the corresponding Fermi level in order to determine the aforementioned degeneracy. In addition, some considerations upon optical emission are made.     

Subband structure of a two-dimensional electron gas formed at the polar surface of the strong spin-orbit perovskite KTaO3

We demonstrate the formation of a two-dimensional electron gas (2DEG) at the (100) surface of the 5d transition-metal oxide KTaO3. From angle-resolved photoemission, we find that quantum confinement lifts the orbital degeneracy of the bulk band structure and leads to a 2DEG composed of ladders of subband states of both light and heavy carriers. Despite the strong spin-orbit coupling, our measurements provide a direct upper bound for the potential Rashba spin splitting of only Δk(parallel)}~0.02 ?(-1) at the Fermi level. The polar nature of the KTaO3(100) surface appears to help mediate the formation of the 2DEG as compared to nonpolar SrTiO3(100).     

Parametric optimum analysis of an irreversible Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas

An irreversible model of an Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas is established, which is composed of two isothermal and two isobaric processes. The influence of both the quantum degeneracy and the finite-rate heat transfer between the working fluid and the heat reservoirs on the performance of the cycle is investigated, based on the theory of statistical mechanics and thermodynamic properties of an ideal Fermi gas. The inherent regeneration losses of the cycle are analyzed. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the cycle is optimized for a given power input. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal regions of the coefficient of performance and power input are determined. Especially, the optimal performance of the cycle in the strong and weak gas degeneracy cases and the high temperature limit is discussed in detail. The analytic expressions of some optimized parameters are derived. Some optimum criteria are given. The distinctions and connections between the Ericsson refrigeration cycles working with the Fermi and classical gases are revealed.      

Two-dimensional transport and strong spin-orbit interaction in SrMnSb_2

We have carried out magneto-transport measurements for single crystal SrMnSb_2. Clear Shubnikov-de Haas oscillations were resolved at relatively low magnetic field around 4 T, revealing a quasi-2D Fermi surface. We observed a development of quantized plateaus in Hall resistance(R_(xy)) at high pulsed fields up to 60 T. Due to the strong 2D confinement and layered properties of the samples, we interpreted the observation as bulk quantum Hall effect that is contributed by the parallel 2D conduction channels. Moreover, the spin degeneracy was lifted leading to Landau level splitting. The presence of anisotropic g factor and the formation of the oscillation beating pattern reveal a strong spin-orbit interaction in the SrMnSb_2 system.     

Reaching fermi degeneracy in two-species optical dipole traps

We propose the use of a combined optical dipole trap to achieve Fermi degeneracy by sympathetic cooling with a different bosonic species. Two far-detuned pairs of laser beams focused on the atomic clouds are used to confine the two atomic species with different trapping strengths. We show that a deep Fermi degeneracy regime can be potentially achieved earlier than Bose-Einstein condensation, as discussed in the favorable situation of a 6Li-23Na mixture. This opens up the possibility of experimentally investigating a mixture of superfluid Fermi and normal Bose gases.     

Self-consistent perturbation theory of the anderson model: Ground state properties

The zero temperature limit of the self-consistent perturbation theory of a degenerate Anderson impurityin a metal is partially solved with analytical methods. In particular, the energy scales relevant to the system are made explicit and closed expressions are derived for the local level propagator around the Fermi energy and for the dynamical susceptibility. Results are compared with what is known from Fermi liquid theory. The argument that the theory is valid for large degeneracy is disturbed by certain pathologies.Supported by DFG through the research program of Sonderforschungsbereich 125 (Aachen-Jülich-Köln)     

All-optical production of a degenerate Fermi gas

We achieve degeneracy in a mixture of the two lowest hyperfine states of 6Li by direct evaporation in a CO2 laser trap, yielding the first all optically produced degenerate Fermi gas. More than 10(5) atoms are confined at temperatures below 4 microK at full trap depth, where the Fermi temperature for each state is 8 microK. This degenerate two-component mixture is ideal for exploring mechanisms of superconductivity ranging from Cooper pairing to Bose-Einstein condensation of strongly bound pairs.     

Effect of degenerate carriers on Si band gap narrowing

Various mechanisms causing band gap narrowing in strongly heated silicon are considered. In the high-temperature region, it becomes necessary to use Fermi–Dirac quantum statistics to describe carriers, since the silicon chemical potential appears in the valence band and in the conduction band at high carrier concentrations. It is shown that carrier degeneracy under conditions of sufficiently strong heating of intrinsic semiconductor causes strong band gap narrowing. The obtained values of band gap narrowing are compared to experimental results.     

Merging of single-particle levels in finite Fermi systems

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate. The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied. In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations. Implications of this finding are discussed for nuclear, solid-state, and atomic systems. The text was submitted by the authors in English.     

Spectrum of bound fermion states on vortices in <Superscript>3</Superscript>He-B

We study subgap spectra of fermions localized within vortex cores in ³He-B. We develop an analytical treatment of the low-energy states and consider the characteristic properties of fermion spectra for different types of vortices. Due to the removed spin degeneracy the spectra of all singly quantized vortices consist of two different anomalous branches crossing the Fermi level. For singular o and u vortices the anomalous branches are similar to the standard Caroli-de Gennes-Matricon ones and intersect the Fermi level at zero angular momentum yet with different slopes corresponding to different spin states. On the contrary the spectral branches of nonsingular vortices intersect the Fermi level at finite angular momenta which leads to the appearance of a large number of zero modes, i.e. energy states at the Fermi level. Considering the ν, w and uvw vortices with superfluid cores we show that the number of zero modes is proportional to the size of the vortex core.     

Spin splitting induced by spin-orbit interaction in chiral nanotubes

We show that chiral tubes present spin splitting at the Fermi level in the absence of a magnetic field, whereas achiral tubes preserve spin degeneracy, as evidenced by tight-binding electronic structure calculations with the inclusion of spin-orbit interaction. These remarkably different behaviors of chiral and nonchiral nanotubes have a symmetry origin, which may provide a global explanation to recently reported spin-dependent transport experiments which were in apparent contradiction.     

铁热稠密物质状态方程的相对论Hartree-Fock-Slater计算

 本文在球元胞、中心力场、相对论Fermi统计近似下，用平均原子模型计算铁热稠密物质在任意温度和密度下的单电子能级和状态方程。这种算法以Zink的解析拟合势作为初始势，求解满足Wigner-Seitz边界条件的Dirac-Slater径向波函数方程。通过简并度是密度的连续函数，考虑了大密度的压致电离效应。这样从另一个角度考虑了电子的能带结构。     

Splitting of the electronic states near EF in A4C60 compounds (A = alkali metal)

The electronic structure of A₄C6₀ compounds (A=Na, K, Cs) has been studied using electron energy-loss spectroscopy. Both the low energy loss functions and Cls core excitation measurements reveal a strong splitting of the electronic states near the Fermi level in comparison with K₃C₆₀ or K₆C₆₀. This splitting indicates a lowering of the high degeneracy of the C₆₀ molecular orbitals due to a broken symmetry ground state and/or the opening of a correlation gap in these systems.     

Intra-Landau-level cyclotron resonance in bilayer graphene

Interaction driven integer quantum-Hall effects are anticipated in graphene bilayers because of the near degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate k3/2 dispersion. We speculate on the possibility of unusual localization physics associated with these modes.     

Direct transition between a singlet Mott insulator and a superconductor

We argue that a normal Fermi liquid and a singlet, spin-gapped Mott insulator cannot be continuously connected, and that some intermediate phase must intrude between them. By explicitly working out a case study where the singlet insulator is stabilized by orbital degeneracy and an inverted Hund's rule coupling, mimicking a Jahn-Teller effect, we find that the intermediate phase is a superconductor.     

Kondo resonance for orbitally degenerate systems

Formation of the Kondo state in the general two-band Anderson model has been investigated within the numerical renormalization group calculations. The Abrikosov-Suhl resonance is essentially asymmetric for the model with one electron per impurity (quarter filling case) in contrast with the one-band case. An external magnetic (pseudomagnetic) field breaking spin (orbital) degeneracy leads to asymmetric splitting and essential broadening of the many-body resonance. Unlike the standard Anderson model, the "spin-up" Kondo peak is pinned against the Fermi level, but not suppressed by the magnetic field.     

Conductivity of 2D multi-component electron gas partially-quantized by magnetic field

The 2D semimetal consisting of heavy holes and light electrons is studied. The consideration is based on the assumption that electrons are quantized by magnetic field while holes remain classical. We assume also that the interaction between components is weak and the conversion between components is absent. The kinetic equation for holes colliding with quantized electrons is utilized. It has been stated that the inter-component friction and corresponding correction to the dissipative conductivity σ _xx do not vanish at zero temperature due to degeneracy of the Landau levels. This correction arises when the Fermi level crosses the Landau level. The statement will keep in force until the degeneracy remains. The limits of kinetic equation applicability were found. We also study the situation of kinetic memory when particles repeatedly return to their meeting points.     

热稠密物质U92的状态方程

 本文用平均原子模型，对热稠密物质U⁹²的状态方程，进行了Hartree-Fock-Slater计算。以Zink解析拟合势作为初始势及孤立原子的TF能级作为初始能级，求解满足Wigner-Seitz边界条件的Dirac-Slater方程。通过简并度是密度的连续函数来考虑大密度时的压致电离效应。