Pressure-tuned resonance Raman scattering and photoluminescence studies on MBE grown bulk GaAs at theE 0 gap

Hydrostatic pressure has been used to tune in resonance Raman scattering (RRS) in bulk GaAs. Using a diamond anvil cell, both the photoluminescence peak (PL) and the 2 LO and LO-phonon Raman scattered intensities have been monitored, to establish RRS conditions. When theE ₀ gap of GaAs matchesħω _S orħω _L, the 2 LO and LO-phonon intensity, respectively, exhibit resonance Raman scattering maxima, at pressures determined byħω _L. With 647.1 nm radiation (ħω _L = 1.916 eV), a sharp and narrow resonance peak at 3.75 GPa is observed for the 2 LO-phonon. At this pressure the 2 LO-phonon goes through its maximum intensity, and falls right on top of the PL peak, revealing thatħω _S(2 LO) =E ₀. This is the condition for “outgoing” resonance. Experiments with other excitation energies (ħω _L) show, that the 2 LO resonance peak-pressure moves to higher pressure with increasingħω _L, and the shift follows precisely theE ₀ gap. Thus, the 2 LO RRS is an excellent probe to follow theE ₀ gap, far beyond the Γ-X cross-over point. A brief discussion of the theoretical expression for resonance Raman cross section is given, and from this the possibility of a double resonance condition for the observed 2 LO resonance is suggested. The LO-phonon resonance occurs at a pressure whenħω _L ≈E ₀, but the pressure-induced transparency of the GaAs masks the true resonance profile.     

Analytic solution of the BCS gap equation inD dimensions (D=1, 2, 3), at finite temperatures

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically in one, two and three dimensions, for temperatures close to zero andT _c. We work in the weak coupling limit, but allow the interaction widthν≡ħω _m/E _F to lie in the interval (0, ∞) Here,ħω _m is the maximum energy of a force-mediating boson, andE _F denotes the Fermi energy. We obtain expressions forT _c and ΔC, the jump in the electronic specific heat acrossT=T _c, in the limitsν≪1 (the usual phonon pairing) andν>1 (non-phononic pairing). This enables us to see howT _c scales with the mediating boson cut off. Our results predict a larger jump in the specific heat for the caseν>1, compared toν≪1. We also briefly touch upon the role of a van Hove singularity in the density of states.     

Level structure of 99Rh at high spins

High spins states in ⁹⁹Rh were populated via the ⁶⁶Zn(³⁷Cl, 2p2n)⁹⁹Rh reaction at an incident beam energy of 130 MeV. Seventeen new transitions have been observed in the present study and the level scheme has now been extended up to a spin of J∼ 25ħ and an excitation energy of about E _x∼ 10 MeV. The observation of a positive parity E2 cascade based on the 9/2⁺ isomeric level is suggestive of collective behaviour in this nucleus up to high spins. Spherical shell model (within restricted model space) and Cranked shell model calculations were performed to obtain an insight into the observed level structure. The new collective band observed up to a spin of J∼ 25ħ is suggested to be based on (πg _9/2 ³) ⊗ (νg _7/2 ²) quasi-particle excitations. Received: 12 July 1999 / Revised version: 14 September 1999     

Nature of conduction via impurities in uncompensated silicon

The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=10¹⁶−6×10¹⁶ cm⁻³, ionization energy ε₁≃45 meV) with compensation K=10⁻⁴−10⁻⁵ in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the sample. It is found that the conductivity σ(E) is due to carrier motion along the D ⁻ band, which is filled with carriers under the influence of the field E. In fields E<E _q (E _q ≃100–200 V/cm) the carrier motion consists of hops along localized D ⁻ states in a 10–15 meV energy band below the bottom of the free band (energy ε=ε₁); for E>E _q carriers drift along localized D ⁻ states with energy ε∞ε₁−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 232–236 (25 August 1997)     

Spectral behaviour of the two-photon absorption coefficient in ZnO,CuCl and Bi4Ge3O12

Summary The spectral behaviour of the direct interband two-photon absorption coefficient α⁽²⁾ in ZnO, CuCl and Bi₄Ge₃O₁₂ has been investigated in a large excitation energy range. The experimental results have shown that the α⁽²⁾ spectral behaviour is well described by a parametric formula containing terms with different energy dependence. In particular, for 2ħω-E _g>≈400 meV, the first experimental evidence of 2ħω-E _g)^5/2 dependence has been obtained. As a consequence, each of the various models proposed to predict the α⁽²⁾ dispersion curve gives the correct energy dependence in a limited energy range, due to the poor approximation made in the evaluation of dipole matrix elements. To explain the spectral dependence of the two-photon absorption coefficient, consideration of all the intermediate states is required, with the energy dependence of the dipole matrix elements properly considered. It is shown that the greatest contributions to the oscillator strength come from transitions totally allowed at the critical points. Work partially supported by M.P.I.     

Fermion zero modes on vortices in chiral superconductors

The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting state the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in an s-wave superconductor: E=(n+1/2)ω₀, with integral n. In class II the corresponding spectrum is E=nω₀ and thus contains a state with exactly zero energy. The effect of a single impurity on the spectrum of bound states is also considered. For class I the spectrum acquires the doubled period ΔE=2ω₀ and consists of two equidistant sets of levels, in accordance with A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57, 5457 (1998). For the class II states the spectrum is not influenced by a single impurity if the same approximation is applied. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 9, 601–606 (10 November 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Magneto-intersubband zener tunneling in a wide GaAs quantum well at high filling factors

The dependence of the differential resistance r _xx on the dc current density J _dc in a wide GaAs quantum well with two occupied size quantization subbands has been investigated at the temperature T = 4.2 K in the magnetic fields B < 1 T. A peak, whose position is given by the relation 2R _c eE _H = ħω_c/2, where R _c is the cyclotron radius, E _H is the Hall electric field, and ω_c is the cyclotron frequency, has been observed in the r _xx (J _dc) curves at high filling factors. The experimental results are attributed to Zener tunneling of electrons between the Landau levels of different subbands.     

Dynamics of the anisotropic two-dimensional XY model

In this paper we study the dynamics of the two-dimensional XY model with single-ion anisotropy, and spin S = 1, in the large D phase, and low temperatures, using the bond operator formalism. The in-plane structure factor is a delta function. The out of plane shows a three peak structure, which merges in a single peak at the Brillouin zone boundary. We analyze also spin currents generated by a magnetic field gradient. The spin conductivity is calculated, at finite temperature, using the Kubo formula. The model shows unconventional ballistic spin transport at finite temperature. The computed spin conductivity exhibits a nonzero Drude weight at finite temperature. For ω< 2m, where m is the energy gap, the spin conductivity is described solely by the Drude weight. There is a regular contribution to the spin conductivity for ω> 2m, which persist in the zero temperature limit. The conductivity at the critical point, and for small frequencies, is (gμ_B)²/ħ times a universal scaling function of ħω/k_B T.     

Rotational co-existence in selenium isotopes

High spin states of ^72,73,74Se nuclei are discussed using calculations from the cranked Nilsson Strutinsky method with tuning to fixed spins. The low spin anomaly in the yrast bands of these nuclei is interpreted in a rotational co-existence picture. High K rotational isomers are proposed for I ^π =4⁺ in ⁷²Se and 6⁺ in ⁷⁴Se.     

Structure of neutron-rich nuclei around A ⋍ 100

Neutron-rich isotopes of Mo (Z=42) around A ⋍ 100 have been investigated within the formalisms of cranked Nilsson Strutinsky and CHFB, to study several interesting features of nuclear structure in this mass region. The total energy/routhian surfaces have been generated for the isotopes of Mo ranging from A ⋍ 96 − 112, as a function of deformation (β ₂ and γ) for ground state and higher angular momentum states. Results of calculations using two different formalisms have been compared and combined to have a better understanding of the underlying mechanism of shape evolution.     

Extensive γ -ray spectroscopy of normally and superdeformed structures in 61 29Cu32

A largely extended experimental knowledge of the ⁶¹ ₂₉Cu₃₂ nucleus has been obtained from three experiments. Excited states in ⁶¹Cu were produced via the fusion-evaporation reaction ²⁸Si(³⁶Ar, 3p)⁶¹Cu . In addition to the Ge array GAMMASPHERE, neutron and charged-particle detectors placed around the target position were used for high-performance particle spectroscopy. The constructed level scheme includes more than 160 energy levels and 320 γ -ray transitions belonging to both normally deformed as well as superdeformed rotational structures. The multipolarities have been determined for the γ -ray transitions and as a result spin-parity assignments are given for nearly all energy levels. Experimental results in the normally deformed region are compared with predictions from large-scale shell model calculations. The collective structures are compared with results from cranked Nilsson-Strutinsky calculations. The results reveal the need to modify the standard Nilsson parameters in the mass A ∼ 60 region.     

Octupole excitations at high spins in <Emphasis Type="Italic">A</Emphasis> ∼ 160 nuclei

The yrast and yrare states of ¹⁶²Yb are studied within the cranked Nilsson model and random phase approximation. Special attention is paid to the analysis of experimental crossing points between different bands that form the yrast band. We found that, at the rotational frequency ħΩ > 0.3 MeV, there is onset of strong octupole correlations. The results of calculations demonstrate good agreement with available experimental data. The text was submitted by the authors in English.     

Resonance microwave photoresistance of a two-subband electron system at large filling factors

The microwave photoresistance of a double GaAs quantum well with two occupied size-quantization sub-bands E ₁ and E ₂ has been studied at the temperatures T = 1.6–4.2 K in the magnetic fields B < 0.5 T. The microwave photoresistance of such a system has been found to have a maximum amplitude when the maximum of the magneto-intersubband oscillations with the number k = (E ₂ − E ₁)ℏω_c coincides with the maximum or minimum of the ω/ω_c oscillations, where ω is the microwave frequency and ω_c is the cyclotron frequency. It has been shown that the resonance photoresistance that appears in the kth maximum of the magneto-intersubband oscillations is determined by the condition ℏω/(E ₂ − E ₁) = (j ± 0.2)/k, where k and j are positive integers.     

Level statistics inside the core of a superconductive vortex

A microscopic theory of the Efetov supermatrix sigma-model type is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ ⁻¹≫ω ₀∼Δ²/E _F . At low energies ε≪ω _Th∼ (ω ₀/τ)^1/2, the energy level statistics is described by the “zero-dimensional” limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma model increase the mean interlevel distance by the relative amount [2 ln (1/ω ₀ τ)]⁻¹. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 78–83 (10 July 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Experimental study of the <Emphasis Type="Italic">πh</Emphasis><Subscript>11/2</Subscript> band in <Superscript>113</Superscript>Sb

In the present work, the excited states of ¹¹³Sb were populated in the ¹⁰⁰Mo(²⁰Ne, p6n) reaction at a beam energy of 136 MeV. States only up to 59/2⁻ were observed in the ΔJ = 2 band. Mean lifetimes for the five states (from 4460 to 7998 keV) were measured for the first time using Doppler shift attenuation method. An upper limit of the lifetime (0.14 ps) was estimated for the 9061 keV, 47/2⁻ state. The B(E2) values, derived from the present lifetime results, correspond to a large quadrupole deformation of β ₂ = 0.32. The observed reduction in the experimental B(E2) values for the 918.4 keV (spin 39/2⁻ → 35/2⁻) and 985 keV (spin 43/2⁻ → 39/2⁻) transitions may be interpreted as due to the proton alignement in the g _7/2 orbital. The dynamic moment of inertia was observed to be about half of the rigid body value at the highest observed frequency.     

High-spin states in odd-odd 168Lu

High-spin states in the odd-odd ¹⁶⁸Lu nucleus, populated in the ¹⁵⁴Sm(¹⁹F,5n) reaction at a beam energy of 96 MeV, were investigated using in-beam γ-ray spectroscopy techniques. The BC neutron crossing in the yrast band, based on πg _7/2[404]7/2⁺⊗νi _13/2[642]5/2⁺ configuration, occurs at ħω= 0.31 MeV. The two side bands, based on πh _11/2[514]9/2⁻⊗νi _13/2[642]5/2⁺ and πh _9/2[541]1/2⁻⊗νi _13/2[642]5/2⁺ configurations, show anomalous signature-splitting and signature-inversion in the first one, to occur at ħω= 0.24 MeV. A moderately delayed BC-crossing is anticipated in the second one. Received: 15 June 1998 / Revised version: 11 January 1999     

High-spin states in <Superscript>36</Superscript>Ar and their underlying shell model configurations

Eight high-spin states in ³⁶Ar below 10MeV excitation energy, among them a prospective J ^π = 8^- state at 9408keV and the J? 8 levels of the recently discovered superdeformed rotational band, have been observed by n-γ coincidence measurements with the ³³S(α, nγ) reaction at E _α = 14.4 and 13.4MeV. High-spin assignments of, respectively, J ^π = 6⁺ and 5^- were obtained for the E _p = 1209 and 1462keV (E _x = 9682 and 9927keV) resonances of the ³⁵Cl (p,γ) reaction by a measurement of γ-ray angular distributions. The spectrum of the high-spin and of the E _x? 7.4MeV levels is decomposed according to the underlying shell model configurations with n = 0, 1, 2, 4 particles excited from the N = 2 into the N = 3 major shell. The role of four-particle excitations, all connected with large prolate distortions, is elucidated for the entire A = 36-40 mass region. Received: 21 December 2001 / Accepted: 25 March 2002     

A microscopic analysis of moments of inertia

A microscopic analysis of moments of inertia is performed within the cranked Nilsson model. Special emphasis is put on the second-derivative moment of inertia, J⁽²⁾. Contributions to this from changes of rotational frequency and deformation are separately discussed. A simple expression for the latter is derived and it is for a studied series of Yb isotopes usually found to contribute with less than 10% to the total J⁽²⁾ value. J⁽¹⁾, J⁽²⁾ and J_rigid are calculated as functions of spin at the appropriate equilibrium deformations for the even-even nuclei ^160–176Yb. Variations of J⁽²⁾ with particle number and spin are discussed. Relations between J⁽²⁾ and the deformation are studied in detail, especially in connection with the super-backbending.     

Band termination in the Z = N odd-odd nuclei <Superscript>46</Superscript>V and <Superscript>50</Superscript>Mn

The configuration-dependent cranked Nilsson-Strutinsky approach has been employed to study the properties and band structures at high spin in the Z = N odd-odd nuclei ⁴⁶V and ⁵⁰Mn. The observed bands are explained and terminating states are confirmed by the calculations. The calculated and observed bands are in good agreement without normalization, especially for terminating states. Possible bands with rotation around the intermediate axis and the effect of γ-deformation on the total energy of several interesting configurations are discussed. Received: 2 April 2002 / Accepted: 27 January 2003 / Published online: 15 April 2003