Josephson current in superconductor/ferromagnet/ superconductor junctions

The Bogoliubov-de Gennes equation and Nambu spinor Green's function approach are applied to studying the Josephson current in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions in the clean limit. It is found that the critical current exhibits a damped oscillation with the F thickness d, the oscillation period equal to 2πξ_F with ξ_F the coherence length of the F. The change of the critical current from positive to negative is determined by factor cosφ^′ with φ^′=d/ξ_F as the F-induced phase difference. The exponent decay of the critical current is close related to that of the superconductor order parameter in the F, both of them having the same decay length.     

Josephson and quasiparticle currents in tunneling junctions between partially dielectrized (partially gapped) superconductors with spin density waves

The current-voltage characteristics (CVC) are calculated for the Josephson, interference, and quasiparticle components of the current through a tunneling junction formed by two superconductors with spin density waves (SDW). The treatment is based on the model of partial dielectrization (gapping) of the Fermi surface and the assumption of pinning of the spin density waves. The following particular cases are studied in detail: asymmetric SDW superconductor-ordinary superconductor junctions and symmetric junctions between two identical SDW superconductors. The positions and nature of the singularities in the CVC are determined. For a symmetric contact the possibility of the existence of asymmetric CVC’s is predicted. The calculations are in qualitative agreement with the experimentally observed behavior of the CVC’s of tunneling junctions and microcontacts containing the SDW superconductor with heavy fermions URu₂Si₂. Fiz. Tverd. Tela (St. Petersburg) 41, 1743–1749 (October 1999)     

Angular studies of the magnetoresistance in the density wave state of the quasi-two-dimensional purple bronze KMo<Subscript>6</Subscript>O<Subscript>17</Subscript>

The purple molybdenum bronze KMo₆O₁₇ is a quasi-two-dimensional compound which shows a Peierls transition towards a commensurate metallic charge density wave (CDW) state. High magnetic field measurements have revealed several transitions at low temperature and have provided an unusual phase diagram “temperature-magnetic field”. Angular studies of the interlayer magnetoresistance are now reported. The results suggest that the orbital coupling of the magnetic field to the CDW is the most likely mechanism for the field induced transitions. The angular dependence of the magnetoresistance is discussed on the basis of a warped quasi-cylindrical Fermi surface and provides information on the geometry of the Fermi surface in the low temperature density wave state.     

Reconstruction of the Fermi surface in the pseudogap state of cuprates

Reconstruction of the Fermi surface of high-temperature superconducting cuprates in the pseudogap state is analyzed within a nearly exactly solvable model of the pseudogap state, induced by short-range order fluctuations of the antiferromagnetic (AFM), spin-density wave (SDW), or a similar charge-density wave (CDW) order parameter, competing with the superconductivity. We explicitly demonstrate the evolution from “Fermi arcs” (on the “large” Fermi surface) observed in the ARPES experiments at relatively high temperatures (when both the amplitude and phase of the density waves fluctuate randomly) towards the formation of typical “small” electron and hole “pockets,” which are apparently observed in the de Haas-van Alphen and Hall resistance oscillation experiments at low temperatures (when only the phase of the density waves fluctuate and the correlation length of the short-range order is large enough). A qualitative criterion for the quantum oscillations in high magnetic fields to be observable in the pseudogap state is formulated in terms of the cyclotron frequency, the correlation length of fluctuations, and the Fermi velocity. The text was submitted by the authors in English.     

Extraordinary magnetic field behavior of SIFS Josephson junctions with an inhomogeneous transparency of the FS interface

Within the framework of the Usadel equations, the Josephson effect in a superconductor-insulator-ferromagnet-superconductor (SIFS) structure with a spatially heterogeneous transparency of the SF interface has been studied. It is shown that, at a certain thickness of the F layer, a stepwise variation of the transparency leads to the formation of a region of size ∼ξ _F (coherence length in a ferromagnet), where the Josephson supercurrents of different signs may flow. This may lead to the dependence of the junction critical current on the external magnetic field qualitatively different from the Fraunhofer pattern typically observed in usual Josephson junctions. The text was submitted by the authors in English.     

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically T _g≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(T _g/T). The glass cross-over temperature T_g related to correlations among solitons is equal to the average energy barrier and scales like T _g∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap. Received 12 December 2001     

Electronic properties of quasi-one-dimensional compounds with a charge/spin-density wave ground state

First, a review of the general properties of the collective transport induced by the charge (CDW)/spin (SDW) density wave motion in quasi-one-dimensional conductors is presented. Then the three recent developments in this field are emphasized, namely: high spatial resolution x-ray study of the field-induced CDW deformations; quantum interference effects in magnetotransport of a sliding CDW through columnar defects; manifestation of disorder in the CDW/SDW ground state in thermodynamic properties at very low temperatures. Fiz. Tverd. Tela (St. Petersburg) 41, 759–763 (May 1999) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Model for superconducting current in HTSC: How to calculate the maximum intrinsic values

Summary In order to explain the HTSC electrical density values, the authors propose a new original model for these new superconductors, introducing the parameterSc, given by the ratio between the coherence distance ξ₀ and the lattice constant λ₁. The value ofSc is less than 1 in HTSC and higher than 1 in normal s.c. In HTSC the pair electron transport mechanism became different than in other s.c., in which a wave function linear coherence is established. A Josephson intrinsic electrical conduction mechanism is established. The HTSC behaves like a good diamagnetic material but a bad superconductor.     

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T _c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional “eggbox type” charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments. Received 14 June 1999     

Charge dynamics of the spin-density-wave state in BaFe<Subscript>2</Subscript>As<Subscript>2</Subscript>

We report on a thorough optical investigation of BaFe₂As₂ over a broad spectral range and as a function of temperature, focusing our attention on its spin-density-wave (SDW) phase transition at T_SDW = 135 K. While BaFe₂As₂ remains metallic at all temperatures, we observe a depletion in the far infrared energy interval of the optical conductivity below T_SDW, ascribed to the formation of a pseudogap-like feature in the excitation spectrum. This is accompanied by the narrowing of the Drude term consistent with the dc transport results and suggestive of suppression of scattering channels in the SDW state. About 20% of the spectral weight in the far infrared energy interval is affected by the SDW phase transition.     

Supercurrent and its Fano effect in a Josephson Aharonov-Bohm ring

The Josephson current through an Aharonov-Bohm (AB) interferometer, in which a quantum dot (QD) is situated on one arm and a magnetic flux Φ threads through the ring, has been investigated. In the presence of the magnetic flux, the relation between the Josephson current and the superconductor phase is complex, and the system can be adjusted to π junction by either modulating the magnetic flux or the QD’s energy level ε_d. Due to the electron-hole symmetry, the Josephson current I has the property I(ε_d,Φ)=I(-ε_d,Φ+π). The Josephson current exhibits a jump when a pair of Andreev bound states aligns with the Fermi energy. The condition for the current jump is given. Particularly, we find that the position of the current jump and the position of the maximum value of the critical current I_c are identical. Due to the interference between the two paths, the critical current I_c versus the QD’s level ε_d shows a typical Fano shape, which is similar to the Fano effect in the corresponding normal device. However they also show some differences. For example, the critical current never reaches zero for any parameters, while the current in the normal device can reach zero at the destruction point.     

Superconducting decay length in a ferromagnetic metal

The complex decay length ξ characterizing the penetration of superconducting correlations into a ferromagnet due to the proximity effect is studied theoretically in the framework of the linearized Eilenberger equations. The real part ξ₁ and imaginary part ξ₂ of the decay length are calculated as functions of exchange energy and the rates of ordinary, spin-flip, and spin-orbit electronic scattering in a ferromagnet. The lengths ξ_1,2 determine the spatial scales of, respectively, the decay and oscillation of a critical current in SFS Josephson junctions in the limit of a large distance between superconducting electrodes. The developed theory provides the criteria of applicability of the expressions for ξ₁ and ξ₂ in the dirty and clean limits, which are commonly used in the analysis of SF hybrid structures. The text was submitted by the authors in English.     

Coexistence of superconductivity and spin density wave orderings in the organic superconductor (TMTSF) 2 PF 6

The phase diagram of the organic superconductor (TMTSF)₂PF₆has been revisited using transport measurements with an improved control of the applied pressure. We have found a 0.8 kbar wide pressure domain below the critical point (9.43 kbar, 1.2 K) for the stabilisation of the superconducting ground state featuring a coexistence regime between spin density wave (SDW) and superconductivity (SC). The inhomogeneous character of the said pressure domain is supported by the analysis of the resistivity between T _SDW and T _SC and the superconducting critical current. The onset temperature T _SC is practically constant ( 1.20±0.01 K) in this region where only the SC/SDW domain proportion below T _SC is increasing under pressure. An homogeneous superconducting state is recovered above the critical pressure with T _SC falling at increasing pressure. We propose a model comparing the free energy of a phase exhibiting a segregation between SDW and SC domains and the free energy of homogeneous phases which explains fairly well our experimental findings. Received 3 September 2001 and Received in final form 9 November 2001     

Interaction of both charge density waves in NbSe3 from interlayer tunneling experiments

An interlayer tunneling technique has been used for spectroscopy of charge density wave (CDW) energy gaps (Δ_1,2) in NbSe₃ subsequently opened at the Fermi surface on decreasing temperature at T _p1 = 145 K (CDW1) and at T _p2 = 60 K (CDW2). We found that the CDW2 formation is accompanied by an increase of the CDW1 gap below T _p2. The maximum enhancement of Δ₁, δΔ₁ is about 10%. The effect observed has been predicted theoretically as resulting from the joint phase locking of both CDWs with the underlying crystalline lattice below T _p2. The text was submitted by the authors in English.     

Shapiro steps in the torsion of a quasi-one-dimensional conductor TaS<Subscript>3</Subscript>

Features have been observed in the current dependences of the torsion angle, φ(I), for samples of a quasi-one-dimensional conductor TaS₃ irradiated by a high-frequency (HF) field. The features appear at the same current values as the Shapiro steps on the current-voltage characteristics, i.e., correspond to the synchronization of the motion of a charge-density wave (CDW) by the HF field. The shape of the features in the φ(I) dependences indicates a decrease in the inhomogeneous deformation of the CDW under the synchronization conditions. The investigation of torsion appears to be a highly sensitive method for determining the spatial coherence of the CDW.     

Microscopic theory of longitudinal sound velocity in CDW and SDW ordered cuprate systems

We address here the self-consistent calculation of the spin density wave and the charge density wave gap parameters for high-T_c cuprates on the basis of the Hubbard model. In order to describe the experimental observations for the velocity of sound, we consider the phonon coupling to the conduction band in the harmonic approximation and then the expression for the temperature dependent velocity of sound is calculated from the real part of the phonon Green’s function. The effects of the electron–phonon coupling, the frequency of the sound wave, the hole doping concentration, the CDW coupling and the SDW coupling parameters on the sound velocity are investigated in the pure CDW phase as well as in the co-existence phase of the CDW and SDW states. The results are discussed to explain the experimental observations.     

Charge-density-wave partial gap opening in quasi-2D KMo6O17 purple bronze studied by angle resolved photoemission spectroscopy

Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo₆O₁₇ purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ∼40 K well below the Peierls transition temperature for this material, with CDW transition temperature T_CDW ∼120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative k_F point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, E_F, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K_0.3MoO₃ blue bronze.     

SDW in the 2D Compound CuFeTe2

In a previous work (ICAME'97) we presented the Mössbauer results for a non-stoichiometric sample of the quasi-two-dimensional (2D) dichalcogenide CuFeTe₂, where a Spin Density Wave (SDW) ground state with T _SDW=256±15 K was proposed. Here we report the study of the magnetic and electric properties determined by magnetic susceptibility, Mössbauer spectroscopy and resistance measurements, of an almost stoichiometric sample prepared by the vertical Bridgman growth technique. The SDW behavior is supported by the results obtained by the following different techniques: Magnetic susceptibility: A magnetic transition is observed at T _SDW=308 K with a Pauli paramagnetic behavior above this temperature. Mössbauer effect: The shape of the spectra and the thermal evolution of the hyperfine field are characteristic of the SDW's in quasi-2D systems. Electrical resistance: There is a metal–semiconductor transition along the layers as the temperature decreases indicating the opening of a gap at the Fermi level.