Surface of underdoped YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-</Subscript><Subscript>δ</Subscript> as revealed by STM/STS

We performed scanning tunneling microscopy and spectroscopy on untwinned crystals of underdoped YBa₂Cu₃O_{7- δ} at δ = 0.4. A comprehensive statistical analysis of our topographic data indicates a doping dependent cleaving behavior of this material. We find in particular that at δ = 0.4 the material primarily cleaves in multiples of one unit cell along the c-axis with a high corrugation of the topmost layer. Our data suggest that the low temperature cleaving mainly results in a disruption of the CuO chain layers involving a redistribution of the layer atoms onto the two cleaving planes. In a few instances, fractional step heights (in terms of the c-axis lattice constant) are observed as well. Scanning tunneling spectroscopy reveals that such fractional steps connect surfaces which differ significantly in their tunneling conductance.     

Effect of helical edge states on the tunneling conductance in ferromagnet/noncentrosymmetric superconductor junction

Helical edge states exist in the mixed spin-singlet and spin-triplet phase of a noncentrosymmetric (NCS) superconductor [Y. Tanaka, T. Yokoyama, A.V. Balatsky, N. Nagaosa, Phys. Rev. B 79, 060505(R) (2009)]. In this article we have considered a planar ferromagnetic metal/NCS superconductor tunnel junction and have studied the effect of these helical edge states which manifests itself through the charge and spin tunneling conductance across the junction. We have shown the behavior of conductance for the entire range of variation of γ = Δ _-/Δ ₊ where Δ _± are the order parameters in the positive and negative helicity bands of the NCS superconductor. There exists a competition between the Rashba parameter α and the exchange energy E _ex which is crucial for determining the variation of the conductance with the applied bias voltage across the junction. We have found a nonzero spin current across the junction which appears due to the exchange energy in the Ferromagnet and modulates with the bias voltage. It also changes its profile when the strength of the exchange energy is varied.     

Transport through a double barrier in Large Radius Carbon Nanotubes with a transverse magnetic field

We discuss the Luttinger Liquid behaviour of Large Radius Carbon Nanotube e.g. the Multi Wall ones (MWNT), under the action of a transverse magnetic field B. Our results imply a reduction with B in the value of the bulk critical exponent, α_bulk, for the tunneling density of states, which is in agreement with that observed in transport experiments. Then, the problem of transport through a Quantum Dot formed by two intramolecular tunneling barriers along the MWNT, weakly coupled to Tomonaga-Luttinger liquids is studied, including the action of a strong transverse magnetic field B. We predict the presence of some peaks in the conductance G versus B, related to the magnetic flux quantization in the ballistic regime, at a very low temperature T, and also at higher values of T, where the Luttinger behaviour dominates. The temperature dependence of the maximum G_max of the conductance peak according to the Sequential Tunneling follows a power law, G ∝T^γe-1 with γ_e linearly dependent on the critical exponent, α_end, strongly reduced by B.     

Space-time dispersion of graphene conductivity

We present an analytic calculation of the conductivity of pure graphene as a function of frequency ω, wave-vector k, and temperature for the range where the energies related to all these parameters are small in comparison with the band parameter γ≃3 eV, but much larger than the collision rate τ^-1. The simple asymptotic expressions are given in various limiting cases. For instance, the conductivity for kv₀≪ T≪ω is equal to σ(ω,k)=e²/4ħ and independent of the band structure parameters γ and v₀. Our results are also used to explain the known dependence of the graphite conductivity on temperature and pressure.     

Electron-electron scattering and nonequilibrium noise in sharvin contacts

We consider wide ballistic microcontacts with electron-electron scattering in the leads and calculate electric noise and nonlinear conductance in them. Due to a restricted geometry the collisions of electrons result in a shot noise even though they conserve the total momentum of electrons. We obtain the noise and the conductivity for arbitrary relations between voltage V and temperature T. The positive inelastic correction to the Sharvin conductance is proportional to T at low voltages eV ≪ T, and to |V| at high voltages. At low voltages the noise is defined by the Nyquist relation and at high voltages the noise is related with the inelastic correction to the current by the Schottky formula S _in = 2eI _in.     

Coulomb effects in a ballistic one-channel S-S-S device

We develop a theory of Coulomb oscillations in superconducting devices in the limit of small charging energy E _C ≪Δ. We consider a small superconducting grain with finite capacitance connected to two superconducting leads by nearly ballistic single-channel quantum point contacts. The temperature is assumed to be very low, so there are no single-particle excitations on the grain. Then the behavior of the system can be described in terms of the quantum mechanics of the superconducting phase on the island. The Josephson energy as a function of this phase has two minima that become degenerate when the phase difference on the leads equals to π, the tunneling amplitude between them being controlled by the gate voltage on the grain. We find the Josephson current and its low-frequency fluctuations, and predict their periodic dependence with period 2e on the induced charge Q _x =CV _g . Zh. éksp. Teor. Fiz. 114, 640–653 (August 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor     

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.     

Possible observation of coulomb blockade at room temperature

We have studied the (I–V) characteristics of the tunnel junction formed between the tip and the substrate in an STM at room temperature. We find that in such an arrangement it may be possible to get a junction capacitance ⋍10⁻¹⁹ F and junction conductance <1μs. When the junction conductance is <1μs strong nonlinearity is observed in the (I–V) characteristics. We explain this nonlinearity as onset of coulomb blockade of tunneling electrons.     

Tunneling investigations of single crystals of the single-layer cuprate Bi2Sr2CuOz in high magnetic fields

The coexistence of a superconducting gap and a normal-state gap (pseudogap) is observed in tunneling experiments with high-quality single crystals of the single-layer cuprate Bi₂Sr₂CuO_z. At temperatures T< T _c the normal-state gap, whose width is close to that of the super-conducting gap, does not vanish in magnetic fields H>H _c2. The large smearing of the gap structure in the tunneling spectra and the high conductance of tunnel junctions at zero bias voltage are due to the strong angular dependence of the superconducting-and normal-state gaps. The results of the investigations are in good agreement with recently published angle-resolved photoemission data. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 217–222 (10 August 1998)     

Is U(1) H a good family symmetry?

We analyze U(1) _H as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3) _c ⊗SU(2) _L ⊗U(1) _Y ⊗U(1) _H nonsupersymmetric, are able to fit the experimental resultm _b≪m _t.     

c-axis tunneling on YBCO films

We have measured I(V) characteristics of c-axis planar tunnel junctions on Y₁Ba₂Cu₃O _{7 - δ} films. Our results and their analysis provide experimental support for the importance of the two-dimensional character of the YBCO band structure, and a method to measure the ratio between the Fermi energy of YBCO and the barrier height. The analysis is based on the relation between the linear conductance background, related to the inelastic tunneling component, and the zero bias conductance, related to the elastic one. Received 24 September 2000 and Received in final form 15 November 2000     

On the origin of quantum oscillations in the mixed state of an anisotropic superconductor

For the vortex lattice in an anisotropic superconductor with well-separated cores (H _c1≪ B≪H _c2) it is shown that sizable de Haas-van Alphen oscillations are caused by the levels’ crossing of the energy threshold separating localized and extended states of excitations moving in the average magnetic field B. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 9, 705–710 (10 November 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Detection of the proximity effect in Au/YBCO bilayers at 77 K with the aid of a low-temperature scanning tunneling microscope

The characteristic features of the conductance of a tunneling contact, formed by a microscope tip and an Au/YBCO sandwich, are investigated with the aid of a scanning tunneling microscope. It is shown that there exist three types of dependences of the conductance of the structure on the applied voltage, which are distinguished by the position of the characteristic features on the voltage axis. It is established that this difference is due to the local characteristics of the proximity effect in gold films on a high-T _c superconductor surface. It is concluded that the transmittance of the YBCO/Au boundary is spatially strongly nonuniform. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 984–988 (25 June 1996)     

Fluctuation-induced magnetotransport of superconductors in the quasiballistic regime

We study the fluctuation-induced magnetotransport of a two-dimensional superconductor in the quasiballistic regime, where ξ _GL(T) ≪ ℓ (ℓ is the electron mean free path and ξ _GL(T) is the Ginzburg-Landau coherence length). The magnetoconductivity is evaluated in the nonlocal fluctuation regime thereby extending the existing theory valid in the local limit. We show that the Maki-Thompson (MT) and density-of-states (DOS) contributions strongly compensate each other and their sum is negligible in comparison with the Aslamazov-Larkin (AL) term. The hierarchy of the fluctuation contributions to the magnetoconductivity in the high-field limit is also qualitatively discussed. Received 10 July 2002 / Received in final form 21 November 2002 Published online 7 May 2003     

Tunneling conductance in a gapped graphene-based superconducting structure: Case of massive Dirac electrons

The tunneling conductance in a NG/SG graphene junction in which the graphene was grown on a SiC substrate is simulated. The carriers in the normal graphene (NG) and the superconducting graphene (SG) are treated as massive relativistic particles. It is assumed that the Fermi energy in the NG and SG are E_FN400 meV and E_FS400 meV+U, respectively. Here U is the electrostatic potential from the superconducting gate electrode. It is seen that the Klein tunneling disappears in the case where a gap exist in the energy spectrum. As U→∞, the zero bias normalized conductance becomes persistent at a minimal value of G/G₀1.2. The normalized conductance G/G₀ is found to depend linearly on U with constant slope of , where is the size of the gap Δ opening up in the energy spectrum of the graphene grown on the SiC substrate. It is found that G/G₀2+αU for potentials in the range −270 meV<U<0 meV and G=0 for potentials U<−270 meV. As α→∞, the conductance for eV=Δ (V is the bias voltage placed across the NG/SG junction) can be approximated by a unit step function G(eV=Δ,U)/G₀2Θ(U). This last behavior indicates that a NG/SG junction made with gapped graphene could be used as a nano switch having excellent characteristics.     

Parton distributions in the virtual photon target up to NNLO in QCD

Parton distributions in the virtual photon target are investigated in perturbative QCD up to the next-to-next-to-leading order (NNLO). In the case Λ ²≪P ²≪Q ², where −Q ² (−P ²) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NNLO, but they are factorisation-scheme dependent. We analyse parton distributions in two different factorisation schemes, namely the and DIS _γ schemes, and we discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-x behaviours of the quark distributions. The gluon distribution is predicted to be very small in absolute value except in the small-x region.     

Resonance split of ballistic conductance peaks in electric and magnetic superlattices

Resonant peak splitting for ballistic conductance in finite electric superlattices (ES) and magnetic superlattices (MS) was investigated theoretically. It is shown that, for electron tunneling through the ES (MS) of identical n electric (magnetic) barriers, the resonance split of the conductance peak is (n–1)-fold; while for electron tunneling through the ES (MS) made of two different barriers, one resonant window of the former splits into two subwindows, within each of which the resonance split is (m–1)-fold, where m is the number of the renormalized building blocks consisting of two different barriers of the latter. Received 15 February 2000     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.