Fermi surface topology and the upper critical field in two-band superconductors: application to MgB2

Electronic Structure of Boron Flat Holeless Sheet

The electronic band structure, namely energy band surfaces and densities-of-states (DoS), of a hypothetical flat and ideally perfect, i.e., without any type of holes, boron sheet with a triangular network is calculated within a quasi-classical approach. It is shown to have metallic properties as is expected for most of the possible structural modifications of boron sheets. The Fermi curve of the boron flat sheet is found to be consisted of 6 parts of 3 closed curves, which can be approximated by ellipses representing the quadric energy-dispersion of the conduction electrons. The effective mass of electrons at the Fermi level in a boron flat sheet is found to be too small compared with the free electron mass m 0 and to be highly anisotropic. Its values distinctly differ in directions Γ–K and Γ–M: m Γ – K / m 0 ≈ 0.480 and m Γ – M / m 0 ≈ 0.052 , respectively. The low effective mass of conduction electrons, m σ / m 0 ≈ 0.094 , indicates their high mobility and, hence, high conductivity of the boron sheet. The effects of buckling/puckering and the presence of hexagonal or other type of holes expected in real boron sheets can be considered as perturbations of the obtained electronic structure and theoretically taken into account as effects of higher order.

Orbital upper critical field and its anisotropy of clean one- and two-band superconductors

The Helfand-Werthamer (HW) scheme (Helfand and Werthamer 1966 Phys. Rev. 147 288; another part of this work published as a separate paper by Werthamer et al 1966 Phys. Rev. 147 295) of evaluating the orbital upper critical field is generalized to anisotropic superconductors in general, and to two-band clean materials, in particular. Our formal procedure differs from those in the literature; it reproduces not only the isotropic HW limit but also the results of calculations for the two-band superconducting MgB(2) (Miranović et al 2003 J. Phys. Soc. Japan 72 221, Dahm and Schopohl 2003 Phys. Rev. Lett. 91 017001) along with the existing data on H(c2)(T) and its anisotropy γ(T) = H(c2,ab)(T)/H(c2,c)(T) (a, c are the principal directions of a uniaxial crystal). Using rotational ellipsoids as model Fermi surfaces we apply the formalism developed to study γ(T) for a few different anisotropies of the Fermi surface and of the order parameters. We find that even for a single band d-wave order parameter γ(T) decreases on warming; however, relatively weakly. For order parameters of the form Δ(k(z)) = Δ(0)(1 + η cos k(z)a) (Xu et al 2011 Nature Phys. 7 198), according to our simulations γ(T) may either increase or decrease on warming even for a single band depending on the sign of η. Hence, the common belief that the multi-band Fermi surface is responsible for the temperature variation of γ is proven incorrect. For two s-wave gaps, γ decreases on warming for all Fermi shapes examined. For two order parameters of the form Δ(k(z)) = Δ(0)(1 + η cos k(z)a), presumably relevant for pnictides, we obtain γ(T) increasing on warming provided both η(1) and η(2) are negative, whereas for η > 0, γ(T) decreases. We study the ratio of the two order parameters at H(c2)(T) and find that the ratio of the small gap to the large one does not vanish at any temperature, even at H(c2)(T), an indication that this does not happen at lower fields.

Effect of two length scales on the properties of MgB(2) for arbitrary applied magnetic field

Experiments carried out on the intermetallic superconducting material MgB(2) have shown anomalous magnetic field dependence of upper critical field, small angle neutron scattering form factor, specific heat, critical current etc. Similarly, scanning tunnelling microscopy (STM) experiments on vortex structures have shown unusually large vortex core size and two different magnetic and spatial field scales. Also, whereas the specific heat measurements and isotope shift experiments have shown Bardeen-Cooper-Schrieffer-like (BCS-like) behaviour, the temperature dependences of the penetration depth experiments have shown non-BCS-like behaviour. These anomalous behaviours have been attributed to the multiband superconductivity of this material and the nature of the local spatial behaviour of the magnetic induction and the order parameter components having two length scales. We report an analytical investigation of the effect of two length scales on the temperature and the applied magnetic field dependence of several properties of MgB(2), such as, the penetration depth, single vortex and vortex lattice structure, vortex core radius, reversible magnetization, critical current, small angle neutron scattering form factor and the shear modulus of the vortex lattice within the framework of two-order parameter Ginzburg-Landau theory. We solve the corresponding nonlinear Ginzburg-Landau equations numerically exactly using an iterative method for arbitrary applied field H(c1) < H < H(c2), the Ginzburg-Landau parameter and vortex lattice symmetry. This enables us to compute the local spatial behaviour of the magnetic induction and the order parameters accurately for arbitrary applied field and a wide range of temperature. Comparison of the analytical results with experiments on MgB(2) gives very good agreement.

Phase diagram of the electron-doped La2-xCexCuO4 cuprate superconductor from Andreev bound states at grain boundary junctions

We use quasiparticle tunneling across La2-xCexCuO4 grain boundary junctions to probe the superconducting state and its disappearance with increasing temperature and magnetic field. A zero bias conductance peak due to zero energy surface Andreev bound states is a clear signature of the phase coherence of the superconducting state. Hence, such a peak must disappear at or below the upper critical field Bc2(T). For La2-xCexCuO4 this approach sets a lower bound for Bc2(0) approximately 25 T which is substantially higher than reported previously. The method of probing the superconducting state via Andreev bound states should also be applicable to other cuprate superconductors.

Pressure induced effects on the Fermi surface of superconducting 2H-NbSe2

The pressure dependence of the critical temperature T(c) and upper critical field H(c2)(T) has been measured up to 19 GPa in the layered superconducting material 2H-NbSe2. T(c)(P) has a maximum at 10.5 GPa, well above the pressure for the suppression of the charge density wave (CDW) order. Using an effective two-band model to fit H(c2)(T), we obtain the pressure dependence of the anisotropy in the electron-phonon coupling and Fermi velocities, which reveals the peculiar interplay between CDW order, Fermi surface complexity, and superconductivity in this system.

Temperature-dependent anisotropy of the penetration depth and coherence length of MgB2

We report measurements of the temperature-dependent anisotropies (gamma(lambda) and gamma(xi)) of both the London penetration depth lambda and the upper critical field of MgB2. Data for gamma(lambda)=lambda(c)/lambda(a) was obtained from measurements of lambda(a) and lambda(c) on a single crystal sample using a tunnel diode oscillator technique. gamma(xi)=H(perp)c(c2)/H(||c)(c2) was deduced from field-dependent specific heat measurements on the same sample. Gamma(lambda) and gamma(xi) have opposite temperature dependencies, but close to T(c) tend to a common value (gamma(lambda) similar or equal to gamma(xi)=1.75 +/- 0.05). These results are in good agreement with theories accounting for the two-gap nature of MgB2.

Surface superconductivity of dirty two-band superconductors: applications to MgB2

The minimal magnetic field H(c2) destroying superconductivity in the bulk of a superconductor is smaller than the magnetic field H(c3) needed to destroy surface superconductivity if the surface of a superconductor coincides with one of the crystallographic planes and is parallel to the external magnetic field. While for a dirty single-band superconductor the ratio of H(c3) to H(c2) is a universal temperature-independent constant 1.6946, for dirty two-band superconductors this is not the case. I show that in the latter case the interaction of the two bands leads to a novel scenario with the ratio H(c3)/H(c2) varying with temperature and taking values larger and smaller than 1.6946. The results are applied to MgB(2) and compared with recent experiments (A. Rydh, cond-mat/0307445).

Why magnesium diboride is not described by anisotropic Ginzburg-Landau theory

It is well established that the superconductivity in the recently discovered superconducting compound MgB2 resides in the quasi-two-dimensional band (sigma band) and three-dimensional band (pi band). We demonstrate that, due to such band structure, the anisotropic Ginzburg-Landau theory practically does not have a region of applicability, because gradient expansion in the c direction breaks down. In the case of a dirty pi band, we derive the simplest equations, which describe properties of such superconductors near Tc, and explore some consequences of these equations.

Anisotropies of the lower and upper critical fields in MgB2 single crystals

The temperature dependence of the upper (H(c2)) and lower (H(c1)) critical fields has been deduced from Hall probe magnetization measurements of high quality MgB2 single crystals along the two main crystallographic directions. We show that Gamma(H(c2))=H(c2 axially ab)/H(c2 axially c) and Gamma(H(c1))=H(c1 axially c)/H(c1 axially ab) differ significantly at low temperature (being approximately 5 and approximately 1, respectively) and have opposite temperature dependencies. We suggest that MgB2 can be described by a single field dependent anisotropy parameter gamma(H) (=lambda(c)/lambda(ab)=xi(ab)/xi(c)) that increases from Gamma(H(c1)) at low field to Gamma(H(c2)) at high field.