Session Q42: Theory of Superconducting Properties

Optical Integral and Sum Rule violation

We perform direct calculations of conductivities and optical integrals ($W$) in the normal and superconducting states of the cuprates to look at the dependence of their difference($\Delta W$) on the upper cut-off($\omega_c$) placed on the optical integral and the effect of the bandwidth. Our calculations indicate that the frequency cut-off imposed by the bandwidth plays an important role in the sum rule violation. In the presence of lattice $\Delta W$ (as calculated from the Kubo band sum rule) need not approach zero for large $\omega_c$. For BCS model ~$95\%$ of the spectral weight in the optical sum is recovered up to the bandwidth. But for other models - the single mode model and the collective mode model, only ~$70\%$-$80\%$ is recovered. We conclude that for all cases but BCS, there is a significant cut-off dependence as far as the recovery of the optical sum is concerned. We argue that $\Delta W$ between the superconducting and the normal state remains negative and point out the differences with the original mode model that claimed to explain positive shift of $\Delta W$. We find that the collective mode model with moderate coupling exhibits behavior consistent with the measured $\Delta W$ in the cuprates.   

Charge expulsion and Spin Meissner effect in superconductors

I argue that the Meissner effect (expulsion of magnetic field from the interior of a metal going into the superconducting state) cannot be explained by the conventional BCS-London theory, hence that BCS-London theory is incorrect[1]. The theory of hole superconductivity explains the Meissner effect as arising from the expulsion of negative charge from the interior of the superconductor towards the surface, resulting in a non-homogeneous charge distribution, a macroscopic electric field in the interior, and a spin current near the surface (Spin Meissner effect). Electrodynamic equations describing this scenario will be discussed[2]. In the charge sector, these equations are related to electrodynamic equations originally proposed by the London brothers[3] but shortly thereafter discarded by them[4]. [1] J.E. Hirsch, Physica Scripta 80, 035702 (2009). [2] J.E. Hirsch, Ann. Phys. (Berlin) 17, 380 (2008). [3] F. London and H. London, Proc. R. Soc. London A149, 71 (1935). [4] H. London, Proc. R. Soc. London A155, 102 (1936).   

Crossed Andreev reflection and electron transfer in three-terminal devices

Using scattering theory we investigate the transport properties of three-terminal devices where one terminal is superconducting and two are normal metals. The contributions from electron transfer (ET) and crossed Andreev reflection (CAR) to the non-local signal between the two normal terminals are identified. We compute ET and CAR numerically for asymmetric devices. For symmetric devices, analytical expressions for ET and CAR are also found. ET dominates CAR in symmetric devices, but CAR can dominate ET in asymmetric devices if ET is sufficiently suppressed.   

Triplet Andreev reflection off a domain wall in a lateral geometry

We find that geometry is an important ingredient in modeling the triplet Andreev reflection amplitude at the interface between a half-metal and an s-wave superconductor. Considering a domain wall as a source of spin-rotation symmetry breaking we find that while in a serial geometry the Andreev reflection amplitude vanishes at the Fermi energy, it remains finite if the contact is made in a lateral fashion. In addition, if the half metal is a thin film, rather than an extended magnet, the amplitude is enhanced by a factor $l_{\rm d}/d$, where $l_{\rm d}$ is the width of the domain wall and $d$ the film thickness. We conclude that in a lateral geometry, domain walls can be an effective source of the triplet proximity effect.   

A Proposed New Measurement of the Superconducting Gap around $\bar {M}$-point in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$

In previous publications, Zhao et al have presented first-principle calculations of the electronic structure, electron-phonon interaction, Tc, and the superconducting energy gaps on the Fermi surfaces of YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO). However, experimental measurements of the superconducting gaps on the Fermi surfaces of YBCO still face some challenges due to surface problems for YBCO samples. Considering the similarities between the crystal structure, electronic properties, and features of the Fermi surfaces of YBCO and those of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ (BSCCO), we discuss the need to measure \textit{the superconducting gap on the small sheet of the Fermi surface around the}$\bar {M}$\textit{-point in BSCCO}. This gap may be similar to the one of YBCO around the S-point. The superconducting gap on this small sheet of the Fermi surface around the$\bar {M}$-point in BSCCO is expected to show minor variations from about 18 meV to 25 meV, as we found on the small sheet of the Fermi surface around the S-point of YBCO. There is no node on the superconducting gap on this small sheet of the Fermi surface around the$\bar {M}$-point of BSCCO. This work is funded in part by NSF (Award No 0754821) and the Air Force Office of Scientific Research (Award No FA9550-09-1-0367).   

Quantum oscillations in electron doped high temperature superconductors

We have computed Shubnikov-de Haas oscillations in high magnetic fields and low temperatures in the electron doped NCCO compounds for 15, 16, and 17 percent doping within the density wave framework and have found good agreement with the experiments of T. Helm et al., Phys. Rev. Lett. 103, 157002 (2009). The method used is an exact transfer matrix method using the Landauer formula.   

Calculation of the pairing temperature $T_c$ and the gap function in electron-doped cuprates

Using a spin-Fermion model, and applying an Eliashberg-type theory to electron-doped cuprates at quantum criticality, we calculate the pairing transition temperature $T_c$, and the gap function $\Delta(\vec{k}, \omega_n)$ for $T [Preview Abstract]

Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) Phase in (TMTSF)2X Conductors: Theory versus Experiment

We consider a problem of a formation of the LOFF phase in a quasi-one-dimensional (Q!D) conductor, where we take into account both the paramagnetic spin-splitting effects and the orbital effects against superconductivity. We show that due to a weakness of the orbital effects in a Q1D case, the LOFF phase appears in (TMTSF)2X (X=ClO4 and PF6) superconductors for real values of the Q1D band parameters. We compare our theoretical calculations with the recent experimental data by Y. Maeno group, obtained on (TMTSF)2ClO4 superconductor, and show that there is a good qualitative and quantitative agreement between the theory and the experimental data. Note that the LOFF phase naturally appears in a singlet Q1D superconductor, whereas it may also appear in triplet Q1D superconductor under special conditions. Our work is supported by the NSF through the grant DMR-0705986.   

Goldstone modes in Larkin-Ovchinnikov-Fulde-Ferrell superconductors

The order parameter in LOFF superconductors can break translational symmetry, as well as the phase-rotation symmetry, which leads to the existence of additional Goldstone modes. We derive the energy of these modes microscopically, both in the single plane wave (FF) and the two plane wave (LO) phases, and also calculate the superfluid density and the elastic moduli of the nonuniform superconducting phases.   

d-wave pairing instability due to quantum critical fluctuations of the loop current order

The quantum critical fluctuations of the time reversal breaking order parameter observed in the pseudogap regime in the Cuprates couple to the lattice angular momentum of the fermions. Such a coupling is anisotropic in momentum space and unambiguously promotes d-wave pairing. In this talk I will discuss the origin and the nature of the coupling and show that the same parameters that describe the normal state transport properties give the right order of magnitude of the transition temperature and the normalized zero temperature gap.   

Properties of the Abrikosov Lattice in the symmetric gauge

The structure of Abrikosov state (AS) in the type-II superconductors shares many properties of other physical systems, such as electron gases in the regime of the Quantum Hall Effect and the rotating atoms in magnetic traps. Usually, is described using Landau gauge for the magnetic field. We employ the symmetric gauge to reveal deep analogies between the Abrikosov lattice and other systems that can be described in terms of vortices, and derive new analytic results for the vortex lattice. The work was supported by NSF and CEA (France). 1. O.K. Vorov and P. Van Isacker, to be subm. to Phys. Rev. B, in preparation.   

Type-1.5 superconductivity from interband Josephson coupling

In Ginzburg-Landau (GL) theory, the critical value of the GL parameter $\kappa_c=1/\sqrt{2}$ separates regimes of type-I and type-II superconductivity. However, it was found recently that $U(1)\times U(1)$ GL models, possess a distinct ``type-1.5'' phase with vortex excitations which interact attractively at large length scales and repulsively at shorter distances, resulting in a magnetic response which involves phase separation into domains of Meissner and vortex states. Inclusion of the interband Josephson coupling in the $U(1) \times U(1)$ GL model shrinks (or can even eliminate) the parameter range of this ``type-1.5'' regime. Here we report on the situation which is quite generic for multiband systems, but is principally different from $U(1) \times U(1)$ superconductivity: namely a system with only one superconducting band which induces some superfluid density in another band via the interband proximity effect. We show that in this case the role of interband Josephson coupling reverses: instead of suppressing, it promotes type-1.5 superconductivity by producing nontrivial variation of the condensate density at intermediate scales, resulting in nonmonotonic vortex interaction despite the long-range behavior of the condensate densities in both bands being identical.   

Phonons as a probe of electronic nematicity

We propose the use of acoustic phonons for studying signatures of nematic d-wave superconductivity, i.e. a d-wave superconductivity possessing broken $C_4$ symmetry. We We show that the $C_4\rightarrow C_2$ symmetrybreaking in nematic d-wave superconductors would cause broken symmetry in the phonon dispersion and decay rates. These effects result from the symmetry-allowed coupling between the nematic order parameter and deformations. The qualitative difference in the spatial structure of the phonon decay rate between ordinary d-wave and nematic d-wave superconductors suggests that acoustic phonons could be used as a probe of electronic nematicity. Recent developments in triple-axis spin-echo neutron scattering, which provides experimental access to the spatial structure of low-energy acoustic phonon decay rates, could make these effects observable in the near future.