CCP9 - Computational Electronic Structure of Condensed Matter

Workshop on solving the Bogoliubov-de Gennes and Gross-Pitaevskii equations for superconductors, superfluids and BEC

28-30 September 2007

Abstracts

"Ab-initio theory of superconductivity"

E. K. U. Gross   (Berlin, Germany)

A novel density-functional-type approach to the description of phonon-mediated super-conductivity is presented [1]. The goal of this approach is to provide a theory with predictive power, allowing the calculation of material-specific properties such as the critical temperature.To this end, the electron-phonon interaction and the electron-electron repulsion are treated on the same footing. There are no adjustable parameters such as the μ* of Eliashberg theory. The formalism can be viewed as the superconducting generalization of the multi-component density-functional theory [2] for electrons and nuclei. Approximations of the universal xc functionals are derived on the basis of many-body perturbation theory [1,3]. Numerical results for the critical temperature and the gap will be presented for simple metals [4,5], for MgB2 [6], and for Li, Al and K under pressure [7]. In particular, for MgB2, the two gaps and the specific heat as function of temperature are in very good agreement with experimental data. For Li and Al under pressure, the calculations explain why these two metals behave very differently, leading to a strong enhancement of superconductivity for Li and to a clear suppression for Al with increasing pressure. For K we predict a behavior similar to Li, i.e. a strong increase of Tc with increasing pressure. Furthermore, the peculiar features of the superconducting phase of CaC6 will be analyzed [8]. In the figure below, the gap function of CaC6 is shown on the Fermi surface. Finally, results for hydrogen under extreme pressure will be presented. It turns out that hydrogen is a three-gap superconductor whose critical temperature increases with increasing pressure until about 100K (at 500 GPa).

 

  1. M. Lüders, M.A.L. Marques, N.N. Lathiotakis, A. Floris, G. Profeta, L. Fast, A.Continenza, S. Massidda and E.K.U. Gross, Phys. Rev. B 72, 024545 (2005).

  2. T. Kreibich, E.K.U. Gross, Phys. Rev. Lett. 86, 2984 (2001).

  3. S. Kurth, M.A.L. Marques, M. Lüders, E.K.U. Gross, Phys. Rev. Lett. 83, 2628, (1999).

  4. M.A.L. Marques, M. Lüders, N.N. Lathiotakis, G. Profeta, A. Floris, L. Fast, A. Continenza, E.K.U. Gross, S. Massidda, Phys. Rev. B 72, 024546 (2005).

  5. A. Floris, A. Sanna, S. Massidda and E.K.U. Gross, Phys. Rev. B 75, 054508 (2007).

  6. A. Floris, G. Profeta, N.N. Lathiotakis, M. Lüders, M.A.L. Marques, C. Franchini, E.K.U. Gross, A. Continenza, S. Massidda, Phys. Rev. Lett. 94, 037004 (2005).

  7. G. Profeta, C. Franchini, N.N. Lathiotakis, A. Floris, A. Sanna, M.A.L. Marques, M. Lüders, S. Massidda, E.K.U. Gross, A. Continenza, Phys. Rev. Lett. 96, 047003 (2006).

  8. A. Sanna, G. Profeta, A. Floris, A. Marini, E.K.U. Gross, S. Massidda, Phys. Rev. B (Rapid Comm.) 75, 020511 (2007).

 

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"Superconducting phases in strontium ruthenate subject to magnetic field"

Karol Izydor Wysokinski (Lublin, Poland)

The orbital symmetry of the spin triplet superconducting state of strontium ruthenate is widely believed to be chiral one with d-vector along the crystal c-axis. This piece of evidence comes mainly from measurements of the spin susceptibility being constant below T_c when measured in magnetic field in a-b plane. The experimental measurements of the spin susceptibility in a magnetic field along c-axis show that small magnetic field is sufficient to rotate d-vector into the a-b plane. Using the realistic 3 dimensional and 3 band model of the superconductor in tight -binding representation we solve the Bogolubov-deGennes equations and discuss the effect of the (spin-only) magnetic field on the material. The model predicts field induced phase transition characterized by small but finite entropy change thus explaining the lack of its experimental signatures.

 

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"Dynamic cluster simulations of the 2D Hubbard model: What is the cuprate pairing mechanism?"

Thomas A. Maier (ORNL, USA)

We will discuss recent dynamic cluster approximation studies of the doped two-dimensional Hubbard model of the high-temperature superconductors. The phenomena found in these simulations include antiferromagnetic, superconducting and pseudogap behavior, and are thus remarkably similar to what is observed in the cuprate materials. We will discuss how one can combine diagrammatic techniques with numerical results to obtain the momentum, frequency, temperature and spin quantum number that characterize the pairing interaction responsible for d-wave pairing. The effective pairing interaction is found to be attractive between singlets formed between nearest neighbor sites and its dynamics is associated with the antiferromagnetic spin fluctuation spectrum. An exact decomposition of the pairing interaction reveals that it is mediated by antiferromagnetic spin fluctuations. Motivated by these results, we will then discuss a simple spin susceptibility representation of the pairing interaction that provides potential routes to experimental verification. Furthermore, we will present preliminary results for the frequency dependence of the superconducting gap parameter and discuss recent results for a three-band Hubbard model obtained from a combination of density functional and dynamic cluster quantum Monte Carlo calculations.


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"Electron-phonon coupling and superconductivity in intercalated graphites from first-principles"

F. Mauri

Graphite intercalated compounds (GICs) can display a superconducting behavior at low temperature. However, until the discovery of Yb and Ca intercalated graphite [1,2] (Tc(YbC6)=6.5 K and Tc(CaC6)=11.5 K), the critical temperatures achieved were typically less than a Kelvin. Recently, it has been shown that even higher critical temperatures (up to 15.1 K) can be achieved in CaC6 applying hydrostatic pressure [3]. This is presently the highest Tc reported in a GIC. The large number of intercalant available for graphite (more than 100) requires theoretical investigation to guide the experimental work. Moreover since there is not a general consensus on the nature of the superconducting state, the calculation of the superconducting properties in the framework of strong-coupling electron-phonon theory for different intercalants and the consequent comparison with experiments can judge its reliability in predicting the critical temperature. Using density functional theory we investigate the occurrence of superconductivity in AC6 with A=Mg,Ca,Sr,Ba. All the aforementioned GICs posses an intercalant band at the Fermi level, GICs[4]. Comparing the superconducting properties and the calculated critical temperatures of these materials we show that the pairing mechanism is due to the elenctron-phonon interaction. In particular we find CaC6 to be superconducting with Tc=11.5, and we predict Ba and Sr intercalated graphite to be superconducting with Tc 0.2 K and 3.0 K [5]. Our predictions have been confirmed by recent experiments [6]. We study the pressure dependence of Tc and and that the SrC6 and BaC6 critical temperatures should be substantially enhanced by pressure. On the contrary, for CaC6 we find that in the 0 to 5 GPa region, Tc weakly increases with pressure. The increase is much smaller than what shown in several recent experiments. We propose possible explanations for these discrepancies. Finally we argue that, although MgC6 is unstable, the synthesis of intercalated systems of the kind MgxCa1(1-x)C6 could lead to higher critical temperatures.

[1] T. E. Weller, et al., Nature Phys. 1, 39 (2005) and cond-mat/0503570
[2] N. Emery, et al. Phys. Rev. Lett. 95, 087003 (2005)
[3] A. Gauzzi, et al., Phys. Rev. Lett. 98, 067002 (2007)
[4] M. Calandra and F. Mauri, Phys. Rev. Lett. 95, 237002 (2005)
[5] M. Calandra and F. Mauri Phys. Rev. B 74, 094507 (2006)
[6] J. S. Kim, et al. Phys. Rev. Lett. 99, 027001 (2007)


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"BCS-BEC in strongly dissipative systems"

Marzena Szymanska (Oxford, UK)

By confining photons in a semiconductor microcavity, and strongly coupling them to electronic excitations, one may create polaritons: bosonic quasi-particles with an effective mass of 10-9 times that of Rubidium atoms, thus allowing BEC at elevated temperatures. After a long and strenuous search, the comprehensive set of experiments has finally given evidence for BEC of polaritons [1]. However, this new condensate depart from the archetypal BEC in several ways. Most importantly polaritons have short lifetime and so a continues pumping is required to sustain a steady-state. This leads to a new type of condensation which can exist in highly non-equilibrium and dissipative environment [2,3].

We show that, surprisingly, the mechanism of condensation, connected with the chemical potential reaching the bottom of bosonic modes, is the same in closed systems at equilibrium and in open systems with pump and decay. In the latter, the role of the chemical potential is played by the energy at which the non-thermal distribution diverges. We derive the self-consistency condition for an uniform condensed steady state. This condition can be compared both to the laser rate equation and to the Gross-Pitaevskii equation of an equilibrium condensate. However, even when the system is characterised by a thermal distribution, the presence of pumping and decay significantly modifies the spectra of phase fluctuations: the low energy phase mode (Goldstone, Bogoliubov mode) becomes diffusive at small momenta, leading to correlation functions -- and thus condensate lineshape -- that differ both from an isolated condensate and from that for phase diffusion of a single laser mode. These generic features of dissipative condensation can be observed in different optical probes of the microcavity and affect the decay of spatial and temporal coherence in a condensate, and modify its superfluid properties.

  1. "Bose-Einstein condensation of exciton polaritons", J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. M. J. Keeling, F. M. Marchetti, M. H. Szymanska, R. Andre, J. L. Staehli, V. Savona, P. B. Littlewood, B. Deveaud, Le Si Dang, Nature 443, 409 (2006).
  2. "Non-equilibrium quantum condensation in an incoherently pumped dissipative system", M. H. Szymanska, J. Keeling, P. B. Littlewood, Phys. Rev. Lett. 96, 230602 (2006).
  3. "Mean field theory and fluctuation spectrum of a pumped, decaying Bose-Fermi system across the quantum condensation transition", M. H. Szymanska, J. Keeling, P. B. Littlewood, Phys. Rev. B 75, 195331 (2007).

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"Polarised Fermi Superfluids: Phase Diagram and Dynamics"

Francesca Marchetti (Oxford, UK)

Recent advances in the ability to manipulate and control ultra-cold atomic vapours have provided a unique experimental system in which to explore pairing phenomena. Following the successful realisation of the crossover from the BCS state of Cooper pairs to the Bose Einstein condensation of diatomic molecules, attention has turned to the consideration of more exotic Fermi superfluids. A subject that has attracted particular theoretical and experimental interest is that of Fermi condensates with imbalanced spin populations, owing to the potential relevance of polarised Fermi condensates to QCD and magnetised superconductors. I will discuss the topology of the zero and finite temperature phase diagram for both cases of equal and unequal masses [1,2], the relevance of our findings to recent experiments, and the dynamics of phase separation [3].

  1. M. M. Parish, F. M. Marchetti, A. Lamacraft, B. D. Simons, Nature Physics 3, 124 (2007).
  2. M. M. Parish, F. M. Marchetti, A. Lamacraft, B. D. Simons, Phys. Rev. Lett. 98, 160402 (2007).
  3. A. Lamacraft and F. M. Marchetti, http://www.arxiv.org/abs/cond-mat/0701692.

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"Atom optics with Bose-Einstein condensates"

Robin Scott (Nottingham, UK)

Optical effects such as reflection, diffraction, focusing and interferometry, which are traditionally created with laser light, can also be produced with Bose-Einstein condensates. In many ways atom optics is directly analogous to traditional optics, but there are important differences due to atom-atom interactions, scattering events and finite temperature phase fluctuations. We show that these additional effects can have a pronounced effect on the dynamics of the atom cloud, sometimes spoiling the atom optics, but occasionally enhancing it, for example in interferometry. We also explain the different techniques we use to capture the key underlying physics.

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Non-equilibrium dynamics beyond Bogoliubov - de Gennes:
Dissipative bosonic atom dynamics in optical lattices using stochastic phase
space methods
 

J. Roustekoski (Soton, UK)


We study the effect of quantum and thermal fluctuations on bosonic atom dynamics in optical
lattices using stochastic phase space methods. As a first example, we consider the dipolar
motion of bosonic atoms in a very shallow, strongly confined 1D optical lattice [1] using the parameters
of the recent NIST experiment [2]. We find that, due to momentum uncertainty, a small, but non-negligible,
atom population occupies the unstable velocity region of the corresponding classical dynamics,
resulting in the observed dissipative atom transport. The stochastic simulations are able to
produce the observed damping rate of the atomic center-of-mass motion within the experimental
measurement uncertainty.

As a second example we study the splitting of a harmonically trapped atomic Bose-Einstein condensate
when we continuously turn up an optical lattice [3,4]. As the lattice height is increased, quantum fluctuations
of atoms are enhanced. We analyze the resulting nonequilibrium dynamics of the fragmentation process of
the condensate, the loss of the phase coherence of atoms along the lattice, and the reduced atom number
fluctuations in individual lattice sites. The comparisons to the atom number squeezing experiments [5] are
made. We find the atom number squeezing to saturate in deep lattices due to nonadiabaticity in turning up
of the lattice potential that is challenging to avoid in experiments when the occupation number of the lattice
sites is large, making it difficult to produce strongly number squeezed or the Mott insulator states with large
filling factors.

  1. J. Ruostekoski and L. Isella, Phys. Rev. Lett. 95, 110403 (2005).
  2. C. D. Fertig, K. M. O’Hara, J. H. Huckans, S. L. Rolston, W. D. Phillips, and J. V. Porto, Phys. Rev. Lett. 94, 120403 (2005).
  3. L. Isella and J. Ruostekoski, Phys. Rev. A 72, 011601 (2005).
  4. L. Isella and J. Ruostekoski, Phys. Rev. A 74, 063625 (2006).
  5. C. Orzel, A. K. Tuchman, M. L. Fenselau, M. Yasuda, and M. A. Kasevich, Science 291, 2386 (2001).

     

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"Vortex configurations in nanostructured superconductors: direct observations using Bitter decoration"


I.V. Grigorieva (Manchester, UK)

Vortices in superconductors represent a system of interacting particles that can be easily tuned and controlled by the applied field or a specially designed pinning potential. Confining the vortices in a mesoscopic (i.e., no more than a few microns in size) superconductor provides yet another tool to force them into specific configurations, control their number or even make vortices to merge into multiquanta flux lines with a single normal core (giant vortices). I will present our recent experimental findings, where vortices in mesoscopic superconductors were observed directly by the Bitter decoration method. In particular, we found that the circular geometry of superconducting disks leads to the formation of concentric shells of vortices and the filling of the shells is governed by well defined rules (“periodic law”). We were also able to identify ‘magic’ vortex numbers corresponding to the appearance of consecutive new shells. Furthermore, we investigated the effect of pinning on vortex configurations in confined geometry: While weak pinning only leads to distortions of the vortex shells, strong pinning forces up to 10 vortices to merge into tight clusters or, for sufficiently strong pinning, even true giant vortices. The experimental findings are in good agreement with the results of numerical simulations based on Ginzburg-Landau equations.
 


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Role of impurities in Superconductor-Insulator Transition

F. V. Kusmartsev and M. Saarela2

1 Department of Physics, Loughborough University, LE11 3TU, UK

2 Physical Sciences, P.O.Box 3000, FIN-90014 University of Oulu, Finland

We investigate the Nanoscale Structure Formations in underdoped High Temperature superconductors taking into account both phonons and strong correlations. The phonons may be responsible for local pairing that may lead to a formation of bi- tri- and other string and stripy polaron structures. The quantum nature of these structures and the strong Coulomb interaction force us to take into account many body quantum correlations.

The formation of superconducting and insulating states in underdoped cuprates may be well described by a two-dimensional strongly-interacting charged boson gas. This is one of the most fundamental and clean quantum systems. At high densities and zero temperature it is superconducting whereas at very low densities it forms a Wigner crystal where all charged carriers are localized and the system is an insulator. The existence of oxygen impurities with opposite charge equal to -2e lead to a formation of charged structures or the charge density waves symmetrically distributed around the impurities. Moreover, with decreasing density the Coulomb attraction of the impurity collects a cluster of bosons around it and induces oscillations of the boson density in the tail part. When the density decreases the amplitude of these oscillations increases. At the critical density, rs=3, a small cluster of four particles forms a bound state with the impurity. Outside this localized cluster or “an artificial atom” formed by correlations a fraction of positive background is revealed to keep to whole system neutral.That “atom” will attract the next shell of boson when the density is further decreased.

The layered growth of clusters and such specific charge density waves around random, charged impurities continues with decreasing density. The formation of the multi-shell droplets divides the charged boson fluid into two phases: bosons localized in clusters and superfluid bosons. Obviously, when the radius of those clusters is significantly smaller than the distance between impurities the flow of bosons through the system is superfluid. However, when the distance between impurities becomes equal to the cluster diameter then bosons will be fully localized. Such a state is no more superconducting even though some superconducting islands still exist. This is a quantum phase transition which has the first order character. Such a transition reminds the percolation phase transition with the difference that the main role here is played by the over-screening of the Coulomb interaction.

We present detailed results on this system using variation many body method based on the Jastrow type correlated wave function and show that they provide the microscopic explanation for the recent experimental findings in superconducting-insulator transition in high Tc superconductors [1,2] and formation of various structures observed in STM experiments[3].

[1] S. Oh, T. A. Crane, D. J. Van Harlingen and J. N. Eckstein, Phys. Rev. Lett. 96, 107003 (2006)
[2]M. Salluzzo, G. Ghiringhelli, N. B. Brookes, G. M. De Luca, F. Fracassi and R. Vaglio, Phys. Rev. B75, 054519 (2007)
[3] K. McElroy, J. Lee, J. A. Slezak, D.-H. Lee, H. Eisaki, S. Uchida, and J. C. Davis, Science 309, 1048 (2005).
[4] J.-X. Zhu, K. McElroy, J. Lee, T. P. Devereaux, Q. Si, J. C. Davis, and A. V. Balatsky, Phys. Rev. Lett. 97, 177001 (2006).

e_mail: F.Kusmartsev@lboro.ac.uk


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"Andreev edge channels and magnetic focusing in normal-superconductor hybrid systems: a semiclassical analysis"

Andor Kormányos (Lancaster, UK)

We study a transverse electron-hole focusing effect in a normal-superconductor system. The spectrum of the quasiparticles is calculated both quantum mechanically and in semiclassical approximation, showing an excellent agreement. A semiclassical conductance formula is derived which takes into account the effect of electron-like as well as hole-like quasiparticles. At weak magnetic fields the semiclassical conductance shows characteristic oscillations due to the Andreev reflection, while for stronger fields it goes to zero. These findigs are in line with the results of previous quantum calculations and with the expectations based on the classical dynamics of the quasiparticles[1].

  1. Phys. Rev. B 76, 064516 (2007).

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"Superlight small bipolarons in the presence of a strong Coulomb repulsion"

J.P. Hague (Loughborough)

Through the use of analytical results and quantum Monte-Carlo simulations, we show how a combination of lattice geometry, long-range attraction and local repulsion can lead to pairs which are both small and light. In particular, such pairs can be found for reasonable magnitudes of the phonon frequency and electron-phonon coupling. The possible Bose-Einstein condensation of the pairs is discussed. We show that small-light pairs are a precursor to high condensation temperatures. The stability of such a condensate to phase separation and disorder are also discussed.

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"Systematic study of strongly ferromagnetic S/FM/S Pi-junctions"

J. Robinson (Cambridge, UK)

We report a systematic study of Nb/FM/Nb trilayer structures in which the FM layer is one of the strong ferromagnets: Co, Fe, Ni, or Ni80Fe20(Py) [1,2]. Accurate control of the FM layer thickness has enabled detailed studies of the magnetic and transport properties in the superconducting state. In all cases we estimate the thickness of the magnetic dead layer and the exchange energies of the ferromagnetic layers; in doing so we demonstrate inconsistencies between the exchange energies derived elsewhere from S/FM bilayer experiments and from S/FM/S junction measurements compared to their bulk Curie temperatures which may hint at further complexity in the underlying physics.  Finally, we focus in detail on a single 0 to Pi phase-transition in Co based superconducting junctions and show evidence for the appearance of a second-harmonic in the current-phase relation at the minimum of the critical current [2,3].

  1.  J.W.A Robinson, S. Piano, G. Burnell, C. Bell, and M.G. Blamire, Phy. Rev. Lett. 97, 177003 (2006)

  2.  J.W.A Robinson, S. Piano, G. Burnell, C. Bell, and M.G. Blamire, Phy. Rev. B 76, 1 (2007)

  3.  H. Sellier, C. Baraduc, F. Lefloch, and R. Calemczuk, Phys. Rev. Lett. 92, 257005 (2004)

 


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