
General
Superconductivity and superfluidity are manifestations of quantummechanic behavior (i.e. dissipationless flow properties) in the macroscopic world. This means that the concept of a quantummechanical wave function, usually describing elementary particles, atoms or molecules, can be used to describe the entire superconducting or superfluid condensate (macroscopic wave function). The phase of this macroscopic wave function is seen to vary spatially over distances much larger than the atomic radius. The condensate (superflow) velocity can then simply be related to spatial gradients of this phase variable. Not surprisingly, new effects emerge, such as dissipationless electronic and hydrodynamic transport of mass, charge and spin. Sometimes the properties are found to be rather counterintuitive, for example when a supercurrent passes through an insulator or when a constant voltage drop results in an oscillating current.
Many of the phenomena in superconductors are being exploited for modern applications. Magnetic resonance imaging (MRI) which became a standard tool for materials characterization and medical diagnosis relies on large superconducting coils. Similarly, accelerators or fusion technology are impossible without superconductors. Pilot projects were launched for the replacement of copper by superconducting materials in the power grid. The most sensitive detectors for magnetic fields being used in many laboratories around the world exploit the quantum nature of the supercurrent. Since recently, flux quantization in small superconducting rings became one of the potential bases in quantum information technology.
Beyond applications, superconductivity and superfluidity can still be counted to the most fascinating and challenging fields of basic research. At the time Bardeen, Cooper, and Schrieffer explained superconductivity as a subtle (pairing) interaction between the conduction electrons and the lattice, the perception of the ground state was comparably simple. Soon thereafter, the discovery of superfluidity in the isotope ^{3}He opened the pandemonium of exotic pairing states, in which anisotropies in the spin, and orbital angular momentum degrees of freedom are of equal importance. These facts along with the extraordinary purity opened the view of Fermisuperfluids as model systems for more general pair condensates with enormous intellectual impact also on metallic superconductors. The analogies became particularly obvious after the discovery of pairing states with higher angular momentum in heavy fermion systems and cuprates such as UBe_{13} and YBa_{2}Cu_{3}O_{7}, respectively. Specifically, but not only in the cuprates, superconductivity is not the only possible ground state. Rather various types of ordering phenomena including magnetism, charge and spin density waves or ordering fluctuations compete with the Cooper pairing mechanism. This snapshot indicates how far we are away from a sound understanding of systems with complex electronic interactions, with the phenomenon of superconductivity representing just one of several possible instabilities. Clearly, only the synopsis of a larger class of materials opens new insights into fundamental problems which, after all, may lead to novel applications.
The related research activities at the WMI include the following subjects:
 the liquid and solid phases of ^{3}He
 Conventional and unconventional superconductors
 Spin and charge density waves (SDW and CDW) and superconductivity in organic metals and layered systems
 the phase diagram of copperoxygen compounds
 solidstate based quantum information technology
 Theory of unconventional superconductivity and superfluidity (analytic twofluid description, electromagnetic response, electronic Raman response, spin response)
The material classes, methods and main objectives we work on are:
 ^{3}He, ^{4}He and mixtures (structure of solid ^{3}He, transport in quantum liquids)
 Heavy fermion superconductors, cuprate superconductors, Sr_{2}RuO_{4}, noncentrosymmetric superconductors, multigap superconductors
 (BEDTTTF)_{2}X (X = Cu[N(CN)_{2}] Br e.g.) (SDW, CDW, superconductivity, metalinsulator transition)
 CuO_{2} compounds (crystal growth, transport, spectroscopy, antiferromagnetism, ordering fluctuations, pairing mechanism)
Current Projects
 In the field of high temperature superconductivity the WMI participates in the Priority Program "Pnictide Superconductors" SPP1458 of the German Research Foundation (DFG) coordinated by B. Büchner (IFW Dresden), R. Hackl (WMI), C. Honercamp (RWTH Aachen), and D. Johrendt (LMU München). The WMI contributes one project to this coordinated research program: Raman study of the interrelation of electron dynamics and phase transitions in ironpnictide compounds (R. Hackl, R. Gross)
 Quantum oscillations in NCCO (M. Kartsovnik, A. Erb, R. Gross)
 Analytic representation of BCS response functions (D. Einzel, P. Schmidt)
 Analytic solutions of the GinzburgLandau equations (D. Einzel, R. Doll, J. Woste)
 The gauge mode and massive order parameter collective modes in multigap superconductors (D. Einzel, N. Bittner)
Students at any level are invited to participate in the research projects. For practical lab work, Bachelor and Master/Diploma theses please contact the person indicated in the respective projects.
Selected Results:

 Cuprates (R. Hackl)
Superconductivity in the cuprates (Fig.1) remains one of the major open problems in condensed matter physics. There is wide (though not general) consensus that direct electronelectron interactions and magnetism are relevant for Cooper pairing. However, there are only pieces of evidence in support of this hypothesis.
For further insight we study the electronic properties of various cuprate systems as a function of doping and temperature. It turns out that electrons propagating along the diagonal of the CuO_{2} plane have universal properties both in the normal and in the superconducting state wheras those with momenta along the principle direction suffer a substantial dependence on the material class and on sample details. This is particularly striking for doping levels p≤0.21 holes per CuO_{2} f.u. as shown in Fig. 2. A phenomenological analysis demonstrates that Landau Fermi liquid properties apply universally for high doping. Below 0.21, only diagonal particles continue to follow this paradigm. It is one of the challenges to figure out which of the properties is at the origin of the high Tc.
In the period between 2003 and 2010, research into the cuprates was supported by the DFG via the Research Unit "Phase Transitions in CopperOxygen Compounds" (FOR 538) coordinated by the WMI (Rudi Hackl). The results are summarized in the European Physical Journal Special Topics, volume 188 (edited by R. Hackl and W. Hanke).



Fig. 1:
 Crystal structure of YBa_{2}Cu_{3}O_{7} (Y123). Y (blue), Ba (yellow) Cu (red) O (black). The material shown has a doping level p=0.19 free holes per CuO_{2} formula unit. Upon removing oxygen from the chains along b the doping is reduced. For O_{6} there are no free carriers. The CuO_{2} planes (shaded in red) are nearly 2D conductors.
 


Fig. 2:
 Universal phase diagram of the cuprates. At zero doping (O_{6} in Y123) the materials are antiferromagnetic insulators. At p=0.16 the maximal transition temperature is reached. Above p=0.21, the cuprates are nearly isotropic metals. For p<0.21 only electrons with diagonal momenta have metallic properties. Depending on the polarizations, the light scattering experiment can separately project out electrons propagating along the diagonals and the principle axes. 


Recent Publications:
Pair breaking versus symmetry breaking: Origin of the Raman modes in superconducting cuprates
N. Munnikes, B. Muschler, F. Venturini, L. Tassini, W. Prestel, Shimpei Ono, Yoichi Ando, D. C. Peets, W. N. Hardy, Ruixing Liang, D. A. Bonn, A. Damascelli, H. Eisaki, M. Greven, A. Erb, and R. Hackl,
Phys.Rev. B 84, 144523 (2011)
Superconductivity in copperoxygen compounds
R. Hackl,
Z. Kristallogr. 226, 323 (2011)
Electron interactions and charge ordering in CuO_{2} compounds
B. Muschler, W. Prestel, L. Tassini, R. Hackl, M. Lambacher, A. Erb, Seiki Komiya,
Yoichi Ando, D. C. Peets, W. N. Hardy, Ruixing Liang, D. A. Bonn, Eur. Phys. J Special Topics 188, 131 (2010)
Towards a better understanding of superconductivity at high transition temperatures
R. Hackl and W. Hanke,
Eur. Phys. J Special Topics 188, 3 (2010)

 Ironbased systems (R. Hackl)
Hightemperature superconductivity in ironbased compounds (FeSC, Fig. 1) was first observed in 2008 and is considered a surprise similar to that of the discovery of the cuprates. In contrast to the cuprates, the FeSC are true multiband systems. The relative area of the electron and hole bands can be tuned by atomic substitution. Very early, the similarity of the Fermi surfaces was considered crucial for the high Tc since the spin susceptibility develops pronounced maxima which drive instabilities towards spin order and superconductivity. The tunability of the Fermi surfaces makes the FeSC a laboratory for studying pairing channnels beyond electronphonon coupling.
The work on the FeSC is supported by the DFG via the Priority Program "Superconductivity in the Pnictides" (SPP1458) since 2010. The program is coordinated by B. Büchner (IFW Dresden), R. Hackl (WMI), C. Honercamp (RWTH Aachen), and D. Johrendt (LMU München).
At the WMI, we study spin and carrier properties including the momentum dependence of the superconducting gap in compounds with characteristic Fermi surface shapes. In BFCA we observe a strong anisotropy of the gap on the electron bands having minima close to or at zero (Fig.2). Away from optimal doping we find finite gaps. In the future we try to find out how the gap develops in systems with significantly different Fermi surfaces. We hope to establish a connetion between the gap and the pairing potential. More generally, we scrutinize the concepts for unconventional superconductivity beyond the FeSC.



Fig. 1:
 Crystal structure and Raman selection rules of BaFe_{2}As_{2} (BFA). (a) Unit cell: Ba (green), Fe (red) As (black). The parent compound is a metal with spin density wave (SDW) order below 138K. Upon substituting Ba by K, Fe by Co, or As by P the SDW is suppressed and superconductivity appears. (b) The central hole bands and the electron bands encircling M can be projected independently (cum grano salis) using the light polarizations indicated at the bottom. 



Fig. 2:
 Raman spectra of BFCA right above and well below Tc=24K. Isotropic gaps would result in spectra with a sharp onset of the intensity at twice the gap energy 2Δ. The continuous increases of the spectra indicate a broad distribution of gaps on all bands. 


Recent Publications:
RamanScattering Detection of Nearly Degenerate sWave and dWave Pairing Channels in IronBased Ba_{0.6}K_{0.4}Fe_{2}As_{2} and Rb_{0.8}Fe_{1.6}Se_{2} Superconductors
F. Kretzschmar, B. Muschler, T. Böhm, A. Baum, R. Hackl, HaiHu Wen, V. Tsurkan, J. Deisenhofer, A. Loidl, Phys. Rev. Lett. 110, 187002 (2013)
Pinpointing Gap Minima in Ba(Fe_{0.94}Co_{0.06})_{2}As_{2} via Band Structure Calculations and Electronic Raman Scattering
I. I. Mazin, T. P. Devereaux, J. G. Analytis, JiunHaw Chu, I. R. Fisher,
B. Muschler, R. Hackl, Phys. Rev. B 82, 180502(R) (2010)
Band and momentum dependent electron dynamics in superconducting
B. Muschler, W. Prestel, R. Hackl, T.P. Devereaux, J. G. Analytis, JiunHaw Chu,
I. R. Fisher, Phys. Rev. B 80, 180510(R) (2009))

 Tritellurides (R. Hackl)
Charge density wave (CDW) formation is an abundant phenomenon in condensed matter physics. Originally, it was considered an instability in onedimensional (1D) systems resulting from parallel or nested portions of the Fermi surface (Peierls). More generally, phonons have a reduced energy at twice the Fermi momentum 2k_{F} also in higher dimensions and even for spherical Fermi surfaces (Kohn). If, in addition, parts of the Fermi surface are nested the phonon energy may be renormalized down to zero. Then the lattice becomes soft and distorts with a modulation given by the inverse nesting vector which by and large coincides with 2k_{F}.
The tritellurides (RTe_{3}, Fig. 1) are model systems for the study of CDWs. The transition temperatures can be tuned in a wide range by varying the lattice parameters using chemical or applied pressure. In addition, those RTe_{3} systems with heavy rare earth atoms (R = Dy, Ho, Er, Tm) have two consecutive transitions with orthogonal ordering vectors. TbTe_{3} was reported to exhibit superconductivity if the CDW is suppressed by pressure. Hence, the experiments can be considered complemetary to the studies in the organic metals, the cuprates and the ironbased compounds where spin and charge density waves are in close proximity to superconductivity.
Our experiments reveal the amplitude modes (AM) of all transitions (Fig. 2). We show how the collective modes couple to the phonons and how the transition can be suppressed by pressure. Using the AM for identifying the CDW the phase diagram can be mapped out.



Fig. 1:
 Crystal structure and reciprocal space of RTe_{3} (R = rare earth, here Dy, La). (a) Unit cell: Te (violet), R (green). (b) An isolated Te plane is sufficient to capture most of the electronic properties. The Te 5p_{x} (green) and p_{z} (yellow) orbitals have substantial overlaps only along their axes (V_{pσ}) constituting orthogonal Fermi surface sheets. The hopping perpendicular to those chains (V_{pπ}) gives rise to warping. (c) Fermi surface and energetically possible ordering vectors Q* and Q_{1}. (d) Hybridization between the p_{x} and p_{z} orbitals leads to closed Fermi surfaces. 



Fig. 2:
 Energies and intensities of CDW amplitude modes and of phonons. The upper panels show the energies of amplitude modes of (a) DyTe_{3} at ambient pressure and (b) LaTe_{3} at 6GPa applied pressure. (c) and (d) show the Variation of the intensities of phonons and AMs with temperature. 


Recent Publications:
Alternative route to charge density wave formation in multiband systems
H.M. Eiter, M. Lavagnini, R. Hackl, E.A. Nowadnick, A.F. Kemper, T.P. Devereaux, J.H. Chu, J.G. Analytis, I.R. Fisher, L. Degiorgi,
Proc. Nat. Ac. Sci. 110, 64 (2013)
Raman scattering evidence for a cascadelike evolution of the chargedensitywave collective amplitude mode
M. Lavagnini, H.M. Eiter, L. Tassini, B. Muschler, R. Hackl, R. Monnier, J.H. Chu, I. R. Fisher, and L. Degiorgi,
Phys. Rev. B 81, 081101(R) (2010)

