Correlated Electron Systems Group Research Highlights

In conventional superconductors, lattice vibrations (phonons) mediate the attraction between electrons that is responsible for superconductivity. The high transition temperatures (high-T_c) of the copper oxide superconductors has led to collective spin excitations being proposed as the mediating excitations in these materials. The mediating excitations must be strongly coupled to the conduction electrons, have energy greater than the pairing energy, and be present at T_c. The most obvious feature in the magnetic excitations of high-T_c superconductors such as YBa₂Cu₃O_6-x is the so-called ‘resonance’. Although the resonance may be strongly coupled to the superconductivity, it is unlikely to be the main cause, because it has not been found in the La_2-x(Ba,Sr)_xCuO₄ family and is not universally present in Bi₂Sr₂CaCu₂O_8-x. In this work we used inelastic neutron scattering to characterize possible mediating excitations at higher energies in YBa₂Cu₃O_6.6. We observed a square-shaped continuum of excitations peaked at incommensurate positions. These excitations have energies greater than the superconducting pairing energy, are present at T_c, and have spectral weight far exceeding that of the ‘resonance’. The discovery of similar excitations in La_2–xBa_xCuO₄ suggests that they are a general property of the copper oxides, and a candidate for mediating the electron pairing.
  More details can be found in the following publication : The structure of the high-energy spin excitations in a high-transition temperature superconductor, S.M. Hayden et al., Nature 429, 531 (2004).
 
  The image shows magnetic excitations in YBa₂Cu₃O_6.6. Note the peaks at incommensurate positions.

Magnesium diboride (MgB₂) is a unusual superconducting for two reasons. Firstly it has the highest critical temperature (39 K) of any material besides the high T_c cuprate superconductors, and secondly it has two distinct superconducting gaps. This latter property means that the energy needed to break apart a Cooper pair depends on which sheet of Fermi surface they have formed. In all other superconductors the electrons in the Cooper pair scatter rapidly between the different Fermi surface sheets and so there is only one effective energy gap.  This two gap property of MgB₂ has been established by many experiments including our own magnetic penetration depth measurements [1,2]. In anisotropic superconductors the lower and upper critical fields H_c1 and H_c2 depend on which direction the field is applied.  However, in most materials the ratio of H_c1 say along the crystallographic a direction to that along the c direction is independent of temperature. In MgB₂ the behaviour is quite different. Our work combined measurements of the magnetic penetration depth (λ) with measurements of the specific heat to determine the anisotropies of H_c1 and H_c2 (γ_λ and γ_ξ respectively) [3]. We found that they have opposite temperature dependencies, but tend to a common value at T_c. This has been understood theoretically as a direct consequence of the two gap nature of the superconductivity in MgB₂. [1] Exponential temperature dependence of the penetration depth in single crystal MgB₂, Phys. Rev. Lett. 88, 047002 (2002) [2] Magnetic penetration depth of MgB₂”, Physica 385C, 205 (2003) [3] Temperature dependent anisotropy of the penetration depth and coherence length in MgB₂, Phys. Rev. Lett. 95 097005 (2005).
  The figure shows the temperature dependence of the anisotropy in the London penetration depth (γ_λ) and upper critical field ( γ_ξ) of MgB₂.
 

In addition to their obvious technological potential, high temperature superconductors also represent one of the most challenging materials for fundamental physicists. Not only do they superconduct at such phenomenally high temperatures (the current record stands at 166K), many of their physical properties are so unusual, they challenge our basic understanding of how electrons interact inside a solid. One reason for their anomalous behaviour is believed to be their highly two-dimensional electronic state. High temperature superconductors are constructed of layers of copper and oxygen arranged in a kind of chequerboard configuration. Owing to this highly layered texture, current flow within these copper-oxide planes can be as much as 10,000 times higher than between adjacent planes. We are familiar with the notion of an electron having an associated spin and charge as given by fundamental constants. Electrons in lower dimensions however obey different statistics and therefore show strikingly different properties. When electrons are confined to two dimensions, the charge can take fractional values, whilst in one dimension, the spin and the charge can separate altogether. Indeed, the notion of spin-charge separation has been suggested as a possible origin of the anomalous behaviour of high temperature superconductors, but as yet, no consensus has been reached within the community. Clearly though, confirmation of the dimensionality of the electronic system will go a long way to achieve this.
One way to determine the dimensionality of a metal is to examine the energy contour of its most energetic (i.e. fastest moving) electrons, those which dominate the electrical properties of the material. In an isotropic three dimensional metal, this contour, or Fermi surface, takes the form of a sphere. The velocity vectors of these high-octane electrons emanate at right angles to the Fermi surface, rather like the spikes of a sea urchin. In two dimensions, this surface is a cylinder and the velocity vectors resemble the tongues of a hair curler. The crucial point here is that now the vectors only have components in two dimensions. The energy contour of the high temperature superconductors has remained elusive for seventeen years. In this work we have succeeded in measuring this energy contour for the first time. Detailed analysis of the results has shown that whilst the energy contour resembles a cylinder, it contains faint ripples running along the cylindrical axis as shown schematically in the figure. These ripples signify that the electrons have a small but finite velocity component in the third direction and so confirm the three dimensionality of this particular high temperature superconductor. The puzzle now is to understand why, if these materials really are three-dimensional in nature, are their physical properties so unusual. A paper containing the main results is available for download. A coherent three-dimensional Fermi surface in a high-transition temperature superconductor, Nature 425, 814 (2003).
 
  Ripples on the Fermi surface of the overdoped superconductor Tl₂Ba₂CuO_6+δ.

The Electronic structure of MgB₂ is unusual in that there are two distinct types of Fermi surface sheet which couple very differently to the phonons. Band structure calculations (Kortus et al, PRL 2001) show that there are two quasi-two-dimensional warped tubes which couple strongly to the phonons and two more three dimensional tubular networks which couple weakly to the phonons. This unusual structure is key to understanding the high T_c and unique two superconducting gap behaviour of this compound. Our study of the the de Haas-van Alphen (dHvA) effect has been very important in verifying this model of the electronic structure. We were able to measure accurately the cross-sections of the various Fermi surface sheets and compare them to theory, thus confirming the topology of the calculated Fermi surface . In addition we were able to measure the quasiparticle effective masses on the various sheets and thus deduce the strength of the electron phonon coupling. We were able to show directly for the first time, that the electron-phonon coupling on the 2D σ sheets is (as predicted) about 3 times stronger than on 3D π sheets. Recently we have extended this work to looking at the electronic structure of Al-doped MgB₂. The Al substitutes for the Mg, effectively doping electrons. It is observed that adding Al causes T_c to decrease. In principle, this could result either from a bandstructure effect (i.e., directly from the electron doping) or from increased scattering between the σ and π sheets. We were able to observed dHvA oscillations in 7% Al doped MgB₂ using a 33T magnet at NHMFL in Tallahassee, Florida. Our results [4] give quantitative experimental backing to theoretical bandstructure calculations and show that the main cause of T_c reduction is the band filling effect of the doping not scattering. An important remaining question is whether can T_c be raised significantly by doping holes into the structure. [1] Determination of the Fermi Surface of MgB₂ by the de Haas-van Alphen effect, Phys. Rev. Lett. 91, 037003 (2003)
  [2] de Haas-van Alphen effect in single crystal MgB₂, Phys. Rev. Lett. 88, 217002 (2002).
  [3] de Haas-van Alphen effect in MgB₂ crystals, Physica 385C 75 (2003).
  [4] de Haas-van Alphen effect investigation of the electronic structure of Al-substituted MgB₂,Physical Review B 72, 060507(R), (2005)
 
  Calculated Fermi surface of MgB₂, showing various extremal orbits.

PrBa₂Cu₄O₈ (Pr124) is isostructural with the high-temperature superconductor YBa₂Cu₄O₈ (T_c ~ 80K) with 1D CuO chains sandwiched between 2D CuO₂ planes (see figure below). In Pr124, holes on the CuO₂ planes are localised, hence non-superconducting. The double chain, however, remains metallic and thus offers a unique opportunity to study the quasi-1D cuprate chain in isolation. Despite the extremely 1D nature of the chain carriers (ρ_a/ρ_b ~ 1000 at 4.2K), we found that ρ(T) varies as T² below 50 K along all three axes [1], suggesting that Pr124 is an anisotropic yet still 3D Fermi-liquid at low T. Above 100K, ρ_a and ρ_c become semiconducting. In addition to this 3D-1D temperature-induced dimensional crossover, we also found a 3D-1D magnetic-field-induced dimensional crossover occurs at low-T and high magnetic fields [2]. Analysis of the various crossover energy scales allowed us to determine the degree of warping on the Fermi surface in Pr124 and revealed a new route towards achieving a purely 1D metallic state at low T [3].
  [1] Metallic c-axis transport across insulating planes in PrBa₂Cu₄O₈, J. Phys. Soc. Jpn., 71 704 (2002).
  [2] Three-dimensional Fermi-liquid ground state in a quasi-one-dimensional cuprate, Phys. Rev. Lett., 89 086601 (2002).
  [3] PrBa₂Cu₄O₈: a new laboratory for low dimensional physics, NHMFL Reports, 10 (2) 4 (2003).
  Structure of PrBa₂Cu₄O₈
 

Smart alloys which exhibit shape-memory and super-elastic phenomena have been deployed in a wide variety of applications ranging from actuators in aircraft wings to surgical instruments. However, an atomic-scale understanding of the origin of the martensitic transformation (MT), the structural transformation at the heart of these phemomana, is still lacking. It has been hypothesised that lattice vibrations are the key, an idea supported by first-principles calculations indicating that strong coupling of certain phonons to the electrons (phonon softening), due to particular features in the Fermi surface, plays a crucial role. Owing principally to the compositional disorder inherent to many of these alloys, a Fermi surface determination in these materials is experimentally challenging, with traditional quantum oscillatory techniques suffering due to their reliance on a long electronic mean free path. We have been able to provide experimental evidence in support of the intimate relationship between the phonon softening and the Fermi surface through a Compton scattering. More details can be found in the paper below.
  Observation of a strongly nested Fermi surface in the shape-memory alloy Ni_0.62Al_0.38, Phys. Rev. Lett. 96 , 046406 (2006).
  Fermi surface of Ni_0.62Al_0.38.