Research HighlightsA. I. Coldea et al., Phys. Rev. Lett. 101, 216402 (2008)
LaFePO was the one of the first of the ferro-oxypnictide superconductors to be discovered1 and has a transition temperature of Tc ~ 6 K. Substituting the pnictogen P for As results in the isostructural compound LaFeAsO, which is non-superconducting and has a spin-density wave ground state but a small amount of electron doping (F replaced for O) that makes this system a superconductor with Tc~26 K2. Understanding the details of the Fermi surface of these two isostructural compounds may help to understand the reason for high Tc superconductivity in ferro-oxypnictide. Here we report detailed quantum oscillations measurements, one of the most powerful techniques to determine the details of the Fermi surface topology.
We measure torque magnetometry using piezocantilevers and high quality crystals of LaFePO (size of 200μm x 200μm x 20 μm) in high magnetic fields up to 45 tesla and low temperatures (0.3 K). We find that in the normal state LaFePO has a rich spectra of quantum oscillations (Figures 1a and b) containing at least seven different frequencies associated with the electronic bands centred along the AM direction (α1,2, β1,2 corresponding to minimum and maximum extremal areas of corrugated two-dimensional cylinders) and hole pockets centred along Γ-Z direction (δ, γ, ε) (see Figure 1c). The three-dimensional pocket predicted by band structure calculations is not observed in the current study. The obtained effective mass varies between
1.7-2.1me and the mass enhanced for LaFePO is a factor ~2 suggesting a moderate mass effect due to electronic correlations.
The difference in amplitudes of the dHvA signal between the hole and electron pockets is an indication of different scattering rates affecting these orbits. The near-perfect matching between the hole and the electron orbits that we observe suggests that LaFePO (which is non-magnetic) may be close to a spin/charge density wave transition and that magnetic fluctuations are an important ingredient in the physics of the Fe-based superconductors.
Figure 1a. Torque measurements versus magnetic field in LaFePO obtained in the hybrid magnet at 0.5 K for different orientations between the magnetic field and the c axis. b) Fourier transform spectra showing the frequencies associated with extremal areas of quasi-two dimensional electron and hole cylinders (see text). c). Fermi surface of LaFePO close to near nesting with the vector Q; the 3D pocket centered at Z is not observed in this study.
R.A. Cooper et al., Science 323 603 (2009)
When plunged into liquid nitrogen, a cheap cryogenic coolant, certain oxide materials undergo a phase transition from a metallic resistive state to a superconducting state characterized by the total loss of electrical resistance – meaning that current can flow without the aid of a battery. Historically, this remarkable state had always been considered a very low temperature phenomenon readily destroyed by the thermal agitation of the constituent atoms. Hence these oxide materials were quickly dubbed ‘high temperature superconductors’ in recognition of their surprisingly robust superconductivity, and the world held its breath in anticipation of a new technological revolution. Twenty years on, the revolution is still on hold, partly due to material issues, but also due to the fact that the origin of their superconductivity still remains a mystery. We know that the electrons pair up below the transition, but we yet to identify the “glue” that attracts the electrons together in the first place.
The metallic (resistive) state of these materials, i.e. above the transition temperature, is as enigmatic as the superconductivity itself and many people working within the field believe that the two are inextricably linked. Essentially, what scatters the electrons (and thus gives them their resistance) can also cause them to pair up and form the zero-resistance state. Thus in order to solve one riddle, you need to understand the other.
A metal is characterised by a resistance which decreases with decreasing temperature as the scattering processes become less numerous. At low temperatures, this temperature dependence typically follows a very simple power law with an exponent dependent on whichever scattering process is the more dominant. In typical metals, electron-electron scattering (i.e. electrons scattering off each other) is the dominant process and the corresponding exponent is two - if the temperature doubles, the resistance increases by a factor of four. In certain metals in close proximity to a phase transition to an ordered state (think of water turning into ice, or randomly oriented magnets aligning collinearly) the limiting low temperature exponent can be unity and the system is said to be ‘quantum critical’, as though the electrons themselves are teetering on the brink of becoming ordered. According to theoretical predictions, this exotic form of resistance survives to low temperature only precisely at the quantum critical point where the phase transition is driven to zero temperature. This is shown pictorially in the left-hand panel where the exponent of the electrical resistance is plotted as a function of temperature and some other control parameter, such as pressure, applied magnetic field or chemical composition, that tunes the system towards the quantum critical point, labelled gc at zero kelvin.
At elevated temperatures, e.g. above the superconducting “dome” (indicated by a dashed line in the right-hand panel), the resistance of high temperature superconductors resembles that seen in other putative quantum critical systems, prompting many in the field to consider them from the same viewpoint. Indeed, if one ignores the region below the dashed line, one can convince oneself that the diagram on the right resembles the region on the left very close to gc. In order to really test this hypothesis properly however, one needs to be able to measure the resistance at temperatures below the superconducting dome. In other words, high temperature superconductivity is itself a hindrance in our quest to probe the metallic state from which it emerges.
By using ultra high magnetic fields that last a fraction of a second, an international team led by Nigel Hussey at the University of Bristol and Cyril Proust at LNCMP in Toulouse, have been able to strip away the veil of superconductivity surrounding this putative quantum critical point to reveal the underlying phase diagram for the first time. To their surprise, they found that rather than collapsing to a single point, as in the left-hand panel, the linear-in-temperature resistance regime (the brown color-coded region) fans out to fill the entire superconducting region, in complete contradiction with theory. Intriguingly, the magnitude of the slope of the resistance is a maximum precisely at the critical point (labelled gc* in the right-hand panel), suggesting some form of quantum criticality, but not that envisaged in previous theoretical models. The team duly coined this behavior “anomalous criticality”.
So what is the significance of this finding for high temperature superconductivity? Well, moving from the right of the phase diagram in the right-hand panel (corresponding to a reduction in the number of mobile electrons), Cooper and co-workers discovered that the strength of the linear-in-temperature resistance scales with the superconducting transition temperature, confirming that whatever causes the linear-in-temperature scattering must also cause the electrons to pair up into the superconducting state. At the critical doping concentration gc*, the strength of the electron scattering is sufficiently large as to cause the electrons to become sluggish or even localize around individual atomic sites which in turn causes the superconductivity to collapse. It is as though the interaction that promotes high temperature superconductivity ultimately destroys the very electronic states from which the superconducting pairs form. Now the big question is to identify just what that interaction is and how might it be possible to get around its self-destructive tendencies!
Left-hand panel. Temperature-tuning parameter phase diagram for a conventional quantum critical system described in terms of the power-law exponent of the temperature-dependence of the electrical resistance. Right-hand panel. Comparative phase diagram for high temperature superconductors. The white dashed line indicates the superconducting transition temperature in zero magnetic field. In the presence of a high magnetic field, the veil of superconductivity is stripped away to reveal the metallic ground state underneath and the persistence of the linear-in-temperature resistance across the phase diagram, an observation that is difficult to explain within conventional quantum critical scenarios.