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The Fermi surface of hole-doped cuprates : results from high magnetic field experiments in Toulouse

High magnetic fields generated at the LNCMI-Toulouse recently provided access to a direct measurement of the Fermi surface of underdoped hole-doped cuprates, thanks to the observation of quantum oscillations in the resistance and the magnetisation of those materials (for a review see [1]). Quantum oscillations is a unique tool in the quest for determining the ground state of a fermionic system : the Fermi surface [2]. The frequency of those quantum oscillations is proportional the size of the Fermi surface (see figure 2). Since the Fermi surface defines most of the physical properties of metallic solid, the precise determination of its topology in the k-space is essential in order to understand the physics of a material.


a)Generic phase diagram of hole-doped cuprates. Charge carrier doping allows to modify the ground state of a system from an antiferromagnetic Mott insulator (“AF insulator”), to a superconductor and finally to more conventional metal (“FL” for Fermi Liquid). b) and c) Quantum oscillations in an overdoped cuprate (c, see [8]) and underdoped cuprate (b, see [9]). Quantum oscillations have a much higher frequency in the overdoped regime. This implies that the Fermi surface observed in the underdoped regime is much smaller than that observed in the overdoped regime (see figure 2). The Fermi surface as observed with quantum oscillations is significantly modified with doping. The nature of this modification can be identified thanks to complementary Hall effect measurements (see panels d and e). While in the overdoped regime the Hall effect is positive in the low-T limit, meaning the large Fermi surface out of which fast quantum oscillations arise is hole-like, it is strongly negative in the underdoped regime, meaning in this case that the slow quantum oscillations are due to electron-like carriers. This major transformation, from a large hole-like Fermi surface in the overdoped regime to a small electron-like Fermi surface in the underdoped regime, is sketched in panels f and g. A Fermi surface reconstruction is most probably occuring at a critical doping between the two dopings shown here, where the large hole-like Fermi surface (blue, panel g), reconstructs into small electron pocket (red, panel f) (see text for more details about what migh be occurring at the critical doping).

Combined with Hall effect measurements, quantum oscillations revealed the existence of a quantum critical point (a phase transition occurring at zero temperature (see [3] and [4])) lying beneath the superconducting dome of the phase diagram of hole-doped cuprates. In a classical phase transition, temperature acts as the control parameter driving the system to the transition. Here, the system is driven to the critical point thanks to charge carrier doping. Fluctuations also exist at a quantum phase transition, except that those fluctuations are quantum mechanical in nature, in contrast with thermal fluctuations existing at a classical phase transition. Fluctuations found at a quantum phase transition can have a great influence over a wide range of the phase diagrams. Those fluctuations are thought to be responsible for the heavy-fermion character found in some strongly correlated electron systems (electron mass can be as high as 1000 bare electron mass) and might just as well be responsible for the cooper pairing required for the superconductivity observed in those systems (see [3]). With the existence of a quantum critical doping lying underneath the superconducting dome in high-Tc cuprates, it is now reasonable to think that the associated fluctuations are the origin of the pairing mechanism in high-Tc cuprate superconductors.

Figure 2 :The quantum oscillation frequency F is proportionnal to area (Ak) of the electron orbit (red dashed line) around the Fermi surface (blue) which occurs in a plane perpendicular to the magnetic field (B, red arrow).


Recent work

Recently we worked in order to determine more accurately the topology of the Fermi surface in the underdoped cuprates [5], modifications made to that Fermi surface upon doping [6], and consequences of the Fermi surface transformation mentioned earlier on high magnetic field transport properties [7].


References :

[1] B. Vignolle et al.,  Comptes Rendus de l’Académie des Sciences 12, 446 (2011)

[2] D. Schoenberg, University of Cambridge (1984)

[3] D. M. Broun, Nature Physics 4, 170 (2008)


[5] B. J. Ramshaw et al., Nature Physics 7, 234 (2011)

[6] D. LeBoeuf et al., Phys. Rev. B 83, 054506 (2011)

[7] B. Vignolle et al., arXiv:1107.5422

[8] B. Vignolle et al., Nature 455, 952 (2008)

[9] N. Doiron-Leyraud et al., Nature 447, 565 (2007)