# Focus on fermiology of the cuprates

Michael Norman, Cyril Proust

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Michael Norman, Cyril Proust. Focus on fermiology of the cuprates. New Journal of Physics, 2014, 16, pp.045004. 10.1088/1367-2630/16/4/045004. hal-01048669

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EDITORIAL • OPEN ACCESS

Focus on fermiology of the cuprates

To cite this article: Michael R Norman and Cyril Proust 2014 *New J. Phys.* **16** 045004

View the [article online](#) for updates and enhancements.

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Editorial

**Focus on fermiology of the cuprates**

**Michael R Norman<fnref n="1" /> and Cyril Proust<fnref n="2" />**

E-mail: cyril.proust@lncmi.cnrs.fr

Received 5 February 2014

Accepted for publication 5 February 2014

Published 8 April 2014

New Journal of Physics **16** (2014) 045004

doi:10.1088/1367-2630/16/4/045004

**Abstract**

Almost three decades after the discovery of high temperature cuprate superconductors, the origin of their high critical temperature remains an enigma. But it is now possible to discuss the ‘fermiology’ of the cuprates thanks to the discovery of quantum oscillations, which give valuable information about the Fermi surface and therefore the physical properties of a metal. The aim of this ‘focus on’ collection is to bring together experimentalists and theorists in order to provide new insights into the Fermi surface of cuprate superconductors. This new direction of research has definitely stimulated further progress in the field of high temperature superconductivity.

The Fermi surface of a metal delimits in reciprocal space the occupied electronic states from the empty ones. It is a basic property of solid state physics, which underlies many of the electrical and thermal properties of a metal. Even in the presence of interactions, this concept remains robust. In superconductors, the instability of the normal state leads to the opening of an energy gap around the Fermi surface, as described by the theory of Bardeen, Cooper and Schrieffer [1]. This has proved to be a successful description of low $T_c$ superconductors.

The discovery of high $T_c$ cuprate superconductors by Bednorz and Müller in 1986 is considered a major event for the condensed matter physics community [2]. Not only has the critical temperature for superconductivity reached unexpected values (the record is 135 K at

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<footnote n="1">¹Materials Science Division, Argonne National Laboratory, Argonne, IL 60439, USA</footnote>

<footnote n="2">²Laboratoire National des Champs Magnétiques Intenses, Toulouse, France</footnote>
ambient pressure), but many new theoretical ideas have emerged in an attempt to describe the electronic properties of these materials. After almost 28 years of intense research, some fundamental questions remain. What is the source of pairing that causes the appearance of superconductivity? What is the nature of the normal phase from which superconductivity arises? Over much of the phase diagram, this normal state exhibits an energy gap. In this so-called pseudogap phase, well-defined quasiparticle excitations do not exist in large regions of momentum space [3]. Although discovered only three years after the pioneering work of Bednorz and Müller, the physical origin of this pseudogap behavior, and whether it constitutes a distinct phase of matter, is still the subject of much debate.

In 2007, a breakthrough occurred with the unambiguous observation of quantum oscillations in underdoped $YBa_2Cu_3O_{6.5}$ [4]. This effect is a direct consequence of quantization of closed cyclotron orbits, establishing the existence of a well-defined Fermi surface in the ground state of underdoped cuprates [5, 6].

While there was little doubt about the existence of a Fermi surface with sharply defined excitations on the overdoped side of the phase diagram of the cuprates [7, 8], the discovery of quantum oscillations in the underdoped regime was a surprise. Combined with other probes sensitive to the electronic structure, such as ARPES [9, 10] and STM [11], and to magnetic order, like neutron diffraction [12], along with theoretical modeling [13–16], this field has moved forward rapidly with the goal of understanding the origin of the pseudogap.

In electron-doped cuprates, it is believed that below a critical doping, commensurate antiferromagnetic order breaks translational symmetry and a Fermi surface reconstruction occurs, leading to small Fermi pockets [17].

In hole-doped cuprates, the obvious candidate for the broken symmetry associated with the Fermi surface reconstruction was first detected by high field nuclear magnetic resonance (NMR) measurements, which have revealed the emergence of a modulation of the charge density at low temperature [18]. In zero field, short range static charge correlations in underdoped YBCO were subsequently observed with resonant soft x-ray scattering [19, 20], hard x-ray scattering [21], and inelastic x-ray scattering [22] experiments. High field sound velocity measurements in YBCO have provided a thermodynamic signature of this charge order [23]. Both x-ray and ultrasound measurements point to biaxial charge order. A Fermi surface reconstruction due to such order can lead to an electron pocket in the ‘nodal’ region of the Brillouin zone along the zone diagonals [24]. This can explain the negative Hall [25] and Seebeck [26] coefficients measured at low temperatures.

But the link between the pseudogap and the charge order is still an open question. Many recent theories have been proposed to explain the presence of charge order in the phase diagram of hole-doped cuprates [27–33]. Its elucidation will surely lead to a better understanding of the mechanism of high temperature superconductivity.

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[32] Lee P A 2014 arXiv:1401.0519

[33] Wang Y and Chubukov A 2014 arXiv:1401.0712