Fermi pockets and quantum oscillations of the Hall coefficient in high-temperature superconductors

Abstract

Recent quantum oscillation measurements in high-temperature superconductors in high magnetic fields and low temperatures have ushered in a new era. These experiments explore the normal state from which superconductivity arises and provide evidence of a reconstructed Fermi surface consisting of electron and hole pockets in a regime in which such a possibility was previously considered to be remote. More specifically, the Hall coefficient has been found to oscillate according to the Onsager quantization condition, involving only fundamental constants and the areas of the pockets, but with a sign that is negative. Here, we explain the observations with the theory that the alleged normal state exhibits a hidden order, the d-density wave, which breaks symmetries signifying time reversal, translation by a lattice spacing, and a rotation by an angle /2, while the product of any two symmetry operations is preserved. The success of our analysis underscores the importance of spontaneous breaking of symmetries, Fermi surface reconstruction, and conventional quasiparticles. We primarily focus on the version of the order that is commensurate with the underlying crystalline lattice, but we also touch on the consequences if the order were to incommensurate. It is shown that whereas commensurate order results in two independent oscillation frequencies as a function of the inverse of the applied magnetic field, incommensurate order leads to three independent frequencies. The oscillation amplitudes, however, are determined by the mobilities of the charge carriers comprising the Fermi pockets. Fermi surface reconstruction ͉ Hall effectA ny prospect of elucidating the mechanism of hightemperature superconductivity in cuprates is remote without answering some of the basic questions in clear terms. The most important of which is the notion of a Fermi surfacewhether or not it exists or is reconstructed because of a broken symmetry in the pseudogap state (1). An equally basic question is the extent to which a featureless spin liquid ground state, the resonating valence bond state (RVB), is important (2). In this respect, the recent experiments on quantum oscillations in high magnetic fields in high-quality samples of YBa 2 Cu 3 O y (Y123) and YBa 2 Cu 4 O 8 (Y124) have been striking (3-7).The quantum oscillations in the magnetization [de Haas-van Alphen effect (dHvA)], in the conductivity [Shubnikov-de Haas effect (SdH)], and in the Hall coefficient (R H ) have long been used to map out the Fermi surface and its topology in metals and semimetals (8). A Fermi surface differentiates the occupied electronic states from the unoccupied states in the momentum space and plays a fundamental role in quantum theory of matter. The highest occupied energy is an important parameter called the Fermi energy. The excitations from this surface determine the quasiparticles, which behave in many ways like bare particles, but their properties are modified by the collective interactions. An important notion is that a Fermi surface is a topological invarian...

Coexistence of Fermi arcs and Fermi pockets in a high-Tc copper oxide superconductor

“…This is distinct from that reported in Nd−LSCO system [23] which is symmetrical with respect to the (π,0)−(0,π) line, similar to the "shadow band" commonly observed in Bi2201 and Bi2212 [18]. This particular location makes it impossible to originate from the d-density-wave "hidden order" that gives a holelike Fermi pocket centered around (π/2,π/2) point [24,25]. Among other possible origins of Fermi pocket formation [26,27,28], the phenomenological resonant valence bond picture [27] shows a fairly good agreement with our observations, in terms of the location, shape and area of the hole-like Fermi pocket and its doping dependence.…”

“…This makes it impossible to correspond to the electron-like Fermi pocket suggested from quantum oscillation experiments [11,24].…”

Fermi surface reconstruction in hole-dopedt−Jmodels without long-range antiferromagnetic order

“…Recent observations of pocket-like Fermi surfaces in quantum oscillation experiments 1-5 as well as new angle resolved photo emission measurements 6 have triggered a renewed theoretical interest in this matter. [7][8][9] One possible, well known route to a Fermi surface reconstruction is the onset of spin-density wave (SDW) order, which breaks a large Fermi surface into small electron-and hole-pockets centered at the magnetic Brillouin zone boundary. 10,11 In fact, many of the unresolved theoretical problems in strongly correlated electron materials, from heavy-Fermion compounds to high-T c cuprates, are related to the fate of electronic excitations close to antiferromagnetic quantum critical points.…”

Chemical potential oscillations from nodal Fermi surface pocket in the underdoped high-temperature superconductor YBa2Cu3O6+x

“…A lthough high-T c cuprate superconductors have a history spanning a quarter of a century 1,2 , quantum oscillations in these materials have only been measured as recently as a few years ago [3][4][5][6][7][8][9][10][11][12] , by employing high magnetic fields to weaken superconductivity. Interestingly, their advent has signalled a reevaluation of the electronic structure in the normal state of the underdoped cuprates.…”

“…Quantum oscillation results have been interpreted in terms of a nodal-antinodal Fermi surface 4,9,11,12 arising from spatial symmetry breaking, where the antinodal sections correspond to electron pockets 12 , and the nodal sections correspond either to closed hole pockets or open sheets 11 in models proposed thus far. Multiple frequencies can arise not only from closed sections such as these, but also from warping, splitting, and magnetic breakdown effects of a single Fermi surface section.…”