Competing order, Fermi surface reconstruction, and quantum oscillations in underdoped high-temperature superconductors

Abstract

We consider incommensurate order parameters for electrons on a square lattice which reduce to d-density wave order when the ordering wavevector Q is close to Q0 = (π/a, π/a), a being the lattice spacing, and describe the associated charge and current distributions within a single-harmonic approximation that conserves current to lowest order. Such incommensurate orders can arise at the mean-field level in extended Hubbard models, but the main goal here is to explore thoroughly the consequences within a Hartree-Fock approximation. We find that Fermi surface reconstruction in the underdoped regime can correctly capture the phenomenology of the recent quantum oscillation experiments that suggest incommensurate order, in particular the de Haas-van Alphen oscillations of the magnetization in high fields and very low temperatures in presumably the mixed state of these superconductors. For 10% hole doping in YBa2Cu3O 6+δ , we find in addition to the main frequency around 530 T arising from the electron pocket and a hole frequency at around 1650 T, a new low frequency from a smaller hole pocket at 250 T for which there are some indications that require further investigations. The oscillation corresponding to the electron pocket will be further split due to bilayer coupling but the splitting is sufficiently small to require more refined measurements. The truly incommensurate d-density wave breaks both time reversal and inversion but the product of these two symmetry operations is preserved. The resulting Fermi surface splits into spin up and spin down sectors that are inversion conjugates. Each of the spin sectors results in a band structure that violates reflection symmetry, which can be determined in spin and angle resolved photoemission spectroscopy. For those experiments such as the current photoemission experiments or the quantum oscillation measurements that cannot resolve the spin components the bands will appear to be symmetric because of the equal mixture of the two spin sectors. There is some similarity of our results with the spiral spin density wave order which, as pointed out by Overhauser, also breaks time reversal and inversion. Calculations corresponding to higher order commensuration produces results similar to anti-phase spin stripes, but appear to us to be an unlikely explanation of the experiments. The analysis of the Gorkov equation in the mixed state shows that the oscillation frequencies are unshifted from the putative normal state and the additional Dingle factor arising from the presence of the mixed state can provide a subtle distinction between the spiral spin density wave and the d-density wave, although this is very difficult to establish precisely.

Violation of the Onsager relation for quantum oscillations in superconductors

“…Alternatives in terms of SF-DDW with electron pockets have also been proposed. 6,8,9 While the electron pocket is rapidly suppressed in the mixed state in our model, it is not clear how general this conclusion is, i.e., whether it is valid beyond the BdG theory. We think that within the Fermi-liquid scenario, both are viable options at this point and further work will be needed to distinguish between them.…”

“…The period of the oscillation is large and implies that the FS has been reconstructed, probably, by some translational symmetry-breaking order in the ground state. [6][7][8][9] However, for both materials that have been studied, the simplest construction, a ͑ , ͒ folding forming four hole pockets in the original Brillouin zone ͑BZ͒, would imply a pocket too small comparing to the nominal doping by about 25%. 1,3 This partly motivated a number of workers to interpret the data in terms of more complicated reconstruction such as incommensurate spin-density wave ͑SDW͒.…”

Novel magnetic order in the pseudogap state of high-Tccopper oxides superconductors

“…The DDW state implies a doubling of the unit cell. The interest for such a state has been recently revived [26,27] owing to the observation of small Fermi pockets in quantum oscillation measurements at high field. In the DDW state, charge loops give rise to orbital-like magnetic moment perpendicular to CuO2 planes.…”

Quantum oscillations in the high- T c cuprates

“…Magnetic field-dependent neutron scattering experiments find evidence of field dependence in samples YBa 2 Cu 3 O 6+x of composition x = 0.45, where a low-magnetic-field nematic phase (or glassy phase exhibiting twofold symmetry) is found to evolve progressively into a phase closely resembling an incommensurate spin-density wave in fields of about 15 T [101,104], and static magnetic order has been found in YBa 2 Cu 3 O 6.6 doped with 2 per cent Zn [105]. Other possibilities suggested for translational symmetry breaking include dynamic forms of magnetism [110][111][112], a d-density wave [63][64][65][66][67] and a charge-density wave, among others.…”