Quantum oscillations in the mixed state ofd-wave superconductors

Abstract

We show that the low-energy density of quasiparticle states in the mixed state of ultraclean d x 2 −y 2-wave superconductors exhibits quantum oscillations even in the regime where the cyclotron frequency ប c Ӷ⌬ 0 , the d-wave pairing gap. Such oscillations as a function of magnetic field B are argued to be due to the internodal scattering of the nodal quasiparticles near wave vectors ͑Ϯk D , Ϯ k D ͒ by the vortex lattice as well as their Zeeman coupling. While the nominal periodicity of the oscillations is set by the condition k D ͓hc / ͑eB͔͒ 1/2 ϵ k D Ј ͓hc / ͑eBЈ͔͒ 1/2 ͑mod 2͒, we find that there is additional structure within each period that grows in complexity as the Dirac node anisotropy increases.The behavior of d x 2 −y 2-wave superconductors in magnetic field has recently come into sharp focus due to the experimental observation of the oscillations in the longitudinal and Hall electrical transport, as well as magnetization, at extremely high magnetic fields for very clean underdoped YBa 2 Cu 3 O 6.5 ͑Ref. 1͒ and YBa 2 Cu 4 O 8 . 2,3 At temperatures about 2 K and for magnetic fields in excess of about 30 T, the Hall resistance is finite, negative ͑i.e., electron like͒, and oscillates as a function of magnetic field, with approximately four pronounced peaks between ϳ45 and 60 T. Below about 30 T, the system is in the mixed superconducting state, and the electrical Hall conductivity vanishes. The current interpretation of these oscillations involves charge-or spin-orderinduced reconstruction of the Fermi surface with electron pockets, 1,3-6 which result from the appropriate tuning of the strength of the charge or spin potentials in the particle-hole channel. [4][5][6] As the estimated mean field H c2 for the YBCO samples in question significantly exceeds 60 T, 7 it is at present unclear why one should expect the superconducting order parameter amplitude to collapse at the fields applied in Refs. 1-3. Instead, the local superconducting correlations should persist, and rather the system is expected to be in the vortex liquid state. 8-10 Additionally, the sign reversal of the Hall effect, from positive to negative, with decreasing temperature near T c in optimally doped YBCO has been observed and interpreted earlier as resulting from the flux flow. 11-13 The structure factor of such a liquid state is expected to closely resemble that of a vortex solid. In this context, the natural question is the existence, the periodicity, and the physical nature of such magnetic-field-induced oscillations in the vortex state.In this work, we therefore examine the properties of the d-wave quasiparticles ͑qps͒ in the vortex solid state at intermediate magnetic fields, i.e., we examine the particle-particle channel. For the square vortex lattice observed in the smallangle neutron scattering, 14 we find that the combined effect of the orbital and spin coupling of the qps to the magnetic field does induce oscillations in the low-energy density of states ͑DOS͒, N͑E͒, and that the nature of these oscillations depends on the Dirac c...

Mean-field analysis of quantum oscillations, Fermi-surface topology, and magnetic breakdown in high-Tccuprates

“…16 Shortly after the experimental discoveries, several theoretical proposals have been made. [17][18][19][20][21][22][23][24][25][26][27][28] Most of them share the underlying idea that the quantum oscillation arise due to a broken symmetry. [19][20][21][22][23][24][25][26][27][28] Some have further offered a missing link between the Fermi arc and quantum oscillation from a closed Fermi surface.…”

Quantum oscillations in the high- T c cuprates

“…Among possibilities suggested for an unconventional origin of magneto-oscillations are spinless fermions [45,46], charge 2e bosons [47], low-energy Andreev-type bound states [48], oscillations originating from the vortex lattice [49,50,51], or Fermi points accompanied by a shift in chemical potential [52]. These possibilities, however, need to be examined for their agreement with Fermi-Dirac statistics observed by quantum oscillations and measured 1/B periodicity over an extended field range (discussed in §2), as well as the doping dependence of the frequency and effective mass (discussed in §3).…”

In situ doping control of the surface of high-temperature superconductors

“…Angle-resolved photoemission spectroscopy (ARPES) on the surfaces of easily cleaved materials such as Bi 2 Sr 2 CaCu 2 O 8+δ shows that in zero magnetic field the Fermi surface breaks up into disconnected arcs [4][5][6] . However, in high magnetic field, quantum oscillations 7 at low temperatures in YBa 2 Cu 3 O 6.5 indicate the existence of small Fermi surface pockets [8][9][10][11][12][13][14][15][16][17][18] . Reconciling these two phenomena through ARPES studies of YBa 2 Cu 3 O 7−δ (YBCO) has been hampered by the surface sensitivity of the technique [19][20][21] .…”