BCS-Like Bogoliubov Quasiparticles in High-TcSuperconductors Observed by Angle-Resolved Photoemission Spectroscopy

Abstract

We performed high-resolution angle-resolved photoemission spectroscopy on triple-layered high-Tc cuprate Bi2Sr2Ca2Cu3O 10+δ . We have observed the full energy dispersion (electron and hole branches) of Bogoliubov quasiparticles and determined the coherence factors above and below EF as a function of momentum from the spectral intensity as well as from the energy dispersion based on BCS theory. The good quantitative agreement between the experiment and the theoretical prediction suggests the basic validity of BCS formalism in describing the superconducting state of cuprates.PACS numbers: 74.72. Hs, 74.20Fg, 79.60.Bm It is well known that BCS (Bardeen, Cooper, and Schrieffer) theory [1] explains many of fundamental thermodynamic, transport and magnetic properties of superconductors by introducing a simple picture that two electrons with opposite momenta and spins near the Fermi surface form a pair (Cooper pair) in the superconducting state. In the language of Fermi liquids [2], the quasiparticles (QPs) of the Cooper pairs are called Bogoliubov quasiparticles (BQPs) [3] which are defined as excitation of a single electron "dressed" with an attractive interaction between paired electrons. The BQPs play an essential role in characterizing the superconducting state via quantities such as the superconducting gap and its symmetry. Despite the excellent description of the BQPs in BCS theory, there has been no direct experimental observation of the predicted full energy dispersion (electron and hole branches) of BQPs, although the pairing of electrons is evidenced by ac Josephson-junction experiment [4]. For high-T c cuprates, the direct observation of the BQPs is even more significant, since many microscopic ideas of BCS theory have been seriously challenged. Since the BQPs are a natural consequence of the starting Hamiltonian including the two-body attractive interaction assumed by BCS theory [1], the existence of BQPs would prove the validity of the basic BCS description of the superconducting state in the cuprates.In this Letter, we report the direct observation of BQPs in triple-layered high-T c cuprate Bi 2 Sr 2 Ca 2 Cu 3 O 10+δ by angle-resolved photoemission spectroscopy (ARPES). By using ultrahigh resolution in energy and momentum, we have succeeded in directly observing the full energy dispersion (electron and hole branches) of BQPs below and above the Fermi level (E F ). We have determined experimentally the coherence factors as a function of momentum from ARPES intensity and compared the result with the prediction from BCS theory to investigate the basic

Electronic structure of cuprate superconductors in a full charge-spin recombination scheme

“…We have performed a series of calculations for the electron spectral Using an reasonably estimative value of J ∼ 100 meV in cuprate superconductors, the position of the low-energy SC quasiparticle peak at δ = 0.15 is located at ω peak ≈ 0.5J ≈ 50 meV, which is not too far from the ω peak ≈ 40 meV observed 20 in the optimally doped Bi 2 Sr 2 CaCu 2 O 8+x . However, the electron spectrum is doping dependent, and the weight of the lowenergy SC quasiparticle peak in the underdoped regime increases with the increase of doping, while the position of the low-energy SC quasiparticle peak shifts towards to the electron Fermi energy, in qualitative agreement with the experimental results 5,6,[15][16][17][18][19][20][21][22][23] .…”

“…In particular, it should be emphasized that the Bogoliubov-type dispersion of cuprate superconductors in the SC-state, and the momentum dependence of the coherence factors U k and V k in Eq. (16) have been confirmed experimentally from the ARPES measurements [15][16][17][18][19] . On the other hand, the electron quasiparticle coherent weight Z F reduces the electron quasiparticle bandwidth, and suppresses the spectral weight of the single-particle excitation spectrum, then the energy scale 58 of the electron quasiparticle band is controlled by the magnetic exchange coupling J.…”

“…Later, the ARPES experimental studies show that in the underdoped and optimally doped regimes, although the antinodal region of the electron Fermi surface is gapped out, leading to the notion that only part of the electron Fermi surface survives as the disconnected Fermi arcs around the nodes [28][29][30][31][32] , the underlying electron Fermi surface determined from the low-energy spectral weight still fulfills Luttinger's theorem in the entire doping range 32 . These ARPES experimental facts [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] on the other hand provide strong evidences supporting the notion of the charge-spin recombination 13,14 . Since the electron Fermi surface is a fundamental property of interacting electron systems, the study of the nature of the electron Fermi surface should be crucial for understanding the electronic structure of cuprate superconductors.…”

“…In this case, the characteristic feature (A) of the charge-carrier pairing state is therefore satisfied by the standard d-wave BCS formalism in Eqs. (15) and (16). In particular, it should be emphasized that the Bogoliubov-type dispersion of cuprate superconductors in the SC-state, and the momentum dependence of the coherence factors U k and V k in Eq.…”

“…However, one of the most striking dilemmas is that the SC coherence of the low-energy quasiparticle excitations in cuprate superconductors seems to be described by the standard Bardeen-Cooper-Schrieffer (BCS) formalism [15][16][17][18][19] , although the normal-state is undoubtedly not the standard Landau Fermi-liquid on which the conventional electron-phonon theory is based. Angle-resolved photoemission spectroscopy (ARPES) experiments reveal sharp spectral peaks in the singleparticle excitation spectrum 5,6,[15][16][17][18][19][20][21][22][23] , indicating the presence of quasiparticle-like states, which is also consistent with the long lifetime of the electronic state as it has been determined by the conductivity measurements 10,11 . In particular, as a direct method for probing the electron Fermi surface, the early ARPES measurements indicate that in the entire doping range, the underlying electron Fermi surface satisfies Luttinger's theorem [24][25][26][27] , i.e., the electron Fermi surface with the area is proportional to 1 − δ.…”