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Physical Review Letters

Spin Dynamics of the Electron-Doped High- Tc Superconducting Cuprates

F. P. Onufrieva, Pierre M. Pfeuty

Published Jun 14, 2004• 13 citations
Publisher

Abstract

We show that a basic difference between the electron- and hole-doped cuprates is their proximity to two different quantum critical points in a 2D free fermion system on a square lattice and that the spin dynamics observed recently for the first time in the electron-doped Nd2-xCexCuO4, very different from that in the hole-doped cuprates, can be understood as a consequence of this effect.

DOI
10.1103/physrevlett.92.247003

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We show that a basic difference between the electron- and hole-doped cuprates is their proximity to two different quantum critical points in a 2D free fermion system on a square lattice and that the spin dynamics observed recently for the first time in the electron-doped Nd2-xCexCuO4, very different from that in the hole-doped cuprates, can be understood as a consequence of this effect.
We show that the presence of two topological quantum critical points (QCP's) in 2D electronic system on a square lattice imposes strong constraints on density-wave (DW) correlations in the high-T(c) cuprates. Electronic properties of the corresponding strongly correlated system are highly reminiscent of the experimental trends in the high-T(c) cuprates. The most interesting results are the existence at low doping of two single-particle gaps different by order of magnitude both increasing towards low doping and of the specific insulating state characterized by a small chemical potential jump.
Recent experiments revealed a striking asymmetry in the phase diagram of the high temperature cuprate superconductors. The correlation effect seems strong in the hole-doped systems and weak in the electron-doped systems. On the other hand, a recent theoretical study shows that the interaction strengths (the Hubbard U) are comparable in these systems. Therefore, it is difficult to explain this asymmetry by their interaction strengths. Given this background, we analyze the one-particle spectrum of a single band model of a cuprate superconductor near the Fermi level using the dynamical mean field theory. We find the difference in the "visibility" of the strong correlation effect between the hole- and electron-doped systems. This can explain the electron-hole asymmetry of the correlation strength without introducing the difference in the interaction strength.
Asymmetric features of various physical quantities in the normal and superconducting states between hole- and electron-doped cuprate high-temperature superconductors have been an issue of debate for a long time. Their exploration is very important for the understanding not only of the mechanism of high-Tc superconductivity but also of the nature of doped-Mott insulators. Presented in this review is the present status of theoretical understanding of the electronic states in hole- and electron-doped high- Tc cuprates as well as the origin of the electron-hole asymmetry of the electronic states. In particular, it is shown that numerically exact diagonalization calculations for small clusters in a t-J model with long-range hoppings, t and t nicely reproduce the electron-hole asymmetry observed experimentally in various quantities and thus make it possible to extract the physical origin of the asymmetry. These results give a deep insight on the asymmetric behaviors in hole- and electron-doped high-Tc cuprates and on the nature of doped Mott insulators.
We show that a two-dimensional (2D) metal in a superconducting (SC) state with wave-vector-dependent gap behaves as a quantum-spin liquid characterized by a collective mode of resonance type. Formally the mode exists whatever is a form of Fermi surface (FS). However, when the latter is spherical the effect is rather formal: any factor leading to an even weak electron scattering, like finite T, impurity, etc., easily kills the mode. On the contrary, for the type of FS observed in the high-Tc{T}_{c}Tc​ cuprates (characterized by a proximity to the saddle-point wave vectors) the resonance mode exists in a true sense being well separated from the electron-hole continuum and well defined. The effect is due to the effective 1D dimension in a proximity of electronic topological transition quantum critical point. The physical nature of the collective mode varies progressively between two possibilities. In the case of a weak interaction, the resonance mode is a typical effect of a two-particle bound state that appears slightly below the bottom of the two-particle continuum. The effect exists even in the case of infinitesimally weak interaction (of relevant sign). In the case of a strong or intermediate interaction, it is a critical mode existing as a precursor of spin-density wave (SDW) instability. The gap of the collective mode is not related directly to the value of the SC gap (being, however, limited by the latter from above) but rather to a proximity to SDW instability. We predict also a second collective mode lying inside the two-particle continuum. The existence of these two modes and the particular form of their dispersion in the case corresponding to the underdoped cuprates ${(d}_{{x}^{2}\ensuremath{\sim}{y}^{2}}$ symmetry of SC gap, exchange interaction of antiferromagnetic sign, etc.) allows one to understand the main features observed experimentally in the underdoped cuprates, namely the so-called ``41 meV resonance peak'' and ``24 meV incommensurability'' and their two-dimensional wave vector dependences, the doping evolution of the spin dynamics and many other features. The theory also predicts new features to be tested experimentally.
The effects of the electron-phonon interaction on charge and spin dynamics are studied for the one-dimensional two-band Hubbard model by the exact diagonalization method. The parameters of the model are chosen to represent a hole-doped Cu-O system. Local charge fluctuations induced by phonons are expressed in terms of microscopic current and polarization, and it is shown that the dynamic charge transfer is strongly dependent on the phonon wave vector when the system is doped with holes. The dynamic magnetic structure factor is also found to be significantly modified by lattice distortion. In particular the lowest-energy spin excitations are greatly softened, indicating significant spin-phonon coupling. It is shown that the optical response is significantly modified as well due to coupling with the lattice over an energy range far exceeding the phonon energy. These results demonstrate the unconventional nature of the electron-phonon coupling in the strongly correlated electron systems. Its possible implications to the pairing mechanism in the cuprates are discussed.
We have discovered a new nontrivial aspect of electronic topological transition (ETT) in a 2D free fermion system on a square lattice. The corresponding exotic quantum critical point, $\ensuremath{\delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\delta}}_{c}$, T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0 ( $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\ensuremath{-}\ensuremath{\delta}$ is the electron concentration), is at the origin of anomalous behavior in the interacting system on one side of ETT, $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}$. Most important is the appearance of the line of characteristic temperatures, ${T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta}$. Application of the theory to high- Tc{T}_{c}Tc​ cuprates reveals a striking similarity to the behavior observed experimentally in the underdoped regime.