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arXiv:cond-mat/0604488 · Journal of Physics Condensed Matter

On the origin of the tunnelling asymmetry in the cuprate superconductors: a variational perspective

Hong-Yu Yang, Fan Yang, Yong-Jin Jiang, Tao Li

Published Dec 8, 2006• 13 citations
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Abstract

Through variational Monte Carlo calculations on Gutzwiller projected wavefunctions, we study the quasiparticle weight for adding and removing an electron from a high-temperature superconductor. We find that the quasiparticle weight is particle–hole symmetric at sufficiently low energy. We propose to use the tunnelling asymmetry as a tool to study the mechanism of electron incoherence in high-temperature superconductors.

DOI
10.1088/0953-8984/19/1/016217

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Through variational Monte Carlo calculations on Gutzwiller projected wavefunctions, we study the quasiparticle weight for adding and removing an electron from a high-temperature superconductor. We find that the quasiparticle weight is particle–hole symmetric at sufficiently low energy. We propose to use the tunnelling asymmetry as a tool to study the mechanism of electron incoherence in high-temperature superconductors.
With the use of Gutzwiller-projected variational states, we study the renormalization of the current carried by the quasiparticles in high-temperature superconductors and of the quasiparticle spectral weight. The renormalization coefficients are computed by the variational Monte Carlo technique, under the assumption that quasiparticle excitations may be described by Gutzwiller-projected BCS quasiparticles. We find that the current renormalization coefficient decreases with decreasing doping and tends to zero at zero doping. The quasiparticle spectral weight Z+{Z}_{+}Z+​ for adding an electron shows an interesting structure in k\mathbf{k}k space, which corresponds to a depression of the occupation number nk{n}_{\mathbf{k}}nk​ just outside the Fermi surface. The perturbative corrections to those quantities in the Hubbard model are also discussed.
The spectral weights (SW's) for adding and removing an electron of the Gutzwiller projected ddd-wave superconducting (SC) state of the $t\text{\ensuremath{-}}J$-type models are studied numerically on finite lattices. We restrict the study to the uniform system but exactly treat the strong correlation between electrons, we show that the product of weights is equal to the pairing amplitude squared, the same as in the weakly coupled case. In addition, we derive a rigorous relation of SW with doping in the electron doped system and obtain particle-hole asymmetry of the conductance-proportional quantity within the SC gap energy and, also, the anticorrelation between gap sizes and peak heights observed in tunneling spectroscopy on high Tc{T}_{c}Tc​ cuprates.
Recent measurements of quasiparticles in hole-doped cuprates revealed highly unusual features: (i) the doping-independent Fermi velocity, (ii) two energy scales in the quasiparticle spectral function, and (iii) a suppression of the low-energy spectral weight near the zone center. We explain these important facts by a novel two-mode variational Monte Carlo (VMC) study of the t-J model, which resolves a long-standing issue of the sum rule for quasiparticle spectral weights in VMC studies. The electron-doped case is also discussed.
We study the Hubbard model with parameters relevant to cuprates using variational Monte Carlo for projected d-wave states. For doping 0<x approximately less than or equal to 0.35 we obtain a superconductor whose order parameter Phi(x) tracks the observed nonmonotonic T(c)(x). The variational parameter Delta(var)(x) scales with the (pi,0) "hump" and T* seen in photoemission. Projection leads to incoherence in the spectral function and from the singular behavior of its moments we obtain the nodal quasiparticle weight Z approximately x though the Fermi velocity remains finite as x-->0. The Drude weight D(low) and superfluid density are consistent with experiment and D(low) approximately Z.
We present variational Monte Carlo (VMC) results for the Gutzwiller-projected coexisting state including both antiferromagnetic (AFM) order and superconducting (SC) order in the two-dimensional t-t'-t"-J model. By further considering off-site spin correlation between electrons, in contrast to earlier VMC results [Phys. Rev. Lett. 102, 027002 (2009)], we find the apparent competition between AFM order and SC order near the underdoped regime instead of coexistence. The local ferromagnetic correlation introduced by spin-spin Jastrow correlators seem to be responsible for the disappearance of the coexisting state. We also demonstrate that the quasiparticle spectral weight from upper (lower) AFM band are strongly diminished (enhanced) by the spin-spin correlation. This result obviously leads to the loss of antinodal electron pockets and the appearance of nodal hole pockets as passing from the AFM phase to the SC phase in hole-doped cuprates, which is in consistent with the observation by angle-resolved photoemission spectroscopy.