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arXiv:cond-mat/0510001 · Physical Review B

Variational Monte Carlo study of the current carried by a quasiparticle

Cody P. Nave, Dmitri A. Ivanov, Patrick A. Lee

Published Mar 7, 2006• 27 citations

Abstract

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 ${Z}_{+}$ for adding an electron shows an interesting structure in $\mathbf{k}$ space, which corresponds to a depression of the occupation number ${n}_{\mathbf{k}}$ just outside the Fermi surface. The perturbative corrections to those quantities in the Hubbard model are also discussed.

DOI: 10.1103/physrevb.73.104502

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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}_{+}

for adding an electron shows an interesting structure in

\mathbf{k}

space, which corresponds to a depression of the occupation number

{n}_{\mathbf{k}}

just outside the Fermi surface. The perturbative corrections to those quantities in the Hubbard model are also discussed.

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 analyze the electronic Green's functions in the superconducting ground state of the $t\text{\ensuremath{-}}J$ model using Gutzwiller-projected wave functions, and compare them to the conventional BCS form. Some of the properties of the BCS state are preserved by the projection: the total spectral weight is continuous around the quasiparticle node and approximately constant along the Fermi surface. On the other hand, the overall spectral weight is reduced by the projection with a momentum-dependent renormalization, and the projection produces electron-hole asymmetry in renormalization of the electron and hole spectral weights. The latter asymmetry leads to the bending of the effective Fermi surface, which we define as the locus of equal electron and hole spectral weight.

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 study the electronic structure of a strongly correlated d-wave superconducting state. Combining a renormalized mean field theory with direct calculation of matrix elements, we obtain explicit analytical results for the nodal Fermi velocity upsilon(F), the Fermi wave vector k(F), and the momentum distribution n(k) as a function of hole doping in a Gutzwiller projected d-wave superconductor. We calculate the energy dispersion E(k) and spectral weight of the Gutzwiller-Bogoliubov quasiparticles and find that the spectral weight associated with the quasiparticle excitation at the antinodal point shows a nonmonotonic behavior as a function of doping. Results are compared to angle resolved photoemission spectroscopy of the high-temperature superconductors.

The effects of the Gutzwiller projection on a BCS wave function with varying particle number are considered. We show that a fugacity factor has to be introduced in these wave functions when they are Gutzwiller projected, and derive an expression for this factor within the Gutzwiller approximation. We examine the effects of the projection operator on BCS wave functions by calculating the average number of particles before and after projection. We also calculate particle number fluctuations in a projected BCS state. Finally, we point out the differences between projecting BCS wave functions in the micro- and grand-canonical schemes, and discuss the relevance of our results for variational Monte Carlo studies.