Fermi surface reconstruction in underdoped cuprates: Origin of electron pockets

Ilya Ivantsov, Alvaro Ferraz, and Evgenii Kochetov

Phys. Rev. B 98, 214511 – Published 17 December 2018

Abstract

A new phenomenological model is proposed to describe the evolution of the Fermi surface (FS) in a wide range of dopings. It reproduces the key features of the cuprates in the underdoped phase above the superconducting temperature $T_{c}$ . It is shown that the explicit accounting of strong electron correlation in the framework of the $t - J$ model taken in complementary to the translational symmetry breaking induced by the charge density wave (CDW) gives rise to the Fermi surface reconstruction (FSR) into small electron pockets. While the strong Coulomb repulsion leads to an emergence of the arclike Fermi surface in the pseudogap (PG) phase, the Bragg reflection on the boundaries of the reduced Brillouin zone (BZ) opens up a possibility to close the quasiparticle orbits. Direct calculation of the FS properties allows us to unveil the scenario of the experimentally observed transition to the CDW phase that sets in at the doping level $δ \approx 0.08$ and is accompanied by a divergence of the carriers effective mass and the sign reversals of the Hall and Seebeck coefficients.

Received 21 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.214511

Physics Subject Headings (PhySH)

Charge density waves Fermi surface Impurities in superconductors Pseudogap

Cuprates High-temperature superconductors

Cluster methods Hubbard model Tight-binding model t-J model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ilya Ivantsov^1,2, Alvaro Ferraz³, and Evgenii Kochetov^1,3

¹Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
²L.V. Kyrensky Institute of Physics, Siberian Branch of Russian Academy of Sciences, 660036 Krasnoyarsk, Russia
³International Institute of Physics - UFRN, Department of Experimental and Theoretical Physics - UFRN, Natal 59078-970, Brazil

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Vol. 98, Iss. 21 — 1 December 2018

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Images

Figure 1
(a) The picture of the original tight-binding model on a square lattice with the nearest $t$ , next nearest $t^{'}$ , and next-next-nearest $t^{''}$ neighbors hopping. The inset schematically represents the $s$ -wave hopping mode corresponding to the well known dispersion relation $ɛ (k) = 2 t (\cos (k_{x}) + \cos (k_{y})) + 4 t^{'} \cos (k_{x}) \cos (k_{y}) + 2 t^{''} (\cos (2 k_{x}) + \cos (2 k_{y}))$ . (b) A schematic representation of the Hamiltonian in the superlattice representation. (c) The superlattice consisting of the $3 \times 3$ clusters. The spatial distribution of the charge density projected on the original lattice corresponds to the color bar. The inset schematically represents the modes of the intercluster interaction.
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Figure 2
The Fermi surfaces calculated for the different doping levels $δ$ with [(a)–(d)] and without [(e) and (f)] taking into consideration the distribution of the spectral weight. The solid lines $k_{x} = π / 3$ and $k_{y} = π / 3$ represent the Bragg “planes” in the reconstructed BZ. The parameters of the $t - J$ model used in the calculation are $t^{'} = - 0.27$ , $t^{''} = 0.2$ , $J = 0.5$ , and temperature $T = 10^{- 4}$ (here and below the energy scale is in units of $t$ ).
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Figure 3
(a) The FS calculated by the CPT method at the doping level $δ = 0.14$ and with the Lorentzian broadening value $η = 0.01$ . The slices of the spectral function in the direction 1,2 and 3 (depicted in green) are presented in panel (b). The horizontal solid line denotes the Fermi level. $Δ$ denotes the value of the gap resulting from the band splitting. (c) Schematic representation of the electron pocket formation. The reconstructed FS is depicted in the repeated BZ representation. Enumerated dots correspond to the Bragg reflection points. The sides of the electron pockets giving rise to the FS spectral weight are indicated in red and the area contributing to the full area of pocket is depicted by shading. The inset schematically represents the resulted closed pocket. (d) Schematic representation of the formation of the hole pockets due to the Bragg reflection. In the panels (a), (c), and (d) the first reconstructed Brillouin zone is depicted as the cyan square, the Bragg planes correspond to the solid lines $k_{x}, k_{y} = \pm π / 3$ , $Q_{x}$ and $Q_{y}$ correspond to the CDW modulation vectors. (e) The distribution of the FS spectral weights in the direction specified by the angle $φ$ [panel (a)] with various doping levels calculated by the CPT method. To each horizontal slice corresponds a doping $δ$ denoted on the vertical axis. The slices indicated by the Roman numerals correspond to the “phases” depicted in Fig. 4. The line III also corresponds to the FS depicted in panel (b). (f) The dependence of the value of the gap maximum on the Coulomb repulsion $U$ .
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Figure 4
(a) Panel displays the doping dependence of the density of states (DOS) at the Fermi level. Red and blue solid lines correspond to the DOS associated with the electron/hole carriers, respectively. (b) The black line shows the doping dependence of the calculated $σ$ coefficient (left vertical axis). The green line shows the doping dependence of $Δ$ (right vertical axis). The dashed black line in panels (a) and (b) correspond to the “pure” PG phase without FSR.
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