Fermi-surface reconstruction and transport coefficients from a mean-field bidirectional charge-density wave state in the high-${T}_{c}$ cuprates

Fermi-surface reconstruction and transport coefficients from a mean-field bidirectional charge-density wave state in the high- $T_{c}$ cuprates

Kangjun Seo and Sumanta Tewari

Phys. Rev. B 90, 174503 – Published 7 November 2014

Abstract

The recent discovery of an incipient charge-density wave (CDW) instability competing with superconductivity in a class of high-temperature cuprate superconductors has brought the role of charge order in the phase diagram of the cuprates under renewed focus. Here, we take a mean field $Q_{1} = (2 π / 3, 0)$ and $Q_{2} = (0, 2 π / 3)$ biaxial CDW state and calculate the Fermi-surface topology and the resulting Hall and Seebeck coefficients as a function of temperature and hole doping. We establish that, in the appropriate doping ranges where the low-temperature state (in the absence of superconductivity) is a CDW, the Fermi surface consists of electron pockets, resulting in the Hall and Seebeck coefficients becoming negative at low temperatures, as seen in experiments.

Received 26 February 2014
Revised 12 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.174503

Authors & Affiliations

Kangjun Seo

School of Natural Sciences, University of California, Merced, California 95343, USA

Sumanta Tewari

Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA

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Vol. 90, Iss. 17 — 1 November 2014

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Images

Figure 1
(a) The CDW band structure from the eigenvalues $E_{n} (k)$ of the matrix $H (k)$ [Eq. (4)]. The chemical potential, corresponding to hole doping $p = 0.125$ , is noted by a dashed line. Here, the CDW order parameter $W = 0.069$ eV at $T = 0$ . (b) The Fermi surface for $p = 0.125$ in the first Brillouin zone. The green dashed square in the middle represents the reduced Brillouin zone (RBZ) boundary determined by the CDW momenta $Q_{1}$ and $Q_{2}$ . Note that the Fermi surface in the CDW state consists of two electron pockets in RBZ: one large electron pocket at the center $(0, 0)$ and the corners $(π / 3, π / 3)$ of the RBZ (red) and two hole pockets at the boundary $(π / 3, 0)$ and $(0, π / 3)$ (red).
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Figure 2
Temperature dependence of the Seebeck and Hall coefficients in the CDW state. (a) Normal-state Seebeck coefficients $S / T$ at various doping concentrations $p$ are plotted as a function of temperature $T$ . The negative Seebeck coefficients at low temperature for $p = 0.092$ and $0.125$ are ascribed to the electron pockets in the Fermi surface due to the CDW, while $S / T$ at $p = 0.08 (W = 0)$ remains positive. (b) Hall coefficients $R_{H}$ in arbitrary units for various $p$ are plotted as a function of $T$ . The sign of the Hall coefficient changes at lower temperature for $p = 0.092$ and 0.125, while it remains positive at all temperatures for $p = 0.08$ .
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Figure 3
Doping dependencies of Seebeck and Hall coefficients in the biaxial CDW state with $Q_{1} = (2 π / 3, 0)$ and $Q_{2} = (0, 2 π / 3)$ . (a) With increasing doping concentration $p$ , Seebeck coefficients $S / T$ for $T = 20$ and 30 K change the sign from positive to negative, while $S / T$ at $T = 60$ K $(W = 0)$ remains positive throughout. (b) Hall coefficients $R_{H}$ vs $p$ show the similar behavior as the doping dependence of Seebeck coefficient $S / T$ .
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Figure 4
(a) The CDW band structure from the eigenvalues $E_{n} (k)$ of the $3 \times 3$ matrix in Eq. (10). The chemical potential, corresponding to hole doping $p = 0.125$ , is displayed by a dashed line ( $μ = - 1.0027 t$ for $W = 0.2267 t$ at $T = 0$ ). (b) The Fermi surface in the first Brillouin zone is depicted. In this case, the reduced Brillouin zone (RBZ) boundary is determined by the CDW momentum $Q = (2 π / 3, 0)$ . Note that the Fermi surface in the RBZ consists of a hole pocket centered at $(π / 3, π)$ depicted in red.
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Figure 5
Temperature and doping dependencies of the Seebeck and Hall coefficients in the unidirectional $Q = (2 π / 3, 0)$ CDW state. (a), (b) The temperature dependence for $p = 0.08$ , 0.092, and 0.125. (c), (d) The doping dependence for $T = 20$ , 30, and 60 K.
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