Quasiparticle Dynamics in the Vicinity of Metal-Insulator Phase Transition in ${\mathrm{Na}}_{x}{\mathrm{CoO}}_{2}$

Quasiparticle Dynamics in the Vicinity of Metal-Insulator Phase Transition in ${Na}_{x} {CoO}_{2}$

D. Qian, L. Wray, D. Hsieh, D. Wu, J. L. Luo, N. L. Wang, A. Kuprin, A. Fedorov, R. J. Cava, L. Viciu, and M. Z. Hasan

Phys. Rev. Lett. 96, 046407 – Published 2 February 2006

Abstract

Layered cobaltates embody novel realizations of correlated matter on a spin- $1 / 2$ triangular lattice. We report a high-resolution systematic photoemission study of the insulating cobaltates. The observation of a single-particle gap opening and band folding provides direct evidence of anisotropic particle-hole instability on the Fermi surface due to its unique topology. Overlap of the measured Fermi surface is observed with the $\sqrt{3} \times \sqrt{3}$ charge-order Brillouin zone near $x = 1 / 3$ but not at $x = 1 / 2$ where the insulating transition is actually observed. Unlike conventional density waves, charge stripes, or band insulators, the onset of the gap depends on the quasiparticle’s quantum coherence which is found to occur well below the disorder-order symmetry breaking temperature of the crystal (the first known example of its kind).

Received 9 October 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.046407

Authors & Affiliations

D. Qian¹, L. Wray¹, D. Hsieh¹, D. Wu², J. L. Luo², N. L. Wang², A. Kuprin³, A. Fedorov³, R. J. Cava⁴, L. Viciu⁴, and M. Z. Hasan^1,5,*

¹Department of Physics, Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, China
³Advanced Light Source, Lawrence Berkeley Laboratory, Berkeley, California 94305, USA
⁴Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
⁵Princeton Center for Complex Materials, Princeton University, Princeton, New Jersey 08544, USA

^*Electronic address: mzhasan@princeton.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 4 — 3 February 2006

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Phase transitions in ${Na}_{x} {CoO}_{2}$ : (a) Electron diffraction image along the $[001]$ axis. The rectangular supercell is observed due to the ${Na}^{+}$ charge ordering (Wigner crystallization). (b) Phase diagram of ${Na}_{x} {CoO}_{2}$ [2]. PM stands for paramagnetic. Metal-insulator phase transitions are observed in doping near $x = 1 / 2$ where (c) the Na layer undergoes a disorder to order transition above room temperature [2, 3, 4].Reuse & Permissions
Figure 2
Quasiparticle dynamics: Single-particle removal spectra of samples with doping at (a) $x = 0.3$ , (b) $x = 0.5$ , and (c) $x = 0.55$ . (d) and (e) show spectra and color images along $Γ \to K$ , while (f) and (g) are spectra measured along $Γ \to M$ . (h) Doping and temperature dependence of $e_{g^{'}}$ -band dispersions in the vicinity of $x = 0.5$ which show no changes. (i) Experimental band dispersion is compared with local-density approximation (LDA) theory (dotted line) [24]. The measured band is less dispersive. It exhibits folding and a gap opens at the Fermi level.Reuse & Permissions
Figure 3
Gap anisotropy: (a) High energy-resolution ( $k$ integrated on 4% BZ) spectra of ${Na}_{0.5} {CoO}_{2}$ measured at 10 K near the folding points along different $k$ -space cuts. Comparison of the spectra with the Fermi edge of Au and metallic ${Na}_{0.55} {CoO}_{2}$ demonstrates the gap in ${Na}_{0.5} {CoO}_{2}$ . (b) $k$ dependence of quasiparticle (leading-edge) gap in $K_{0.5} {CoO}_{2}$ measured at 10 K. Open circles are the expected $k$ dependence of the gap in case where nesting occurring only along $Γ \to K$ line. The $k$ -space angle $θ$ is defined from the $Γ \to K$ to the $Γ \to M$ line.Reuse & Permissions
Figure 4
Particle-hole instabilities on the Fermi surface: Fermi surface reconstruction: ${Na}^{+}$ charge order vs $\sqrt{3} \times \sqrt{3}$ Co charge order. (a) Momentum distribution of quasiparticles (two-color image), $n (k)$ , within 20 meV of Fermi energy. The white dots reflect the FS topology. (b) Temperature dependence of the “FS topology” in $x = 1 / 2$ samples. The solid rectangle is the BZ of Na supercell. Measured FS topology almost coincides with the Na supercell. (c) The $\sqrt{3} \times \sqrt{3}$ Co charge-order BZ (solid hexagon) has no overlap with $x = 0.5$ FS but coincides with $x = 0.3$ (superconducting doping) FS. (d) Reconstructed FS contours based on experimental folding behavior, which is consistent with the geometry of the Na supercell defined by $\vec{b_{1}^{'}}$ and $\vec{b_{2}^{'}}$ .Reuse & Permissions
Figure 5
Charge-gap amplitude and quasiparticle coherence: Temperature dependence of (a) in-plane dc resistivity, (b) quasiparticle signal along $Γ \to K$ cut. Inset shows the quasiparticle after linear background subtraction. (c) Evolution of leading-edge gap with temperature. (d) The integrated spectral weight of quasiparticle (coherence) in insulating doping ( $x = 0.5$ ) is compared with the metallic dopings ( $x = 0.6 - 0.7$ ) as a function of temperature.Reuse & Permissions

Physical Review Letters

Quasiparticle Dynamics in the Vicinity of Metal-Insulator Phase Transition in NaxCoO2

D. Qian, L. Wray, D. Hsieh, D. Wu, J. L. Luo, N. L. Wang, A. Kuprin, A. Fedorov, R. J. Cava, L. Viciu, and M. Z. Hasan

Phys. Rev. Lett. 96, 046407 – Published 2 February 2006

Abstract

Authors & Affiliations

Article Text (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Quasiparticle Dynamics in the Vicinity of Metal-Insulator Phase Transition in ${Na}_{x} {CoO}_{2}$