[Paper Review] Charge carriers of different origin in cuprates as revealed by experiment

L. P. Gor’kov, G. B. Teǐtel'Baum|arXiv (Cornell University)|Jul 1, 2006

Particle accelerators and beam dynamics3 citations

TL;DR

This paper demonstrates experimentally that the number of charge carriers in cuprates exceeds the external doping concentration $x$ at higher doping and elevated temperatures, indicating dynamic spin and charge fluctuations. Using Hall coefficient measurements and ARPES data, it shows that thermally activated carriers near van Hove singularities contribute to a temperature-dependent carrier density, implying that Cu spins are not localized and that the pseudogap regime involves coexisting metallic and antiferromagnetic phases.

ABSTRACT

The Hall coefficient data for cuprates show that number of carriers exceeds external doping $x$ at higher $x$ and varies with temperature. Hence, spins on the Cu-sites are not conserved. Activation energy for thermally excited carriers equals the energy between the Fermi surface "arc" and the band bottom near the van Hove singularities. Crossover from marginal Fermi liquid- to pseudogap- regime happens at temperatures at which number of activated carriers gets comparable with the number of externally doped holes. Implications for the $(T,x)$-phase diagram of cuprates are discussed.

Motivation & Objective

• To determine whether the number of charge carriers in cuprates equals the externally doped hole concentration $x$.
• To investigate the origin and temperature dependence of charge carriers in the pseudogap and marginal Fermi liquid regimes.
• To assess the stability of Cu $d^{9}$-hole configurations and the role of spin degrees of freedom in carrier dynamics.
• To reconcile Hall coefficient data with ARPES measurements and understand the energy scale of carrier activation.
• To clarify the nature of the $T^*$ crossover and its relation to phase coexistence in cuprates.

Proposed method

• Analysis of high-temperature Hall coefficient data (up to 1000 K) for La$_{2-x}$Sr$_x$CuO$_4$ across a range of doping levels $x$.
• Fitting the Hall carrier concentration $n_{\text{Hall}}$ to the exponential form $n_{\text{Hall}} = n_0(x) + n_1(x) \exp(-\Delta(x)/T)$, where $\Delta(x)$ is the activation energy.
• Comparison of the extracted activation energy $\Delta(x)$ with ARPES data on Fermi surface arcs and band structure near van Hove singularities.
• Correlation of $n_0(x)$ and $n_1(x)$ with the onset of topological changes in the Fermi surface at $x \sim 0.2$.
• Use of NMR and neutron scattering data to support the existence of coexisting antiferromagnetic and metallic phases in the pseudogap regime.
• Interpretation of temperature-independent resistivity at low doping as a signature of thermally activated carriers forming scattering centers.

Experimental results

Research questions

• RQ1 Does the number of charge carriers in cuprates exceed the externally doped hole concentration $x$?
• RQ2 What is the origin of the temperature-dependent Hall carrier concentration, and how does it relate to electronic structure?
• RQ3 How do the activation energy $\Delta(x)$ and carrier density $n_{\text{Hall}}$ vary with doping and temperature?
• RQ4 What is the role of Cu spin dynamics in carrier generation, and does spin localization break down in the pseudogap regime?
• RQ5 How do the observed carrier dynamics relate to the $T^*$ crossover and the coexistence of metallic and antiferromagnetic phases?

Key findings

• The Hall carrier concentration $n_{\text{Hall}}$ exceeds the external doping $x$ at higher $x$ and elevated temperatures, indicating additional thermally activated carriers.
• The activation energy $\Delta(x)$ extracted from the Hall data matches the energy difference between the Fermi surface arc and the band bottom near van Hove singularities.
• A plateau in the activation energy $\Delta(x)$ is observed at $x \sim 0.2$, coinciding with a topological change in the Fermi surface from hole-like to electron-like.
• The $x$-dependence of $n_0(x)$ and the drop in $n_1(x)$ at $x \sim 0.2$ suggest a quantum critical point (QCP) at this doping level.
• The temperature-independent resistivity at low doping arises from thermally activated carriers forming scattering centers with the same activation energy as the Hall response.
• The data support a dynamic coexistence of metallic (MFL-like) and antiferromagnetic (ICAF) phases in the pseudogap regime, with the latter becoming static at low temperatures.