Lifshitz critical point in the cuprate superconductor YBa2Cu3Oy from high-field Hall effect measurements

Abstract: The Hall coefficient R_H of the cuprate superconductor YBa2Cu3Oy was measured in magnetic fields up to 60 T for a hole concentration p from 0.078 to 0.152, in the underdoped regime. In fields large enough to suppress superconductivity, R_H(T) is seen to go from positive at high temperature to negative at low temperature, for p > 0.08. This change of sign is attributed to the emergence of an electron pocket in the Fermi surface at low temperature. At p < 0.08, the normal-state R_H(T) remains positive at all temperatures, increasing monotonically as T \to 0. We attribute the change of behaviour across p = 0.08 to a Lifshitz transition, namely a change in Fermi-surface topology occurring at a critical concentration p_L = 0.08, where the electron pocket vanishes. The loss of the high-mobility electron pocket across p_L coincides with a ten-fold drop in the conductivity at low temperature, revealed in measurements of the electrical resistivity $\rho$ at high fields, showing that the so-called metal-insulator crossover of cuprates is in fact driven by a Lifshitz transition. It also coincides with a jump in the in-plane anisotropy of $\rho$, showing that without its electron pocket the Fermi surface must have strong two-fold in-plane anisotropy. These findings are consistent with a Fermi-surface reconstruction caused by a unidirectional spin-density wave or stripe order.

Lifshitz Critical Point in YBa$_2$Cu$_3$O$_y$ Superconductor: Hall Effect Measurements

The paper "Lifshitz critical point in the cuprate superconductor YBa$_2$Cu$_3$O$_y$ from high-field Hall effect measurements" explores a sophisticated aspect of the cuprate superconductor, namely the detection and interpretation of a Lifshitz transition in its electronic structure. This transition, reflected through high-field Hall effect measurements, marks a pivotal point in understanding the complex phase behavior of these materials.

The research primarily focuses on the Hall coefficient, $R_{\rm H}$, of YBa$_2$Cu$_3$O$_y$ (YBCO), measured across various doping levels, specifically within the underdoped regime (hole concentration $0.078 \leq p \leq 0.152$). The experiments employed magnetic fields reaching up to 60 T to quench superconductivity, facilitating the observation of underlying electronic properties. The results reveal a striking change in the sign of $R_{\rm H}$ from positive at high temperatures to negative at low temperatures for hole concentrations greater than $p=0.08$, implicating the emergence of an electron pocket in the Fermi surface. Conversely, for hole concentrations below $p=0.08$, $R_{\rm H}(T)$ remains positive and increases monotonically as the temperature approaches zero, indicating the absence of this electron pocket below this critical doping.

This alteration in electronic behavior is attributed to a Lifshitz transition at the critical concentration $p_{\rm L} = 0.08$, where a transformation in the Fermi surface topology effectively eliminates the electron pocket. Such a transition not only affects the electronic structure but manifests in electrical transport properties. The disappearance of the electron pocket corresponds to a substantial reduction in conductivity at cryogenic temperatures and a tenfold drop in electrical resistivity when superconductivity is suppressed, validating an intrinsic connection to the Lifshitz transition rather than a metal-insulator crossover previously assumed.

Furthermore, the study presents a compelling correlation between the disappearance of the electron pocket and the jump in in-plane anisotropy of resistivity $\rho$. The resulting Fermi surface, without the contribution from the electron pocket, exhibits a pronounced two-fold in-plane anisotropy. This aligns with hypotheses involving Fermi-surface reconstructions driven by unidirectional spin-density wave or stripe order, a well-discussed mechanism within the complex landscape of cuprate physics.

These findings have critical implications, extending beyond the empirical observations to theoretical paradigms in correlated electron systems, challenging previous notions and directing toward more precise models describing electron interactions and superconductivity in cuprates. The presence and subsequent vanishing of high-mobility electron pockets at specific dopings could refine models predicting superconducting properties, paving the way for enhanced design in materials with engineered electronic behavior.

From a practical perspective, this insight into Lifshitz transitions opens avenues to manipulate electronic properties in cuprates, potentially enhancing their applicability in technology reliant on superconductors. The precise modulation of doping levels to control electronic properties holds promise in areas like quantum computing, where superconductors play a pivotal role.

In conclusion, the paper delivers significant insights into the complex electronic phase diagram of YBCO cuprates by identifying a Lifshitz critical point. The sophisticated analysis and implications of this research contribute meaningfully to understanding high-temperature superconductivity and will significantly impact both theoretical exploration and technological exploitation of these remarkable materials.