Vortex core spectroscopy links pseudogap and Lifshitz critical point in a cuprate superconductor

TL;DR

Using high-resolution STM/STS, the study maps vortex-core spectra in Bi-2212 across a broad hole-doping range to connect vortex electronic structure with pseudogap physics and Fermi-surface topology. It identifies two distinct vortex-core classes separated at $p^* \approx 0.21$: below this, vortices exhibit subgap states and $4a_{o} \times 4a_{o}$ checkerboard modulations, while above this, cores display a zero-bias conductance peak consistent with conventional d-wave superconductivity. The results link the pseudogap endpoint to a Lifshitz transition from open hole-like to closed electron-like Fermi surfaces and show concomitant changes in zero-field quasiparticle interference patterns. Overall, the vortex core emerges as a powerful local probe of the cuprate ground state and its electronic topology, clarifying the relationship between pseudogap physics and vortex-state spectra in Bi-2212.

Abstract

Understanding how superconductivity competes with other electronic phases in cuprates requires direct access to the hidden non-superconducting low temperature phase, for which Abrikosov vortices provide a unique local probe. We map the doping- and field-dependent evolution of vortex-core states in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ across a broad doping range spanning the Fermi-surface Lifshitz transition. High-resolution scanning tunneling spectroscopy reveals a striking transformation of the vortex-core spectrum from unconventional, pseudogap-like signatures at moderate doping to more BCS-like behavior beyond a critical doping $p^* \approx 0.21$. This crossover aligns with the pseudogap endpoint and the onset of Fermi-surface reconstruction, indicating a direct link between pseudogap physics and vortex electronic structure. Our findings highlight the vortex core as a sensitive local probe of the cuprate ground state.

Figures (11)

• Figure 1: Electronic vortex core structure in Bi-2212 at $p < p^*=$ 0.21.$dI/dV(r, 5 mV)$ conductance maps acquired in the exact same field of view at (a) 1 Tesla and (b) 0 Tesla. (c) Fourier transform of panel (a) with yellow and black circles indicating the atomic Bragg peaks and the $q_{1}$ checkerboard peaks, respectively. (d) Topography acquired in the same field of view as panels (a) and (b) at 0 T ($V_{\text{b}} =$ 250 mV, $I =$ 20 pA, dashed circle identifies the vortex position). (e) Tunneling spectra as a function of position along the arrow in panel (a) showing the spatial dependence of the SGSs. (f) $dI/dV(V)$ spectra averaged over the regions marked by a solid blue circle at 1 Tesla in (a) and a solid red circle at 0 Tesla in (b). The corresponding local doping is $p_{\text{local}}= 0.13\pm0.02$; the bulk $T_{c}\approx$ 80 K; Data was acquired at 4.4 K, with $V_{\text{b}} =$ 110 mV and $I =$ 50 pA.
• Figure 2: Electronic vortex core structure in Bi-2212 at $p > p^*=$ 0.21. (a) $dI/dV(r, 0~mV)$ conductance map measured at 2.8 T. (b) Tunneling spectra as a function of position and (c) corresponding gray-scale plot measured along the black arrow in panel (a). (d) Zero-bias conductance as a function of distance from the vortex center along the (100) direction ($\textcolor{blue}{\bullet}$) and along the ($\overline{1}$10) direction ($\circ$). The red curve is a fit to $\sigma(x) = 1 - (1 - \sigma_0) \cdot \tanh(x/\xi)$ of the data along the (100) direction, where $\sigma_0$ is the normalized zero bias conductance away from the vortex region and $x$ is the distance from the core center EskildsenPRL2002. The local doping is $p_{\text{local}}= 0.24\pm0.01$; Data was acquired at 4.4 K, with $V_{\text{b}} =$ 110 mV and $I =$ 50 pA.
• Figure 3: Field-Doping phase diagram of Abrikosov vortex cores in hole-doped Bi-2212. Each data point corresponds to a complete $dI/dV(r, V, B)$ grid map with a vortex in the field of view. Different marker colors represent different bulk $T_{\text{c}}$ values, whereas individual samples are distinguished by distinct symbols. The local doping is extracted from the gap distribution outside the vortex core region within a radius of $2\xi$ where $\xi \approx$ 2.7 nm is the coherence length. The bulk $T_{\text{c}}$ curve corresponds to $T_{\text{c}} = T_{\text{c}}^{\text{max}}[1 - 82.6(p-0.16)^{2}]$ where $T_{\text{c}}^{\text{max}} =$ 95 K at $p = p_{\text{opt}} =$ 0.16, following Presland et al.PRESLAND1991.
• Figure 4: Tunneling conductance spectra measured at the center of vortex cores in Bi-2212 as a function of local doping $p$. Spectra are spatially averaged, normalized, and vertically offset for clarity.
• Figure S1: STM topography and tunneling spectroscopy of Bi-2212 as a function of hole doping. (a) Underdoped-52K. (b) Underdoped-80K. (c) Overdoped-70K. (d) Overdoped-52K. Scan conditions: $V_{\text{b}} =$ +250 mV, $I =$ 20 pA, $T\sim$ 4.4 K. (e) Representative tunneling spectrum for each doping level. The OD70K spectrum is normalized and vertically offset for clarity.