Sign-Reversing Hall Effect in Atomically Thin High-Temperature ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}{\mathrm{CaCu}}_{2.0}{\mathrm{O}}_{8+\delta }$ Superconductors

We developed novel techniques to fabricate atomically thin ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}{\mathrm{CaCu}}_{2.0}{\mathrm{O}}_{8+\delta }$ van der Waals heterostructures down to two unit cells while maintaining a transition temperature $T_c$ close to the bulk, and carry out magnetotransport measurements on these van der Waals devices. We find a double sign change of the Hall resistance $R_{xy}$ as in the bulk system, spanning both below and above $T_c$. Further, we observe a drastic enlargement of the region of sign reversal in the temperature-magnetic field phase diagram with decreasing thickness of the device. We obtain quantitative agreement between experimental $R_{xy}(T,B)$ and the predictions of the vortex dynamics-based description of Hall effect in high-temperature superconductors both above and below $T_c$.

Figure 1

van der Waals BSCCO device. (a) Optical image of Hall bar device, showing BSCCO with contacts and hexagonal boron nitride ($h$-BN) cover, as drawn in the inset below. (b) Cross-sectional view of a typical device in scanning TEM. Columns of atoms are visible as dark spots. Black arrows point to the location of bismuth oxide layers (darkest spots), while gray arrows show their extrapolated positions. (c) Resistivity as a function of temperature for vdW devices of a different thickness.

Figure 2

Hall effect measurements. (a) Hall resistance for a 2 UC sample. The curves are vertically shifted for clarity, the horizontal dashed lines mark $R_{xy}=0$. Below 60 K, the Hall effect has the same sign as in the normal state. Above 60 K the sign reversal appears at magnetic fields $B<5\mathrm{T}$. Dashed and dash-dotted lines show fits to the data (solid lines). (b) Inverse Hall resistance increases linearly with sample thickness in our devices, demonstrating good oxygen dopant retention down to 2 UCs. Data taken at 100 K. (c) Device mobility increases as samples become thicker, eventually saturating at 5 UC.

Figure 3

The double sign change. (a) Temperature dependencies $R_{xy}(T)$ at fixed magnetic fields for the 2 UC device. Fits above (dash-dotted) and below (dashed lines) $T_c$ are superimposed on experimental data (symbols). Inset: Superconducting gap extracted from fits for all samples using Eq. (1). $T_c$ is the temperature extracted from the analysis of $R_{xx}(T)$ in the framework of superconducting fluctuations (SF). (b) The Hall sign-reversal phase diagram. Shading shows Hall resistance $R_{xy}(B,T)$ for a 2 UC device with $T_c=81.5\mathrm{K}$. The blue region shows the area of negative Hall resistance. Symbols show the locus $R_{xy}=0$ for different thicknesses, and the lines are generated from fits to $R_{xy}=0$ using Eq. (2) [13] (solid) and using Eq. (3) (dash). As thickness decreases, the Hall sign-reversed region becomes larger.