Dimensionality switching and superconductivity transition in dense $1T\text{−}{\mathrm{HfSe}}_2$

The quest for new transition metal dichalcogenides (TMDs) with outstanding electronic properties is a particularly significant and interesting subject. The use of nonconventional methods of materials synthesis, especially pressure engineering, shows great potential for breakthrough discoveries in TMDs. Here, we employ the high-pressure techniques to successfully realize the transformation of two-dimensional semiconductor into three-dimensional superconducting states in $1T\text{−}{\mathrm{HfSe}}_2$. We unambiguously demonstrate that the enhancement of the interlayer coupling and the bonding between interlayer Se-Se atoms contribute to the emergence of nonlayered $C2/m$ and $I4/mmm$ phases. The discovered three-dimensional (3D) structures present excellent superconductivity compared to the original layered structure, and the superconducting critical temperature reaches a maximum of 5.8 K at around 50 GPa. Theoretical calculations reveal that the realization of superconductivity in these two 3D structures is related to the increase in the density of states at the Fermi surface $\left[N\left({\varepsilon }_f\right)\right]$. The present results in ${\mathrm{HfSe}}_2$ may provide a platform for our deep understanding of the relationship among dimensionality, structure, and superconductivity phenomena in TMDs.

Figure 1

Results of the Rietveld refinements and crystal structures of ${\mathrm{HfSe}}_2$ at high pressure. Rietveld refinement of XRD patterns at (a) 0.7 GPa, (b) 28.5 GPa, and (c) 60.9 GPa $\left(\lambda =0.6199\AA \right)$. The solid lines and open circles represent the calculated and experimental data, respectively, and the green solid lines at the bottom are the residual intensities. The vertical bars indicate the diffraction peak positions. Inset shows the crystal structures of hexagonal $P\overline{3}m1$, monoclinic $C2/m$ and tetragonal $I4/mmm$ phases. (d) Pressure dependence of the $c/a$ ratio in the ambient $P\overline{3}m1$ phase. (e) The unit-cell volume versus pressure for ${\mathrm{HfSe}}_2$. The data were fitted by the third-order Birch-Murnaghan equation. The dotted lines mark the phase transition pressures.

Figure 2

Experimental Raman spectra and calculated electron localization function (ELF) of ${\mathrm{HfSe}}_2$ at pressures. (a) Raman spectra of ${\mathrm{HfSe}}_2$ for various pressures up to 60 GPa at room temperature. The dashed arrows are guides for the eyes. (b) Evolution of Raman shift frequencies with pressure. The insets show in-plane phonon modes $E_{\mathrm{g}}$ and the out-of-plane phonon modes $A_{1\mathrm{g}}$. The calculated ELF of (c) $C2/m\text{−}{\mathrm{HfSe}}_2$ at 30 GPa for the (010) plane and (d) $I4/mmm\text{−}{\mathrm{HfSe}}_2$ at 60 GPa for the (110) plane.

Figure 3

Electrical transport properties of ${\mathrm{HfSe}}_2$ as a function of pressure. (a) Temperature-dependent resistance under pressures ranging 6.6–21.6 GPa. The inset displays the photograph of $1T\text{−}{\mathrm{HfSe}}_2$ using the standard four-probe method for electrical transport measurements. (b) Electrical resistance as a function of temperature under various pressures. Inset shows a significant resistance drop below superconductivity onset $T_{\mathrm{c}} \sim 5$ K at 22.1 GPa. (c) $R_{\mathrm{normalized}}$ vs T(K) below 8 K from 22.1 to 74.3 GPa. (d) Temperature dependence of resistance under different magnetic fields up to 1 T at 24.4 GPa. (e) The ${\mu }_0{H}_{\mathrm{c}2}$ plots at various $T$ below $T_{\mathrm{c}}$ and the solid line in blue and purple represent fitting by the WHH and GL formulas, respectively. (f) The evolution of upper critical field ${\mu }_0{H}_{\mathrm{c}2}\left(0\right)$ under pressure.

Figure 4

The calculated Fermi surface and DOS of ${\mathrm{HfSe}}_2$. The 3D Fermi surface at the left side and 2D Fermi surface of (a) $C2/m\text{−}{\mathrm{HfSe}}_2$ along the (001) surface of primitive cell at 30 GPa, (b) $I4/mmm\text{−}{\mathrm{HfSe}}_2$ along the ($11\overline{1}$) surface of primitive cell at 50 GPa. (c) Total and projected electronic DOS at 15 GPa, 40 GPa, and 70 GPa, respectively. (d) The electronic and structural phase diagrams of ${\mathrm{HfSe}}_2$.