Local corrugation and persistent charge density wave in $\mathrm{ZrTe}{}_3$ with Ni intercalation

The mechanism of emergent bulk superconductivity in transition-metal intercalated ${\mathrm{ZrTe}}_3$ is investigated by studying the effect of Ni doping on the band structure and charge density wave (CDW). The study reports theoretical and experimental results in the range of ${\mathrm{Ni}}_{0.01}{\mathrm{ZrTe}}_3$ to ${\mathrm{Ni}}_{0.05}{\mathrm{ZrTe}}_3$. In the highest doped samples, bulk superconductivity with $T_c<T_{\text{CDW}}$ is observed, with a reduced $T_{\text{CDW}}$ compared with pure ${\mathrm{ZrTe}}_3$. Relativistic ab initio calculations reveal that Ni incorporation occurs preferentially through intercalation in the van der Waals gap. Analysis of the structural and electronic effects of intercalation indicate buckling of the Te sheets adjacent to the Ni site akin to a locally stabilized CDW-like lattice distortion. In contrast to the changes of $T_{\text{CDW}}$ observed in resistivity, experiments with low-temperature x-ray diffraction, angle-resolved-photoemission spectroscopy, as well as temperature-dependent resistivity reveal the nearly unchanged persistence of the CDW into the regime of bulk superconductivity. The CDW gap is found to be unchanged in its extent in momentum space, with the gap size also unchanged or possibly slightly reduced upon Ni intercalation. Both experimental observations suggest that superconductivity coexists with the CDW in ${\mathrm{Ni}}_x{\mathrm{ZrTe}}_3$.

Figure 1

(a) Resistance $R$ normalized to the value at $T=300$ K as a function of temperature for samples $A\text{−}C$ and SC as well as pure ${\mathrm{ZrTe}}_3$ (reference sample). Details of the superconducting transition in the zoomed region from 2 to 5 K are shown in the inset. (b) Extracted charge density wave transition temperatures $T_{\text{CDW}1}$ and $T_{\text{CDW}2}$ for all samples (filled and open squares, left scale) as well as the resistivity anomaly height $\mathrm{\Delta }R/R_1$ (circles, right scale). The inset shows details of the definition of $T_{\text{CDW}1}$, $T_{\text{CDW}2}$, $\mathrm{\Delta }R$, and $R_1$.

Figure 2

Calculated band structure and converged unit cell of ${\mathrm{ZrTe}}_3$.

Figure 3

Converged $3\times 2\times 2$ supercell of ${\mathrm{ZrTe}}_3$ containing a ${\mathrm{Ni}}_i^1$ defect (a,b) and a ${\mathrm{Ni}}_i^3$ defect (c,d). Zr, Te, and Ni atoms are indicated by green, gold, and silver spheres, respectively. Displacements of Zr and Te due to the presence of Ni are shown in (b) and (d). Positive values correspond to displacements away from the van der Waals gap.

Figure 4

Unfolded band structure of ${\mathrm{ZrTe}}_3$ for the supercells with Ni concentrations of $2.1\%$ (a) and $4.2\%$ (b). Panel (c) shows the extracted momentum-resolved density of states at three momentum positions marked by arrows. Overlaid as sharp curves are the band dispersions of ${\mathrm{ZrTe}}_3$. All data are calculated using PBEsol+SOC.

Figure 5

Fermi surface maps of samples $A$ (a) and SC (e) acquired by ARPES at a temperature $T=7$ K. Band dispersion maps along lines of constant $k_x$ indicated in (a,e) are shown for samples $A$ (b)–(d) and SC (e)–(g).

Figure 6

(a)–(d) Spectra at specific high-symmetry points as indicated at the top of each panel for all four samples at cuts at $T=7$ K. (e) Extracted peak positions from panel (a) and lower edge positions from panel (d) as a function of sample name with increasing Ni content.

Figure 7

Diffraction plane ($h0l$) of samples $A$ (a), $B$ (b), $C$ (c), and SC (d), each spanning from (300) in the top left to ($50\overline{2}$) in the bottom right corner. Blue (yellow) corresponds to low (high) intensity, and the strong main lattice spots are overexposed. The measurement temperature was $T=20$ K. The position of the superstructure spots due to the PLD is marked with green circles.

Figure 8

Density of states for ${\mathrm{ZrTe}}_3$ (a) as well as for the supercells with Ni concentrations of 2.1% (b) and 4.2% (c).