Scanning tunneling microscopy and spectroscopy studies of the heavy-electron superconductor ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$

We report on the structural and superconducting electronic properties of the heavy-electron superconductor ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$. By using a variable-temperature scanning tunneling microscopy (VT-STM) the coexistence of $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$ and $(2\times 1)$ surface reconstructions is observed. Similar to earlier observations on the “122” family of Fe-based superconductors, we find that their respective surface fraction strongly depends on the temperature during cleavage, the measurement temperature, and the sample's history. Cleaving at low temperature predominantly results in the $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$-reconstructed surface. A detailed analysis of the $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$-reconstructed domains identifies $(2\times 1)$-ordered dimers, tertramers, and higher order even multimers as domain walls. Higher cleaving temperatures and the warming of low-temperature–cleaved samples increases the relative weight of the $(2\times 1)$ surface reconstruction. By slowly increasing the sample temperature $T_{\mathrm{s}}$ inside the VT-STM we find that the $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$ surface reconstructions transforms into the $(2\times 1)$ structure at $T_{\mathrm{s}}=123$ K. We identify the polar nature of the ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$(001) surface as the most probable driving mechanism of the two reconstructions, as both lead to a charge density $\rho =0.5e^{-}$, thereby avoiding divergent electrostatic potentials and the resulting “polar catastrophe.” Low-temperature scanning tunneling spectroscopy (STS) performed with normal metal and superconducting probe tips shows a superconducting gap which is best fit with an isotropic $s$ wave. We could not detect any correlation between the local surface reconstruction, suggesting that the superconductivity is predominantly governed by ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ bulk properties. Correspondingly, temperature- and field-dependent data reveal that both the critical temperature and critical magnetic field are in good agreement with bulk values obtained earlier from transport measurements. In the superconducting state the formation of an Abrikosov lattice is observed without any zero bias anomaly at the vortex core.

Figure 1

(a) Crystal structure of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ and probable cleavage plane (gray). (b) Top view illustrates a ${45}^{\circ }$ rotation between nearest neighbor directions of Tl and Ni layers. (c) Topographic image with occasionally occurring dislocation lines (black arrow). The blue box of the $\sqrt{2}\times \sqrt{2}$ unit cell in the higher resolution image (e) is one of two typical structures for LT-cleaved samples. (d) Line section along the blue line in (c). The terraces are separated by step heights of the half-unit-cell as visualized in the lower left sketch. Scan parameters are as follows: $U=500/10$ mV, $I=10/250$ pA, and $T_{\mathrm{s}}=5$ K for (c) and (e), respectively.

Figure 2

Cleaving temperature dependence of the ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ surface structure. In either case an overview image (left panel), a zoom-in to the region within the black square (middle), and a model of the surface (right) are shown. Atoms of the topmost Se layer and the Tl cleavage plane are shown in red and blue, respectively. To highlight Tl atom rows, nearest-neighbor Tl atom with a Tl–Tl distance $a=3.870$ Å are not resolved individually but as a continuous blue line. (a) If cleaved at 5 K the surface topography is dominated by large domains of a $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$ superstructure [imaging parameters (inset) are as follows: $U=1\left(0.5\right)$ V, $I=20\left(500\right)$ pA, $T_{\mathrm{s}}=5$ K]. (b) Cleavage at a temperature of 50 K lead to substantial stripes formation and smaller $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$ domains ($U=50$ mV, $I=20$ pA, $T_{\mathrm{s}}=50$ K). (c) A twofold symmetric “wormlike” structure is observed for room-temperature–cleaved ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ ($U=1$ V, $I=300$ pA, $T_{\mathrm{s}}=5$ K).

Figure 3

(a) and (b) STM topographic images of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ single crystal surfaces cleaved at $T_{\mathrm{s}}=5$ K. Scan parameters are as follows: $U=1$ V, $I=20$ pA. The surface is governed by $(\sqrt{2}\times \sqrt{2})\mathrm{R}{45}^{\circ }$-ordered patches labeled A or B, which are separated by boundaries that consist of short stripes. Four such regions marked by black squares and labeled 1–4 in panels (a) and (b) are schematically represented in (c). Analysis reveals that the stripes exhibit different length and represent dimers (1), trimers (2), tetramers (3), and pentamers (4). Whereas dimers and tetramers separate the inequivalent domains A and B, trimer and pentamer walls are always surrounded by the same domain.

Figure 4

(a) Both LT structures of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ coexist on a sample cleaved at $T_{\mathrm{cleave}}=50$ K. This already changes at a temperature of $T_{\mathrm{s}}=120$ K in (b) where no square lattice is observed. By warming up to $T_{\mathrm{s}}=123$ K further changes are observed in (c). The transition into the “wormlike” structure in (d) is completed at $T=126$ K. Circles serve as markers for same sample positions and black arrows for an example of restructuring. Scan parameters are as follows: $U=50$ mV, $I=20$ pA for (a) and $U=1$ V, $I=200...300$ pA for (b)–(d).

Figure 5

STS signal of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ recorded with a normal conducting W tip. The data are fitted by an isotropic [red, Eq. (1)]. Stabilization parameters are as follows: $U=-5$ mV, $I_{\mathrm{set}}=200$ pA, $U_{\mathrm{mod}}=0.1$ mV, $T=1.2$ K.

Figure 6

(a) Topographic image of a ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ showing the “wormlike” structure. (b) Normalized $dI/dU$ spectra measured along the 10-nm-long blue line marked in (a). No significant influence of the surface reconstruction on the width or shape of the superconducting gap is detected. Stabilization parameters are as follows: $U=-5$ mV, $I_{\mathrm{set}}=200$ pA, $U_{\mathrm{mod}}=0.1$ mV, $T=1.2$ K.

Figure 7

(a) Temperature-dependent STS data of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$. A pronounced superconducting gap is clearly visible at the lowest accessible temperature, $T=1.2$ K (purple line). With increasing temperature the gap size is reduced and vanishes at about $T\gtrsim 3.2$ K (orange line). (b) Plot of the temperature-dependent gap size determined by fitting the STS data presented in (a) with Eq. (2) expected for a BCS-type superconductor (see main text for details). Stabilization parameters are as follows: $U=-5$ mV, $I_{\mathrm{set}}=200$ pA, $U_{\mathrm{mod}}=0.1$ mV.

Figure 8

(a) Magnetic field-dependent spectroscopy of ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$ at $T=1.2$ K. The gap becomes smaller with increasing magnetic field and vanishes for $B\ge 400$ mT. Stabilization parameters are as follows: $U=-5$ mV, $I_{\mathrm{set}}=200$ pA, $U_{\mathrm{mod}}=0.1$ mV. (b) Plot of the field-dependent gap size determined by fitting the data in (a).

Figure 9

(a) Topographic image of cleaved ${\mathrm{TlNi}}_2{\mathrm{Se}}_2$. (b) Differential conductance maps of the same area as in (a) at a perpendicular magnetic field of 100 mT, showing the Abrikosov lattice. The unit cell of the vortex lattice as theoretically expected from Eq. (3) is indicated in green. The experimentally observed density of the vortices is in excellent agreement. (c) Some examples of scanning tunneling spectra measured directly at and at some selected distances from the vortex core. The superconducting gap is decreasing with decreasing distance to the vortex core where the gap vanishes completely. (d) Normalized $dI/dU$ spectra as a function of their distance from the vortex core as measured along the 200-nm-long blue trajectory marked in (b). Scan parameters are as follows: $U=-1$ mV, $I_{\mathrm{set}}=50$ pA, $U_{\mathrm{mod}}=0.1$ mV, $T=1.2$ K.