Temperature-Induced Lifshitz Transition and Possible Excitonic Instability in ZrSiSe

The nodal-line semimetals have attracted immense interest due to the unique electronic structures such as the linear dispersion and the vanishing density of states as the Fermi energy approaching the nodes. Here, we report temperature-dependent transport and scanning tunneling microscopy (spectroscopy) [STM(S)] measurements on nodal-line semimetal ZrSiSe. Our experimental results and theoretical analyses consistently demonstrate that the temperature induces Lifshitz transitions at 80 and 106 K in ZrSiSe, which results in the transport anomalies at the same temperatures. More strikingly, we observe a $V$-shaped dip structure around Fermi energy from the STS spectrum at low temperature, which can be attributed to co-effect of the spin-orbit coupling and excitonic instability. Our observations indicate the correlation interaction may play an important role in ZrSiSe, which owns the quasi-two-dimensional electronic structures.

Figure 1

(a) Crystal structure of ZrSiSe. (b) The first-principles calculated band structure of ZrSiSe with SOC along high-symmetry lines. The dashed blue line, dotted red and long dashed green lines label three different Fermi levels corresponding to the cases with temperature $T=5\mathrm{K}$ (intrinsic case), 102 and 106 K according to Fig. 2, respectively. (c),(d),(e) The three-dimensional Fermi surface with the Fermi energy labeled by the dashed blue, dotted red, and long dashed green lines in (b), respectively.

Figure 2

(a),(b) The field dependence of the ${\rho }_{yx}(H)$ and ${\rho }_{xx}(H)$ for several temperatures ranging from $T=5\mathrm{K}$ to 300 K. (c),(d) The field dependence of the Hall conductivity ${\sigma }_{xy}(H)$ for temperatures ranging from $T=5$ to 300 K. Open symbols represent the experimental results and the red solid lines represent the fitting results based on two-component model. (e),(f) The temperature dependence of fitting parameter, namely, the densities and mobility of the carriers extracted from the two-component model analysis of ${\sigma }_{xy}$. The left dashed red and right dashed green lines in (f) label two anomalies of the mobility ${\mu }_2$ at 80 and 106 K, respectively.

Figure 3

(a) Top view of crystal structure of ZrSiSe. (b) Atomically resolved STM topographic image of the cleaved ZrSiSe surface at $T=4.5\mathrm{K}$ with $V_b=600\mathrm{mV}$ and $I_t=200\mathrm{pA}$. The inset shows the fast Fourier transform (FFT) image. (c),(d) Enlarged views of the cleaved surface at $T=4.5\mathrm{K}$ ($V_b=600\mathrm{mV}$ and $I_t=500\mathrm{pA}$) and $T=77\mathrm{K}$ ($V_b=600\mathrm{mV}$ and $I_t=200\mathrm{pA}$). (e) Line-cut averaged $dI/dV$ spectrum acquired in ZrSiSe at $T=4.5\mathrm{K}$ (black curve) and $T=77\mathrm{K}$ (red curve) along the Zr-Se-Zr direction. All spectra are normalized at $V=200\mathrm{mV}$. The black-solid arrow labels the $V$-shaped dip structure. The solid-red arrow in Fig. 3 labels the line-cut direction. (f),(h) The STS line-cut map along the Zr-Se-Zr direction at $T=4.5$ and 77 K, respectively. (g),(i) The calculated ratio of $e/h$ asymmetry based on the spectra measurement in (f) and (h), respectively.

Figure 4

(a),(b) The calculated Dirac nodal-line structure and Fermi surface of trivial quadratic band with the model in the Supplemental Material, respectively. (c),(d) The calculated DOS with the model in SMs for $k_{B}T=0.004$ ($T=4.5\mathrm{K}$) in (c) and $k_{B}T=0.05$ ($T=77\mathrm{K}$) in (d). Bottom curves 1 and 3 are from Dirac nodal-line bands in (a) with $({\lambda }_{\mathrm{soc}},{\mathrm{\Delta }}_{\mathrm{ex}})=(0.06,0)$ and (0.06, 0.02), respectively. Top curve 8 and 10 are from the sum of blue curve and bottom curves 1 and 3, respectively. (e) and (f) The enlargement of the bottom and top parts of (c), respectively. Curves 1 and 3 in (e) and (f) are same to these in (c). The curves 2, 4–7 with $({\lambda }_{\mathrm{soc}},{\mathrm{\Delta }}_{\mathrm{ex}})=(0.06,0.01)$, (0.06, 0.03–0.06). The curves 9, 11–14 have the same values as the curves 2, 4–7. In (a)–(f), other parameters are present in the Supplemental Material.