Surface charge induced Dirac band splitting in a charge density wave material ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$

${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$, a quasi-one-dimensional (1D) crystal, shows a characteristic temperature-driven metal-insulator phase transition. Above the charge density wave (CDW) temperature $T_c$, ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ has been predicted to harbor a Weyl semimetal phase. Below $T_c$, it becomes an axion insulator. Here, we performed angle-resolved photoemission spectroscopy measurements on the (110) surface of ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ and observed two sets of Dirac-like energy bands in the first Brillouin zone, which agree well with our first-principles calculations. Moreover, we found that each Dirac band exhibits an energy splitting of hundreds of millielectron volts under certain circumstances. In combination with core level measurements, our theoretical analysis showed that this Dirac band splitting is a result of surface charge polarization due to the loss of surface iodine atoms. Our findings here shed light on the interplay between band topology and CDW order in Peierls compounds and will motivate more studies on topological properties of strongly correlated quasi-1D materials.

Figure 1

Crystal structure and sample characterization. (a) Crystal structure of ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$. The (110) surface is shown in blue. (b) Scanning tunneling microscopy (STM) image of ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. The $c$ axis of the crystal and the charge-density-wave (CDW) wavevector ${\vec{q}}_{\mathrm{CDW}}$ are shown. This image is acquired at −1 V and current of 30 pA. Inset: the Fourier transform of the STM image. (c) Enlarged STM image of the green dashed rectangle area shown in (b). About 50% of iodine atoms remain on the freshly cleaved (110) surface. (d) The logarithmic normalized longitudinal resistivity $\rho /\rho \left(T=300\mathrm{K}\right)$ (blue) and its derivative (red) as a function of ${10}^3{T}^{\text{–}1}$. (e) Bulk Brillouin zone of ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ and the surface planes on which the Fermi surface mappings are taken. (f) Constant energy contour (CEC) mapping acquired on the $\overline{\mathrm{Y}\mathrm{\Gamma }\mathrm{Z}}$ plane at $E\text{−}{E}_F=-0.6\mathrm{eV}$. (g) CEC mapping acquired on the $\overline{\mathrm{X}\mathrm{\Gamma }\mathrm{Z}}$ plane at $E\text{−}{E}_F=-0.6\mathrm{eV}$. (h) Angle-resolved photoemission spectroscopy (ARPES) band map of ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ measured along the $\overline{\mathrm{\Gamma }\mathrm{Z}}$ direction. The linear horizontal (LH) polarized light with photon energy of 23 eV is used in (g) and (h).

Figure 2

Observation of Dirac bands on ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. (a) Angle-resolved photoemission spectroscopy (ARPES) spectra along the $\overline{\mathrm{\Gamma }\mathrm{Z}}$ direction acquired at room temperature. The linear vertical light with photon energy of 23 eV is used. The black curves are the calculated band structures. (b) The corresponding ARPES band spectra after normalizing the momentum distribution curves (MDC). (c) The MDC of the ARPES band spectra shown in (b).

Figure 3

Temperature dependence of Dirac band splitting on ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. (a)–(c) Angle-resolved photoemission spectroscopy (ARPES) spectra along the $\overline{\mathrm{\Gamma }\mathrm{Z}}$ direction acquired at (a) $T=350\mathrm{K}$, (b) 265 K, and (c) 120 K. Right panels of (a)–(c): two energy distribution curve (EDC) lines extracted at two momenta marked with red and blue arrows above the left ARPES spectra. (d) and (f) The corresponding second derivative spectra of the ARPES data shown in (a)–(c). (g) The EDC line extracted at the same $k\sim 0.246{\AA }^{-1}$ (i.e., π/$c$). Two dip features of each EDC line are fitted by two Gaussian functions, which can quantitatively estimate the Dirac band splitting observed on the ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface.

Figure 4

Core levels of Se and iodine (I) and corresponding angle-resolved photoemission spectroscopy (ARPES) band maps of the ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. (a) Core levels of Se $3d_{3/2}$, Se $3d_{5/2}$, I $4d_{3/2}$, and I $4d_{5/2}$. The core level photoemission measurement is performed at room temperature, and both spectra are normalized to the intensity maximum of the Se $3d_{5/2}$ peak. The photon energy of 110 eV is used. The sample is heated to $T=350\mathrm{K}$ for ∼1 h. (b) and (c) ARPES band spectra along the $\overline{\mathrm{\Gamma }\mathrm{Z}}$ direction on (b) the freshly cleaved and (c) heat-treated ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. The linear horizontal (LH) polarized light with photon energy of 47eV is used. The blue arrows indicate the Dirac band crossing points. The ARPES measurements are performed at room temperature.

Figure 5

Circular dichroism (CD) effect of the Dirac band splitting in ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$. (a) Experimental geometry for CD-angle-resolved photoemission spectroscopy (CD-ARPES) measurement on ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$. (b) Constant energy contour (CEC) mapping acquired on the $\overline{\mathrm{X}\mathrm{\Gamma }\mathrm{Z}}$ plane at $E\text{−}{E}_F=-1.06\mathrm{eV}$. (c) CEC mapping of the normalized CD data at $E\text{−}{E}_F=-1.06\mathrm{eV}$. (d) and (e) ARPES spectra along the $\overline{\mathrm{\Gamma }\mathrm{Z}}$ direction measured with right circularly polarized (RCP) and left circularly polarized (LCP) light with photon energy of 47 eV, respectively. (f) Normalized CD spectra along the $\overline{\mathrm{\Gamma }\mathrm{Z}}$ direction. All ARPES data shown in (b)–(f) are taken at $T=350\mathrm{K}$.

Figure 6

Surface charge-induced Dirac band splitting on the ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. (a) Shechamic for the volatile iodine atoms on the ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. (b)–(d) Calculated band structures of ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ along the $\mathrm{\Gamma }\mathrm{Z}$ direction with the integrated $k_z$. (a) 100%, (b) 50%, and (c) 0% of iodine atoms on the ${\left(\mathrm{Ta}{\mathrm{Se}}_4\right)}_2\mathrm{I}$ (110) surface. The size of the red (blue) dots represents the fraction of electronic charge on the outermost (second outermost) $\mathrm{Ta}{\mathrm{Se}}_4$ layers, while the size of the gray dots represents that of the rest bulk atoms.