Measurement of electronic structure and surface reconstruction in the superionic ${\mathrm{Cu}}_{2-x}\mathrm{Te}$

Recently, layered copper chalcogenides ${\mathrm{Cu}}_{2}X$ family $(X=\mathrm{S}, \mathrm{Se}, \mathrm{Te})$ has attracted tremendous research interests due to their high thermoelectric performance, which is partly due to the superionic behavior of mobile Cu ions, making these compounds “phonon liquids.” Here, we systematically investigate the electronic structure and its temperature evolution of the less studied single crystal ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ by the combination of angle resolved photoemission spectroscopy (ARPES) and scanning tunneling microscope/spectroscopy (STM/STS) experiments. While the band structure of the ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ shows agreement with the calculations, we clearly observe a $2\times 2$ surface reconstruction from both our low temperature ARPES and STM/STS experiments which survives up to room temperature. Interestingly, our low temperature STM experiments further reveal multiple types of reconstruction patterns, which suggests the origin of the surface reconstruction being the distributed deficiency of liquidlike Cu ions. Our findings reveal the electronic structure and impurity level of ${\mathrm{Cu}}_2\mathrm{Te}$, which provides knowledge about its thermoelectric properties from the electronic degree of freedom.

Figure 1

Schematic drawing of the crystal structure of ${\mathrm{Cu}}_2\mathrm{Te}$ (a) and top view of (001) plane (b). (c) Bulk and projected surface Brillouin zone (BZ) of (001) surface with high symmetry points indicated. (d) Photoemission core level spectrum of our ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ sample. (e) Extracted lattice constant from single crystal x-ray diffraction measurements at different temperatures. (f) Large scale STM topographic image on (001) plane with a sharp step, $40\mathrm{nm}\times 80\mathrm{nm}$, $U_s=1\mathrm{V}$, $I_s=250\mathrm{pA}$, 5.2 K. (g) Line profile along the red line in the (f) showing the step height.

Figure 2

(a) Broad Fermi surface (FS) map covering more than 1 BZ collected in 140-eV photons with linear horizontal polarization. (b) Band dispersions along $\overline{K}-\overline{\mathrm{\Gamma }}-\overline{K}$ from ARPES measurements. (c) Band dispersions along $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ from ARPES measurements. (d) The constant energy contours around $\overline{\mathrm{\Gamma }}$ point at (i) $E_F$, (ii) $E_b=0.1\mathrm{eV}$, (iii) $E_b=0.2\mathrm{eV}$, (iv) $E_b=0.3\mathrm{eV}$. FS map (e) and $\overline{\mathrm{\Gamma }}-\overline{M}$ dispersion (f) showing folded bands at $\overline{M}$ point. Data in (b)–(f) were collected using 21-eV photons with circularly right polarization.

Figure 3

(a) Schematic drawing of the crystal structure of ${\mathrm{Cu}}_2\mathrm{Te}$ (001) plane, with $1\times 1$ primitive cell and $2\times 2$ supercell indicated by red and green parallelogram, respectively. (b) STM image showing clear $2\times 2$ reconstruction on ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ (001) surface, $15\mathrm{nm}\times 15\mathrm{nm}$, $U_s=-1\mathrm{V}$, $I_s=250\mathrm{pA}$. (c) Line profile along the blue line in (b). (d) STM topographic image on ${\mathrm{Cu}}_{2-x}\mathrm{Te}$, $30\mathrm{nm}\times 30\mathrm{nm}$, $U_s=-1\mathrm{V}$, $I_s=250\mathrm{pA}$. (e) A series of $dI/dV$ spectra along the defined blue dots in (d) with sample bias from −1 to +1.2 V. (f) $dI/dV$ spectrum with high energy resolution with sample bias from −200 to +200 mV showing detailed density of states near $E_F$. All data were collected at 5.2 K.

Figure 4

(a) Band structures of ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ measured along $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ at different temperatures. (b) Fermi surface of ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ measured at 5.2 and 280 K, respectively. All data were collected using 21.2-eV photons. (c) Temperature evolution of integrated photoemission intensity of main bands [integrated over the green dashed rectangle area in (a)], reconstructed bands [integrated over the red dashed rectangle area in (a)], and their ratio.

Figure 5

(a)–(d) STM topographic images showing several reconstruction phases found in our ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ samples: (a) $2\times 2$ phase. (b) Type A $\sqrt{3}\times \sqrt{3}$ phase. (c) $2\times 2$ and $2\sqrt{3}\times 2\sqrt{3}$ mixed phase. (d) Type B $\sqrt{3}\times \sqrt{3}$ phase. The measurement settings are (a) $50\mathrm{nm}\times 50\mathrm{nm}$, $U_s=-1\mathrm{V}$, $I_s=250\mathrm{pA}$, 5.2 K; (b) $30\mathrm{nm}\times 30\mathrm{nm}$, $U_s=1\mathrm{V}$, $I_s=350\mathrm{pA}$, 5.2 K; (c) $50\mathrm{nm}\times 50\mathrm{nm}$, $U_s=1\mathrm{V}$, $I_s=250\mathrm{pA}$, 77 K; (d) $50\mathrm{nm}\times 50\mathrm{nm}$, $U_s=1\mathrm{V}$, $I_s=250\mathrm{pA}$, 77 K.

Figure 6

Fermi surface of ${\mathrm{Cu}}_{2-x}\mathrm{Te}$.

Figure 7

Calculated total density of states (DOS) of ${\mathrm{Cu}}_2\mathrm{Te}$.

Figure 8

(a) Band dispersions along $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ directions obtained by our ARPES experiments data overlapped with calculation results from Ref. [20] (black curves). (b) The calculated band structure along $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ directions extracted from Ref. [20].

Figure 9

Calculated dispersions along (a) $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ and (b) $\overline{K}-\overline{\mathrm{\Gamma }}-\overline{K}$ direction at different $k_z$ values.

Figure 10

Calculated dispersions at different $k_z$ values (orange: $k_z=\pi /5$; yellow: $k_z=2\pi /5$) were appended to experimental data along (a) $\overline{M}-\overline{\mathrm{\Gamma }}-\overline{M}$ and (b) $\overline{K}-\overline{\mathrm{\Gamma }}-\overline{K}$ direction. The coordinate axis on the left and right are the binding energy of the experiment results and calculation results, respectively.

Figure 11

(a) Photoemission intensity of the band dispersion along $\overline{M}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{M}$. (b) Momentum distribution curve at $E_F$. Data were collected using 21-eV photons with circularly right polarization.

Figure 12

(a) Electron diffraction pattern obtained by TEM measurement. (i)–(vi) show diffraction results obtained at six different locations. (b) (i) Zoomed-in image in the white square given in (a) (iv) showing clearer diffraction pattern. (ii) ${\mathrm{Cu}}_2\mathrm{Te}$ (001) plane diffraction pattern simulated by crystalmaker software.

Figure 13

(a) (i) The photography of ${\mathrm{Cu}}_{2-x}\mathrm{Te}$ single crystal; the red grid in the picture indicates $1\mathrm{mm}\times 1\mathrm{mm}$ area; (ii) photo of the sample at the XPS test position; clearly seen is the sample profile surrounded by three black lines as shown in (i). (b) The XPS spectrum of Cu $2p$. The binding energy position of the peaks are 932.2 eV (Cu $2p_{3/2}$) and 952.0 eV (Cu $2p_{1/2}$). (c) Stack of the 55 XPS spectra for the Cu $2p_{1/2}$ peak in different positions with the 55 positions shown in the green dots of (a) (ii). The background of these spectra have been normalized.