Emergence of Fermi Pockets in a New Excitonic Charge-Density-Wave Melted Superconductor

A superconducting state ($T_c\sim 4.2\mathrm{K}$) has very recently been observed upon successful doping of the charge-density-wave (CDW) ordered triangular lattice ${\mathrm{TiSe}}_2$, with copper. Using state-of-the-art photoemission spectroscopy we identify, for the first time, momentum-space locations of doped electrons that form the Fermi sea of the superconductor. With doping, we find that kinematic nesting volume increases, whereas coherence of the CDW collective order sharply drops. In superconducting doping, as chemical potential rises, we observe the emergence of a large density of states in the form of a narrow electron pocket near the $L$ point of the Brillouin zone with $d$-like character. The $k$-space spectral evolution directly demonstrates, for the first time, that the CDW order parameter microscopically competes with superconductivity in the same band.

Figure 1

Sample characterization: (a) Brillouin zone layout of ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$ where $M(\frac{1}{2},0,0)$, $K(\frac{1}{3},\frac{1}{3},0)$, $L(\frac{1}{2},0,\frac{1}{2})$, $H(\frac{1}{3},\frac{1}{3},\frac{1}{2})$, and $A(0,0,\frac{1}{2})$. (b) Doping-temperature phase diagram suggests CDW is a competing phase for superconductivity. (c) High resolution valence band profile of ${\mathrm{Cu}}_x{\mathrm{TiSe}}_2$ along the $M/L\mathrm{\text{−}}\Gamma /A\mathrm{\text{−}}M/L$ momentum-space cut measured at 20 K. The top two bands are the ${\Gamma }^3(A^{3-})$ and ${\Gamma }^{2-}$ bands (in agreement with LDA calculations [16]).

Figure 2

CDW state melts near superconducting doping: low temperature ($T\ll T_{\mathrm{CDW}}$ at $x=0$) doping evolution of bands in the vicinity of the $L$ point (top row) and $\Gamma$ points (bottom row). With increasing doping the intensity of the folded band decreases and spectral weight concentrates near the $L$ points in the form of an electron pocket with bandwidth about 0.1 eV. Bottom row: with increasing doping spectral weight near the $M\mathrm{\text{−}}\Gamma \mathrm{\text{−}}M$ cuts continues to shift to lower energies and deeper-lying bands tend to split further from each other.

Figure 3

Temperature evolution of spectral function with doping: energy distribution curves for $k=L+0.1{\AA }^{-1}$ are shown for $x=0$, 0.04, and 0.06 dopings. The peak at 0.25 eV in $x=0$ at $T=20\mathrm{K}$ is due to band folding. With increasing doping the intensity of the 0.25 eV peak drops while the quasiparticle peak grows dramatically.

Figure 4

Rise of chemical potential with doping: Electron pockets emerge and grow with doping: high temperature ($T\gg T_{\mathrm{CDW}}$) band evolution in the vicinity of the $L$ point. With increasing doping the Fermi level rises up. At the $\Gamma$ point this is seen as a lowering of the Se $4p$ bands [(a)–(c), top row] and the emergence of low-energy states. At the $L$ point, doping gives rise to an electron pocket with a bandwidth of about 0.1 eV. The $L$ pocket grows with increasing doping.

Figure 5

Electron distribution of superconductor ${\mathrm{Cu}}_{0.06}{\mathrm{TiSe}}_2$: with increasing copper doping, electrons near the $L$ point form a narrow pocket and generate a sixfold symmetric Fermi contour. A finite but weak intensity is also observed at the $\Gamma /A$ point. The presented summary of data above is measured in the first quadrant at $T=20\mathrm{K}$ then symmetrized over the Brillouin zone.