Relation between the structural phase transition and superconductivity in ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$

We have investigated the relation between structural transition with Ir-dimer formation and superconductivity in ${\mathrm{IrTe}}_2$ by combining the Se substitution and the Cu intercalation. Regardless of the structural transition temperature ($T_{\mathrm{s}}$), which increases with increasing the Se content ($y$) in ${\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$, superconductivity emerges robustly by the Cu intercalation. As the Cu content $x$ in ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$ increases, $T_{\mathrm{s}}$ tends to decrease, followed by the emergence of superconductivity with showing the highest critical temperature ($T_{\mathrm{c}}$) at the optimum Cu concentration ($x_{\mathrm{opt}}$) close to the structural phase boundary. Based on the transport and thermodynamic properties, the electron-phonon coupling constant is found to be enhanced near the structural phase boundary, which suggests an essential role of the structural instability for the superconductivity in doped ${\mathrm{IrTe}}_2$. With increasing $y$ from 0 to 0.5 in ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y, T_{\mathrm{s}}$ at $x=0$ increases by about 80%, whereas $T_{\mathrm{c}}$ at $x=x_{\mathrm{opt}}$ decreases by about 20%. This can be understood by the weakening of the interlayer hybridization upon the Se substitution, resulting in the weak but negative correlation between $T_{\mathrm{s}}$ and $T_{\mathrm{c}}$ through $y$.

Figure 1

(a) Crystal structure of ${\mathrm{IrTe}}_2$. (b) Variation of in-plane ($a, a^{\prime }$) lattice constant and lattice anisotropy ratio ($c/a, c^{\prime }/a^{\prime }$) of ${\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$. $a^{\prime }$ and $c^{\prime }$ represent the in-plane and out-of-plane lattice parameters of the pseudotrigonal cell converted from the monoclinic cell (see the main text for detailed definitions), respectively. Solid and dashed lines are guides to the eyes. (c) Variation of $T_{\mathrm{s}}$ as a function of $y$. Solid line is a guide to the eye. (d) Hall coefficient at 2 K for ${\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$ obtained by linear fitting of Hall resistivity vs magnetic field data. (e) Electronic specific-heat coefficient $\gamma$ (left) and Debye temperature ${\mathrm{\Theta }}_{\mathrm{D}}$ (right) as a function of $y$. Black dotted line in (b)–(e) is a boundary separating the 1/5 and 1/6 stripe phases. Solid lines in (d) and (e) are merely guides to the eyes.

Figure 2

Variation of the in-plane ($a, a^{\prime }$) and out-of-plane ($c, c^{\prime }$) lattice constants for (a) $y=0$, (b) $y=0.2$, (c) $y=0.3$, and (d) $y=0.5$ as a function of $x$ in ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$. Lattice anisotropy ratio ($c/a, c^{\prime }/a^{\prime }$) for (e) $y=0$, (f) $y=0.2$, (g) $y=0.3$, and (h) $y=0.5$ as a function of $x$. Filled triangles and circles correspond to the lattice parameters of the monoclinic phase and the trigonal phase, respectively. Solid and dashed lines are guides to the eyes.

Figure 3

Temperature dependence of normalized resistivity $\rho /\rho$(300 K) of ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$ with $x$ ($0\le x\le 0.20$) for (a) $y=0$, (b) $y=0.2$, (c) $y=0.3$, and (d) $y=0.5$. Temperature dependence of $\rho /\rho$(3.5 K) for (e) $y=0$, (f) $y=0.2$, (g) $y=0.3$, and (h) $y=0.5$ under zero magnetic fields. Black dotted arrows indicate the structural phase transition temperature (see the detailed definition described in the text). For Cu doped samples, the data are shifted by 0.2 for clarity. Black curved arrows marked for ${\mathrm{IrTe}}_2$ indicate the warming and cooling processes. For samples without showing the first-order phase transitions, we show only the data collected on warming.

Figure 4

Electronic phase diagram of ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$ as functions of $x, y$, and temperature. Blue filled circles indicate the critical temperatures for the structural phase transition averaged over the cooling and warming processes. Filled and open red circles denote the onset values of the superconducting transition temperature with zero resistivity above 1.8 K and ones with finite resistivity down to 1.8 K, respectively. The superconducting transition temperatures are multiplied by 30 for clarity.

Figure 5

Temperature dependence of specific heat $C$ of ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$ for (a) $y=0$ and (b) $y=0.3$, plotted as $C/T$ versus $T^2$. Cu content ($x$) dependence of (c) Debye temperature, (d) electron-phonon coupling constant, and (e) electronic specific heat coefficient of ${\mathrm{Cu}}_x{\mathrm{IrTe}}_{2-y}{\mathrm{Se}}_y$. Filled red and blue circles indicate the data for $y=0$ and $y=0.3$, respectively. Vertical dashed lines correspond to the optimum composition ($x_{\mathrm{opt}}$) for superconductivity of compounds with $y=0$ (red) and $y=0.3$ (blue). Solid lines in (c), (d), and (e) are guides to the eyes.