Superconducting phase diagram and the evolution of electronic structure across charge density wave in underdoped $1T\text{−}{\mathrm{Cu}}_{\delta }\mathrm{Ti}{\mathrm{Se}}_2$ under hydrostatic pressure

We revisit a superconducting phase diagram and electronic structures across the charge density wave (CDW) phase transition of Cu-underdoped $1T\text{−}{\mathrm{Cu}}_{\delta }\mathrm{Ti}{\mathrm{Se}}_2$ ($\delta \sim 0.03$) under hydrostatic pressure. Superconductivity appears right after the complete collapse of the long-range CDW at a critical pressure of $P_{\mathrm{c}}\sim 2.48\mathrm{GPa}$, apart from the reported superconducting phase diagrams; it is found that the superconducting transition temperature shows a domelike pressure dependence covering a narrow pressure range with a maximum of ${T_{\mathrm{c}}}^{\max }\sim 2.80\mathrm{K}$ at 4.80 GPa. Accordingly, the residual resistivity ${\rho }_0$ and temperature exponent $n$ of normal-state resistivity (from ∼3.30 at ambient pressure to ∼2.38 at $P_{\mathrm{c}}$ and ∼4.0 at 6.50 GPa) reduce sizably while the quadratic temperature coefficient $A$ of normal-state resistivity is enhanced by one order in magnitude; these results indicate the importance of CDW quantum fluctuation in superconducting pairing; low-$T$ resistivity upwarps with a −ln$T$ dependence below a characteristic temperature $T^{*}$ which has a domelike shape in the pressure range of 2.82–4.80 GPa. Based on two-band analysis of Hall conductivity and Kohler-fitting of magnetotransport (MR), energy bands are dominated by electron-type carriers across the CDW phase transition for $P<P_{\mathrm{c}}$, and they reverse into hole-type for $P>P_{\mathrm{c}}$; interestingly, the mobility of carriers increases up to five times at $P_{\mathrm{c}}$, but carrier concentration shows a weak pressure dependence. The MR value increases with the pressure for $P<P_{\mathrm{c}}$ and then jump up to a saturated value after the collapse of the CDW. Our results show that the collapse of the CDW is accompanied by the reconstruction of the Fermi surface, and the enhancement in MR can be mainly attributed to the change of mobility. Possible mechanisms are discussed.

Figure 1

ρ($T$) under pressures for $1T\text{−}{\mathrm{Cu}}_{0.03}\mathrm{Ti}{\mathrm{Se}}_2$ in different runs: (a) S1#, run1; (b) S1#, run2; and (c) S2#, run3. The derivatives $d\rho /dT$ are exported from ρ($T$) for (d) S1#, run1; (e) S1#, run2; and (f) S2#, run3, respectively. The black arrows indicate CDW transition and transition temperature $T_{\mathrm{CDW}}$ where $d\rho /dT$ reaches the minimum.

Figure 2

Low-T ρ($T$) for (a) S1#, run1 and (b) S1#, run2; the arrows indicate the onset superconducting transition ${T_{\mathrm{c}}}^{\mathrm{onset}}$ (blue) and zero resistivity temperature ${T_{\mathrm{c}}}^{\mathrm{zero}}$ (black) where the resistivity starts to decrease and reaches zero. ρ($T$) and the fittings (solid lines), denoted by $\rho \left(T\right)={\rho }_0+A{T}^n$ with the residual resistivity ${\rho }_0$, the temperature coefficient $A$, and the exponent $n$, respectively: (c) 3.0–6.5 GPa, run1; (d) 3.0–7.0 GPa, run3. The insets of (c) and (d) show the enlargement of ρ($T$); the upturn temperature $T^{*}$ in ρ($T$) is marked by red arrows; the blue arrows indicate ${T_{\mathrm{c}}}^{\mathrm{onset}}$. The pressure dependence of ${\rho }_0$ and $n$ is summarized in Fig. 3.

Figure 3

(a) Temperature-pressure phase diagram of $1T\text{−}{\mathrm{Cu}}_{0.03}\mathrm{Ti}{\mathrm{Se}}_2$. $T_{\mathrm{CDW}}, T^{*}$, and ${T_{\mathrm{c}}}^{\mathrm{onset}}$ represents the CDW transition temperature, the upturn temperature in resistivity, and the superconducting transition temperature, respectively. The square points represent $T_{\mathrm{CDW}}$ and the black solid line is the fittings by $T_{\mathrm{CDW}}\left(P\right)=T_0{(1-P/P_{\mathrm{c}})}^{\beta }$; where $T_0, P_{\mathrm{c}}$, and β represent $T_{\mathrm{CDW}}$ at AP, the critical pressure where $T_{\mathrm{CDW}}$ reduces to zero, and the pressure exponent characterizing the suppression of CDW, respectively. The fittings of normal-state resistivity by $\rho \left(T\right)={\rho }_0+A{T}^n$ give (b) ${\rho }_0$, (c) $A$, and (d) $n$. $A$ is linearly fitted with $n=2$. The solid lines show the changing trends.

Figure 4

Field dependence of transverse magnetoresistance $\mathrm{MR}=\left[{\rho }_{xx}\left(H\right)-{\rho }_{xx}\left(0\right)\right]/{\rho }_{xx}\left(0\right)$ and longitudinal Hall resistivity ${\rho }_{xy}\left(H\right)$ at various temperatures and pressures: (a) MR at AP; (b) MR at 1.50 GPa; (c) MR at 5 K for various pressures; (d) ${\rho }_{xy}\left(H\right)$ at AP; (e) ${\rho }_{xy}\left(H\right)$ at 1.50 GPa; (f) ${\rho }_{xy}\left(H\right)$ at 5 K for various pressures; the black arrows indicate the changes of pressures and temperatures.

Figure 5

The normalization of MR vs ${({\mu }_{0}H/{\rho }_0)}^2$ and linear fittings with Kohler slope; the MR and the linear fittings at various temperatures and pressures: (a) at AP for various temperatures; (b) at 1.50 GPa for various temperatures; (c) at 5 K for various pressures; solid lines indicate the fitting results; field dependence of Hall conductivity ${\sigma }_{xy}\left(H\right)$ and the fittings on the basis of two-band models: (d) ${\sigma }_{xy}\left(H\right)$ at AP; (e) ${\sigma }_{xy}\left(H\right)$ at 1.50 GPa; (f) ${\sigma }_{xy}\left(H\right)$ at 5 K; the black arrows indicate the changes of pressures and temperatures.

Figure 6

Temperature dependence of carrier concentration, the electron-type $n_e$ and the hole-type $n_h$ at (a) AP and (b) 1.50 GPa; (c) $n_e$ and $n_h$ at 5 K, respectively; the mobility, ${\mu }_e$ and ${\mu }_h$ at (d) AP and (e) 1.50 GPa; (f) ${\mu }_e$ and ${\mu }_h$ at 5 K, respectively; ρ($T$) and $d\rho /dT$ at (g) AP and (h) 1.50 GPa; (i) ρ($P$) and $d^2\rho /d{P}^2$ at 5 K, respectively; MR at (j) AP and (k) 1.5 GPa under various fields; (l) pressure dependence of MR under various fields; Kohler slope $K$ at (m) AP for $1T\text{−}{\mathrm{Cu}}_{0.03}\mathrm{Ti}{\mathrm{Se}}_2$ (pink) and $1T\text{−}\mathrm{Ti}{\mathrm{Se}}_2$ (black) and (n) 1.50 GPa; (o) pressure dependence of $K$; the dashed lines and the arrows in (g),(h) and (m)–(o) indicate CDW phase transition; and the arrow in (i) indicates the $P_{\mathrm{c}}$ determined from the derivative $d^2\rho /d{P}^2$.