Dimensional tuning and coexisting electronic orders in single-crystalline $$1T\text {-Cu}_x\text {TiSe}_2$$ quantum materials

Abstract We report a detailed study of moderate-coupling superconductivity coexisting with charge-density-wave (CDW) order in single-crystalline $$1T\\text {-Cu}_x\\text {TiSe}_2$$ ( $$x = 0\\text {--}0.1$$ ) down to $$60\\text { mK}$$ . Millikelvin specific-heat measurements on underdoped samples reveal a sharp superconducting anomaly with a vanishing residual electronic specific heat coefficient ( $$\\gamma _r \\rightarrow 0$$ ) in the ground state, signaling a fully gapped superconducting state clear of uncondensed normal electrons. Concurrently, distinct thermodynamic anomalies near $$200\\text { K}$$ and $$25\\text { K}$$ confirm the robust persistence of CDW order in the undoped and underdoped regimes, respectively. Upper critical-field measurements display a nearly temperature-independent anisotropy, $$H_{\\text {c2}}^{ab}/H_{\\text {c2}}^c \\simeq 1.7$$ , consistent with conventional single-gap s -wave pairing. Analysis of the reduced specific-heat jump, $$\\Delta C_{\\text {el}}/\\gamma _n T_{\\text {c}}$$ , alongside the Werthamer-Helfand-Hohenberg (WHH) framework, establishes moderate electron-phonon coupling ( $$\\lambda _{\\text {el-ph}} = 0.62$$ ) and conventional superconductivity coexisting with a partially suppressed CDW state. These findings present $$1T\\text {-Cu}_x\\text {TiSe}_2$$ as a clean model platform for investigating the systematic modulation of competing quantum phases via transition-metal intercalation, offering a strategic framework for the architectural design of low-dimensional functional electronics.