Unconventional superconductivity in CuxBi2Se3 from magnetic susceptibility and electrical transport

Although the Cu doped Bi _2 Se _3 topological insulator was discovered and intensively studied for almost a decade, its electrical and magnetic properties in normal state, and the mechanism of ‘high- T _c ’ superconductivity regarding the relatively low-carrier density are still not addressed yet. In this work, we report a systematic investigation of magnetic susceptibility, critical fields, and electrical transport on the nominal Cu _0.20 Bi _2 Se _3 single crystals with ${T}_{\mathrm{c}}^{\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{e}\mathrm{t}}$ = 4.18 K, the highest so far. The composition analysis yields the Cu stoichiometry of x = 0.09(1). The magnetic susceptibility shows considerable anisotropy and an obvious kink at around 96 K was observed in the magnetic susceptibility for H ∥ c , which indicates a charge density anomaly. The electrical transport measurements indicate the two-dimensional (2D) Fermi liquid behavior at low temperatures with a high Kadowaki–Woods ratio, A / γ ^2 = 30.3 a _0 . The lower critical field at 0 K limit was extracted to be 6.0 Oe for H ∥ ab . In the clean limit, the ratio of energy gap to T _c was determined to be Δ _0 / k _B T _c = 2.029 ± 0.124 exceeding the standard BCS value 1.764, suggesting Cu _0.09 Bi _2 Se _3 is a strong-coupling superconductor. The in-plane penetration depth at 0 K was calculated to be 1541.57 nm, resulting in an unprecedented high ratio of T _c / λ ^−2 (0) ≅ 9.86. Moreover, the ratio of T _c to Fermi temperature is estimated to be ${T}_{\mathrm{c}}/{T}_{\mathrm{F}}^{2\mathrm{D}}$ = 0.034. Both ratios fall into the region of unconventional superconductivity according to Uemura’s regime, supporting the unconventional superconducting mechanism in Cu _x Bi _2 Se _3 . Finally, the enhanced T _c value higher than 4 K is proposed to arise from the increased density of states at Fermi energy and strong electron–phonon interaction induced by the charge density instability.