Pressure-Induced Unconventional Superconducting Phase in the Topological Insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

Simultaneous low-temperature electrical resistivity and Hall effect measurements were performed on single-crystalline ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ under applied pressures up to 50 GPa. As a function of pressure, superconductivity is observed to onset above 11 GPa with a transition temperature $T_c$ and upper critical field $H_{c2}$ that both increase with pressure up to 30 GPa, where they reach maximum values of 7 K and 4 T, respectively. Upon further pressure increase, $T_c$ remains anomalously constant up to the highest achieved pressure. Conversely, the carrier concentration increases continuously with pressure, including a tenfold increase over the pressure range where $T_c$ remains constant. Together with a quasilinear temperature dependence of $H_{c2}$ that exceeds the orbital and Pauli limits, the anomalously stagnant pressure dependence of $T_c$ points to an unconventional pressure-induced pairing state in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ that is unique among the superconducting topological insulators.

Figure 1

Longitudinal resistivity of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ for various applied pressures as a function of (a) temperature and (b) magnetic field oriented parallel to the crystallographic $c$ axis of the ambient pressure phase, at a fixed temperature of 0.5 K. (Data at 20.8 GPa were obtained with a different lead configuration resulting in larger measurement uncertainty, and are, therefore, scaled by a factor of 2.5 to match the overall trend reported previously [23].)

Figure 2

Transverse Hall resistance of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ as a function of applied pressure, showing linear behavior with a negative slope indicative of a single, electronlike band. The slope decreases with applied pressure until 46.7 GPa, implying an increasing carrier concentration with pressure; 50.1 GPa presents a larger slope and concordantly smaller carrier concentration (see text for details).

Figure 3

Phase diagram of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ showing the evolution of carrier concentration $n_H$ (diamonds), superconducting transition temperature $T_c$ (circles), and upper critical field $H_{c2}$ at zero temperature (squares) as a function of pressure for fields orientation along the crystallographic $c$ axis of the ambient-pressure structure; $n_H$ data below 21 GPa are from Ref. 23. Dotted vertical lines correspond to known structural phase transitions between rhombohedral ($R\mathrm{\text{−}}3m$) and monoclinic ($C2/m$) structures near 10 GPa, and a transition to a bcc-like ($C2/m$) structure near 28 GPa, respectively [21, 23, 28].

Figure 4

(a) Upper critical field $H_{c2}$ of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ for various pressures up to 50 GPa, with fields applied parallel to the ambient-pressure crystallographic $c$ axis (values determined from 50% resistive transition, with error bars indicating 10%–90% values). Solid lines are guides, but all have the same functional dependence as $H_{c2}(T)$ for 34.4 GPa data. Error bars for 24.7 GPa (not shown for clarity) are $\pm 1\mathrm{T}$. Panels (b) and (c) present the reduced upper critical field, $h^{*}(t)$ with reduced temperature $t=T/T_c$, for applied pressures of 34.4 and 50.1 GPa, respectively. Solid and dashed lines indicate the calculated $h^{*}(t)$ dependence for orbital limited $s$-wave superconductors [31] and for a polar $p$-wave state [32, 33], respectively (see text).