Evolution of Electronic States and Emergence of Superconductivity in the Polar Semiconductor GeTe by Doping Valence-Skipping Indium

GeTe is a chemically simple IV–VI semiconductor which bears a rich plethora of different physical properties induced by doping and external stimuli. Here, we report a superconductor-semiconductor-superconductor transition controlled by finely-tuned In doping. Our results reveal the existence of a critical doping concentration $x_c=0.12$ in ${\mathrm{Ge}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$, where various properties, including structure, resistivity, charge carrier type, and the density of states, take either an extremum or change their character. At the same time, we find indications of a change in the In-valence state from ${\mathrm{In}}^{3+}$ to ${\mathrm{In}}^{1+}$ with increasing $x$ by core-level photoemission spectroscopy, suggesting that this system is a new promising playground to probe valence fluctuations and their possible impact on structural, electronic, and thermodynamic properties of their host.

Figure 1

(a) Schematic of the unit cell of GeTe. The grey cube denotes the high-$T$ cubic unit cell, green the low-$T$ rhombohedrally distorted modification. The black arrow indicates the cubic [111] direction along which the distortion takes place, cf. Ref. [32]. (b) Band structure of cubic GeTe. The direct band gap of $\sim 0.2\mathrm{eV}$ is located at the $L$ point of the Brillouin zone. The valence-band maximum (VBM) is set to be zero energy. (c) Sketch of the density of states for ${\mathrm{Ge}}_{1-\delta }\mathrm{Te}$ [46] and the atomic energy levels of the In dopant. The blue dotted line indicates $E_F$ for ideal GeTe without Ge vacancies ($\delta =0$). The more realistic case of ${\mathrm{Ge}}_{1-\delta }\mathrm{Te}$ is indicated with a red dashed line. Temperature-dependent resistivities ${\rho }_{xx}(T)$ of ${\mathrm{Ge}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ for (d) $0\le x\le x_c$ and (e) $x_c\le x\le 1$. (f) Expanded view of (e) for $T\le 5\mathrm{K}$.

Figure 2

Specific heat of ${\mathrm{Ge}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ for selected $x$ measured in $B=0\mathrm{T}$ (blue filled symbols) and $B=2\mathrm{T}$ (red open symbols), which is sufficient to suppress the superconductivity. Dotted black lines denote the normal-state electronic specific-heat coefficient ${\gamma }_n$, dashed lines the electronic specific heat in weak [green in (c)–(e)] or strong-coupling [red in (f)] BCS theory, see text. Specific-heat anomalies are observed for $x\ge 0.16$, indicating the formation of bulk superconductivity, which does not yet develop over the whole sample for $x=0.16$ as indicated by a residual nonsuperconducting phase ${\gamma }_n-{\gamma }_{\mathrm{s}}$.

Figure 3

Variation of physical quantities in ${\mathrm{Ge}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$. (a) Pseudocubic unit-cell volume for rhombohedral ($x<0.12$) and cubic structure ($x>0.12$) at 300 K. (b) Zero-field resistivity at 300 K (red open symbols) and at low $T$ (blue filled symbols; at 2 K for $x\le 0.25$ and above $T_c$ for larger $x$). (c) Charge-carrier concentration $n$ at 300 K. Note that $n$ for $x\ge 0.25$ (dashed-dotted vertical line) are multiplied by 0.1 for clarity. (d) Superconducting $T_c$ as estimated from resistivity, specific heat, and magnetization. The error bars for data points below $x=0.16$ indicate that these samples do not superconduct down to approx. 400 mK. (e) Normal-state electronic specific-heat coefficients ${\gamma }_n$. (f) Electron-phonon coupling strength deduced from specific-heat data. Dotted lines are guides to the eyes, solid horizontal lines in (c)–(e) indicate baselines, and the dashed vertical lines denote $x_c=0.12$.

Figure 4

(a) Valence-band photoemission spectra of ${\mathrm{Ge}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ for $x\le 0.25$ recorded by the photon energy of $h\nu =90\mathrm{eV}$. Data for different $x$ are shifted with respect to each other for clarity. The vertical solid line represents $E_F$. At each data set, horizontal solid lines indicate the baseline and dotted lines are linear fits to the data below $E_F$. The arrows denote the energies where these lines intersect as a measure of the VBM energy. (b) Replotted VBM energies as a function of $x$. The sign change indicates where $E_F$ shifts above the VBM, coinciding with $x_c=0.12$. The dotted line is a guide to the eyes. (c) Peak energies of In-$3d_{5/2}$-core-level photoemission spectra are plotted against $x$, demonstrating the two different In-valence states. Gradations indicate the coexistence region of both valence states, and the change from mainly ${\mathrm{In}}^{3+}$ (blue; low doping) to mainly ${\mathrm{In}}^{1+}$ (red; high doping). Dashed horizontal lines indicate the average peak energy of each feature which differ by approximately 200 meV. (d) Schematic illustration of the evolution of the band structure [46] in ${\mathrm{Ge}}_{1-x}{\mathrm{In}}_x\mathrm{Te}$ with $x$, see text.