Quasiparticle Evidence for the Nematic State above $T_{\mathrm{c}}$ in ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$

In the electronic nematic state, an electronic system has a lower symmetry than the crystal structure of the same system. Electronic nematic states have been observed in various unconventional superconductors such as cuprate, iron-based, heavy-fermion, and topological superconductors. The relation between nematicity and superconductivity is a major unsolved problem in condensed matter physics. By angle-resolved specific heat measurements, we report bulk quasiparticle evidence of nematicity in the topological superconductor ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. The specific heat exhibited a clear twofold symmetry despite the threefold symmetric lattice. Most importantly, the twofold symmetry appeared in the normal state above the superconducting transition temperature. This is explained by the angle-dependent Zeeman effect due to the anisotropic density of states in the nematic phase. Such results highlight the interrelation between nematicity and unconventional superconductivity.

Figure 1

(a) Crystal structure of ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ in the hexagonal plane. The orange and blue circles represent the elements Bi and Se. The $x$ and $y$ axes and the azimuthal angle $\varphi$ are defined in the main text. (b) Laue diffraction pattern of the analyzed crystal. (c) Temperature dependence of the in-plane resistivity measured at zero field. (d) Temperature dependence of the magnetic susceptibility $\chi$ measured under 1 Oe field perpendicular to the $xy$ plane. (e) Upper critical fields for $H\parallel x$ axis, $H\parallel y$ axis and $H\perp xy$ plane, obtained from the resistive transition under fields. (f) Polar plot of resistance versus angle $\varphi$ at 2 K under various magnetic fields ($1\sim 5\mathrm{T}$).

Figure 2

(a) Azimuthal angle dependence of the specific heat $\mathrm{\Delta }C(\varphi )/T$ measured under various magnetic fields at 0.35 K. $\mathrm{\Delta }C(\varphi )/T$ is defined as $C(\varphi )/T–C(0°)/T$, and each subsequent curve is shifted vertically by $0.2\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$. Symbols with black outlines are measured data, and those without are mirrored points to show the symmetry. (b)–(g) Polar plots of $\mathrm{\Delta }C(\varphi )/T$ at 0.35 K under various magnetic fields: (b) 0.3 T, (c) 0.7 T, (d) 1 T, (e) 2 T, (f) 4 T, and (g) 5 T. The colored lines indicate the symmetry axes of the twofold oscillation.

Figure 3

(a) Azimuthal angle dependence of the specific heat $\mathrm{\Delta }C(\varphi )/T$ that is measured under various magnetic fields at 2.1 K. $\mathrm{\Delta }C(\varphi )/T$ is defined as $C(\varphi )/T–C(0°)/T$, and each subsequent curve is shifted vertically by $0.8\mathrm{mJ}/\mathrm{mol}{\mathrm{K}}^2$. Symbols with black outlines are measured data, and those without are mirrored points to show the symmetry. (b)–(d) Polar plots of $\mathrm{\Delta }C(\varphi )/T$ at 2.1 K under fields of 3 T, 4 T, and 6 T, respectively. Sketches of the spin-helical structure in the situations of (e) isotropic density of states without nematicity, and (f) anisotropic density of states with nematicity. Paired spins are indicated by orange and blue arrows. The blue and orange patterns in (e) and (f) represent the spatial distributions of the magnitude of the Zeeman effect under fields along the $k_y$ and $k_x$ directions, respectively. Sketches of the band shift due to the Zeeman effect under fields along the $k_y$ and $k_x$ directions in the situations of (g) isotropic density of states without nematicity, and (h) anisotropic density of states with nematicity.