We report an observation of coherent phonons of $E_g^1, E_u^1, A_{1g}^1$, and $E_g^2$ symmetry generated in a single-crystal film of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ by an intense single-cycle THz pulse. The atomic vibrations reveal themselves through periodic modulation of the refractive index of the film. The largest signal is detected at the frequency of 4.05 THz that corresponds to the $E_g^2$ mode. The generation of $E_g^2$ phonons is interpreted as resonant excitation of the Raman mode by the second harmonic of THz-driven nonlinear $E_u^1$ oscillator, the fundamental frequency of which (2.05 THz) is approximately half that of $E_g^2$. The origin of nonlinearity in this case is cubic lattice anharmonicity, while generation of $E_g^1$ (1.1 THz) and $A_{1g}^1$ (2.25 THz) phonons is a manifestation of quartic anharmonicity enhanced by the occasional combination relations between phonon frequencies in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

In this paper, we present novel experimental evidence for the odd-parity nematic superconductivity in high-quality single crystals of doped topological insulator ${\mathrm{Sr}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$. The x-ray diffraction shows that the grown single crystals are either weakly stretched or compressed uniaxially in the basal plane along one of the crystal axis. We show that in the superconducting state, the upper critical magnetic field $H_{c2}$ has a twofold rotational symmetry and depends on the sign of the strain: in the stretched samples the maximum of $H_{c2}$ is achieved when the in-basal-plane magnetic field is transverse to the strain axis, while in the compressed samples this maximum is observed when the field is along the strain direction. This result is naturally explained within a framework of the odd-parity nematic superconductivity coupled to the strain. Magnetoresistance in the normal state is independent of the current direction and also has a twofold rotational symmetry that demonstrates the nematicity of the electronic system in the normal state.

Bismuth chalcogenides are the most studied 3D topological insulators. As a rule, at low temperatures, thin films of these materials demonstrate positive magnetoresistance due to weak antilocalization. Weak antilocalization should lead to resistivity decrease at low temperatures; in experiments, however, resistivity grows as temperature decreases. From transport measurements for several thin films (with various carrier density, thickness, and carrier mobility), and by using a purely phenomenological approach, with no microscopic theory, we show that the low-temperature growth of the resistivity is accompanied by growth of the Hall coefficient, in agreement with the diffusive electron-electron interaction correction mechanism. Our data reasonably explain the low-temperature resistivity upturn.

Topological superconductivity is an exotic phase of matter in which the fully gapped superconducting bulk hosts gapless Majorana surface states protected by topology. Intercalation of copper, strontium, or niobium between the quintuple layers of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ increases the carrier density and leads to superconductivity that is suggested to be topological. Here we study the electronic structure of strontium-intercalated ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ using angle-resolved photoemission spectroscopy and Shubnikov–de Haas oscillations. Despite the apparent low Hall number of $\sim 2\times {10}^{19}{\mathrm{cm}}^{-3}$, we show that the Fermi surface has the shape of an open cylinder with a larger carrier density of $\sim {10}^{20}{\mathrm{cm}}^{-3}$. We suggest that superconductivity in intercalated ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ emerges with the appearance of a quasi-two-dimensional open Fermi surface.

Selective excitation of coherent high-amplitude vibrations of atoms in a solid can induce exotic nonequilibrium states, in which the character of interactions between electronic, magnetic and lattice degrees of freedom is considerably altered and the underlying symmetries are broken. Here we use intense single-cycle terahertz pulses to drive coherently the dipole-active $E_u^1$ phonon mode of a ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ crystal. As a result, several Raman-active modes are simultaneously excited in a nonlinear process, while one of them, having the $E_g^2$ symmetry, experiences dynamical splitting during the first two picoseconds after excitation. The corresponding angular scattering pattern is modified indicating the coexistence of two phonon modes characteristic of a nonequilibrium state with a lower crystal symmetry. We observe also a short-lived frequency splitting of the original $E_g^2$ mode that immediately after excitation amounts to $\sim 25\%$ of the unperturbed value. This transient state relaxes with a characteristic time of $\sim 1$ ps, that is close to the decay time of the squared amplitude of the resonantly excited infrared-active $E_u^1$ mode. We discuss possible mechanisms of the dynamical splitting: nonlinear lattice deformation caused by the intense $E_u^1$ vibrations and excitation of anisotropic electronic distribution due to nonlinear electron-phonon interaction. Our data also contain an evidence in favor of the sum-frequency Raman mechanism of generation of the coherent $E_g^2$ phonons in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ excited by terahertz pulses.