In Kondo insulator samarium hexaboride SmB6, strong correlation and band hybridization lead to an insulating gap and a diverging resistance at low temperature. The resistance divergence ends at about 5 Kelvin, a behavior recently demonstrated to arise from the surface conductance. However, questions remain whether and where a topological surface state exists. Quantum oscillations have not been observed to map the Fermi surface. We solve the problem by resolving the Landau Level quantization and Fermi surface topology using torque magnetometry. The observed Fermi surface suggests a two dimensional surface state on the (101) plane. Furthermore, the tracking of the Landau Levels in the infinite magnetic field limit points to -1/2, which indicates a 2D Dirac electronic state.The recent development of topological insulators is a triumph of single electron band theory [1][2][3][4][5][6][7][8] . It is interesting to understand whether similar exotic states of matter can arise once strong electronic interaction comes into play. Kondo insulators, a strongly-correlated heavyfermion system, offer a good playground for the exploration of this question. In a Kondo insulator 9,10 , the hybridization between itinerant electrons and localized orbitals opens a gap and makes the material insulating. Once the sample temperature is cold enough, the electronic structure in the strongly correlated system can be mapped to a rather simple electronic state that resembles a normal topological insulator 11 . As a result, in the ground state of the Kondo insulator there exists a bulk insulating state and a conductive surface state. In samarium hexaboride (SmB 6 ), the existence of the surface state has been suggested by recent experimental observations of the surface conductance as well as a map of the hybridization gap 12-14 . However, a direct observation of the Fermi surface has not yet been achieved by transport measurements in Kondo insulators. In this letter we report the observation of quantum oscillations in Kondo insulator SmB 6 using torque magnetometry. The observed Fermi surface is shown to be two-dimensional (2D) and arises from the crystalline (101) surface, and the Landau Level index plot shows a Berry phase contributed -1/2 factor in the infinite field limit, which indicates that this Fermi surface encloses Dirac points, a characteristic property of topological insulators.The direct observation of quantum oscillations is an essential step in understanding the electronic state of the bulk and surfaces of Kondo insulator. Wolgast et al. have argued strongly that the great robustness and certain other properties of the low T surface conductivity of SmB 6 are best understood as a consequence of having TI surface states 12 . Nonetheless there is yet no direct evidence for this interpretation of the surface conduction. Such evidence should come from microscopic measurements of the electronic structure, as has been accomplished for the weakly correlated TI materials, such as Bi 2 Se 3 , Bi 2 Te 3 , and graphene [15][16][17][18][19...

Applied magnetic fields underlie exotic quantum states, such as the fractional quantum Hall effect 1 and Bose-Einstein condensation of spin excitations 2 . Superconductivity, on the other hand, is inherently antagonistic towards magnetic fields. Only in rare cases 3-5 can these effects be mitigated over limited fields, leading to reentrant superconductivity. Here, we report the unprecedented coexistence of multiple high-field reentrant superconducting phases in the spin-triplet superconductor UTe 2 6 . Strikingly, we observe superconductivity in the highest magnetic field range identified for any reentrant superconductor, beyond 65 T. These extreme properties reflect a new kind of exotic superconductivity rooted in magnetic fluctuations 7 and boosted by a quantum dimensional crossover 8 .

Low-temperature electrical and thermal transport, heat capacity and magnetic penetration depth measurements were performed on single crystals of the actinide superconductor UTe2 to determine the structure of the superconducting energy gap. Millikelvin specific heat measurements reveal an upturn below 300 mK that is well described by a divergent quantum-critical contribution to the density of states (DOS). Modeling this contribution with a T −1/3 power law allows restoration of the full entropy balance in the superconducting state below Tc = 1.6 K, revealing a perfect T 3 power law for the electronic DOS below Tc. Heat transport measurements performed with currents directed along both crystallographic a-and b-axes reveal a vanishingly small residual fermionic component of the thermal conductivity that grows as T 3 for both directions and exhibits an a/b anisotropy ratio of ∼ 2.5 in the T = 0 limit. The magnetic field dependence of the residual term follows a quasilinear increase consistent with the presence of nodal quasiparticles, rising rapidly toward the a-axis upper critical field where the Wiedemann-Franz (WF) law is recovered. Together with a quadratic temperature dependence of the magnetic penetration depth up to T /Tc = 0.3, these measurements provide definitive evidence for an unconventional spin-triplet superconducting order parameter with point nodes positioned along the crystallographic a-axis.

An unconventional superconducting state was recently discovered in UTe2, where spin-triplet superconductivity emerges from the paramagnetic normal state of a heavy fermion material. The coexistence of magnetic fluctuations and superconductivity, together with the crystal structure of this material, suggest that a unique set of symmetries, magnetic properties, and topology underlie the superconducting state. Here, we report observations of a non-zero polar Kerr effect and of two transitions in the specific heat upon entering the superconducting state, which together suggest that the superconductivity in UTe2 is characterized by a two-component order parameter that breaks time reversal symmetry. These data place constraints on the symmetries of the order parameter and inform the discussion on the presence of topological superconductivity in UTe2.