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Introducing the concept of topology into material science has sparked a revolution from classic electronic and optoelectronic devices to topological quantum devices. The latter has potential for transferring energy and information with unprecedented efficiency. Here, we demonstrate a topological diode effect on the surface of a three-dimensional material, SmB ${}_6$, a candidate topological Kondo insulator. The diode effect is evidenced by pronounced rectification and photogalvanic effects under electromagnetic modulation and radiation at radio frequency. Our experimental results and modeling suggest that these prominent effects are intimately tied to the spatially inhomogeneous formation of topological surface states (TSS) at the intermediate temperature. This work provides a manner of breaking the mirror symmetry (in addition to the inversion symmetry), resulting in the formation of $\mathit{pn}$-junctions between puddles of metallic TSS. This effect paves the way for efficient current rectifiers or energy-harvesting devices working down to radio frequency range at low temperature, which could be extended to high temperatures using other topological insulators with large bulk gap. 

Abstract The quantum limit in a Fermi liquid, realized when a single Landau level is occupied in strong magnetic fields, gives rise to unconventional states, including the fractional quantum Hall effect and excitonic insulators. Stronger interactions in metals with nearly localizedf-electron degrees of freedom increase the likelihood of these unconventional states. However, access to the quantum limit is typically impeded by the tendency off-electrons to polarize in a strong magnetic field, consequently weakening the interactions. In this study, we propose that the quantum limit in such systems must be approached in reverse, starting from an insulating state at zero magnetic field. In this scenario, Landau levels fill in the reverse order compared to regular metals and are closely linked to a field-induced insulator-to-metal transition. We identify YbB₁₂as a prime candidate for observing this effect and propose the presence of an excitonic insulator state near this transition. 

Transition-metal and rare-earth borides are of considerable interest due to their electronic, mechanical, and magnetic properties as well as their structural stability under extreme conditions. Here, we report on a series of high-pressure Raman and x-ray diffraction experiments on the cubic rare-earth hexaboride EuB6 to an ultrahigh pressure of 187 GPa in a diamond anvil cell. In EuB6, divalent europium ions occupy the corners of the cubic structure, which encloses a rigid boron-bonded cage. So far, no structural phase transitions have been reported, while the nanoindentation studies indicate amorphization in nanoscale shear bands during plastic deformation. Our x-ray diffraction studies have revealed that the ambient cubic phase of EuB6 shows broadening and splitting of diffraction peaks starting at 72 GPa and the broadening continuing to 187 GPa. The high-pressure phase is recovered on decompression, and the Raman spectroscopy of the recovered sample from 187 GPa shows a downward frequency shift and broadening of T2g, Eg, and A1g modes of boron octahedron. The density functional theory simulations of EuB6 at 100 GPa have identified five possible lowest energy crystal structures. The experimental x-ray diffraction data at high pressures is compared with the theoretical predictions and the role of structural distortions induced by shear stresses is also discussed.