Electrically pumped topological laser with valley edge modes.

Quantum cascade lasers are compact, electrically pumped light sources in the technologically important mid-infrared and terahertz region of the electromagnetic spectrum1,2. Recently, the concept of topology3 has been expanded from condensed matter physics into photonics4, giving rise to a new type of lasing5-8 using topologically protected photonic modes that can efficiently bypass corners and defects4. Previous demonstrations of topological lasers have required an external laser source for optical pumping and have operated in the conventional optical frequency regime5-8. Here we demonstrate an electrically pumped terahertz quantum cascade laser based on topologically protected valley edge states9-11. Unlike topological lasers that rely on large-scale features to impart topological protection, our compact design makes use of the valley degree of freedom in photonic crystals10,11, analogous to two-dimensional gapped valleytronic materials12. Lasing with regularly spaced emission peaks occurs in a sharp-cornered triangular cavity, even if perturbations are introduced into the underlying structure, owing to the existence of topologically protected valley edge states that circulate around the cavity without experiencing localization. We probe the properties of the topological lasing modes by adding different outcouplers to the topological cavity. The laser based on valley edge states may open routes to the practical use of topological protection in electrically driven laser sources.

Fermi-Arc-Induced Vortex Structure in Weyl Beam Shifts.

In periodic media, despite the close relationship between geometrical effects in the bulk and topological surface states, the two are typically probed separately. We show that when beams in a Weyl medium reflect off an interface with a gapped medium, the trajectory is influenced by both bulk geometrical effects and the Fermi arc surface states. The reflected beam experiences a displacement, analogous to the Goos-Hänchen or Imbert-Fedorov shifts, that forms a half-vortex in the two-dimensional surface momentum space. The half-vortex is centered where the Fermi arc of the reflecting surface touches the Weyl cone, with the magnitude of the shift scaling as an inverse square root away from the touching point, and diverging at the touching point. This striking feature provides a way to use bulk transport to probe the topological characteristics of a Weyl medium.

Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures.

The supermoiré lattice, built by stacking two moiré patterns, provides a platform for creating flat mini-bands and studying electron correlations. An ultimate challenge in assembling a graphene supermoiré lattice is in the deterministic control of its rotational alignment, which is made highly aleatory due to the random nature of the edge chirality and crystal symmetry. Employing the so-called "golden rule of three", here we present an experimental strategy to overcome this challenge and realize the controlled alignment of double-aligned hBN/graphene/hBN supermoiré lattice, where the twist angles between graphene and top/bottom hBN are both close to zero. Remarkably, we find that the crystallographic edge of neighboring graphite can be used to better guide the stacking alignment, as demonstrated by the controlled production of 20 moiré samples with an accuracy better than ~ 0.2°. Finally, we extend our technique to low-angle twisted bilayer graphene and ABC-stacked trilayer graphene, providing a strategy for flat-band engineering in these moiré materials.

Active Ultrahigh-Q (0.2 × 106 ) THz Topological Cavities on a Chip.

Rapid scaling of semiconductor devices has led to an increase in the number of processor cores and integrated functionalities onto a single chip to support the growing demands of high-speed and large-volume consumer electronics. To meet this burgeoning demand, an improved interconnect capacity in terms of bandwidth density and active tunability is required for enhanced throughput and energy efficiency. Low-loss terahertz silicon interconnects with larger bandwidth offer a solution for the existing inter-/intrachip bandwidth density and energy-efficiency bottleneck. Here, a low-loss terahertz topological interconnect-cavity system is presented that can actively route signals through sharp bends, by critically coupling to a topological cavity with an ultrahigh-quality (Q) factor of 0.2 × 106 . The topologically protected large Q factor cavity enables energy-efficient optical control showing 60 dB modulation. Dynamic control is further demonstrated of the critical coupling between the topological interconnect-cavity for on-chip active tailoring of the cavity resonance linewidth, frequency, and modulation through complete suppression of the back reflection. The silicon topological cavity is complementary metal-oxide-semiconductor (CMOS)-compatible and highly desirable for hybrid electronic-photonic technologies for sixth (6G) generation terahertz communication devices. Ultrahigh-Q cavity also paves the path for designing ultrasensitive topological sensors, terahertz topological integrated circuits, and nonlinear topological photonic devices.