Observation of spin–orbit coupling induced Weyl points in a two-electron double quantum dot

Abstract

Recent years have brought an explosion of activities in the research of topological aspects of condensed-matter systems. Topologically nontrivial phases of matter are typically accompanied by protected surface states or exotic degenerate excitations such as Majorana end states 1,2 or Haldane's localized spinons. 3,4 Topologically protected degeneracies can, however, also appear in the bulk. An intriguing example is provided by Weyl semimetals, where topologically protected electronic band degeneracies and exotic surface states emerge even in the absence of interactions. 5-7 Here we demonstrate experimentally and theoretically that Weyl degeneracies appear naturally in an interacting quantum dot system, for specific values of the external magnetic field. These magnetic Weyl points are robust against spin-orbit coupling unavoidably present in most quantum dot devices. 8,9 Our transport experiments through an InAs double dot device placed in magnetic field reveal the presence of a pair of Weyl points, exhibiting a robust ground state degeneracy and a corresponding protected Kondo effect.Mathematical tools borrowed from topology find more and more applications in contemporary condensedmatter physics. In Weyl semimetals, 7,10 for example, the electronic band structure exhibits isolated degeneracy points, 5 where two bands touch. In three-dimensional systems, these degeneracy points can be protected by topology -and classified by a suitably chosen Chern number: continuous perturbations may displace these Weyl points in momentum space, but cannot break their degeneracy. Weyl point related degeneracies of electronic states in molecules termed conical intersections are also thought to play a fundamental role in various phenomena in photochemistry. 11 They have also been predicted to appear in the context of multi-terminal Josephson junctions 12 and that of photonics, 13 and have also been engineered and demonstrated in coupled superconducting qubits. 14,15 The simplest example of a Weyl point arises when a spin-1/2 electron is placed in a homogeneous magnetic field (see Fig. 1a-c). In this example, the parameter space is spanned by the magnetic-field vector B = (B x , B y , B z ), and the two energy eigenstates are degenerate at B = 0. We can associate a nonzero topological charge to this degeneracy point: the ground state Chern number C(S) = 1 evaluated on an arbitrary closed surface S surrounding the degeneracy point (see Methods and Supplementary Information for details). This nonzero Chern number promotes this B = 0 degeneracy point to a Weyl point, and underlines the robustness of its (Kramers) degeneracy against perturbations.Let us now turn to the case of two coupled interacting spins, and investigate the fate of Weyl points in the presence of -possibly strong -spin-orbit in-↑ ↑ ↑

Uncovering topographically hidden features in 2D MoSe2 with correlated potential and optical nanoprobes

“…Since interaction with the tip creates excess carriers in an extremely localized region due to the small tip radius (~20 nm), exciton density in the region is dramatically higher as opposed to far-field excitation at same total power, hence the formation of stable biexcitons at room temperature. The stable biexciton formation in our case is supported by the prior report about resonant excitation of CsPbBr 3 perovskite nanoplate inside the Ag nanowire-Ag film plasmonic nanogaps 53 , which reported that the necessary exciton occupancy for excitation was significantly reduced by~10 6 times from the plasmonic gap. We rule out the possibility of detrimental influence of the Purcell effect on MoSe 2 since plasmonic resonators are well known for large and reproducible enhancement of spontaneous emission 52,[54][55][56] .…”

Mixed topological semimetals driven by orbital complexity in two-dimensional ferromagnets

“…6(d,e) reflects unique local fingerprints and colossal magnitude of the orbital magnetization m z (k) in momentum space which correlate with the emergence of we anticipate that these coupling phenomena can play a key role even in finite systems such as quantum dots (see, for example, Ref. 64). Analogously, we envisage that complementing the topological classification of matter by magnetic information rooting in the electronic degrees of freedom will be valuable for other research fields as well, e.g., for topological magnon semimetals 65,66 .…”

Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors

“…In Refs. [81,82], the authors find that topologically protected magnetic degeneracy points (referred to as magnetic Weyl points) can appear in DQDs for arbitrary SOI; i.e., for certain orientations of the magnetic field ±B W , the singlet |S and the lower triplet state |T − become degenerate: the levels cross as function of magnetic field and are protected from hybridization. In the DQD system considered here, the decoupling of the T ± states from the ST 0 states also leads to magnetic degeneracy points at fine-tuned magnetic fields.…”

“…Furthermore, many of the recent experimental setups seem to be invariant under reflection with respect to a certain plane, e.g., the plane being perpendicular to the plunger gates in Refs. [40,81]. Since the orientation of the magnetic field is usually tunable via a two-or threedimensional vector magnet, the study of anisotropic effects is well within the reach of state-of-the-art experiments.…”