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Register a new userImaging two-component nature of Dirac-Landau levels in the topological surface state of Bi2Se3
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Massless Dirac electrons in condensed matter have attracted considerable attention. Unlike conventional electrons, Dirac electrons are described in the form of two-component wave functions. In the surface state of topological insulators, these two components are associated with the spin degrees of freedom, hence governing the magnetic properties. Therefore, the observation of the two-component wave function provides a useful clue for exploring the novel spin phenomena. Here we show that the two-component nature is manifested in the Landau levels (LLs) whose degeneracy is lifted by a Coulomb potential. Using spectroscopic-imaging scanning tunneling microscopy, we visualize energy and spatial structures of LLs in a topological insulator Bi2Se3. The observed potential-induced LL splitting and internal structures of Landau orbits are distinct from those in a conventional electron system and are well reproduced by a two-component model Dirac Hamiltonian. Our model further predicts non-trivial energy-dependent spin-magnetization textures in a potential variation. This provides a way to manipulate spins in the topological surface state.
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We investigate Dirac fermions on the surface of the topological insulator Bi2Se3 using scanning tunneling spectroscopy. Landau levels (LLs) are observed in the tunneling spectra in a magnetic field. In contrast to LLs of conventional electrons, a field independent LL appears at the Dirac point, which is a hallmark of Dirac fermions. A scaling analysis of LLs based on the Bohr-Sommerfeld quantization condition allowed us to determine the dispersion of the surface band. Near the Fermi energy, fine peaks mixed with LLs appear in the spectra, which may be responsible for the anomalous magneto-fingerprint effect [J. G. Checkelsky et al., Phys. Rev. Lett. 103, 246601 (2009)].
The three dimensional (3D) topological insulators are predicted to exhibit a 3D Dirac semimetal state in critical regime of topological to trivial phase transition. Here we demonstrate the first experimental evidence of 3D Dirac semimetal state in topological insulator Bi2Se3 with bulk carrier concentration of ~ 10^19 cm^{-3}, using magneto-transport measurements. At low temperatures, the resistivity of our Bi2Se3 crystal exhibits clear Shubnikov-de Haas (SdH) oscillations above 6T. The analysis of these oscillations through Lifshitz-Onsanger and Lifshitz-Kosevich theory reveals a non-trivial pi Berry phase coming from 3D bands, which is a decisive signature of 3D Dirac semimetal state. The large value of Dingle temperature and natural selenium vacancies in our crystal suggest that the observed 3D Dirac semimetal state is an outcome of enhanced strain field and weaker effective spin-orbit coupling.
The wavefunction of massless Dirac fermions is a two-component spinor. In graphene, a one-atom-thick film showing two-dimensional Dirac-like electronic excitations, the two-component representation reflects the amplitude of the electron wavefunction on the A and B sublattices. This unique property provides unprecedented opportunities to image the two components of massless Dirac fermions spatially. Here we report atomic resolution imaging of the two-component Dirac-Landau levels in a gapped graphene monolayer by scanning tunnelling microscopy and spectroscopy. A gap of about 20 meV, driven by inversion symmetry breaking by the substrate potential, is observed in the graphene on both SiC and graphite substrates. Such a gap splits the n = 0 Landau level (LL) into two levels, 0+ and 0-. We demonstrate that the amplitude of the wavefunction of the 0- LL is mainly at the A sites and that of the 0+ LL is mainly at the B sites of graphene, characterizing the internal structure of the spinor of the n = 0 LL. This provides direct evidence of the two-component nature of massless Dirac fermions.
The intense search for topological superconductivity is inspired by the prospect that it hosts Majorana quasiparticles. We explore in this work the optimal design for producing topological superconductivity by combining a quantum Hall state with an ordinary superconductor. To this end, we consider a microscopic model for a topologically trivial two-dimensional p-wave superconductor exposed to a magnetic field, and find that the interplay of superconductivity and Landau level physics yields a rich phase diagram of states as a function of $mu/t$ and $Delta/t$, where $mu$, $t$ and $Delta$ are the chemical potential, hopping strength, and the amplitude of the superconducting gap. In addition to quantum Hall states and topologically trivial p-wave superconductor, the phase diagram also accommodates regions of topological superconductivity. Most importantly, we find that application of a non-uniform, periodic magnetic field produced by a square or a hexagonal lattice of $h/e$ fluxoids greatly facilitates regions of topological superconductivity in the limit of $Delta/trightarrow 0$. In contrast, a uniform magnetic field, a hexagonal Abrikosov lattice of $h/2e$ fluxoids, or a one dimensional lattice of stripes produces topological superconductivity only for sufficiently large $Delta/t$.
Recently, Weyl semimetals have been experimentally discovered in both inversion-symmetry-breaking and time-reversal-symmetry-breaking crystals. The non-trivial topology in Weyl semimetals can manifest itself with exotic phenomena which have been extensively investigated by photoemission and transport measurements. Despite the numerous experimental efforts on Fermi arcs and chiral anomaly, the existence of unconventional zeroth Landau levels, as a unique hallmark of Weyl fermions which is highly related to chiral anomaly, remains elusive owing to the stringent experimental requirements. Here, we report the magneto-optical study of Landau quantization in Weyl semimetal NbAs. High magnetic fields drive the system towards the quantum limit which leads to the observation of zeroth chiral Landau levels in two inequivalent Weyl nodes. As compared to other Landau levels, the zeroth chiral Landau level exhibits a distinct linear dispersion in z momentum direction and allows the optical transitions without the limitation of zero z momentum or square root of magnetic field evolution. The magnetic field dependence of the zeroth Landau levels further verifies the predicted particle-hole asymmetry of the Weyl cones. Meanwhile, the optical transitions from the normal Landau levels exhibit the coexistence of multiple carriers including an unexpected massive Dirac fermion, pointing to a more complex topological nature in inversion-symmetry-breaking Weyl semimetals. Our results provide insights into the Landau quantization of Weyl fermions and demonstrate an effective tool for studying complex topological systems.
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