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Register a new userComparative study of Weyl semimetal, topological and Chern insulators: thin-film point of view
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Regarding three-dimensional (3D) topological insulators and semimetals as a stack of constituent 2D topological (or sometimes non-topological) layers is a useful viewpoint. Primarily, concrete theoretical models of the paradigmatic 3D topological phases such as Weyl semimetal (WSM), strong and weak topological insulators (STI/WTI), and Chern insulator (CI), are often constructed in that way. Secondarily, fabrication of the corresponding 3D topological material is also done in the same spirit; epitaxial growth technique is employed, making the resulting sample in the form of a thin film. Here, in this paper we calculate $mathbb{Z}$- and $mathbb{Z}_2$-indices and study evolution of the topological properties of such thin films of 3D topological systems, making also a comparative study of CI- vs. TI-type models belonging to different symmetry classes in this respect. Through this comparative study we suggest that WSM is to CI as STI is to WTI. Finally, to test the robustness of our scenario against disorder and relevance to experiments we have also studied numerically the two-terminal conductance of the system using transfer matrix method.
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The Fermi surface of a conventional two-dimensional electron gas is equivalent to a circle, up to smooth deformations that preserve the orientation of the equi-energy contour. Here we show that a Weyl semimetal confined to a thin film with an in-plane magnetization and broken spatial inversion symmetry can have a topologically distinct Fermi surface that is twisted into a $mbox{figure-8}$ $-$ opposite orientations are coupled at a crossing which is protected up to an exponentially small gap. The twisted spectral response to a perpendicular magnetic field $B$ is distinct from that of a deformed Fermi circle, because the two lobes of a mbox{figure-8} cyclotron orbit give opposite contributions to the Aharonov-Bohm phase. The magnetic edge channels come in two counterpropagating types, a wide channel of width $beta l_m^2propto 1/B$ and a narrow channel of width $l_mpropto 1/sqrt B$ (with $l_m=sqrt{hbar/eB}$ the magnetic length and $beta$ the momentum separation of the Weyl points). Only one of the two is transmitted into a metallic contact, providing unique magnetotransport signatures.
We propose characterization of the three-dimensional topological insulator by using the Chern number for the entanglement Hamiltonian (entanglement Chern number). Here we take the extensive spin partition of the system, that pulls out the quantum entanglement between up spin and down spin of the many-body ground state. In three dimensions, the topological insulator phase is described by the section entanglement Chern number, which is the entanglement Chern number for a periodic plane in the Brillouin zone. The section entanglement Chern number serves as an interpolation of the $Z_2$ invariants defined on time-reversal invariant planes. We find that the change of the section entanglement Chern number protects the Weyl point of the entanglement Hamiltonian and the parity of the number of Weyl points distinguishes the strong topological insulator phase from the weak topological insulator phase.
We present a comprehensive study of the crystal structure of the thin-film, ferromagnetic topological insulator (Bi, Sb)$_{2-x}$V$_x$Te$_3$. The dissipationless quantum anomalous Hall edge states it manifests are of particular interest for spintronics, as a natural spin filter or pure spin source, and as qubits for topological quantum computing. For ranges typically used in experiments, we investigate the effect of doping, substrate choice and film thickness on the (Bi, Sb)$_2$Te$_3$ unit cell using high-resolution X-ray diffractometry. Scanning transmission electron microscopy and energy-dispersive X-ray spectroscopy measurements provide local structural and interfacial information. We find that the unit cell is unaffected in-plane by vanadium doping changes, and remains unchanged over a thickness range of 4--10 quintuple layers (1 QL $approx$ 1 nm). The in-plane lattice parameter ($a$) also remains the same in films grown on different substrate materials. However, out-of-plane the $c$-axis is reduced in films grown on less closely lattice-matched substrates, and increases with the doping level.
We carried out point contact (PC) investigation of WTe2 single crystals. We measured Yanson d2V/dI2 PC spectra of the electron-phonon interaction (EPI) in WTe2. The spectra demonstrate a main phonon peak around 8 meV and a shallow second maximum near 16 meV. Their position is in line with the calculation of the EPI spectra of WTe2 in the literature, albeit phonons with higher energy are not resolved in our PC spectra. An additional contribution to the spectra is present above the phonon energy, what may be connected with the peculiar electronic band structure and need to be clarified. We detected tiny superconducting features in d2V/dI2 close to zero bias, which broadens by increasing temperature and blurs above 6K. Thus, (surface) superconductivity may exist in WTe2 with a topologically nontrivial state. We found a broad maximum in dV/dI at large voltages (>200 mV) indicating change of conductivity from metallic to semiconducting type. The latter might be induced by the high current density (~10^8 A/cm^2) in the PC and/or local heating, thus enabling the manipulation of the quantum electronic states at the interface in the PC core.
Within a relativistic quantum formalism we examine the role of second-order corrections caused by the application of magnetic fields in two-dimensional topological and Chern insulators. This allows to reach analytical expressions for the change of the Berry curvature, orbital magnetic moment, density of states and energy determining their canonical grand potential and transport properties. The present corrections, which become relevant at relatively low fields due to the small gap characterizing these systems, unveil a zero-field diamagnetic susceptibility which can be tuned by the external magnetic field.
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