Engineering of Chern insulators and circuits of topological edge states (original) (raw)
Related papers
2010
Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. These states are possible due to the combination of spin orbit interactions and time reversal symmetry. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for topological insulators and superconductors and describe recent experiments in which the signatures of topological insulators have been observed. We will describe transport experiments on HgTe/CdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi 1−x Sbx, Bi 2 Se 3 , Bi 2 Te 3 and Sb 2 Te 3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, as well as other potential device applications of topological insulators.
Impurity-induced states on the surface of three-dimensional topological insulators
Physical Review B, 2010
We calculate the modification of the local electronic structure caused by a single local impurity on the surface of a 3D Topological Insulator. We find that the LDOS around the Dirac point of the electronic spectrum at the surface is significantly disrupted near the impurity by the creation of low-energy resonance state(s)-however, this is not sufficient to (locally) destroy the Dirac point. We also calculate the non-trivial spin textures created near the magnetic impurities and discover anisotropic RKKY coupling between them.
Edge states of a three-dimensional topological insulator
Journal of Physics: Condensed Matter, 2014
We use the bulk Hamiltonian for a three-dimensional topological insulator such as Bi2Se3 to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based on a lattice discretization of the bulk Hamiltonian. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge is studied as a function of the edge potential. We show that a magnetic field in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states.
Physical Review B, 2012
Two-dimensional 2-bands insulators breaking time reversal symmetry can present topological phases indexed by a topological invariant called the Chern number. Here we first propose an efficient procedure to determine this topological index. This tool allows in principle to conceive 2-bands Hamiltonians with arbitrary Chern numbers. We apply our methodology to gradually construct a quantum anomalous Hall insulator (Chern insulator) which can be tuned through five topological phases indexed by the Chern numbers {0, ±1 ± 2}. On a cylindrical finite geometry, such insulator can therefore sustain up to two edge states which we characterize analytically. From this non-trivial Chern insulator and its time reversed copy, we build a quantum spin Hall insulator and show how the phases with a ±2 Chern index yield trivial Z2 insulating phases.
Colloquium: Topological insulators
2010
Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator but have protected conducting states on their edge or surface. These states are possible due to the combination of spin-orbit interactions and time-reversal symmetry. The two-dimensional ͑2D͒ topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A three-dimensional ͑3D͒ topological insulator supports novel spin-polarized 2D Dirac fermions on its surface. In this Colloquium the theoretical foundation for topological insulators and superconductors is reviewed and recent experiments are described in which the signatures of topological insulators have been observed. Transport experiments on HgTe/ CdTe quantum wells are described that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. Experiments on Bi 1−x Sb x , Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 are then discussed that establish these materials as 3D topological insulators and directly probe the topology of their surface states. Exotic states are described that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions and may provide a new venue for realizing proposals for topological quantum computation. Prospects for observing these exotic states are also discussed, as well as other potential device applications of topological insulators.
Tuning topological surface states by cleavage angle in topological crystalline insulators
Physical Review B
The conducting states, recently discovered at the surface of two special class of insulatorstopological insulators and topological crystalline insulators-are distinguished by their insensitivity to local and non-magnetic surface defects at a level of disorder, sufficiently small to be described within the perturbation theory. However, the behavior of the surface states in case of non local macroscopic imperfections is not clear. Here, we propose a systematic study of the topological surface states on vicinal planes (deviations from perfect surface cleavage) in a topological crystalline insulator of the tin telluride family, by using realistic first-principles-derived tight-binding models. The theoretical framework proposed is quite general and easily permits the extensions to other topological insulator families.
Controlling Topological States in Topological/Normal Insulator Heterostructures
ACS Omega, 2018
We have performed a systematic investigation of the nature of the nontrivial interface states in topological/normal insulator (TI/NI) heterostructures. On the basis of first principles and a recently developed scheme to construct ab initio effective Hamiltonian matrices from density functional theory calculations, we studied systems of realistic sizes with high accuracy and control over the relevant parameters such as TI and NI band alignment, NI gap, and spin−orbit coupling strength. Our results for IV−VI compounds show the interface gap tunability by appropriately controlling the NI thickness, which can be explored for device design. Also, we verified the preservation of an in-plane spin texture in the interface-gaped topological states.
Topological insulators in random potentials
Physical Review B, 2016
We investigate the effects of magnetic and nonmagnetic impurities on the two-dimensional surface states of three-dimensional topological insulators (TIs). Modeling weak and strong TIs using a generic four-band Hamiltonian, which allows for a breaking of inversion and time-reversal symmetries and takes into account random local potentials as well as the Zeeman and orbital effects of external magnetic fields, we compute the local density of states, the single-particle spectral function, and the conductance for a (contacted) slab geometry by numerically exact techniques based on kernel polynomial expansion and Green's function approaches. We show that bulk disorder refills the suface-state Dirac gap induced by a homogeneous magnetic field with states, whereas orbital (Peierlsphase) disorder perserves the gap feature. The former effect is more pronounced in weak TIs than in strong TIs. At moderate randomness, disorder-induced conducting channels appear in the surface layer, promoting diffusive metallicity. Random Zeeman fields rapidly destroy any conducting surface states. Imprinting quantum dots on a TI's surface, we demonstrate that carrier transport can be easily tuned by varying the gate voltage, even to the point where quasi-bound dot states may appear.