Three-dimensional (3D) topological insulators (TIs) have generated tremendous research interest over the past decade due to their topologically-protected surface states with linear dispersion and helical spin texture. The topological surface states offer an important platform to realize topological phase transitions, topological magnetoelectric effects and topological superconductivity via 3D TI-based heterostructures. In this review, we summarize the key findings of magneto and quantum transport properties in 3D TIs and their related heterostructures with normal insulators, ferromagnets and superconductors. For intrinsic 3D TIs, the experimental evidences of the topological surface states and their coupling effects are reviewed. Whereas for 3D TI related heterostructures, we focus on some important phenomenological magnetotransport activities and provide explanations for the proximity-induced topological and quantum effects.

Van der Waals heterostructures based on three-dimensional topological insulators

A bulk crystal of cadmium arsenide is a three-dimensional Dirac semimetal, but, in a thin film, it can behave like a three-dimensional topological insulator. This tunability provides unique opportunities to manipulate and explore a topological insulator phase. However, an obstacle to engineering such tunability is the subtlety of transport-based discriminants for topological phases. In this work, the quantum capacitance of cadmium arsenide–based heterostructures provides two direct experimental signatures of three-dimensional topological insulator physics: an insulating three-dimensional bulk and a Landau level at zero energy that does not disperse in a magnetic field. We proceed to join our ability to see these fingerprints of the topological surface states with flexibility afforded by our epitaxial heterostructures to demonstrate a route toward controlling the energy of the Dirac nodes on each surface. These results point to new avenues for engineering topological insulators based on cadmium arsenide.

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Controlling and visualizing Dirac physics in topological semimetal heterostructures

BiSbTeSe2 is a 3D topological insulator (3D-TI) with Dirac type surface states and low bulk carrier density, as donors and acceptors compensate each other. Dominating low-temperature surface transport in this material is heralded by Shubnikov-de Haas oscillations and the quantum Hall effect. Here, we experimentally probe and model the electronic density of states (DOS) in thin layers of BiSbTeSe2 by capacitance experiments both without and in quantizing magnetic fields. By probing the lowest Landau levels, we show that a large fraction of the electrons filled via field effect into the system ends up in (localized) bulk states and appears as a background DOS. The surprisingly strong temperature dependence of such background DOS can be traced back to Coulomb interactions. Our results point at the coexistence and intimate coupling of Dirac surface states with a bulk many-body phase (a Coulomb glass) in 3D-TIs.

Two-Dimensional-Dirac Surface States and Bulk Gap Probed via Quantum Capacitance in a Three-Dimensional Topological Insulator.

As the thickness of a three-dimensional (3D) topological insulator (TI) becomes comparable to the penetration depth of the surface states, quantum tunneling between surfaces turns their gapless Dirac electronic structure into a gapped surface state. Analytical formulation suggests that the hybridization gap scales exponentially with decrease in number of layers while the system oscillates between topologically trivial and non-trivial insulators. This work explores the transport properties of a 3D TI in the inter-surface hybridization regime. By experimentally probing the hybridization gap as a function of BiSbTeSe2 thickness using three different methods, we map the crossover from the 3D to 2D state. In the 2D topological state, we observe a finite longitudinal conductance at ~2e2/h when the Fermi level is aligned within the surface gap, indicating a quantum spin Hall (QSH) state. Additionally, we study the response of trivial and non-trivial hybridization gapped states modulated by external out-of-plane magnetic and electric fields. Our revelations of surface gap-closing and/or reopening features are strongly indicative of topological phase transitions (TPTs) in the hybridization gap regime, realizing magnetic/electric field switching between band insulating and QSH states with immense potential for practical applications.

Topological Phase Transitions in a Hybridized Three-Dimensional Topological Insulator

We theoretically investigate the Landau levels (LLs) and magneto-capacitance (MC) of monolayer black phosphorus under a perpendicular magnetic field, on which a parabolic potential is applied along with the armchair and zigzag directions, respectively By both analytically perturbative calculation and numerical diagonalization based on an effective k ⋅ p Hamiltonian, we find that the LLs parabolically depend on the wave vectors and show strong anisotropy as the parabolic potential is applied along with different crystal directions Specifically, the analytical LLs obtained by perturbative calculation from a decoupled single-band Hamiltonian are in good agreement with the numerical results Importantly, the LLs are no longer linearly dependent on the magnetic field and level index even in the low energy regime due to the confinement of parabolic potential which repaints the cyclotron orbits Moreover, the MC spectrum clearly reflects the structure of the LLs and exhibits strong anisotropic oscillating patterns It can be used to determine the band parameters of phosphorene, ie, the effective masses and inter-band coupling in the absence of magnetic and electric fields

https://iopscience.iop.org/article/10.1088/1361-648X/aba016/pdf

Probing the anisotropy of Landau levels in phosphorene by magneto-capacitance with a parabolic potential confinement.

Spectroscopy of discrete Landau levels (LLs) in bulk-insulating three-dimensional topological insulators (3D TIs) in perpendicular magnetic field characterizes the Dirac nature of their surface sta...

Jared Harmer

Papers

Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance