Films Of Three-dimensional Topological Insulators Research Articles

Robustness of negative low-field magnetoconductance in ultrathin topological insulator films

In the ultrathin films of three-dimensional topological insulators (TIs), modification of the Berry phase caused by surface hybridization was predicted to allow for a crossover between weak antilocalization (WAL) and weak localization (WL). Here we report on a systematic study of the magnetotransport properties of ${({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{2}{\mathrm{Te}}_{3}$ (BST) thin films with well-controlled thickness, doping level, and chemical potential. We found that the sign of magnetoconductance in perpendicular magnetic field remains negative in all circumstances, suggesting absence of global WL in the ultrathin BST films. This is attributed to long-range disorder, as well as conductance corrections by quantum interference and electron-electron interaction. Our work shows that the electron transport in ultrathin TIs is distinctively different from the WAL regime in the systems with symplectic symmetry, and the WL or weak insulator regime associated with the orthogonal symmetry class.

Conductivity of Two-Dimensional Small Gap Semiconductors and Topological Insulators in Strong Coulomb Disorder

We are honored to dedicate this article to Emmanuel Rashba on the occasion of his 95 birthday. In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap, $\Delta$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $\Delta$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional narrow gap semiconductor on a substrate containing Coulomb impurities, mostly focusing on the case when amplitude of the random potential $\Gamma \gg \Delta$. We show that the conductivity generically exhibits three regimes and only the highest temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through nearest-neighbor or variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We arrive at a similar disorder driven steep insulator-metal transition in thin films of three-dimensional topological insulators with very large dielectric constant, where due to confinement of electric field internal Coulomb impurities create larger disorder potential. Away from neutrality point this unconventional insulator-to-metal transition is augmented by conventional metal-insulator transition at small impurity concentrations, so that we arrive at disorder-driven re-entrant metal-insulator-metal transition.

Conductivity of two-dimensional narrow gap semiconductors subjected to strong Coulomb disorder

In the ideal disorder-free situation, a two-dimensional band-gap insulator has an activation energy for conductivity equal to half the band gap $\mathrm{\ensuremath{\Delta}}$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $\mathrm{\ensuremath{\Delta}}$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional insulator on a substrate containing Coulomb impurities, with random potential amplitude $\mathrm{\ensuremath{\Gamma}}\ensuremath{\gg}\mathrm{\ensuremath{\Delta}}$. We show that the conductivity generically exhibits three regimes of conductivity, and only the highest-temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through activated hopping or Efros-Shklovskii variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We also arrive at a similar steep disorder driven insulator-metal transition in thin films of three-dimensional topological insulators with large dielectric constant, for which Coulomb impurities inside the film create a large disorder potential due to confinement of their electric field inside the film.

Ambipolar Seebeck power generator based on topological insulator surfaces

We propose a thermoelectric (TE) energy conversion device based on the surface of a three-dimensional topological insulator (TI) that is magnetically gap-opened and ionically disordered. A pair of top and bottom surfaces of a single TI film takes the role of a vertical p–n junction with ambipolar conduction, which can be considered as a TE module consisting of two dissimilar TE materials. By tuning the surface carrier screening by means of electric gating, we find that the figure of merit ZT of the device exceeds 1 in the low-temperature-regime below 300 K. Our model may represent one direction for the implementation of TE energy conversion and heat management in nanodevices.

Ultrathin films of three-dimensional topological insulators by vapor-phase epitaxy: Surface dominant transport in a wide temperature range as revealed by measurements of the Seebeck effect

Realization of intrinsic surface dominant transport in a wide temperature region for a topological insulators (TIs) is an important frontier research in order to promote the progresses of TIs towards the future electronics. We report here systematic measurements of longitudinal electrical transport, Shubnikov-de-Haas (SdH) quantum oscillations, Hall coefficient (R_H^2D), and Seebeck coefficient as a function of film thickness (d) and temperature using high quality Bi2-xSbxTe3-ySey (BSTS) single crystal thin films grown by physical vapor-phase deposition. The thickness dependence of sheet conductance and Seebeck coefficient clearly show the suppression of semiconducting hole carriers of bulk states by reducing film thickness, reaching to the surface dominant transport at below dc=14 nm. Quantitative arguments are made as to how the contribution of itinerant carrier number (n) can be suppressed, using both R_H^2D (n_Hall^2D) and SdH (n_SdH). Intriguingly, the value of n_Hall^2D approaches to be twice of n_SdH below dc. While R_H^2D shows a negative sign in whole temperature region, a change from negative to positive polarity is clearly observed for S at high temperatures when d is thick. We point out that this inconsistency observed between R_H^2D and S is intrinsic in 3D-TIs and its origin is the large difference in carrier mobility between the bulk and the topological surface. We propose that Seebeck coefficient can become a convenient and powerful tool to evaluate the intrinsic carrier concentration for the topological surface in 3D-TIs even in the absence of magnetic field.

Interface effects on the magnetic-proximity-induced quantized Hall response in heterostructures based on three-dimensional topological insulators

We report a theoretical study of the spin-dependent transport properties in heterostructures containing a three-dimensional topological insulator (TI) thin film and ferromagnetic normal insulator (FMNI) slab. Within the framework of a continual approach for the FMNI/TI/FMNI trilayer model, we reveal how the magnetic proximity effect at the TI/FMNI interface can influence an intrinsic Hall response of the system. We predict that the FMNI/TI/FMNI trilayer undergoes a transition into the quantum anomalous Hall phase either from the topologically trivial phase or from the quantum spin Hall phase, which is controlled by tuning the proximity-induced exchange field, the TI film thickness, and the TI band structure parameters. We draw the corresponding phase diagram of the FMNI/TI/FMNI trilayer. Moreover, we argue that the roughness at the TI/FMNI interfaces can cause the decomposition of the TI film into topologically distinct domains, which affects the Hall conductivity. We discuss the specifics of manifestation and complexities of observation of quantized conductivity in realistic TI/FMNI heterostructures.

Interface induced quantized spin Hall response in three-dimensional topological insulator/normal insulator heterostructures

We report analytic investigation of the electronic properties of heterostructures comprised by films of three-dimensional topological insulator (TI) and normal insulator (NI) revealing strong interface and size effects on their spin transport characteristics. Imposing at the TI/NI interfaces the natural boundary conditions within a continual scheme, we show that the intrinsic spin Hall response of the NI/TI/NI trilayer can be controlled by tuning the interface potential (IP) together with the TI film thickness. We predict a series of interface induced quantum transitions between topological insulating phase and trivial band insulator phase. We calculate the phase diagram of the NI/TI/NI trilayer and establish an appropriate range of the IP strength and the TI film thickness to realize the regime of quantum spin Hall effect. Our results can provide a useful guide in choosing the relevant material parameters to facilitate the detection of quantum spin Hall conductivity in the TI/NI heterostructures.

Quantum anomalous Hall conductivity in 3D magnetic topological insulator/normal insulator heterostructures

Today, searching for materials hosting quantum anomalous Hall effect (QAHE) at high temperature and with long conductivity plateau is an important issue for next generation spintronic applications at nanoscale. In this article, we discuss a quantized spin Hall response in heterostructures composed of a three-dimensional topological insulator (TI) film and a ferromagnetic normal insulator (FMNI). The magnetic proximity effect at the TI/FMNI interface provides exchange splitting of the topological states in the TI film. We predict analytically that the FMNI/TI/FMNI trilayer can be driven into the QAHE state either from the topologically trivial state or the quantum spin Hall state, depending on the TI film thickness and the interface potential. We calculate the corresponding phase diagram of the FMNI/TI/FMNI trilayer. Our results provide a useful guide to realize the QAHE regime in the TI/FMNI heterostructures.

Interface electronic structure at the topological insulator–ferrimagnetic insulator junction

An interface electron state at the junction between a three-dimensional topological insulator film, Bi2Se3, and a ferrimagnetic insulator film, Y3Fe5O12 (YIG), was investigated by measurements of angle-resolved photoelectron spectroscopy and x-ray absorption magnetic circular dichroism. The surface state of the Bi2Se3 film was directly observed and localized 3d spin states of the Fe3+ in the YIG film were confirmed. The proximity effect is likely described in terms of the exchange interaction between the localized Fe 3d electrons in the YIG film and delocalized electrons of the surface and bulk states in the Bi2Se3 film.

Anomalous Hall and spin Hall conductivities in three-dimensional ferromagnetic topological insulator/normal insulator heterostructures

In this letter we theoretically demonstrate how an interface perturbation and size effect can be used to manipulate the transport properties of semiconductor heterostructures composed of a thin film of a three-dimensional topological insulator (TI) doped with magnetic impurities and sandwiched between topologically normal insulators. In the framework of a continual scheme, we argue that electron states of the TI film are strongly dominated by its thickness and magnetization as well as by an interface potential whose variation can lead to the modification of topological properties of the heterostructure. This opens diverse possibilities to efficiently tune intrinsic Hall conductivity in the system. We calculate a phase diagram of the heterostructure, which demonstrates a series of quantum transitions between distinct regimes of conductivity. We derive the anomalous Hall conductivity and the spin Hall conductivity dependences on the chemical potential. Applicability conditions of the used approach are also discussed.

Observation of Anderson localization in ultrathin films of three-dimensional topological insulators.

Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here, we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi_{1-x}Sb_{x})_{2}Te_{3} films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually, positive magnetoconductivity emerges when the electron system becomes strongly localized. This work reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.

Disorder effect on the quantum Hall effect in thin films of three-dimensional topological insulators

We numerically study the quantum Hall effect (QHE) in three-dimensional topological insulator (3DTI) thin film in the presence of the finite Zeeman energy g and the hybridization gap Δ under a strong magnetic field and disorder. For Δ = 0 but g ≠ 0, the Hall conductivity remains to be odd-integer quanti-zed σ xy = ν(e 2/h) , where ν = 2l + 1 with l being an integer. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and the higher plateaus disappear first. The two central plateaus with ν = ± 1 around the band center are strongest against disorder scattering. With the increasing of the disorder strength, Hall plateaus are destroyed faster for the system with a weaker magnetic field. If g = 0 but Δ ≠ 0, there is a splitting of the central (n = 0) Landau level, yielding a new plateau with ν = 0, in addition to the original odd-integer plateaus. In the strong-disorder regime, the QHE plateaus can be destroyed due to the float-up of extended levels toward the band center. The ν = 0 plateau around the band center is strongest against disorder scattering, which eventually disappears. For both g ≠ 0 and Δ ≠ 0, the simultaneous presence of nonzero g and Δ causes the splitting of the degenerating Landau levels, so that all integer Hall plateaus ν = l appear. The ν = 0,1 plateaus are the most stable ones. In the strong-disorder regime, all QHE states are destroyed by disorder, and the system transits into an insulating phase.

Thermoelectric transport in thin films of three-dimensional topological insulators

We numerically study the thermoelectric transport properties based on the Haldane model of the three-dimensional topological insulator (3DTI) thin film in the presence of an exchange field $g$ and a hybridization gap $\ensuremath{\Delta}$. The thermoelectric coefficients exhibit rich behaviors as a consequence of the interplay between $g$ and $\ensuremath{\Delta}$ in the 3DTI thin film. For $\ensuremath{\Delta}=0$ but $g\ensuremath{\ne}0$, the transverse thermoelectric conductivity ${\ensuremath{\alpha}}_{xy}$ saturates to a universal value $1.38{k}_{B}e/h$ at the center of each Landau level (LL) in the high-temperature regime, and displays a linear temperature dependence at low temperatures. The semiclassical Mott relation is found to remain valid at low temperatures. If $g=0$ but $\ensuremath{\Delta}\ensuremath{\ne}0$, the thermoelectric coefficients are consistent with those of a band insulator. For both $g\ensuremath{\ne}0$ and $\ensuremath{\Delta}\ensuremath{\ne}0$, ${\ensuremath{\alpha}}_{xy}$ saturates to a universal value $0.69{k}_{B}e/h$ at the center of each LL in the high-temperature regime. We attribute this behavior to the split of all the LLs, caused by the simultaneous presence of nonzero $g$ and $\ensuremath{\Delta}$, which lifts the degeneracies between Dirac surface states.

A honeycomb lattice model simulating the surface states of topological insulators

A honeycomb lattice model exhibiting the quantum spin-Hall effect is proposed, where the low-energy properties of the electrons are mainly determined by the energy spectrum in the vicinity of the Γ point, for suitable parameters. The nontrivial topology of the energy bands is revealed by calculating the Chern numbers, Berry curvature distribution, and edge state spectrum. We further show that in the continuum limit, the model Hamiltonian is equivalent to the effective model for the surface states in thin films of three-dimensional topological insulators. As a consequence, this lattice model provides a useful tool for numerical simulation of the physical properties of the surface states.

Quantum phase transitions in ultrathin films of three-dimensional topological insulators in the presence of an electrostatic potential and a Zeeman field

We investigate transport properties of the surface states of three-dimensional topological insulator thin films in the presence of an electrostatic potential $\ensuremath{\gamma}$ and a spin-splitting Zeeman field $g$. It is shown that there exist a quantum pseudospin Hall phase, a quantum anomalous Hall phase, and a common insulator phase in this system. By tuning $g$ and $\ensuremath{\gamma}$, three quantum phase transitions between them can occur accompanied with energy-band closing, each of which is characterized by a change of the quantized pseudospin Chern numbers.

Quantum Hall effect in thin films of three-dimensional topological insulators

We show that a thin film of a three-dimensional topological insulator (3DTI) with an exchange field is a realization of the famous Haldane model for quantum Hall effect (QHE) without Landau levels. The exchange field plays the role of staggered fluxes on the honeycomb lattice, and the hybridization gap of the surface states is equivalent to alternating on-site energies on the AB sublattices. A peculiar phase diagram for the QHE is predicted in 3DTI thin films under an applied magnetic field, which is quite different from that either in traditional QHE systems or in graphene.

Parallel magnetic field driven quantum phase transition in a thin topological insulator film

It is well-known that helical surface states of a three-dimensional topological insulator (TI) do not respond to a static in-plane magnetic field. Formally this occurs because the in-plane magnetic field appears as a vector potential in the Dirac Hamiltonian of the surface states and can thus be removed by a gauge transformation of the surface electron wavefunctions. Here we show that when the top and bottom surfaces of a thin film of TI are hybridized and the Fermi level is in the hybridization gap, a nonzero diamagnetic response appears. Moreover, a quantum phase transition occurs at a finite critical value of the parallel field from an insulator with a diamagnetic response to a semimetal with a vanishing response to the parallel field.

Quantized Anomalous Hall Effect in Magnetic Topological Insulators

The anomalous Hall effect is a fundamental transport process in solids arising from the spin-orbit coupling. In a quantum anomalous Hall insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically nontrivial electronic structure, leading to the quantized Hall effect without an external magnetic field. Based on first-principles calculations, we predict that the tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in contrast to conventional dilute magnetic semiconductors where free carriers are necessary to mediate the magnetic coupling. In two-dimensional thin films, this magnetic order gives rise to a topological electronic structure characterized by a finite Chern number, with the Hall conductance quantized in units of e2/h (where e is the charge of an electron and h is Planck's constant).

Effective continuous model for surface states and thin films of three-dimensional topological insulators

Two-dimensional (2D) effective continuous models are derived for the surface states and thin films of a three-dimensional topological insulator (3DTI). Starting from an effective model for 3DTI based on first-principles calculations (Zhang et al 2009 Nat. Phys.5 438), we present solutions for both the surface states in a semi-infinite boundary condition and those in a thin film with finite thickness. The coupling between opposite topological surfaces and structure inversion asymmetry (SIA) gives rise to gapped Dirac hyperbolas with Rashba-like splittings in the energy spectrum. In addition, SIA leads to asymmetric distributions of wavefunctions for the surface states along the film growth direction, making some branches in the energy spectra much harder than others to probe by light. These features agree well with the recent angle-resolved photoemission spectra of Bi2Se3 films grown on SiC substrate (Zhang et al 2009 arXiv:0911.3706). More importantly, using the parameters fitted by experimental data, the result indicates that the thin film Bi2Se3 lies in the quantum spin Hall (QSH) region based on the calculation of the Chern number and Z2 invariant. In addition, strong SIA always tends to destroy the QSH state.