Surface state charge dynamics of a high-mobility three-dimensional topological insulator

Time-domain terahertz spectroscopy in high magnetic fields

There are a variety of elementary and collective terahertz-frequency excitations in condensed matter whose magnetic field dependence contains significant insight into the states and dynamics of the electrons involved. Often, determining the frequency, temperature, and magnetic field dependence of the optical conductivity tensor, especially in high magnetic fields, can clarify the microscopic physics behind complex many-body behaviors of solids. While there are advanced terahertz spectroscopy techniques as well as high magnetic field generation techniques available, a combination of the two has only been realized relatively recently. Here, we review the current state of terahertz time-domain spectroscopy (THz-TDS) experiments in high magnetic fields. We start with an overview of time-domain terahertz detection schemes with a special focus on how they have been incorporated into optically accessible high-field magnets. Advantages and disadvantages of different types of magnets in performing THz-TDS experiments are also discussed. Finally, we highlight some of the new fascinating physical phenomena that have been revealed by THz-TDS in high magnetic fields.

Polarimetric Three-Dimensional Topological Insulators/Organics Thin Film Heterojunction Photodetectors

As a state of quantum matter with insulating bulk and gapless surface states, topological insulators (TIs) have huge potential in optoelectronic devices. On the other hand, polarization resolution photoelectric devices based on anisotropic materials have overwhelming advantages in practical applications. In this work, the 3D TIs Bi₂Te₃/organics thin film heterojunction polarimetric photodetectors with high anisotropic mobility ratio, fast response time, high responsivity, and EQE in broadband spectra are presented. At first, the maximum anisotropic mobility ratio of the Bi₂Te₃/organics thin film can reach 2.56, which proves that Bi₂Te₃ can serve as a sensitive material for manufacturing polarization photoelectric devices. Moreover, it is found that the device can exhibit a broad bandwidth and ultrahigh response photocurrent from visible to middle wave infrared spectra (405-3500 nm). The highest responsivity (R_i) of optimized devices can reach up to 23.54 AW^-1; surprisingly, the R_i of the device can still reach 1.93 AW^-1 at 3500 nm. In addition, the ultrahigh external quantum efficiency is 4534% with a fast response time (1.42 ms). Excellent properties mentioned above indicate that TIs/organics heterojunction devices are suitable for manufacturing high-performance photoelectric devices in infrared region.

Fluctuation-Induced Torque on a Topological Insulator out of Thermal Equilibrium

Topological insulators with the time reversal symmetry broken exhibit strong magnetoelectric and magneto-optic effects. While these effects are well understood in or near equilibrium, nonequilibrium physics is richer yet less explored. We consider a topological insulator thin film, weakly coupled to a ferromagnet, out of thermal equilibrium with a cold environment (quantum electrodynamics vacuum). We show that the heat flow to the environment is strongly circularly polarized, thus carrying away angular momentum and exerting a purely fluctuation-driven torque on the topological insulator film. Utilizing the Keldysh framework, we investigate the universal nonequilibrium response of the TI to the temperature difference with the environment. Finally, we argue that experimental observation of this effect is within reach.

Three-Dimensional Topological Insulator Bi2Te3/Organic Thin Film Heterojunction Photodetector with Fast and Wideband Response from 450 to 3500 Nanometers

In the pursuit of broadband photodetection materials from visible to mid-IR region, the fresh three-dimensional topological insulators (3D TIs) are theoretically predicted to be a promising candidate due to its Dirac-like stable surface state and high absorption rate. In this work, a self-powered inorganic/organic heterojunction photodetector based on n-type 3D TIs Bi₂Te₃ combined with p-type pentacene thin film was designed and fabricated. Surprisingly, it was found that the Bi₂Te₃/pentacene heterojunction photodetector exhibited a fast and wideband response from 450 to 3500 nm. The optimized responsivity of photodetector reached 14.89 A/W, along with the fast response time of 1.89 ms and the ultrahigh external quantum efficiency of 2840%. Moreover, at the mid-IR 3500 nm, our devices demonstrated a responsivity of 1.55 AW^-1, which was several orders of magnitude higher than that of previous 3D TIs photodetector. These excellent properties indicate that the inorganic/organic heterojunction, that is, the combination of 3D TIs with organic materials, is an exciting structure for high performance photodetectors in the wideband detection region. On account of the fact that the device is constructed on mica substrate, this work also represents a potential scenario for flexible optoelectronic devices.

Nanomaterial-Based Plasmon-Enhanced Infrared Spectroscopy

Surface-enhanced infrared absorption (SEIRA) has attracted increasing attention due to the potential of infrared spectroscopy in applications such as molecular trace sensing of solids, polymers, and proteins, specifically fueled by recent substantial developments in infrared plasmonic materials and engineered nanostructures. Here, the significant progress achieved in the past decades is reviewed, along with the current state of the art of SEIRA. In particular, the plasmonic properties of a variety of nanomaterials are discussed (e.g., metals, semiconductors, and graphene) along with their use in the design of efficient SEIRA configurations. To conclude, perspectives on potential applications, including single-molecule detection and in vivo bioassays, are presented.

Observation of ultrahigh mobility surface states in a topological crystalline insulator by infrared spectroscopy

Topological crystalline insulators possess metallic surface states protected by crystalline symmetry, which are a versatile platform for exploring topological phenomena and potential applications. However, progress in this field has been hindered by the challenge to probe optical and transport properties of the surface states owing to the presence of bulk carriers. Here, we report infrared reflectance measurements of a topological crystalline insulator, (001)-oriented Pb_1−xSn_xSe in zero and high magnetic fields. We demonstrate that the far-infrared conductivity is unexpectedly dominated by the surface states as a result of their unique band structure and the consequent small infrared penetration depth. Moreover, our experiments yield a surface mobility of 40,000 cm² V⁻¹ s⁻¹, which is one of the highest reported values in topological materials, suggesting the viability of surface-dominated conduction in thin topological crystalline insulator crystals. These findings pave the way for exploring many exotic transport and optical phenomena and applications predicted for topological crystalline insulators.

Probing optical and transport properties of the surface states in topological crystalline insulators remains a challenge. Here, Wang et al. demonstrate that the far-infrared conductivity of Pb_1−xSn_xSe (x = 0.23−0.25) single crystals is dominated by the surface states where carriers show a high surface mobility of 40,000 cm² V⁻¹ s⁻¹.

Observation of the universal magnetoelectric effect in a 3D topological insulator

The electrodynamics of topological insulators (TIs) is described by modified Maxwell's equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e2/2hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.

Universal Faraday Rotation in HgTe Wells with Critical Thickness

The universal value of the Faraday rotation angle close to the fine structure constant (α≈1/137) is experimentally observed in thin HgTe quantum wells with a thickness on the border between trivial insulating and the topologically nontrivial Dirac phases. The quantized value of the Faraday angle remains robust in the broad range of magnetic fields and gate voltages. Dynamic Hall conductivity of the holelike carriers extracted from the analysis of the transmission data shows a theoretically predicted universal value of σ_{xy}=e^{2}/h, which is consistent with the doubly degenerate Dirac state. On shifting the Fermi level by the gate voltage, the effective sign of the charge carriers changes from positive (holes) to negative (electrons). The electronlike part of the dynamic response does not show quantum plateaus and is well described within the classical Drude model.

Terahertz spectroscopy on Faraday and Kerr rotations in a quantum anomalous Hall state

Electrodynamic responses from three-dimensional topological insulators are characterized by the universal magnetoelectric term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental indication of the topological magnetoelectric effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall states of magnetic topological insulator surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (for example, dielectric constant and magnetic susceptibility) well exhibits the trajectory towards the fine structure constant in the quantized limit.

Strong nonlinear terahertz response induced by Dirac surface states in Bi2Se3 topological insulator

Electrons with a linear energy/momentum dispersion are called massless Dirac electrons and represent the low-energy excitations in exotic materials such as graphene and topological insulators. Dirac electrons are characterized by notable properties such as a high mobility, a tunable density and, in topological insulators, a protection against backscattering through the spin-momentum locking mechanism. All those properties make graphene and topological insulators appealing for plasmonics applications. However, Dirac electrons are expected to present also a strong nonlinear optical behaviour. This should mirror in phenomena such as electromagnetic-induced transparency and harmonic generation. Here we demonstrate that in Bi2Se3 topological insulator, an electromagnetic-induced transparency is achieved under the application of a strong terahertz electric field. This effect, concomitantly determined by harmonic generation and charge-mobility reduction, is exclusively related to the presence of Dirac electron at the surface of Bi2Se3, and opens the road towards tunable terahertz nonlinear optical devices based on topological insulator materials.

Topological states on the gold surface

Gold surfaces host special electronic states that have been understood as a prototype of Shockley surface states. These surface states are commonly employed to benchmark the capability of angle-resolved photoemission spectroscopy (ARPES) and scanning tunnelling spectroscopy. Here we show that these Shockley surface states can be reinterpreted as topologically derived surface states (TDSSs) of a topological insulator (TI), a recently discovered quantum state. Based on band structure calculations, the Z₂-type invariants of gold can be well-defined to characterize a TI. Further, our ARPES measurement validates TDSSs by detecting the dispersion of unoccupied surface states. The same TDSSs are also recognized on surfaces of other well-known noble metals (for example, silver, copper, platinum and palladium), which shines a new light on these long-known surface states.

The surfaces of noble metals possess Shockley states which exhibit Rashba-type spin splitting and spin-momentum locking. Here, the authors use ab initio methods and photoemission spectroscopy to demonstrate how such Shockley states may be reinterpreted as topologically protected surface states.

High-Resolution Faraday Rotation and Electron-Phonon Coupling in Surface States of the Bulk-Insulating Topological Insulator Cu_{0.02}Bi_{2}Se_{3}

We have utilized time-domain magnetoterahertz spectroscopy to investigate the low-frequency optical response of the topological insulator Cu_{0.02}Bi_{2}Se_{3} and Bi_{2}Se_{3} films. With both field and frequency dependence, such experiments give sufficient information to measure the mobility and carrier density of multiple conduction channels simultaneously. We observe sharp cyclotron resonances (CRs) in both materials. The small amount of Cu incorporated into the Cu_{0.02}Bi_{2}Se_{3} induces a true bulk insulator with only a single type of conduction with a total sheet carrier density of ~4.9×10^{12}/cm^{2} and mobility as high as 4000 cm^{2}/V·s. This is consistent with conduction from two virtually identical topological surface states (TSSs) on the top and bottom of the film with a chemical potential ~145 meV above the Dirac point and in the bulk gap. The CR broadens at high fields, an effect that we attribute to an electron-phonon interaction. This assignment is supported by an extended Drude model analysis of the zero-field Drude conductance. In contrast, in normal Bi_{2}Se_{3} films, two conduction channels were observed, and we developed a self-consistent analysis method to distinguish the dominant TSSs and coexisting trivial bulk or two-dimensional electron gas states. Our high-resolution Faraday rotation spectroscopy on Cu_{0.02}Bi_{2}Se_{3} paves the way for the observation of quantized Faraday rotation under experimentally achievable conditions to push the chemical potential in the lowest Landau level.

Ultra-broadband and high response of the Bi2Te3-Si heterojunction and its application as a photodetector at room temperature in harsh working environments

Broadband photodetection is central to various technological applications including imaging, sensing and optical communications. On account of their Dirac-like surface state, Topological insulators (TIs) are theoretically predicted to be promising candidate materials for broadband photodetection from the infrared to the terahertz. Here, we report a vertically-constructed ultra-broadband photodetector based on a TI Bi2Te3-Si heterostructure. The device demonstrated room-temperature photodetection from the ultraviolet (370.6 nm) to terahertz (118 μm) with good reproducibility. Under bias conditions, the visible responsivity reaches ca. 1 A W(-1) and the response time is better than 100 ms. As a self-powered photodetector, it exhibits extremely high photosensitivity approaching 7.5 × 10(5) cm(2) W(-1), and decent detectivity as high as 2.5 × 10(11) cm Hz(1/2) W(-1). In addition, such a prototype device without any encapsulation suffers no obvious degradation after long-time exposure to air, high-energy UV illumination and acidic treatment. In summary, we demonstrate that TI-based heterostructures hold great promise for addressing the long lasting predicament of stable room-temperature high-performance broadband photodetectors.

Magneto-optical Kramers-Kronig analysis

We describe a simple magneto-optical experiment and introduce a magneto-optical Kramers-Kronig analysis (MOKKA) that together allow extracting the complex dielectric function for left- and right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below ∼0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45(∘) with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an in-situ polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magneto-optical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.

Nonsinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe

We use superconducting quantum interference device microscopy to characterize the current-phase relation (CPR) of Josephson junctions from the three-dimensional topological insulator HgTe (3D HgTe). We find clear skewness in the CPRs of HgTe junctions ranging in length from 200 to 600 nm. The skewness indicates that the Josephson current is predominantly carried by Andreev bound states with high transmittance, and the fact that the skewness persists in junctions that are longer than the mean free path suggests that the effect may be related to the helical nature of the Andreev bound states in the surface of HgTe. These experimental results suggest that the topological properties of the normal state can be inherited by the induced superconducting state, and that 3D HgTe is a promising material for realizing the many exciting proposals that require a topological superconductor.

Gate-tuned quantum oscillations of topological surface states in β-Ag2Te

We report the strong experimental evidence of the existence of topological surface states with large electric field tunability and mobility in β-Ag2Te. Pronounced 2D Shubnikov-de Haas oscillations have been observed in β-Ag2Te nanoplates. A Berry phase is determined to be near π using the Landau level fan diagram for a relatively wide nanoplate while the largest electric field ambipolar effect in topological insulator so far (~2500%) is observed in a narrow nanoplate. The π Berry phase and the evolution of quantum oscillations with gate voltage (Vg) in the nanoplates strongly indicate the presence of topological surface states in β-Ag2Te. Moreover, the mobility of the narrow Ag2Te nanoplate is about several thousand cm(2)s(-1)V(-1). Our results suggest that β-Ag2Te has the potential to become an important material in the investigation of topological insulators.

Magnetization of the metallic surface states in topological insulators

We calculate the magnetization of the helical metallic surface states of a topological insulator. We account for the presence of a small sub-dominant Schrödinger piece in the Hamiltonian in addition to the dominant Dirac contribution. This breaks particle-hole symmetry. The cross-section of the upper Dirac cone narrows while that of the lower cone broadens. The sawtooth pattern seen in the magnetization of the pure Dirac limit as a function of chemical potential (μ) is shifted; but, the quantization of the Hall plateaus remains half integral. This is verified by taking the derivative of the magnetization with respect to μ. We compare our results with those when the non-relativistic piece dominates over the relativistic contribution and the quantization is integral. Analytic results for the magnetic oscillations are obtained where we include a first order correction in the ratio of non-relativistic to relativistic magnetic energy scales. Our fully quantum mechanical derivations confirm the expectation of semiclassical theory except for a small correction to the expected phase. There is a change in the overall amplitude of the magnetic oscillations. The Dingle and temperature factors are modified.

One-dimensional weak antilocalization due to the berry phase in HgTe wires

We study the weak antilocalization (WAL) effect in the magnetoresistance of narrow HgTe wires fabricated in quantum wells with normal and inverted band ordering. Measurements at different gate voltages indicate that the WAL is only weakly affected by Rashba spin-orbit splitting and persists when the Rashba splitting is about zero. The WAL amplitude in wires with normal band ordering is an order of magnitude smaller than for wires with an inverted band structure. These observations are attributed to the Dirac-like dispersion of the energy bands in HgTe quantum wells. From the magnetic-field and temperature dependencies we extract the dephasing lengths and band Berry phases. The weaker WAL for samples with a normal band structure can be explained by a nonuniversal Berry phase which always exceeds π, the characteristic value for gapless Dirac fermions.

Terahertz time-domain spectroscopic ellipsometry: instrumentation and calibration

We present a new instrumentation and calibration procedure for terahertz time-domain spectroscopic ellipsometry (THz-TDSE) that is a newly established characterization technique. The experimental setup is capable of providing arbitrary angle of incidence in the range of 15°-85° in the reflection geometry, and with no need for realignment. The setup is also configurable easily into transmission geometry. For this setup, we successfully used hollow core photonic band gap fiber with no pre-chirping in order to deliver a femtosecond laser into a THz photoconductive antenna detector, which is the first demonstration of this kind. The proposed calibration scheme can compensate for the non-ideality of the polarization response of the THz photoconductive antenna detector as well as that of wire grid polarizers used in the setup. In the calibration scheme, the ellipsometric parameters are obtained through a regression algorithm which we have adapted from the conventional regression calibration method developed for rotating element optical ellipsometers, and used here for the first time for THz-TDSE. As a proof-of-principle demonstration, results are presented for a high resistivity silicon substrate as well as an opaque Si substrate with a high phosphorus concentration. We also demonstrate the capacity to measure a few micron thick grown thermal oxide on top of Si. Each sample was characterized by THz-TDSE in reflection geometry with different angle of incidence.

Measurement of intrinsic dirac fermion cooling on the surface of the topological insulator Bi2Se3 using time-resolved and angle-resolved photoemission spectroscopy

We perform time- and angle-resolved photoemission spectroscopy of a prototypical topological insulator (TI) Bi(2)Se(3) to study the ultrafast dynamics of surface and bulk electrons after photoexcitation. By analyzing the evolution of surface states and bulk band spectra, we obtain their electronic temperature and chemical potential relaxation dynamics separately. These dynamics reveal strong phonon-assisted surface-bulk coupling at high lattice temperature and total suppression of inelastic scattering between the surface and the bulk at low lattice temperature. In this low temperature regime, the unique cooling of Dirac fermions in TI by acoustic phonons is manifested through a power law dependence of the surface temperature decay rate on carrier density.

Spintronics and pseudospintronics in graphene and topological insulators

The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin-relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analogue of giant magnetoresistance in bilayer graphene.