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Topological Materials

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Topological insulators are a newly discovered state of quantum matter. They feature a bulk gap and an odd number of relativistic Dirac fermions on their surfaces. While their bulk is insulating, the surfaces can conduct electric current with a well-defined spin texture. Spin-orbit interaction plays an important role. As a result, these materials are classified differently from the traditional Landau theory of phase transitions in matter. Instead, they are categorized by a topological quantity in the electron's wave-function, the Chern number. In addition, the linear energy-momentum relationship (E = pv) of electrons in these materials also appears in relativity (E = pc). As the velocity (v) of massless particles here are about 200 times slower than the speed of light (c) in vacuum, they are a great way to study the physics of relativity manifest in a condensed matter system.

Surface conduction of topological insulators. (A) The spin of electrons on the surface is correlated with their direction of motion. (B) The lattice structure of Bi2Te3 and the predicted relativistic "Dirac cone"-like electronic structure formed by the surface electrons. (C) The electronic structure measured by angle-resolved photoemission that confirmed the theoretical prediction and the topological nature of Bi2Te3.

Unlike non-topological ('trivial') materials, where fragile surface states can be easily altered by imperfections in surface geometry and chemistry, topological insulators are predicted to have unusually robust surface states protected by time-reversal symmetry. These unique states are protected against all time-reversal-invariant perturbations, such as scattering by non-magnetic impurities, crystalline defects, and distortion of the surface itself. This can produce striking quantum phenomena such as quantum spin Hall (QSH) and quantum anomalous Hall (QAH) effects, image magnetic monopoles induced by electric charges, and Majorana fermions (which are their own anti-particle — expected for bosons but not fermions) induced by proximity to a superconductor.

Extracting the electronic and structural properties of topological insulators is essential for both understanding the underlying physics and potential applications. As ARPES is a direct method to study the electron band structures of solids, it obtains detailed information on the electronic bands of topological insulators, and can even demonstrate control over the electronic surface states of topological insulators in the time domain. ARPES has emerged as the leading tool to elucidate the topological nature of 3D topological insulators.

Electronic structure of the 3D topological Insulator Bi2Te3
Probing the unoccupied states in topological insulator Bi2Se3
Spin-resolved imaging of the surface state of topological insulator Bi2Se3
Massive Dirac fermion on the surface of the magnetically doped topological insulator Bi2Se3
Discovery of the topological semimetal Na3Bi
Quantum Spin Hall Insulator WTe2


Electronic structure of the 3D topological Insulator Bi2Te3

Crystal and electronic structures of Bi2Te3. (A) Tetradymite-type crystal structure of Bi2Te3. (B) Calculated bulk conduction band (BCB) and bulk valence band (BVB) dispersions along high symmetry directions of the surface Brillouin zone (BZ) (see inset), with the chemical potential rigidly shifted to match the experimental result. (C) kz dependence of the calculated bulk Fermi surface (FS) projected on the surface BZ. (D) ARPES measurements of band dispersions along K-Γ-K and M-Γ-M (bottom) directions. (E) Measured wide range FS map covering three BZs, where the red hexagons represent the surface BZ. (F) Photon energy-dependent FS maps. The shape of the inner FS changes dramatically with photon energies, indicating a strong kz dependence due to its bulk nature as predicted in panel (C), while the non-varying shape of the outer hexagram FS confirms its surface state origin.

Bi2Te3 has been proposed to be the simplest 3D topological insulator, with a surface state consisting of a single Dirac cone at the Γ point (k = 0 in the Brillouin zone). By scanning across the Brillouin zone, our ARPES results on Bi2Te3 demonstrate that the surface state consists of a single non-degenerate Dirac cone. Furthermore, we explicitly showed the existence of a 100 meV energy gap for the bulk state by tuning the Fermi level. Our results demonstrate that Bi2Te3 is a possible candidate for high-temperature spintronic applications.

Probing unoccupied states in the topological insulator Bi2Se3 

Just like Bi2Te3, Bi2Se3 is also predicted to be a near-ideal topological insulator with a single Dirac cone. Bi2Se3 offers the potential for topologically protected behavior in ordinary crystals at room temperature and zero magnetic field. It has a large band gap of 0.3 eV at 360 K, which is promising for spintronic applications. For topological insulators, understanding the interplay of spin-polarized surface electrons with non-spin-polarized bulk electrons is critical for these potential applications. Our work reveals the coupling between bulk and surface electrons of the topological insulator Bi2Se3 by probing the dynamics of optically excited electrons directly in the electronic band structure using time-resolved ARPES (trARPES).


This femtosecond 'movie' on Bi2Se3 depicts how excited electrons fill unoccupied bands, and are subsequently prevented from relaxing immediately back to equilibrium due to the bulk band gap. These hot electrons accumulate at the bulk conduction band edge and act as a reservoir, which continues to populate the spin-polarized surface states for more than 10 picoseconds. This finding may pave the way for development of ultrafast optical switches of spin-polarized conduction channels. By resonantly exciting electrons in Bi2Se3 to unoccupied states, we obtain a complete picture of the electronic structure from the Fermi level up to the vacuum level. We found that the unoccupied states host a second, topologically protected Dirac surface state which can be resonantly excited by 1.5 eV photons.

Resonant transitions of the photocurrents. (a) Difference between the populations of the unoccupied bands when excited by left and right circularly polarized light. (b) Three resonant optical transitions between occupied and unoccupied states of Bi2Se3 with a 3 eV excitation. Blue dashed lines mark the initial states upshifted by the resonant excitations. (c) Time-dependent contributions to the photocurrent from each of the resonant optical transitions in (b).

In addition, our knowledge of the unoccupied band structure was instrumental in our investigation of photocurrents generated via circularly polarized optical excitations in Bi2Se3. These photocurrents can be measured in conventional transport configurations and are carried by topological surface states. Light helicity controls the photocurrent direction, making such systems interesting for electronic applications. The spectroscopic signature of photocurrents in trARPES is an asymmetric electron population in momentum space. We found that in Bi2Se3, only resonant optical transitions lead to momentum-asymmetric electron populations and therefore contribute to photocurrent generation. We also observed that different bands contribute to the net current in opposite directions. Our work provides a microscopic understanding of how to control photocurrents in topological materials and sets the stage for further studies leading toward spintronic applications.

Spin-resolved imaging of the surface state of topological insulator Bi2Se3

Spin-orbital texture in topological surface states is a special characteristic of topological insulators in which spin direction is locked to the wave vector and winds twice around the Fermi surface. Probing spin texture in topological insulators is thus crucial for understanding them. Our newly-developed spin-ARPES technique has the ability to probe spin texture in electronic band structure. The figure above shows spin-polarized surface states we have measured in Bi2Se3. Red and blue colors indicate opposite in-plane spin polarization. The spin-momentum locking feature of the topological surface state is clearly shown, where opposite momenta possess opposite spin polarizations.

Massive Dirac fermion on the surface of the magnetically doped topological insulator Bi2Se3

Realization of the insulating massive Dirac fermion state by simultaneous magnetic and charge doping. (A) Gap formation at the Dirac point and the in-gap Fermi level position. The occupied and unoccupied Dirac cones are shown in blue and gray.(B) ARPES spectra intensity plot of the band structure of Mn-doped Bi2Se3 showing the Fermi level inside the surface Dirac gap.

Topological insulators accommodate a conducting, linearly dispersed Dirac surface state in addition to the bulk energy gap. This state is predicted to become massive — that is, they form a gap and lose their linear dispersion — if time reversal symmetry is broken. It is also insulating if the Fermi energy (EF) is positioned inside both the surface and bulk gaps. This is shown in the diagram above. We can force an insulating massive Dirac fermion state to form by tuning EF into the surface-state gap. This state may then support many striking topological phenomena, such as an image magnetic monopole induced by a point charge, the half quantum Hall effect on the surface, and a topological contribution to the Faraday and Kerr effects.

We introduced long-range magnetic order to the 3D topological insulator Bi2Se3, breaking time-reversal symmetry by adding magnetic dopants. We positioned the EF inside the gaps by simultaneous magnetic and charge doping. Using ARPES, we studied the electronic structures of undoped and doped Bi2Se3. For undoped Bi2Se3, EF was found to always reside above the Dirac fermion state. Introducing Mn dopants to Bi2Se3 lifted the degeneracy at the Dirac point, forming an approximately 7 meV time-reversal symmetry-broken gap. It also tuned the EF into this gap, removing excess n-type carriers while maintaining the magnetic doping effect. In other words, Mn dopants not only introduce magnetic moments into the system, but also naturally p-dope the samples. The resulting insulating massive Dirac fermion state we discovered paves the way for studying a range of topological phenomena relevant to both condensed matter and particle physics.


Discovery of the topological semimetal Na3Bi

[Left] A 3D intensity plot of the photoemission spectra at the Dirac point of Na3Bi, showing cone-shape dispersion. [Right] Broad FS map from ARPES measurements that covers three BZs. The Fermi surface in each Brillioun zone is shown as a single point for the Dirac semimetal.

In contrast to 2D Dirac fermions in graphene, or the surfaces of 3D topological insulators, topological Dirac semimetals (TDS) possess 3D Dirac fermions in the bulk and can be viewed as a 3D counterpart of graphene. The bulk conduction and valence bands touch only at Dirac points and disperse linearly along momentum directions, forming 3D Dirac fermions in the bulk. The TDS state is proximate to various quantum states, ranging from regular band insulators to topological superconductors, and is thus useful for studying topological phase transitions.

We have performed angle-resolved photoemission spectroscopy (ARPES) measurements to investigate the electronic structures of Na3Bi single crystals, and validated its description as a 3D counterpart of graphene. Our data clearly observed the Dirac cone in Na3Bi and showed that it is 3D (bulk) in nature. We also found that the bulk Dirac cone persists despite surface deterioration, supporting the notion that the Dirac fermion observed is protected by the bulk crystal symmetry. The discovery of the topological Dirac semimetal Na3Bi opens the door to exploring other 3D TDSs and is potentially useful for spintronic applications.


Quantum Spin Hall Insulator WTe2

(a) Calculated band structure of WTe2, both with Spin Orbit Coupling (SOC) and without. (b) ARPES data equivalent to the calculated band structure shown in (a). (c) Scanning tunneling spectroscopy (STS) spectra taken across the step edge of a 1T’-WTe2 monolayer island (top), and its corresponding height profile (bottom). Near the edge, the gap is partially filled compared to the bulk, indicating conduction in the edge. ARPES data with a larger energy scale can be found here.

A quantum spin Hall insulator (QSH), or a two-dimensional topological insulator, possesses an insulating bulk, and topologically protected dissipationless edge states that bridge the energy gap opened by band inversion and strong spin-orbit coupling. A QSH state features quantized Hall conductance in the absence of a magnetic field and is thus promising for spintronic applications.

In our study, we demonstrated successful growth of monolayer 1T’ phase of WTe2 on a bilayer graphene substrate using molecular beam epitaxy (MBE). Using ARPES and STS (scanning tunneling spectroscopy), we established that monolayer 1T’-WTe2 is a new class of QSH insulator, with nontrivial band inversion, opening of a 55 meV bulk band gap, and a conducting edge state coexistent with an insulating bulk. This finding provides a platform for studying QSH insulators in 2D transition metal dichalcogenides, and for developing novel device applications. More information on thin films and 2D materials may be found here.