Topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The bulk of such materials is insulating but the surface can conduct electric current with well-defined spin texture. These materials, with spin-orbit interaction playing an important role, are classified differently from the traditional Landau theory of phase transitions in matter, rather they are classified by quantities in the electrons wave-function, the so-called Chern number. In addition, the relativistic energy-momentum relationship of electrons in these materials provides a great opportunity to study the physics of relativity in a condensed matter system with the velocity of massless particles about 200 times slower than the light speed in vacuum.
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 Bi2Te3and 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 other materials where the fragile surface states can be easily altered by details in the surface geometry and chemistry, topological insulators are predicted to have unusually robust surface states due to the protection of 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, and can lead to striking quantum phenomena such as quantum spin Hall and quantum anomalous Hall effects, an image magnetic monopole induced by an electric charge, and Majorana fermions [whose anti-particle is itself] induced by proximity effect from a superconductor.
Extracting the electronic and structural properties of topological insulators is essential for both the understanding of the underlying physics and potential applications. As a direct method to study the electron band structures of solids, ARPES can yield rich information of the electronic bands of topological insulators and even demonstrate control over the electronic surface states of the topological insulators in the time domain. For 3D topological insulators, ARPES has emerged as the leading tool to elucidate the topological nature of these materials.
Electronic structure of the 3D topologic 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] The kz dependence of the calculated bulk Fermi surface [FS] projection 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 insulators whose surface states consist of a single Dirac cone at the Γ point. Our ARPES results on Bi2Te3 demonstrate that the surface state consists of a single non-degenerate Dirac cone by scanning over the Brillouin zone. Furthermore, we explicitly showed the 100 meV energy gap for the bulk state by tuning the Fermi Level. Our results prove that Bi2Te3 is among the possible candidates for high-temperature spintronics applications.
"Experimental realization of a three-dimensional topological insulator, Bi2Te3" Science 325, 178 [2009]
Probing the unoccupied states in topological insulator Bi2Se3
In addition to Bi2Te3, Bi2Se3 is also predicted to be a nearly idealized single Dirac cone topological insulator. 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 3600 K, which is promising for spintronics applications. For topological insulators, understanding the interplay of spin-polarized surface electrons with non-spin-polarized bulk electrons is critical for potential spintronics applications. Therefore, 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 material's electronic band structure using time-resolved ARPES[trARPES].
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, the knowledge of the unoccupied band structure was instrumental in our investigations of the 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. The 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 such 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.
"Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3", Phys. Rev. Lett. 108, 117403 [2012]
"Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3", Phys. Rev. Lett. 111, 136802 [2013]
"Band-Resolved Imaging of Photocurrent in a Topological Insulator" Phys. Rev. Lett. 122,167401 [2019]
Spin-resolved imaging of the surface state of topological insulator Bi2Se3
Spin-orbital texture in topological surfaces states is a special character in topological insulators where the spin direction is locked to the wave vector and winds by 2 around the Fermi surface. Probing the spin texture in TI is thus crucial for understanding topological insulators. Our newly-developed spin-ARPES technique has the ability to probe the spin texture in the electronic band structures. As shown in the figure is our measured spin-polarized surface states of 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 Bi2Se3showing 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 if time reversal symmetry [TRS] is broken, and to become insulating if the Fermi energy is positioned inside both the surface and bulk gaps. Furthermore, if Fermi energy [EF] can be tuned into this surface-state gap, an insulating massive Dirac fermion state is formed; this state may support many striking topological phenomena, such as the 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 to break the time-reversal symmetry by adding magnetic dopants and further position the Fermi energy inside the gaps by simultaneous magnetic and charge doping. Using ARPES, we studied electronic structures of both undoped and doped Bi2Se3. For undoped Bi2Se3, EF was found to always reside above the Drac fermion state. By introducing Mn dopants to Bi2Se3, we not only lifted the degeneracy at the Dirac point with an approximately 7meV large TRS gap formed, but also tuned the EF into this gap, removing the 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.
"Massive Dirac Fermion on the surface of a magnetically doped topological insulator" Science 329, 5992 [2010]
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 on the surface 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. TDS state is the neighbor to various quantum states ranging from regular band insulators to topological superconductors, hence is 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 found that it is a 3D counterpart of graphene. Our ARPES data clearly observed the Dirac cone in Na3Bi and showed that the Dirac cone is 3D/bulk in nature. We also found that the bulk Dirac cone persists despite such 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 spintronics applications given its unique properties.
"Discovery of a three-dimensional topological Dirac semimetal, Na3Bi" Science 343, 6173 [2014]
Quantum Spin Hall Insulator WTe2
[a] Calculated band structure of WTe2, both with Spin Orbit Coupling [SOC] and without SOC. [b] ARPES data that shows the same result of WTe2 as the calculated band structure in [a]. [c] ] Scanning Tunneling Spectroscopy [STS] spectra taken across the step edge of a 1T-WTe2 monolayer island [top], and corresponding height profile [bottom]. Near the edge the gap is partially filled compared to the bulk, indicating conduction in the edge. Larger energy scale ARPES data can be found in this section.
A quantum spin Hall insulator [QSH], or a 2-dimentional topological insulator results from topologically protected dissipationless edge states with an insulating bulk 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 spintronics applications.
In our study, we demonstrated successful growth of monolayer 1T phase of WTe2 using molecular beam epitaxy [MBE] on a bilayer graphene substrate. More information on Thin Films and 2D materials can be found in this section. Using ARPES and STS [Scanning tunneling spectroscopy], we established evidence that monolayer 1T-WTe2 is a new class of QSH insulator, with nontrivial band inversion, the opening of a 55meV bulk band gap, and a conducting edge state in contrast to the insulating bulk. Such findings provide a platform for studying QSH insulator in 2D transition metal dichalcogenides and for developing novel device applications.
"Quantum spin Hall state in monolayer 1T-WTe2", Nature Physics volume 13, 683687[2017]