Plasmons are quantized collective oscillations of electrons and have been observed in metals and doped semiconductors. The plasmons of ordinary, massive electrons have been the basic ingredients of research in plasmonics and in optical metamaterials for a long time. However, plasmons of massless Dirac electrons have only recently been observed in graphene, a purely two-dimensional electron system. Their properties are promising for novel tunable plasmonic metamaterials in the terahertz and mid-infrared frequency range. Dirac fermions also occur in the two-dimensional electron gas that forms at the surface of topological insulators as a result of the strong spin-orbit interaction existing in the insulating bulk phase. One may therefore look for their collective excitations using infrared spectroscopy. Here we report the first experimental evidence of plasmonic excitations in a topological insulator (Bi2Se3). The material was prepared in thin micro-ribbon arrays of different widths W and periods 2W to select suitable values of the plasmon wavevector k. The linewidth of the plasmon was found to remain nearly constant at temperatures between 6 K and 300 K, as expected when exciting topological carriers. Moreover, by changing W and measuring the plasmon frequency in the terahertz range versus k we show, without using any fitting parameter, that the dispersion curve agrees quantitatively with that predicted for Dirac plasmons.

With high quality topological insulator Bi(2)Se(3) thin films, we report thickness-independent transport properties over wide thickness ranges. Conductance remained nominally constant as the sample thickness changed from 256 to ∼8  QL (where QL refers to quintuple layer, 1  QL≈1  nm). Two surface channels of very different behaviors were identified. The sheet carrier density of one channel remained constant at ∼3.0×10(13)  cm(-2) down to 2 QL, while the other, which exhibited quantum oscillations, remained constant at ∼8×10(12)  cm(-2) only down to ∼8  QL. The weak antilocalization parameters also exhibited similar thickness independence. These two channels are most consistent with the topological surface states and the surface accumulation layers, respectively.

Topological insulators (TIs) are newly discovered states of matter with robust metallic surface states protected by the topological properties of the bulk wavefunctions [1][2][3][4][5][6]. A quantum phase transition (QPT) from a TI to a conventional insulator and a change in topological class can only occur when the bulk band gap closes [3]. In this work, we have utilized time-domain terahertz spectroscopy (TDTS) to investigate the low frequency conductance in (Bi 1−x In x ) 2 Se 3 as we tune through this transition by indium substitution. Above certain substitution levels we observe a collapse in the transport lifetime that indicates the destruction of the topological phase. We associate this effect with the threshold where states from opposite surfaces hybridize. The substitution level of the threshold is thickness dependent and only asymptotically approaches the bulk limit x ≈ 0.06 where a maximum in the midinfrared absorption is exhibited. This absorption can be identified with the bulk band gap closing and a change in topological class. The correlation length associated with the QPT appears as the evanescent length of the surface states. The observation of the thickness-dependent collapse of the transport lifetime shows the unusual role that finite size effects play in this topological QPT.The topological character of TIs is determined by the nature of their valence-band wave functions, which can be quantified by 4 Z 2 invariants. Fu and Kane have shown that for inversion symmetric crystals it is possible to evaluate these invariants directly with knowledge of the parity of Bloch wave functions for the occupied electronic states at high symmetry points in the Brillouin zone [10]. Although their argument is formulated for inversion symmetric systems, a material's topological classification does not require inversion or translation symmetry. Therefore the expectation is that the alloying of known TIs with lighter elements by reducing spin-orbit coupling or the tuning of lattice constant can cause the bulk band gap ∆ to close and invert at a quantum critical point where the topological class changes (See cartoon * Electronic address: npa@pha.jhu.edu Fig. 1a). This has been investigated in the thalliumbased ternary chalcogenide alloy TlBi(S 1−x Se x ) 2 [7-9], but thus far only with photoemission (Supplementary Information (SI) section B). Although signatures of topological surface state (TSS) conduction have been found in Bi 2 Se 3 [11-14], a demonstration that the surface transport changes dramatically when the band gap closes and the bulk changes topological class [15] would be strong evidence for the topological nature of these materials and is still lacking. In this regard, it was pointed out recently that indium (In) substitutes for bismuth to form a solid solution in Bi 2 Se 3 and that the non-topological end member In 2 Se 3 of the (Bi 1−x In x ) 2 Se 3 series shares the common rhombohedral D 5 3d structure with Bi 2 Se 3 [6]. In Ref.[6] a topological to trivial transition was observed in a range x ∼ 0.0...

We show that a number of transport properties in topological insulator (TI) Bi 2 Se 3 exhibit striking thickness-dependences over a range of up to five orders of thickness (3 nm -170 µm). Volume carrier density decreased with thickness, presumably due to diffusion-limited formation of selenium vacancies. Mobility increased linearly with thickness in the thin film regime and saturated in the thick limit. The weak anti-

By combining transport and photoemission measurements on (Bi(1-x)In(x))(2)Se(3) thin films, we report that this system transforms from a topologically nontrivial metal into a topologically trivial band insulator through three quantum phase transitions. At x ≈ 3%-7%, there is a transition from a topologically nontrivial metal to a trivial metal. At x ≈ 15%, the metal becomes a variable-range-hopping insulator. Finally, above x ≈ 25%, the system becomes a true band insulator with its resistance immeasurably large even at room temperature. This material provides a new venue to investigate topologically tunable physics and devices with seamless gating or tunneling insulators.

Atomically sharp epitaxial growth of Bi 2 Se 3 films is achieved on Si (111) substrate with MBE (Molecular Beam Epitaxy). Two-step growth process is found to be a key to achieve interfacial-layer-free epitaxial Bi 2 Se 3 films on Si substrates. With a single-step high temperature growth, second phase clusters are formed at an early stage. On the other hand, with low temperature growth, the film tends to be disordered even in the absence of a second phase. With a low temperature initial growth followed by a high temperature growth, secondphase-free atomically sharp interface is obtained between Bi 2 Se 3 and Si substrate, as verified 2 by RHEED (Reflection High Energy Electron Diffraction), TEM (Transmission Electron Microscopy) and XRD (X-Ray Diffraction). The lattice constant of Bi 2 Se 3 is observed to relax to its bulk value during the first quintuple layer according to RHEED analysis, implying the absence of strain from the substrate. TEM shows a fully epitaxial structure of Bi 2 Se 3 film down to the first quintuple layer without any second phase or an amorphous layer.

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