PHYSICAL REVIEW X 4, 041022 (2014) Phase Coherence and Andreev Reflection in Topological Insulator Devices A. D. K. Finck,1 C. Kurter,1 Y. S. Hor, 2 and D. J. Van Harlingen1 1Department of Physics and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 2Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA (Received 3 June 2014; published 4 November 2014) Topological insulators (TIs) have attracted immense interest because they host helical surface states. Protected by time-reversal symmetry, they are robust to nonmagnetic disorder. When superconductivity is induced in these helical states, they are predicted to emulate p-wave pairing symmetry, with Majorana states bound to vortices. Majorana bound states possess non-Abelian exchange statistics that can be probed through interferometry. Here, we take a significant step towards Majorana interferometry by observing pronounced Fabry-Pérot oscillations in a TI sandwiched between a superconducting and a normal lead. For energies below the superconducting gap, we observe a doubling in the frequency of the oscillations, arising from an additional phase from Andreev reflection. When a magnetic field is applied perpendicular to the TI surface, a number of very sharp and gate-tunable conductance peaks appear at or near zero energy, which has consequences for interpreting spectroscopic probes of Majorana fermions. Our results demonstrate that TIs are a promising platform for exploring phase-coherent transport in a solid-state system. DOI: 10.1103/PhysRevX.4.041022 Subject Areas: Condensed Matter Physics, Superconductivity, Topological Insulators I. INTRODUCTION bound states (MBSs) can be realized in a topological insulator (TI) with induced superconductivity [6–8]. When electrons travel far distances without scattering MBSs can encode quantum information nonlocally, real- off of impurities, their wavelike nature becomes apparent izing topologically protected qubits whose states can be through signatures of interference. A prominent example is read out through interferometry [9–11]. Recently, there ballistic transmission through a barrier between two semi- has been much experimental progress in realizing super- infinite leads. Imperfect transmission through the interfaces conductivity in topological systems through the study of causes partial reflection of impinging electrons. Within the Josephson junctions constructed on the surface of various barrier, constructive interference of reflected waves leads 3D TIs [12–21]. to periodic modulation of total transmission through the In this paper, we describe direct studies of phase barrier, resulting in resonant transmission whenever the coherence and Andreev reflection in TI devices. In each electron wavelength is an integer multiple of twice of our samples, a thin flake of the 3D TI Bi2Se3 is placed in the barrier length. This is equivalent to kFL ¼ πn, where contact with both a superconducting lead and a normal kF is the Fermi wave vector, L is the barrier length, and n is a nonzero integer. metal lead. The contacts are highly transparent, permitting This quantum phenomenon, known as Fabry-Pérot Andreev reflection between the Bi2Se3 and the super- interference due to its similarity to the eponymous classical conducting lead. The chemical potential of the Bi2Se3 is optical effect, has been observed in a variety of mesoscopic tuned with electrostatic gating. In more resistive devices, systems, including nanotubes [1], nanowires [2], and we find evidence of Fabry-Pérot oscillations, demonstrat- graphene [3]. In topological systems with protected edge ing gate-tunable, phase-coherent transport in a TI. For states [4], interferometry takes on a new significance as source-drain biases below the energy gap of the super- particles traveling through the edge states can acquire an conducting lead, we observe a doubling of the frequency additional phase if their paths enclose exotic quasiparticles of the conductance oscillations. This provides firm evi- – known as anyons [5]. A class of anyons known as Majorana dence of de Gennes Saint-James resonances [22,23],in which an additional phase accumulated from Andreev- reflected holes changes the period of geometric resonances by a factor of 2. When a large magnetic field is applied Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- perpendicular to the TI surface, an intricate set of low- bution of this work must maintain attribution to the author(s) and energy resonances emerges. These features include zero- the published article’s title, journal citation, and DOI. energy peaks that can persist for a range of chemical 2160-3308=14=4(4)=041022(9) 041022-1 Published by the American Physical Society FINCK et al. PHYS. REV. X 4, 041022 (2014) potential and magnetic field, sharing many properties of f ¼ 73 Hz. Unless stated otherwise, all measurements anomalies observed in nanowires [24–28]. Although such are performed at a base mixing chamber temperature anomalies were interpreted in terms of MBSs, the coex- of 20 mK. istence of the low-energy resonances with phase-coherent signatures at high magnetic fields in our devices suggests III. TRANSPORT IN ZERO FIELD that alternative explanations are possible, including weak antilocalization [29]. Our results encourage further studies A. Andreev reflection and reentrant of gate-tunable phase coherence in Bi2Se3 in order to resistance effect perform interferometric searches for MBSs. For example, it We study Andreev reflection in thin (∼10 nm) flakes of is necessary to discern what role topological surface states the 3D topological insulator Bi2Se3 connected to both play in the Fabry-Pérot oscillations. superconducting and normal metal leads separated by L ¼ 100–250 nm. An example of a device with L ¼ II. EXPERIMENTAL METHODS 230 nm is pictured in Fig. 1(a). Either top or back gates Single crystals of Bi2Se3 are grown by melting a mixture are used to tune the chemical potential of the surface states, of pureBiandSeinastoichiometricratioof1.9975∶3 (Bi∶Se) depicted in Fig. 1(b). Here, we focus on one sample, with in a vacuum quartz tube at 800 °C. Thin flakes qualitatively similar results obtained from others [30].At (7–20 nm) of Bi2Se3 are exfoliated onto silicon substrates low temperature, we observe an enhancement in conduct- V covered by a 300 nm thick SiO2 layer. Such thin flakes ance at source-drain biases ( ) below the niobium gap, as N ≈ 1013–1014 −2 – typically have a 2D carrier density of 2D cm expected for Andreev reflection [Fig. 2(a)] [32 34]. Near and low temperature mobility μ ≈ 102–103 cm2=Vs, as V ¼ 0, however, there is a downturn in the conductance. determinedfrommeasurementsof separateHall bardevices This is consistent with the reentrant resistance effect with similar thicknesses as the devices mentioned in the [35,36], in which Andreev reflection is canceled out by main section and Supplemental Material [30].Forestimates the proximity effect in the limit of zero energy and zero 5 of the Fermi velocity, we use the value vF ¼ 4.2 × 10 m=s temperature [36,37]. Maximum conductance occurs at from angle-resolved photoemission spectroscopy measure- either a characteristic temperature or V that is governed 2 mentsofsimilarcrystalsofBi2Se3 [31]. Weak antilocal- by the Thouless energy ET ¼ ℏD=L , where D is the ization measurements of the Hall bar devices give typical diffusion constant and L is the separation between the phase-coherence lengths of lϕ ¼ 300–1000 nm at 10 mK. superconducting and normal metal leads on the bismuth For the Andreev reflection devices, superconducting leads selenide. Magnetotransport and angle-resolved photoemis- are defined by conventional e-beam lithography and a sion spectroscopy measurements [31]pffiffiffiffiffiffiffiffiffiffiffiffiffiffiallow us to calculate 1 1 2 subsequent dc sputtering of 50 nm of Nb at room temper- ET through D¼ vFl¼ vFμðh=2eÞ N2D=π≈0.0025m =s, = = 2 2 ature. Tunnel junctions of Au Al2O3 Nb reveal a super- where vF is the Fermi velocity, l is the mean-free path, μ is conducting gap of Δ ¼ 1.5 meV for our Nb films N the mobility, and 2D is the 2D carrier density. This results immediately after sputtering; in top-gated TI-Nb devices, the inverse proximity effect and additional nanofabrication processing will likely reduce the gap below this pristine value. Normal metal leads are deposited through e-beam evaporation of 5 nm of Ti and 50 nm of Au. Brief Ar ion milling is employed before metallization in situ to ensure goodcontact between the Bi2Se3 and the leads.This process yields reliably transparent contacts, as demonstrated by the consistent observation of supercurrents in topological insulator Josephson junctions [16,18,19,21]. Contact re- sistance is estimated to be much less than 100 Ω and is thus negligible. Typical Nb-Au lead separation is 100–250 nm. FIG. 1. (a) AFM image of N-TI-S device, where N stands for Applying a bias to the silicon substrate permits backgating. the normal metal lead (Au) and S is the superconducting lead A top gate is created by covering the samplewith 30 nm of (Nb). The Bi2Se3 segment originally consisted of two adjacent alumina via atomic layer deposition and deposition of nanoribbons that are each 9 nm thick, but subsequent AFM imaging after measurements revealed only one nanoribbon Ti=Au over the exposed Bi2Se3. The device discussed in remaining under the niobium lead [30]. Separation between N the main section is covered with alumina but lacks a top and S leads is L ¼ 230 nm, as determined from SEM. White gate. The devices are thermally anchored to the mixing scale bar is 1 μm. (b) Energy diagram for the three materials in chamber of a cryogen-free dilution refrigerator equipped the device. The TI (whose dispersion relation is depicted with with a vector magnet and filtered wiring. We perform low- both gapless helical surface states and gapped trivial states) is frequency transport measurements with standard lock-in sandwiched between a compressible normal metal and a super- techniques, typically with a 10 nA ac excitation at conductor with an energy gap Δ.