Aharonov-Bohm Interference and Phase-Coherent Surface-State Transport in Topological Insulator Rings.

We present low-temperature magnetotransport measurements on selectively grown Sb2Te3-based topological insulator ring structures. These devices display clear Aharonov-Bohm oscillations in the conductance originating from phase-coherent transport around the ring. The temperature dependence of the oscillation amplitude indicates that the Aharonov-Bohm oscillations originate from ballistic transport along the ring arms. We attribute these oscillations to the topological surface states. Further insight into the phase coherence is gained by comparing with similar Aharonov-Bohm-type oscillations in topological insulator nanoribbons exposed to an axial magnetic field. Here, quasi-ballistic phase-coherent transport is confirmed for closed-loop topological surface states in the transverse direction enclosing the nanoribbon. In contrast, the appearance of universal conductance fluctuations indicates phase-coherent transport in the diffusive regime, which is attributed to bulk carrier transport. Thus, it appears that even in the presence of diffusive p-type charge carriers in Aharonov-Bohm ring structures, phase-coherent quasi-ballistic transport of topological surface states is maintained over long distances.

Phase-coherent loops in selectively-grown topological insulator nanoribbons.

We succeeded in the fabrication of topological insulator (Bi0.57Sb0.43)2Te3 Hall bars as well as nanoribbons by means of selective-area growth using molecular beam epitaxy. By performing magnetotransport measurements at low temperatures information on the phase-coherence of the electrons is gained by analyzing the weak-antilocalization effect. Furthermore, from measurements on nanoribbons at different magnetic field tilt angles an angular dependence of the phase-coherence length is extracted, which is attributed to transport anisotropy and geometrical factors. For the nanoribbon structures universal conductance fluctuations were observed. By performing a Fourier transform of the fluctuation pattern a series of distinct phase-coherent closed-loop trajectories are identified. The corresponding enclosed areas can be explained in terms of nanoribbon dimensions and phase-coherence length. In addition, from measurements at different magnetic field tilt angles we can deduce that the area enclosed by the loops are predominately oriented parallel to the quintuple layers.

Phase-coherent transport in selectively grown topological insulator nanodots.

Oxidized Si(111) substrates were pre-structured by electron beam lithography and used as a substrate for the selective growth of three-dimensional topological insulators (TI) by molecular beam epitaxy. The patterned holes were filled up by the TI, i.e. Sb2Te3 and Bi2Te3, to form nanodots. Scanning electron microscopy and focused ion beam cross-sectioning was utilized to determine the morphology and depth profile of the nanodots. The magnetotransport measurements revealed universal conductance fluctuations originating from electron interference in phase-coherent loops. We find that these loops are oriented preferentially within the quintuple layers of the TI with only a small perpendicular contribution. Furthermore, we found clear indications of an conductivity anisotropy between different crystal orientations.

Electron Interference in Hall Effect Measurements on GaAs/InAs Core/Shell Nanowires.

We present low-temperature magnetotransport measurements on GaAs/InAs core/shell nanowires contacted by regular source-drain leads as well as laterally attached Hall contacts, which only touch parts of the nanowire sidewalls. Low-temperature measurements between source and drain contacts show typical phase coherent effects, such as universal conductance fluctuations in a magnetic field aligned perpendicularly to the nanowire axis as well as Aharonov-Bohm-type oscillations in a parallel aligned magnetic field. However, the signal between the Hall contacts shows a Hall voltage buildup, when the magnetic field is turned perpendicular to the nanowire axis while current is driven through the wire using the source-drain contacts. At low temperatures, the phase coherent effects measured between source and drain leads are superimposed on the Hall voltage, which can be explained by nonlocal probing of large segments of the nanowire. In addition, the Aharonov-Bohm-type oscillations are also observed in the magnetoconductance at magnetic fields aligned parallel to the nanowire axis, using the laterally contacted leads. This measurement geometry hereby directly corresponds to classical Aharonov-Bohm experiments using planar quantum rings. In addition, the Hall voltage is used to characterize the nanowires in terms of charge carrier concentration and mobility, using temperature- and gate-dependent measurements as well as measurements in tilted magnetic fields. The GaAs/InAs core/shell nanowire used in combination with laterally attached contacts is therefore the ideal system to three-dimensionally combine quantum ring experiments using the cross-sectional plane and Hall experiments using the axial nanowire plane.

Anisotropic phase coherence in GaAs/InAs core/shell nanowires.

Low-temperature transport in nanowires is accompanied by phase-coherent effects, which are observed as modulation of the conductance in an external magnetic field. In the GaAs/InAs core/shell nanowires investigated here, these are h/e flux periodic oscillations in a magnetic field aligned parallel to the nanowire axis and aperiodic universal conductance fluctuations in a field aligned perpendicularly to the nanowire axis. Both electron interference effects are used to analyse the phase coherence of the system. Temperature-dependent measurements are carried out, in order to derive the phase coherence lengths in the cross-sectional plane as well as along the nanowire sidewalls. It is found that these values show a strong anisotropy, which can be explained by the crystal structure of the GaAs/InAs core/shell nanowire. For nanowires with a radius as low as 45 nm, flux periodic oscillations were observed up to a temperature of 55 K.

Crystal Phase Transformation in Self-Assembled InAs Nanowire Junctions on Patterned Si Substrates.

We demonstrate the growth and structural characteristics of InAs nanowire junctions evidencing a transformation of the crystalline structure. The junctions are obtained without the use of catalyst particles. Morphological investigations of the junctions reveal three structures having an L-, T-, and X-shape. The formation mechanisms of these structures have been identified. The NW junctions reveal large sections of zinc blende crystal structure free of extended defects, despite the high stacking fault density obtained in individual InAs nanowires. This segment of zinc blende crystal structure in the junction is associated with a crystal phase transformation involving sets of Shockley partial dislocations; the transformation takes place solely in the crystal phase. A model is developed to demonstrate that only the zinc blende phase with the same orientation as the substrate can result in monocrystalline junctions. The suitability of the junctions to be used in nanoelectronic devices is confirmed by room-temperature electrical experiments.

Simultaneous integration of different nanowires on single textured Si (100) substrates.

By applying a texturing process to silicon substrates, we demonstrate the possibility to integrate III-V nanowires on (100) oriented silicon substrates. Nanowires are found to grow perpendicular to the {111}-oriented facets of pyramids formed by KOH etching. Having control of the substrate orientation relative to the incoming fluxes enables not only the growth of nanowires on selected facets of the pyramids but also studying the influence of the fluxes on the nanowire nucleation and growth. Making use of these findings, we show that nanowires with different dimensions can be grown on the same sample and, additionally, it is even possible to integrate nanowires of different semiconductor materials, for example, GaAs and InAs, on the very same sample.

Amphoteric nature of Sn in CdS nanowires.

High-quality CdS nanowires with uniform Sn doping were synthesized using a Sn-catalyzed chemical vapor deposition method. X-ray diffraction and transmission electron microscopy demonstrate the single crystalline wurtzite structure of the CdS/Sn nanowires. Both donor and acceptor levels, which originate from the amphoteric nature of Sn in II-VI semiconductors, are identified using low-temperature microphotoluminescence. This self-compensation effect was cross examined by gate modulation and temperature-dependent electrical transport measurement. They show an overall n-type behavior with relatively low carrier concentration and low carrier mobilities. Moreover, two different donor levels due to intrinsic and extrinsic doping could be distinguished. They agree well with both the electrical and optical data.

Quantum dots in InAs nanowires induced by surface potential fluctuations.

Back-gated InAs nanowire field-effect transistors are studied focusing on the formation of intrinsic quantum dots, i.e. dots not intentionally defined by electrodes. Such dots have been studied before, but the suggested explanations for their origin leave some open questions, which are addressed here. Stability diagrams of samples with different doping levels are recorded at electron temperatures below 200 mK, allowing us to estimate the number and size of the dots as well as the type of connection, i.e. in series or in parallel. We discuss several potential physical origins of the dots and conclude that they are most probably induced by potential fluctuations at the nanowire surface. Additionally, we show that via gate voltage and doping, the samples can be tuned to different regimes of Coulomb blockade.

In-Plane Anisotropy of Electrical Transport in Y0.85Tb0.15Ba2Cu3O7-x Films.

We fabricated high-quality c-axis-oriented epitaxial YBa2Cu3O7-x films with 15% of the yttrium atoms replaced by terbium (YTBCO) and studied their electrical properties. The Tb substitution reduced the charge carrier density, resulting in increased resistivity and decreased critical current density compared to pure YBa2Cu3O7-x films. The electrical properties of the YTBCO films showed an in-plane anisotropy in both the superconducting and normal states that, together with the XRD data, provided evidence for, at least, a partially twin-free film. Unexpectedly, the resistive transition of the bridges also demonstrated the in-plane anisotropy that could be explained within the framework of Tinkham's model of resistive transition and the Berezinskii-Kosterlitz-Thouless (BKT) model, depending on the sample parameters. Measurements of the differential resistance in the temperature range of the resistive transition confirmed the occurrence of the BKT transition in the YTBCO bridges. Therefore, we consider the YTBCO films to be a promising platform for both the fabrication of devices with high kinetic inductance and fundamental research on the BKT transition in cuprate superconductors.

Growth and Electrical Characterization of Hybrid Core/Shell InAs/CdSe Nanowires.

Core-only InAs nanowires (NWs) remain of continuing interest for application in modern optical and electrical devices. In this paper, we utilize the II-VI semiconductor CdSe as a shell for III-V InAs NWs to protect the electron transport channel in the InAs core from surface effects. This unique material configuration offers both a small lattice mismatch between InAs and CdSe and a pronounced electronic confinement in the core with type-I band alignment at the interface between both materials. Under optimized growth conditions, a smooth interface between the core and shell is obtained. Atom probe tomography (APT) measurements confirm substantial diffusion of In into the shell, forming a remote n-type doping of CdSe. Moreover, field-effect transistors (FETs) are fabricated, and the electron transport characteristics in these devices is investigated. Finally, band structure simulations are performed and confirm the presence of an electron transport channel in the InAs core that, at higher gate voltages, extends into the CdSe shell region. These results provide a promising basis toward the application of hybrid III-V/II-VI core/shell nanowires in modern electronics.

Molecular beam epitaxy growth of GaAs/InAs core-shell nanowires and fabrication of InAs nanotubes.

We present results about the growth of GaAs/InAs core-shell nanowires (NWs) using molecular beam epitaxy. The core is grown via the Ga droplet-assisted growth mechanism. For a homogeneous growth of the InAs shell, the As(4) flux and substrate temperature are critical. The shell growth starts with InAs islands along the NW core, which increase in time and merge giving finally a continuous and smooth layer. At the top of the NWs, a small part of the core is free of InAs indicating a crystal phase selective growth. This allows a precise measurement of the shell thickness and the fabrication of InAs nanotubes by selective etching. The strain relaxation in the shell occurs mainly via the formation of misfit dislocations and saturates at ~80%. Additionally, other types of defects are observed, namely stacking faults transferred from the core or formed in the shell, and threading dislocations.

Supercurrent in Bi4Te3 Topological Material-Based Three-Terminal Junctions.

In this paper, in an in situ prepared three-terminal Josephson junction based on the topological insulator Bi4Te3 and the superconductor Nb the transport properties are studied. The differential resistance maps as a function of two bias currents reveal extended areas of Josephson supercurrent, including coupling effects between adjacent superconducting electrodes. The observed dynamics for the coupling of the junctions is interpreted using a numerical simulation of a similar geometry based on a resistively and capacitively shunted Josephson junction model. The temperature dependency indicates that the device behaves similar to prior experiments with single Josephson junctions comprising topological insulators' weak links. Irradiating radio frequencies to the junction, we find a spectrum of integer Shapiro steps and an additional fractional step, which is interpreted with a skewed current-phase relationship. In a perpendicular magnetic field, we observe Fraunhofer-like interference patterns in the switching currents.

Fully in situ Nb/InAs-nanowire Josephson junctions by selective-area growth and shadow evaporation.

Josephson junctions based on InAs semiconducting nanowires and Nb superconducting electrodes are fabricated in situ by a special shadow evaporation scheme for the superconductor electrode. Compared to other metallic superconductors such as Al, Nb has the advantage of a larger superconducting gap which allows operation at higher temperatures and magnetic fields. Our junctions are fabricated by shadow evaporation of Nb on pairs of InAs nanowires grown selectively on two adjacent tilted Si (111) facets and crossing each other at a small distance. The upper wire relative to the deposition source acts as a shadow mask determining the gap of the superconducting electrodes on the lower nanowire. Electron microscopy measurements show that the fully in situ fabrication method gives a clean InAs/Nb interface. A clear Josephson supercurrent is observed in the current-voltage characteristics, which can be controlled by a bottom gate. The large excess current indicates a high junction transparency. Under microwave radiation, pronounced integer Shapiro steps are observed suggesting a sinusoidal current-phase relation. Owing to the large critical field of Nb, the Josephson supercurrent can be maintained to magnetic fields exceeding 1 T. Our results show that in situ prepared Nb/InAs nanowire contacts are very interesting candidates for superconducting quantum circuits requiring large magnetic fields.

Flux periodic oscillations and phase-coherent transport in GeTe nanowire-based devices.

Despite the fact that GeTe is known to be a very interesting material for applications in thermoelectrics and for phase-change memories, the knowledge on its low-temperature transport properties is only limited. We report on phase-coherent phenomena in the magnetotransport of GeTe nanowires. From universal conductance fluctuations measured on GeTe nanowires with Au contacts, a phase-coherence length of about 280 nm at 0.5 K is determined. The distinct phase-coherence is confirmed by the observation of Aharonov-Bohm type oscillations for parallel magnetic fields. We interpret the occurrence of these magnetic flux-periodic oscillations by the formation of a tubular hole accumulation layer. For Nb/GeTe-nanowire/Nb Josephson junctions we obtained a critical current of 0.2 µA at 0.4 K. By applying a perpendicular magnetic field the critical current decreases monotonously with increasing field, whereas in a parallel field the critical current oscillates with a period of the magnetic flux quantum confirming the presence of a tubular hole channel.

Reappearance of first Shapiro step in narrow topological Josephson junctions.

In Josephson junctions, a supercurrent across a nonsuperconducting weak link is carried by electron-hole bound states. Because of the helical spin texture of nondegenerate topological surface states, gapless bound states are established in junctions with topological weak link. These have a characteristic 4π-periodic current phase relation (CΦR) that leads to twice the conventional Shapiro step separation voltage in radio frequency-dependent measurements. In this context, we identify an attenuated first Shapiro step in (Bi0.06Sb0.94)2Te3 (BST) Josephson junctions with AlO x capping layer. We further investigate junctions on narrow, selectively deposited BST nanoribbons, where surface charges are confined to the perimeter of the nanoribbon. Within these junctions, previously identified signatures of gapless bound states are absent. Because of confinement, transverse momentum sub-bands are quantized and a topological gap opening is observed. Surface states within these quantized sub-bands are spin degenerate, which evokes bound states of conventional 2π-periodic CΦR within the BST nanoribbon weak link.

Selective area growth and stencil lithography for in situ fabricated quantum devices.

The interplay of Dirac physics and induced superconductivity at the interface of a 3D topological insulator (TI) with an s-wave superconductor (S) provides a new platform for topologically protected quantum computation based on elusive Majorana modes. To employ such S-TI hybrid devices in future topological quantum computation architectures, a process is required that allows for device fabrication under ultrahigh vacuum conditions. Here, we report on the selective area growth of (Bi,Sb)2Te3 TI thin films and stencil lithography of superconductive Nb for a full in situ fabrication of S-TI hybrid devices via molecular-beam epitaxy. A dielectric capping layer was deposited as a final step to protect the delicate surfaces of the S-TI hybrids at ambient conditions. Transport experiments in as-prepared Josephson junctions show highly transparent S-TI interfaces and a missing first Shapiro step, which indicates the presence of Majorana bound states. To move from single junctions towards complex circuitry for future topological quantum computation architectures, we monolithically integrated two aligned hardmasks to the substrate prior to growth. The presented process provides new possibilities to deliberately combine delicate quantum materials in situ at the nanoscale.

MBE growth of Al/InAs and Nb/InAs superconducting hybrid nanowire structures.

We report the in situ growth of crystalline aluminum (Al) and niobium (Nb) shells on indium arsenide (InAs) nanowires. The nanowires are grown on Si(111) substrates by molecular beam epitaxy (MBE) without foreign catalysts in the vapor-solid (VS) mode. The metal shells are deposited by electron-beam evaporation in a metal MBE. High quality superconductor/semiconductor (SC/SM) hybrid structures such as Al/InAs and Nb/InAs are of interest for ongoing research in the fields of gateable Josephson junctions and quantum information related research. Systematic investigations of the deposition parameters suitable for metal shell growth are conducted. In the case of Al, the substrate temperature, the growth rate and the shell thickness are considered. The substrate temperature as well as the angle of the impinging deposition flux are explored for Nb shells. The core-shell hybrid structures are characterized by electron microscopy and X-ray spectroscopy. Our results show that the substrate temperature is a crucial parameter in enabling the deposition of smooth Al layers. Contrarily, Nb films are less dependent on substrate temperature but are strongly affected by the deposition angle. At a temperature of 200 °C Nb reacts with InAs, dissolving the nanowire crystal. Our investigations result in smooth metal shells exhibiting an impurity and defect free, crystalline SC/InAs interface. Additionally, we find that the SC crystal structure is not affected by stacking faults present in the InAs nanowires.

Strain relaxation and ambipolar electrical transport in GaAs/InSb core-shell nanowires.

The growth, crystal structure, strain relaxation and room temperature transport characteristics of GaAs/InSb core-shell nanowires grown using molecular beam epitaxy are investigated. Due to the large lattice mismatch between GaAs and InSb of 14%, a transition from island-based to layer-like growth occurs during the formation of the shell. High resolution transmission electron microscopy in combination with geometric phase analyses as well as X-ray diffraction with synchrotron radiation are used to investigate the strain relaxation and prove the existence of different dislocations relaxing the strain on zinc blende and wurtzite core-shell nanowire segments. While on the wurtzite phase only Frank partial dislocations are found, the strain on the zinc blende phase is relaxed by dislocations with perfect, Shockley partial and Frank partial dislocations. Even for ultrathin shells of about 2 nm thickness, the strain caused by the high lattice mismatch between GaAs and InSb is relaxed almost completely. Transfer characteristics of the core-shell nanowires show an ambipolar conductance behavior whose strength strongly depends on the dimensions of the nanowires. The interpretation is given based on an electronic band profile which is calculated for completely relaxed core/shell structures. The peculiarities of the band alignment in this situation implies simultaneously occupied electron and hole channels in the InSb shell. The ambipolar behavior is then explained by the change of carrier concentration in both channels by the gate voltage.

Angle-dependent magnetotransport in GaAs/InAs core/shell nanowires.

We study the impact of the direction of magnetic flux on the electron motion in GaAs/InAs core/shell nanowires. At small tilt angles, when the magnetic field is aligned nearly parallel to the nanowire axis, we observe Aharonov-Bohm type h/e flux periodic magnetoconductance oscillations. These are attributed to transport via angular momentum states, formed by electron waves within the InAs shell. With increasing tilt of the nanowire in the magnetic field, the flux periodic magnetoconductance oscillations disappear. Universal conductance fluctuations are observed for all tilt angles, however with increasing amplitudes for large tilt angles. We record this evolution of the electron propagation from a circling motion around the core to a diffusive transport through scattering loops and give explanations for the observed different transport regimes separated by the magnetic field orientation.