Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator

Topological phase transition without gap closing

Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously connected without gap closing, provided the symmetry of the system changes during the process. Here we propose the generic principles how this is possible by demonstrating various examples such as 1D polyacetylene with the charge-density-wave order, 2D silicene with the antiferromagnetic order, 2D silicene or quantum well made of HgTe with superconducting proximity effects and 3D superconductor Cu doped Bi₂Se₃. It is argued that such an unusual phenomenon can occur when we detour around the gap closing point provided the connection of the topological numbers is lost along the detour path.

Inducing time-reversal-invariant topological superconductivity and fermion parity pumping in quantum wires

We propose a setup to realize time-reversal-invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is ϕ=π a Kramers pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in the presence of both time-reversal-invariant and time-reversal-breaking perturbations. In addition, we show that the system forms a natural realization of a fermion parity pump, switching the local fermion parity of both edges when the relative phase between the superconductors is changed adiabatically by 2π.

Superconductivity of the topological insulator Bi2Se3 at high pressure

The pressure-induced superconductivity and structural evolution of Bi2Se3 single crystals are studied. The emergence of superconductivity at an onset transition temperature (Tc) of about 4.4 K is observed at around 12 GPa. Tc increases rapidly to a maximum of 8.2 K at 17.2 GPa, decreases to around 6.5 K at 23 GPa, and then remains almost constant with further increases in pressure. Variations in Tc with respect to pressure are closely related to the carrier density, which increases by over two orders of magnitude from 2 to 23 GPa. High-pressure synchrotron radiation measurements reveal structural transitions at around 12, 20, and above 29 GPa. A phase diagram of superconductivity versus pressure is also constructed.

Symmetry-protected Majorana fermions in topological crystalline superconductors: theory and application to Sr2RuO4

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.

Pressure-induced unconventional superconducting phase in the topological insulator Bi2Se3

Simultaneous low-temperature electrical resistivity and Hall effect measurements were performed on single-crystalline Bi2Se3 under applied pressures up to 50 GPa. As a function of pressure, superconductivity is observed to onset above 11 GPa with a transition temperature Tc and upper critical field Hc2 that both increase with pressure up to 30 GPa, where they reach maximum values of 7 K and 4 T, respectively. Upon further pressure increase, Tc remains anomalously constant up to the highest achieved pressure. Conversely, the carrier concentration increases continuously with pressure, including a tenfold increase over the pressure range where Tc remains constant. Together with a quasilinear temperature dependence of Hc2 that exceeds the orbital and Pauli limits, the anomalously stagnant pressure dependence of Tc points to an unconventional pressure-induced pairing state in Bi2Se3 that is unique among the superconducting topological insulators.

Time-reversal-invariant topological superconductivity and Majorana Kramers pairs

We propose a feasible route to engineer one- and two-dimensional time-reversal-invariant topological superconductors (SCs) via proximity effects between nodeless s(±) wave iron-based SCs and semiconductors with large Rashba spin-orbit interactions. At the boundary of a time-reversal-invariant topological SC, there emerges a Kramers pair of Majorana edge (bound) states. For a Josephson π junction, we predict a Majorana quartet that is protected by mirror symmetry and leads to a mirror fractional Josephson effect. We analyze the evolution of the Majorana pair in Zeeman fields, as the SC undergoes a symmetry class change as well as topological phase transitions, providing an experimental signature in tunneling spectroscopy. We briefly discuss the realization of this mechanism in candidate materials and the possibility of using s and d wave SCs and weak topological insulators.

Surface spectral function of momentum-dependent pairing potentials in a topological insulator: application to CuxBi2Se3

We propose three possible momentum-dependent pairing potentials as candidates for topological superconductors (for example CuxBi2Se3), and calculate the surface spectral function and surface density of states with these pairing potentials. We find that the first two can give the same spectral functions as the fully gapped and node-contacted pairing potentials given by Fu and Berg (2010 Phys. Rev. Lett. 105 097001), and that the third one can obtain a topological non-trivial case in which there exists a flat Andreev bound state and which preserves the threefold rotation symmetry. We hope our proposals and results will be assessed by future experiment.

Fermiology of the strongly spin-orbit coupled superconductor Sn(1-x)In(x)Te: implications for topological superconductivity

We have performed angle-resolved photoemission spectroscopy on the strongly spin-orbit coupled low-carrier density superconductor Sn(1-x)In(x)Te (x = 0.045) to elucidate the electronic states relevant to the possible occurrence of topological superconductivity, as recently reported for this compound based on point-contact spectroscopy. The obtained energy-band structure reveals a small holelike Fermi surface centered at the L point of the bulk Brillouin zone, together with a signature of a topological surface state, indicating that this material is a doped topological crystalline insulator characterized by band inversion and mirror symmetry. A comparison of the electronic states with a band-noninverted superconductor possessing a similar Fermi surface structure, Pb(1-x)Tl(x)Te, suggests that the anomalous behavior in the superconducting state of Sn(1-x)In(x)Te is related to the peculiar orbital characteristics of the bulk valence band and/or the presence of a topological surface state.

Exchange-coupling-induced symmetry breaking in topological insulators

An exchange gap in the Dirac surface states of a topological insulator (TI) is necessary for observing the predicted unique features such as the topological magnetoelectric effect as well as to confine Majorana fermions. We experimentally demonstrate proximity-induced ferromagnetism in a TI, combining a ferromagnetic insulator EuS layer with Bi(2)Se(3), without introducing defects. By magnetic and magnetotransport studies, including anomalous Hall effect and magnetoresistance measurements, we show the emergence of a ferromagnetic phase in TI, a step forward in unveiling their exotic properties.

Controllable magnetic doping of the surface state of a topological insulator

A combined experimental and theoretical study of doping individual Fe atoms into Bi(2)Se(3) is presented. It is shown through a scanning tunneling microscopy study that single Fe atoms initially located at hollow sites on top of the surface (adatoms) can be incorporated into subsurface layers by thermally activated diffusion. Angle-resolved photoemission spectroscopy in combination with ab initio calculations suggest that the doping behavior changes from electron donation for the Fe adatom to neutral or electron acceptance for Fe incorporated into substitutional Bi sites. According to first principles calculations within density functional theory, these Fe substitutional impurities retain a large magnetic moment, thus presenting an alternative scheme for magnetically doping the topological surface state. For both types of Fe doping, we see no indication of a gap at the Dirac point.

Experimental evidence for s-wave pairing symmetry in superconducting Cu(x)Bi2Se3 single crystals using a scanning tunneling microscope

Topological superconductors represent a newly predicted phase of matter that is topologically distinct from conventional superconducting condensates of Cooper pairs. As a manifestation of their topological character, topological superconductors support solid-state realizations of Majorana fermions at their boundaries. The recently discovered superconductor Cu(x)Bi(2)Se(3) has been theoretically proposed as an odd-parity superconductor in the time-reversal-invariant topological superconductor class, and point-contact spectroscopy measurements have reported the observation of zero-bias conductance peaks corresponding to Majorana states in this material. Here we report scanning tunneling microscopy measurements of the superconducting energy gap in Cu(x)Bi(2)Se(3) as a function of spatial position and applied magnetic field. The tunneling spectrum shows that the density of states at the Fermi level is fully gapped without any in-gap states. The spectrum is well described by the Bardeen-Cooper-Schrieffer theory with a momentum independent order parameter, which suggests that Cu(x)Bi(2)Se(3) is a classical s-wave superconductor contrary to previous expectations and measurements.

Effect of nanoholes on the vortex core fermion spectrum and heat transport in p-wave superconductors

The spectrum of core excitations of the Abrikosov vortex pinned by a nanohole of the size of the coherence length is considered. While the neutral zero energy Majorana core state remains intact due to its topological origin, the energy of charged excitations is significantly enhanced compared to that in the unpinned vortex. As a consequence of the pinning the minigap separating the Majorana state from the charged levels increases from Δ(2)/E(F) (E(F) is the Fermi energy and Δ is the bulk p-wave superconducting gap) to a significant fraction of Δ. Suppression of the thermodynamic and kinetic effects of the charged excitations allows us to isolate the Majorana state so it can be used for quantum computation. It is proposed that thermal conductivity along the vortex cores is a sensitive method to demonstrate the minigap. Using the Butticker-Landauer-Kopnin formula, we calculate the thermal conductance beyond the linear response as a function of the hole radius.

Electromagnetic and thermal responses of Z topological insulators and superconductors in odd spatial dimensions

The relation between bulk topological invariants and experimentally observable physical quantities is a fundamental property of topological insulators and superconductors. In the case of chiral symmetric systems in odd spatial dimensions such as time-reversal invariant topological superconductors and topological insulators with sublattice symmetry, this relation has not been well understood. We clarify that the winding number which characterizes the bulk Z nontriviality of these systems can appear in electromagnetic and thermal responses in a certain class of heterostructure systems. It is also found that the Z nontriviality can be detected in the bulk "chiral polarization," which is induced by magnetoelectric effects.

Dimerization of boron dopant in diamond (100) epitaxy induced by strong pair correlation on the surface

Experiments have shown that boron incorporation in diamond epitaxies is orientation dependent. Our first-principles calculations reveal that at a (100) surface, the formation of the boron dimer is more favored than that of the monomer, indicating a high density of ineffective boron formed under heavy doping. The reconstructed surface layer of carbon dimers in which the electrons are strongly pair correlated provides the mechanism. Hydrogen adsorption affects the correlation and thus the favorability of boron dimer formation, while at a (111) surface, the formation of boron monomer is more favored due to the less correlated surface electrons and hydrogen adsorption has no effect on the favorability.

Structural phase transition in IrTe₂: a combined study of optical spectroscopy and band structure calculations

Ir(1-x)Pt(x)Te₂ is an interesting system showing competing phenomenon between structural instability and superconductivity. Due to the large atomic numbers of Ir and Te, the spin-orbital coupling is expected to be strong in the system which may lead to nonconventional superconductivity. We grew single crystal samples of this system and investigated their electronic properties. In particular, we performed optical spectroscopic measurements, in combination with density function calculations, on the undoped compound IrTe₂ in an effort to elucidate the origin of the structural phase transition at 280 K. The measurement revealed a dramatic reconstruction of band structure and a significant reduction of conducting carriers below the phase transition. We elaborate that the transition is not driven by the density wave type instability but caused by the crystal field effect which further splits/separates the energy levels of Te (p(x), p(y)) and Te p(z) bands.

Stabilization of Majorana modes in magnetic vortices in the superconducting phase of topological insulators using topologically trivial bands

It has been shown that doped topological insulators, up to a certain level of doping, still preserve some topological signatures of the insulating phase such as axionic electromagnetic response and the presence of a Majorana mode in the vortices of a superconducting phase. Multiple topological insulators such as HgTe, ScPtBi, and other ternary Heusler compounds have been identified and generically feature the presence of a topologically trivial band between the two topological bands. In this Letter we show that the presence of such a trivial band can stabilize the topological signature over a much wider range of doping. Specifically, we calculate the structure of vortex modes in the superconducting phase of doped topological insulators, a model that captures the features of HgTe and the ternary Heusler compounds. We show that, due to the hybridization with the trivial band, Majorana modes are preserved over a large, extended doping range for p doping. In addition to presenting a viable system where much less fine-tuning is required to observe the Majorana modes, our analysis opens a route to study other topological features of doped compounds that cannot be modeled using the simple Bi(2)Se(3) Dirac model.

Quantum oscillations in the topological superconductor candidate Cu(0.25)Bi2Se3

Quantum oscillations are generally studied to resolve the electronic structure of topological insulators. In Cu(0.25)Bi(2)Se(3), the prime candidate of topological superconductors, quantum oscillations are still not observed in magnetotransport measurement. However, using torque magnetometry, quantum oscillations (the de Haas-van Alphen effect) were observed in Cu(0.25)Bi(2)Se(3). The doping of Cu in Bi(2)Se(3) increases the carrier density and the effective mass without increasing the scattering rate or decreasing the mean free path. In addition, the Fermi velocity remains the same in Cu(0.25)Bi(2)Se(3) as that in Bi(2)Se(3). Our results imply that the insertion of Cu does not change the band structure and that conduction electrons in Cu doped Bi(2)Se(3) sit in the linear Dirac-like band.

Odd-parity pairing and topological superconductivity in a strongly spin-orbit coupled semiconductor

The existence of topological superconductors preserving time-reversal symmetry was recently predicted, and they are expected to provide a solid-state realization of itinerant massless Majorana fermions and a route to topological quantum computation. Their first likely example, Cu(x)Bi(2)Se(3), was discovered last year, but the search for new materials has so far been hindered by the lack of a guiding principle. Here, we report point-contact spectroscopy experiments suggesting that the low-carrier-density superconductor Sn(1-x)In(x)Te is accompanied by surface Andreev bound states which, with the help of theoretical analysis, would give evidence for odd-parity pairing and topological superconductivity. The present and previous finding of possible topological superconductivity in Sn(1-x)In(x)Te and Cu(x)Bi(2)Se(3) suggests that odd-parity pairing favored by strong spin-orbit coupling is likely to be a common underlying mechanism for materializing topological superconductivity.

Spin-orbit locking as a protection mechanism of the odd-parity superconducting state against disorder

Unconventional superconductors host a plethora of interesting physical phenomena. However, the standard theory of superconductors suggests that unconventional pairing is highly sensitive to disorder, and hence can only be observed in ultraclean systems. We find that due to an emergent chiral symmetry, spin-orbital locking can parametrically suppress pair decoherence introduced by impurity scattering in odd-parity superconductors. Our work demonstrates that disorder is not an obstacle to realize odd-parity superconductivity in materials with strong spin-orbit coupling.

Physics and chemistry of layered chalcogenide superconductors

Structural and physical properties of layered chalcogenide superconductors are summarized. In particular, we review the remarkable properties of the Fe-chalcogenide superconductors, FeSe and FeTe-based materials. Furthermore, we introduce the recently discovered BiS2-based layered superconductors and discuss their prospects.

Topological materials

Recently, topological insulator materials have been theoretically predicted and experimentally observed in both 2D and 3D systems. We first review the basic models and physical properties of topological insulators, using HgTe and Bi(2)Se(3) as prime examples. We then give a comprehensive survey of topological insulators which have been predicted so far, and discuss the current experimental status.

Robust surface doping of Bi2Se3 by rubidium intercalation

Rubidium adsorption on the surface of the topological insulator Bi(2)Se(3) is found to induce a strong downward band bending, leading to the appearance of a quantum-confined two-dimensional electron gas state (2DEG) in the conduction band. The 2DEG shows a strong Rashba-type spin-orbit splitting, and it has previously been pointed out that this has relevance to nanoscale spintronics devices. The adsorption of Rb atoms, on the other hand, renders the surface very reactive, and exposure to oxygen leads to a rapid degrading of the 2DEG. We show that intercalating the Rb atoms, presumably into the van der Waals gaps in the quintuple layer structure of Bi(2)Se(3), drastically reduces the surface reactivity while not affecting the promising electronic structure. The intercalation process is observed above room temperature and accelerated with increasing initial Rb coverage, an effect that is ascribed to the Coulomb interaction between the charged Rb ions. Coulomb repulsion is also thought to be responsible for a uniform distribution of Rb on the surface.

New directions in the pursuit of Majorana fermions in solid state systems

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

Room temperature giant and linear magnetoresistance in topological insulator Bi2Te3 nanosheets

Topological insulators, a new class of condensed matter having bulk insulating states and gapless metallic surface states, have demonstrated fascinating quantum effects. However, the potential practical applications of the topological insulators are still under exploration worldwide. We demonstrate that nanosheets of a Bi(2)Te(3) topological insulator several quintuple layers thick display giant and linear magnetoresistance. The giant and linear magnetoresistance achieved is as high as over 600% at room temperature, with a trend towards further increase at higher temperatures, as well as being weakly temperature-dependent and linear with the field, without any sign of saturation at measured fields up to 13 T. Furthermore, we observed a magnetic field induced gap below 10 K. The observation of giant and linear magnetoresistance paves the way for 3D topological insulators to be useful for practical applications in magnetoelectronic sensors such as disk reading heads, mechatronics, and other multifunctional electromagnetic applications.

Measurement of an exceptionally weak electron-phonon coupling on the surface of the topological insulator Bi2Se3 using angle-resolved photoemission spectroscopy

Gapless surface states on topological insulators are protected from elastic scattering on nonmagnetic impurities which makes them promising candidates for low-power electronic applications. However, for widespread applications, these states should have to remain coherent at ambient temperatures. Here, we studied temperature dependence of the electronic structure and the scattering rates on the surface of a model topological insulator, Bi2Se3, by high-resolution angle-resolved photoemission spectroscopy. We found an extremely weak broadening of the topological surface state with temperature and no anomalies in the state's dispersion, indicating exceptionally weak electron-phonon coupling. Our results demonstrate that the topological surface state is protected not only from elastic scattering on impurities, but also from scattering on low-energy phonons, suggesting that topological insulators could serve as a basis for room-temperature electronic devices.

High-density chemical intercalation of zero-valent copper into Bi2Se3 nanoribbons

A major goal of intercalation chemistry is to intercalate high densities of guest species without disrupting the host lattice. Many intercalant concentrations, however, are limited by the charge of the guest species. Here we have developed a general solution-based chemical method for intercalating extraordinarily high densities of zero-valent copper metal into layered Bi(2)Se(3) nanoribbons. Up to 60 atom % copper (Cu(7.5)Bi(2)Se(3)) can be intercalated with no disruption to the host lattice using a solution disproportionation redox reaction.

Topological superconductivity in bilayer Rashba system

We theoretically study a possible topological superconductivity in the interacting two layers of Rashba systems, which can be fabricated by the heterostructures of semiconductors and oxides. The hybridization, which induces the gap in the single particle dispersion, and the electron-electron interaction between the two layers leads to the novel phase diagram of the superconductivity. It is found that the topological superconductivity without breaking time-reversal symmetry is realized when (i) the Fermi energy is within the hybridization gap, and (ii) the interlayer interaction is repulsive, both of which can be satisfied in realistic systems. Edge channels are studied in a tight-binding model numerically, and the several predictions on experiments are also given.

Charge-orbital density wave and superconductivity in the strong spin-orbit coupled IrTe2:Pd

Using transmission electron microscopy, the anomalies in resistivity and magnetic susceptibility at ~262 K in IrTe2 are found to accompany the superlattice peaks with q[over q=(1/5,0,-1/5). The wave vector is consistent with our theoretical calculation for the Fermi surface nesting vector, indicating that the ~262 K transition is of the charge-orbital density wave (DW) type. We also discovered that both Pd intercalation and substitution induce bulk superconductivity with T(c) up to ~3 K, which competes with DW in a quantum critical pointlike manner.

The coexistence of superconductivity and topological order in the Bi₂Se₃ thin films

Three-dimensional topological insulators (TIs) are characterized by their nontrivial surface states, in which electrons have their spin locked at a right angle to their momentum under the protection of time-reversal symmetry. The topologically ordered phase in TIs does not break any symmetry. The interplay between topological order and symmetry breaking, such as that observed in superconductivity, can lead to new quantum phenomena and devices. We fabricated a superconducting TI/superconductor heterostructure by growing dibismuth triselenide (Bi(2)Se(3)) thin films on superconductor niobium diselenide substrate. Using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we observed the superconducting gap at the Bi(2)Se(3) surface in the regime of Bi(2)Se(3) film thickness where topological surface states form. This observation lays the groundwork for experimentally realizing Majorana fermions in condensed matter physics.

Majorana fermions and exotic surface Andreev bound states in topological superconductors: application to Cu(x)Bi2Se3

The recently discovered superconductor Cu(x)Bi2Se3 is a candidate for three-dimensional time-reversal-invariant topological superconductors, which are predicted to have robust surface Andreev bound states hosting massless Majorana fermions. In this work, we analytically and numerically find the linearly dispersing Majorana fermions at k=0, which smoothly evolve into a new branch of gapless surface Andreev bound states near the Fermi momentum. The latter is a new type of Andreev bound states resulting from both the nontrivial band structure and the odd-parity pairing symmetry. The tunneling spectra of these surface Andreev bound states agree well with a recent point-contact spectroscopy experiment [S. Sasaki et al., Phys. Rev. Lett. 107, 217001 (2011)] and yield additional predictions for low temperature tunneling and photoemission experiments.

Superconductivity in the doped topological insulator Cu{x}Bi{2}Se{3} under high pressure

We report a high-pressure single crystal study of the topological superconductor Cu{x}Bi{2}Se{3}. Resistivity measurements under pressure show superconductivity is depressed smoothly. At the same time the metallic behavior is gradually lost. The upper-critical field data B{c2}(T) under pressure collapse onto a universal curve. The absence of Pauli limiting and the comparison of B{c2}(T) to a polar-state function point to spin-triplet superconductivity, but an anisotropic spin-singlet state cannot be discarded completely.

Cross-correlated responses of topological superconductors and superfluids

We study nontrivial responses of topological superconductors and superfluids to the temperature gradient and rotation of the system. In two-dimensional gapped systems, the Strěda formula for the electric Hall conductivity is generalized to the thermal Hall conductivity. Applying this formula to the Majorana surface states of three-dimensional topological superconductors predicts cross-correlated responses between the orbital angular momentum and thermal polarization (entropy polarization). These results can be naturally related to the gravitoelectromagnetism description of three-dimensional topological superconductors and superfluids, analogous to the topological magnetoelectric effect in Z(2) topological insulators.

Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ∼3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ∼20 K and coexists with the topological superconducting state.

Nano-engineering with a focused helium ion beam

Although Helium Ion Microscopy (HIM) was introduced only a few years ago, many new application fields are budding. The connecting factor between these novel applications is the unique interaction of the primary helium ion beam with the sample material at and just below its surface. In particular, the HIM secondary electron (SE) signal stems from an area that is very well localized around the point of incidence of the primary beam. This makes the HIM well-suited for both high-resolution imaging as well as high resolution nanofabrication. Another advantage in nanofabrication is the low ion backscattering fraction, leading to a weak proximity effect. The lack of a quantitative materials analysis mode (like EDX in Scanning Electron Microscopy, SEM) and a relatively low beam current as compared to the SEM and the Gallium Focused Ion Beam are the present drawbacks of the HIM.

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.

Common origin of the circular-dichroism pattern in angle-resolved photoemission spectroscopy of SrTiO3 and Cu(x)Bi2Se3

Circular dichroism in the angular distribution of photoelectrons from SrTiO(3):Nb and Cu(x)Bi(2)Se(3) is investigated by 7-eV laser angle-resolved photoemission spectroscopy. In addition to the well-known node that occurs in the circular dichroism pattern when the incidence plane matches the mirror plane of the crystal, we show that another type of node occurs when the mirror plane of the crystal is vertical to the incidence plane and the electronic state is two-dimensional. The flower-shaped circular dichroism patterns in the angular distribution occurring around the Fermi level of SrTiO(3):Nb and around the Dirac point of Cu(x)Bi(2)Se(3) are explained on equal footings. We point out that the penetration depth of the topological states of Cu(x)Bi(2)Se(3) depends on momentum.

A precise method for visualizing dispersive features in image plots

In order to improve the advantages and the reliability of the second derivative method in tracking the position of extrema from experimental curves, we develop a novel analysis method based on the mathematical concept of curvature. We derive the formulas for the curvature in one and two dimensions and demonstrate their applicability to simulated and experimental angle-resolved photoemission spectroscopy data. As compared to the second derivative, our new method improves the localization of the extrema and reduces the peak broadness for a better visualization on intensity image plots.

Bulk superconducting phase with a full energy gap in the doped topological insulator Cu(x)Bi₂Se₃

The superconductivity recently found in the doped topological insulator Cu(x)Bi₂Se₃ offers a great opportunity to search for a topological superconductor. We have successfully prepared a single-crystal sample with a large shielding fraction and measured the specific-heat anomaly associated with the superconductivity. The temperature dependence of the specific heat suggests a fully gapped, strong-coupling superconducting state, but the BCS theory is not in full agreement with the data, which hints at a possible unconventional pairing in Cu(x)Bi₂Se₃. Also, the evaluated effective mass of 2.6m(e) (m(e) is the free electron mass) points to a large mass enhancement in this material.

Pressure-induced superconductivity in topological parent compound Bi2Te3

We report a successful observation of pressure-induced superconductivity in a topological compound Bi(2)Te(3) with T(c) of ∼3 K between 3 to 6 GPa. The combined high-pressure structure investigations with synchrotron radiation indicated that the superconductivity occurred at the ambient phase without crystal structure phase transition. The Hall effects measurements indicated the hole-type carrier in the pressure-induced superconducting Bi(2)Te(3) single crystal. Consequently, the first-principles calculations based on the structural data obtained by the Rietveld refinement of X-ray diffraction patterns at high pressure showed that the electronic structure under pressure remained topologically nontrivial. The results suggested that topological superconductivity can be realized in Bi(2)Te(3) due to the proximity effect between superconducting bulk states and Dirac-type surface states. We also discuss the possibility that the bulk state could be a topological superconductor.

Chain of Majorana states from superconducting Dirac fermions at a magnetic domain wall

We study theoretically a strongly type-II s-wave superconducting state of two-dimensional Dirac fermions in proximity to a ferromagnet having in-plane magnetization. It is shown that a magnetic domain wall can host a chain of equally spaced vortices in the superconducting order parameter, each of which binds a Majorana-fermion state. The overlap integral of neighboring Majorana states is sensitive to the position of the chemical potential of the Dirac fermions. Thermal transport and scanning tunneling microscopy experiments to probe the Majorana fermions are discussed.

Odd-parity topological superconductors: theory and application to CuxBi2Se3

Topological superconductors have a full pairing gap in the bulk and gapless surface Andreev bound states. In this Letter, we provide a sufficient criterion for realizing time-reversal-invariant topological superconductors in centrosymmetric superconductors with odd-parity pairing. We next study the pairing symmetry of the newly discovered superconductor CuxBi2Se3 within a two-orbital model, and find that a novel spin-triplet pairing with odd parity is favored by strong spin-orbit coupling. Based on our criterion, we propose that CuxBi2Se3 is a good candidate for a topological superconductor. We close by discussing experimental signatures of this new topological phase.

Tunneling between two helical superconductors via Majorana edge channels

We discuss electric transport through a point contact which bridges Majorana fermion modes appearing at edges of two helical superconductors. The contents focus on the effects of interference and interaction unique to the Majorana fermions and the role of spin-orbit interaction (SOI). Besides the Josephson current, the quasiparticle conductance depends sensitively on the phase difference and relative helicity between the two superconductors. The interaction among the Majorana fermions causes the power-law temperature dependences of conductance for various tunneling channels. Especially, in the presence of SOI, the conductance always increases as the temperature is lowered.

Single-Dirac-cone topological surface states in the TlBiSe(2) class of topological semiconductors

We investigate several strong spin-orbit coupling ternary chalcogenides related to the (Pb,Sn)Te series of compounds. Our first-principles calculations predict the low-temperature rhombohedral ordered phase in TlBiTe₂, TlBiSe₂, and TlSbX₂ (X=Te, Se, S) to be topologically nontrivial. We identify the specific surface termination that realizes the single Dirac cone through first-principles surface state computations. This termination minimizes effects of dangling bonds, making it favorable for photoemission experiments. In addition, our analysis predicts that thin films of these materials could harbor novel 2D quantum spin Hall states, and support odd-parity topological superconductivity.