Fermi-level electronic structure of a topological-insulator/cuprate-superconductor based heterostructure in the superconducting proximity effect regime

Recent Advances in Topological Quantum Materials by Angle-Resolved Photoemission Spectroscopy

Proximity-induced superconductivity in a 3D topological insulator represents a new avenue for observing zero-energy Majorana fermions inside vortex cores. Relatively small gaps and low transition temperatures of conventional s-wave superconductors put hard constraints on these experiments. Significantly larger gaps and higher transition temperatures in cuprate superconductors might be an attractive alternative to considerably relax these constraints, but it is not clear whether the proximity effect would be effective in heterostructures involving cuprates and topological insulators. Here, we present angle-resolved photoemission studies of thin Bi(2)Se(3) films grown in situ on optimally doped Bi(2)Sr(2)CaCu(2)O(8+δ) substrates that show the absence of proximity-induced gaps on the surfaces of Bi(2)Se(3) films as thin as a 1.5 quintuple layer. These results suggest that the superconducting proximity effect between a cuprate superconductor and a topological insulator is strongly suppressed, likely due to a very short coherence length along the c axis, incompatible crystal and pairing symmetries at the interface, small size of the topological surface state's Fermi surface, and adverse effects of a strong spin-orbit coupling in the topological material.

The superconducting proximity effect (SPE) induces a superconductivity transition in otherwise non-superconducting thin films in proximity with a superconductor. The SPE usually occurs in real space and decays exponentially with film thickness. Herein, an abnormal SPE in a topological insulator (TI)/superconductor heterostructure is unveiled, which is attributed to the topologically protected surface state. Surprisingly, such abnormal SPE occurs in momentum space regardless of the TI film thickness, as long as the topological surface states are robust and form a continuous conduction loop. Combining transport measurements and scanning tunneling microscopy/spectroscopy techniques, the SPE in Bi2 Se3 /FeSe0.5 Te0.5 heterostructures is explored, where Bi2 Se3 is an ideal 3D topological insulator and FeSe0.5 Te0.5 a typical iron-based superconductor. As the thickness of the Bi2 Se3 thin film exceeds 400 nm, there still exists SPE-induced superconductivity on the surface of Bi2 Se3 thin film with a transition temperature Tc not less than 10 K. Such an extraordinary behavior is induced by the unique properties of topologically protected surface states of Bi2 Se3 . This research deepens the understanding of the important role of topologically protected surface states in the SPE.

We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulators. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both s-wave and p-wave components, even when the superconducting pair potential only transfers either pure singlets or pure triplets pairs of electrons in and out of the condensate, a corollary to the non-conservation of spin due to the spin-orbit coupling. We identify one single superconducting regime in the case of superconductivity in the topological surface states (Rashba-Dirac limit), irrespective of the relative strength between singlet and triplet pair potentials. In contrast, in the Fermi limit relevant to the noncentrosymmetric materials we find two regimes depending on the value of the chemical potential and the relative strength between singlet and triplet potentials. We construct explicitly the Majorana bound states in these regimes. In the single regime for the case of the Rashba-Dirac limit, there exist one and only one Majorana fermion bound to the core of an isolated vortex. In the Fermi limit, there are always an even number (0 or 2 depending on the regime) of Majorana fermions bound to the core of an isolated vortex. In all cases, the vorticity required to bind Majorana fermions is unity, in contrast to the half-flux in the case of two-dimensional $p_x \pm i p_y$ superconductors that break time-reversal symmetry.

Topological insulator based spin valve devices: Evidence for spin polarized transport of spin-momentum-locked topological surface states

Superconducting proximity effect in topological insulator and superconductor hybrid structure has attracted intense attention in recent years in an effort to search for Majorana fermions in condensed matter systems. Here we report on the superconducting proximity effect in a Bi2Se3/NbSe2 junction fabricated with an all-dry transfer method. Experimentally measured differential conductance spectra exhibit a bias-independent conductance plateau (BICP) in the vicinity of zero bias below 7 K and a zero-bias conductance peak (ZBCP) appears below 2 K. We show that the BICP is due to the strong superconducting proximity effect between the superconductor and the topological surface states while the ZBCP is due to the bulk states of Bi2Se3. Our study gives direct evidence that the topological surface states can be strongly coupled to a superconductor and clarifies the different roles of surface states and bulk states in superconducting proximity effect.

Gapless surface states on topological insulators are protected from elastic scattering on non-magnetic impurities which makes them promising candidates for low-power electronic applications. However, for wide-spread applications, these states should remain coherent and significantly spin polarized at ambient temperatures. Here, we studied the coherence and spin-structure of the topological states on the surface of a model topological insulator, Bi2Se3, at elevated temperatures in spin and angle-resolved photoemission spectroscopy. We found an extremely weak broadening and essentially no decay of spin polarization of the topological surface state up to room temperature. Our results demonstrate that the topological states on surfaces of topological insulators could serve as a basis for room temperature electronic devices.

Topological insulators are electronic materials that have a conventional energy gap as an insulator or semiconductor in the bulk, but possess gapless conducting states around their boundary. They are novel topological states of quantum matters and exhibit a series of exotic physics, such as quantum spin Hall effect, single valley Dirac fermions, Majorana fermions, topological magnetoelectric effect, etc. The conducting edge and surface states have topological origin of the electron band structure, and are protected by time-reversal symmetry such that they are robust or immune against local perturbation. In this dissertation, an effective continuous model for surface states is established from the three-dimensional modified Dirac model, and a theory of ultrathin film for topological insulators is developed. The established electronic model helps us explore spin physics of massive Dirac fermions. The theory has been successfully applied to explain an energy gap opening of the surface states in Bi2Se3 thin film in the measurement of angle-resolved photoemission spectroscopy (ARPES). In-gap bound states are also considered due to vacancy and impurity in topological insulators. It is found that a vacancy can always induce in-gap bound states in both two- and threedimensional topological insulators, and a half quantum magnetic flux inside the vacancy can result in helical Dirac zero modes. Finally the effect of random impurities on the surface transport in topological insulators is investigated, particularly the weak anti-localization of surface electrons in the quantum diffusion regime. It is found that the spin-orbit scattering may suppress the weak localization behaviors of massive Dirac fermions, which suggests an experiment to detect the weak localization in the topological insulator thin film.

Three-dimensional (3D) topological insulator (TI) has emerged as a unique state of quantum matter and generated enormous interests in condensed matter physics. The surfaces of a 3D TI consist of a massless Dirac cone, which is characterized by the Z2topological invariant. Introduction of magnetism on the surface of a TI is essential to realize the quantum anomalous Hall effect and other novel magneto-electric phenomena. Here, by using a combination of first-principles calculations, magneto-transport and angle-resolved photoemission spectroscopy (ARPES), we study the electronic properties of gadolinium (Gd)-doped Sb2Te3. Our study shows that Gd doped Sb2Te3is a spin-orbit-induced bulk band-gap material, whose surface is characterized by a single topological surface state. Our results provide a new platform to investigate the interactions between dilute magnetism and topology in magnetic doped topological materials.

We theoretically study superconducting proximity effect between a topological insulator (TI) and a high-temperature d-wave superconductor (dSC). When the TI-dSC heterostructure violates 90 degree-rotation and certain reflection symmetries, we show that a sizable s-wave pairing, coexisting with a d-wave one, emerges in the proximity-induced superconductivity in the TI's top surface states. Weak disorder further suppresses d-wave pairing but not s-wave one in the TI's surface states. More importantly, the pairing gap in surface states is found to be nodeless and nearly-isotropic when the Fermi pocket of surface states is relatively small. Our theoretical results qualitatively explain recent experimental evidences of a nearly-isotropic pairing gap on surface states of Bi_2Se_3 induced by proximity with high-T_c cuprate Bi_2Ca_2Cu_2O_{8+\delta}. We also demonstrate convincing evidences of Majorana zero modes in a magnetic hc/2e vortex core, which may be detectable in future experiments.

1D topological systems for next-generation electronics

Topological superconductors (TSCs) have a full gap in the bulk and gapless surface states consisting of Majorana fermions, which have potential applications in fault-tolerant topological quantum computation. Because TSCs are very rare in nature, an alternative way to study the TSC is to artificially introduce superconductivity into the surface states of a topological insulator (TI) through proximity effect (PE)1-4. Here we report the first experimental realization of the PE induced TSC in Bi2Te3/NbSe2 thin films as demonstrated by the density of states probed using scanning tunneling microscope. We observe Abrikosov vortices and lower energy bound states on the surface of topological insulator and the dependence of superconducting coherence length on the film thickness and magnetic field, which are attributed to the superconductivity in the topological surface states. This work demonstrates the practical feasibility of fabricating a TSC with individual Majorana fermions inside superconducting vortex as predicted in theory and accomplishes the pre-requisite step towards searching for Majorana fermions in the PE induced TSCs.

The exciton, a bound state of an electron and a hole, is a fundamental quasiparticle induced by coherent light-matter interactions in semiconductors. When the electrons and holes are in distinct spatial locations, spatially indirect excitons are formed with a much longer lifetime and a higher condensation temperature. One of the ultimate frontiers in this field is to create long-lived excitonic topological quasiparticles by driving exciton states with topological properties, to simultaneously leverage both topological effects and correlation1,2. Here we reveal the existence of a transient excitonic topological surface state (TSS) in a topological insulator, Bi2Te3. By using time-, spin- and angle-resolved photoemission spectroscopy, we directly follow the formation of a long-lived exciton state as revealed by an intensity buildup below the bulk-TSS mixing point and an anomalous band renormalization of the continuously connected TSS in the momentum space. Such a state inherits the spin-polarization of the TSS and is spatially indirect along the z axis, as it couples photoinduced surface electrons and bulk holes in the same momentum range, which ultimately leads to an excitonic state of the TSS. These results establish Bi2Te3 as a possible candidate for the excitonic condensation of TSSs3 and, in general, opens up a new paradigm for exploring the momentum space emergence of other spatially indirect excitons, such as moiré and quantum well excitons4-6, and for the study of non-equilibrium many-body topological physics.

We theoretically consider superconducting proximity effect, using the Bogoliubov-de Gennes theory, in heterostructure sandwich-type geometries involving a normal s-wave superconductor and a non-superconducting material with the proximity effect being driven by Cooper pairs tunneling from the superconducting slab to the non-superconducting slab. Applications of the superconducting proximity effect may rely on an induced spectral gap or induced pairing correlations without any spectral gap. We clarify that in a non-superconducting material the induced spectral gap and pairing correlations are independent physical quantities arising from the proximity effect. This is a crucial issue in proposals to create topological superconductivity through the proximity effect. Heterostructures of 3D topological insulator (TI) slabs on conventional s-wave superconductor (SC) substrates provide a platform, with proximity-induced topological superconductivity expected to be observed on the "naked" top surface of a thin TI slab. We theoretically study the induced superconducting gap on this naked surface. In addition, we compare against the induced spectral gap in heterostructures of SC with a normal metal or a semiconductor with strong spin orbit coupling and a Zeeman splitting potential (another platform for topological superconductivity). We find that for any model for the non-SC metal (including metallic TI) the induced spectral gap on the naked surface decays as $L^{-3}$ as the thickness ($L$) of the non-SC slab is increased in contrast to the slower $1/L$ decay of the pairing correlations. Our distinction between proximity-induced spectral gap (with its faster spatial decay) and pairing correlation (with its slower spatial decay) has important implications for the currently active search for topological superconductivity and Majorana fermions in various superconducting heterostructures.

We study the effect of the Fermi surface anisotropy on the odd-frequency spin-triplet pairing component of the induced pair potential. We consider a superconductor/ ferromagnetic insulator (S/FI) hybrid structure formed on the 3D topological insulator (TI) surface. In this case three ingredients ensure the possibility of the odd-frequency pairing: (1) the topological surface states, (2) the induced pair potential, and (3) the magnetic moment of a nearby ferromagnetic insulator. We take into account the strong anisotropy of the Dirac point in topological insulators when the chemical potential lies well above the Dirac cone and its constant energy contour has a snowflake shape. Within this model, we propose that the S/FI boundary should be properly aligned with respect to the snowflake constant energy contour to have an odd-frequency symmetry of the corresponding pairing component and to insure the Majorana bound state at the S/FI boundary. For arbitrary orientation of the boundary, the Majorana bound state is absent. This provides a selection rule to the realization of Majorana modes in S/FI hybrid structures, formed on the topological insulator surface.