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

De Hass-van Alphen and magnetoresistance reveal predominantly single-band transport behavior in PdTe2

Research on two-dimensional transition metal dichalcogenides (TMDs) has grown rapidly over the past several years, from fundamental studies to the development of next generation technologies. Recently, it has been reported that the MX2-type PdTe2 exhibits superconductivity with topological surface state, making this compound a promising candidate for investigating possible topological superconductivity. However, due to the multi-band feature of most of TMDs, the investigating of magnetoresistance and quantum oscillations of these TMDs proves to be quite complicated. Here we report a combined de Hass-van Alphen effect and magnetoresistance studies on the PdTe2 single crystal. Our high-field de Hass-van Alphen data measured at different temperature and different tilting angle suggest that though these is a well-defined multi-band feature, a predominant oscillation frequency has the largest oscillation magnitude in the fast Fourier transformation spectra, which is at least one order of magnitude larger than other oscillation frequencies. Thus it is likely that the transport behavior in PdTe2 system can be simplified into a single-band model. Meanwhile, the magnetoresistance results of the PdTe2 sample can be well-fitted according to the single-band models. The present results could be important in further investigation of the transport behaviors of two-dimensional TMDs.

Superconductivity in CaBi2

Superconductivity is observed with critical temperature Tc = 2.0 K in self-flux-grown single crystals of CaBi2. This material adopts the ZrSi2 structure type with lattice parameters a = 4.696(1) Å, b = 17.081(2) Å and c = 4.611(1) Å. The crystals of CaBi2 were studied by means of magnetic susceptibility, specific heat and electrical resistivity measurements. The heat capacity jump at Tc is ΔC/γTc = 1.41, confirming bulk superconductivity; the Sommerfeld coefficient γ = 4.1 mJ mol(-1) K(-2) and the Debye temperature ΘD = 157 K. The electron-phonon coupling strength is λel-ph = 0.59, and the thermodynamic critical field Hc is low, between 111 and 124 Oe CaBi2 is a moderate coupling type-I superconductor. Results of electronic structure calculations are reported and charge densities, electronic bands, densities of states and Fermi surfaces are discussed, focusing on the effects of spin-orbit coupling and electronic property anisotropy. We find a mixed quasi-2D + 3D character in the electronic structure, which reflects the layered crystal structure of the material.

Superconductivity in alkali metal intercalated iron selenides

Alkali metal intercalated iron selenide superconductors A x Fe2-y Se2 (where A  =  K, Rb, Cs, Tl/K, and Tl/Rb) are characterized by several unique properties, which were not revealed in other superconducting materials. The compounds crystallize in overall simple layered structure with FeSe layers intercalated with alkali metal. The structure turned out to be pretty complex as the existing Fe-vacancies order below ~550 K, which further leads to an antiferromagnetic ordering with Néel temperature fairly above room temperature. At even lower temperatures a phase separation is observed. While one of these phases stays magnetic down to the lowest temperatures the second is becoming superconducting below ~30 K. All these effects give rise to complex relationships between the structure, magnetism and superconductivity. In particular the iron vacancy ordering, linked with a long-range magnetic order and a mesoscopic phase separation, is assumed to be an intrinsic property of the system. Since the discovery of superconductivity in those compounds in 2010 they were investigated very extensively. Results of the studies conducted using a variety of experimental techniques and performed during the last five years were published in hundreds of reports. The present paper reviews scientific work concerning methods of synthesis and crystal growth, structural and superconducting properties as well as pressure investigations.

Topological Superconductivity on the Surface of Fe-Based Superconductors

As one of the simplest systems for realizing Majorana fermions, the topological superconductor plays an important role in both condensed matter physics and quantum computations. Based on ab initio calculations and the analysis of an effective 8-band model with superconducting pairing, we demonstrate that the three-dimensional extended s-wave Fe-based superconductors such as Fe_{1+y}Se_{0.5}Te_{0.5} have a metallic topologically nontrivial band structure, and exhibit a normal-topological-normal superconductivity phase transition on the (001) surface by tuning the bulk carrier doping level. In the topological superconductivity (TSC) phase, a Majorana zero mode is trapped at the end of a magnetic vortex line. We further show that the surface TSC phase only exists up to a certain bulk pairing gap, and there is a normal-topological phase transition driven by the temperature, which has not been discussed before. These results pave an effective way to realize the TSC and Majorana fermions in a large class of superconductors.

Transport spectroscopy on trapped superconducting nano-islands of Pb: signature of unconventional pairing

Elemental bulk lead (Pb) is a conventional type I, spin-singlet (s-wave) superconductor with a critical temperature T c = 7.2 K and a critical magnetic field H c = 800 Oe. However, it is known that at mesoscopic length scales, like in point-contact geometries, Pb shows significantly higher critical field, sometimes up to several Tesla. We have used this property to trap a small superconducting nano-droplet of Pb by forming a metallic point contact on Pb and then applying a magnetic field larger than 800 Oe that drives the bulk of the material non-superconducting. From systematic magnetic field dependent behaviour of the point-contact spectra measured across such a trapped island of Pb we show that the superconducting order parameter of mesoscopic Pb mixes non-trivially with magnetic field possibly due to the emergence of a local spin-triplet component at such length scales. From comparative studies with Nb-based point contacts we surmise that the strong spin-orbit coupling in Pb leads to the emergence of the unconventional component in the order parameter of mesoscopic Pb.

Rotational symmetry breaking in the topological superconductor SrxBi2Se3 probed by upper-critical field experiments

Recently it was demonstrated that Sr intercalation provides a new route to induce superconductivity in the topological insulator Bi2Se3. Topological superconductors are predicted to be unconventional with an odd-parity pairing symmetry. An adequate probe to test for unconventional superconductivity is the upper critical field, Bc2. For a standard BCS layered superconductor Bc2 shows an anisotropy when the magnetic field is applied parallel and perpendicular to the layers, but is isotropic when the field is rotated in the plane of the layers. Here we report measurements of the upper critical field of superconducting SrxBi2Se3 crystals (Tc = 3.0 K). Surprisingly, field-angle dependent magnetotransport measurements reveal a large anisotropy of Bc2 when the magnet field is rotated in the basal plane. The large two-fold anisotropy, while six-fold is anticipated, cannot be explained with the Ginzburg-Landau anisotropic effective mass model or flux flow induced by the Lorentz force. The rotational symmetry breaking of Bc2 indicates unconventional superconductivity with odd-parity spin-triplet Cooper pairs (Δ4-pairing) recently proposed for rhombohedral topological superconductors, or might have a structural nature, such as self-organized stripe ordering of Sr atoms.

Robust two-dimensional superconductivity and vortex system in Bi2Te3/FeTe heterostructures

The discovery of two-dimensional superconductivity in Bi2Te3/FeTe heterostructures provides a new platform for the search of Majorana fermions in condensed matter systems. Since Majorana fermions are expected to reside at the core of the vortices, a close examination of the vortex dynamics in superconducting interface is of paramount importance. Here, we report the robustness of the interfacial superconductivity and 2D vortex dynamics in four as-grown and aged Bi2Te3/FeTe heterostructure with different Bi2Te3 epilayer thickness (3, 5, 7, 14 nm). After two years' air exposure, superconductivity remains robust even when the thickness of Bi2Te3 epilayer is down to 3 nm. Meanwhile, a new feature at ~13 K is induced in the aged samples, and the high field studies reveal its relevance to superconductivity. The resistance of all as-grown and aged heterostructures, just below the superconducting transition temperature follows the Arrhenius relation, indicating the thermally activated flux flow behavior at the interface of Bi2Te3 and FeTe. Moreover, the activation energy exhibits a logarithmic dependence on the magnetic field, providing a compelling evidence for the 2D vortex dynamics in this novel system. The weak disorder associated with aging-induced Te vacancies is possibly responsible for these observed phenomena.

La(1-x)Bi(1+x)S3 (x ≈ 0.08): An n-Type Semiconductor

The new bismuth chalcogenide La(0.92)Bi(1.08)S3 crystallizes in the monoclinic space group C2/m with a = 28.0447(19) Å, b = 4.0722(2) Å, c = 14.7350(9) Å, and β = 118.493(5)°. The structure of La(0.92)Bi(1.08)S3 is built of NaCl-type Bi2S5 blocks and BiS4 and LaS5 infinitely long chains, forming a compact three-dimensional framework with parallel tunnels. Optical spectroscopy and resistivity measurements reveal a semiconducting behavior with a band gap of ∼1 eV and activation energy for transport of 0.36(1) eV. Thermopower measurements suggest the majority carriers of La(0.92)Bi(1.08)S3 are electrons. Heat capacity measurements indicate no phase transitions from 2 to 300 K. Band structure calculations at the density functional theory level confirm the semiconducting nature and the indirect gap of La(0.92)Bi(1.08)S3.

Unconventional Superconductivity in YPtBi and Related Topological Semimetals

YPtBi, a topological semimetal with a very low carrier density, was recently found to be superconducting below T_{c}=0.77  K. In conventional theory, the nearly vanishing density of states around the Fermi level would imply a vanishing electron-phonon coupling and would, therefore, not allow for superconductivity. Based on relativistic density-functional theory calculations of the electron-phonon coupling in YPtBi, it is found that carrier concentrations of more than 10^{21}  cm^{-3} are required to explain the observed critical temperature with the conventional pairing mechanism, which is several orders of magnitude larger than experimentally observed. It is very likely that an unconventional pairing mechanism is responsible for the superconductivity in YPtBi and related topological semimetals with half-Heusler structure.

Electronic structure and relaxation dynamics in a superconducting topological material

Topological superconductors host new states of quantum matter which show a pairing gap in the bulk and gapless surface states providing a platform to realize Majorana fermions. Recently, alkaline-earth metal Sr intercalated Bi2Se3 has been reported to show superconductivity with a Tc ~ 3 K and a large shielding fraction. Here we report systematic normal state electronic structure studies of Sr0.06Bi2Se3 (Tc ~ 2.5 K) by performing photoemission spectroscopy. Using angle-resolved photoemission spectroscopy (ARPES), we observe a quantum well confined two-dimensional (2D) state coexisting with a topological surface state in Sr0.06Bi2Se3. Furthermore, our time-resolved ARPES reveals the relaxation dynamics showing different decay mechanism between the excited topological surface states and the two-dimensional states. Our experimental observation is understood by considering the intra-band scattering for topological surface states and an additional electron phonon scattering for the 2D states, which is responsible for the superconductivity. Our first-principles calculations agree with the more effective scattering and a shorter lifetime of the 2D states. Our results will be helpful in understanding low temperature superconducting states of these topological materials.

A combined method for synthesis of superconducting Cu doped Bi2Se3

We present a two-step technique for the synthesis of superconducting CuxBi2Se3. Cu0.15Bi2Se3 single crystals were synthesized using the melt-growth method. Although these samples are non-superconducting, they can be employed to generate high quality superconducting samples if used as precursors in the following electrochemical synthesis step. Samples made from Cu0.15Bi2Se3 reliably exhibit zero-resistance even under the non-optimal quenching condition, while samples made from pristine Bi2Se3 require fine tuning of the quenching conditions to achieve similar performance. Moreover, under the optimal quenching condition, the average superconducting shielding fraction was still lower in the samples made from pristine Bi2Se3 than in the samples made from Cu0.15Bi2Se3. These results suggest that the pre-doped Cu atoms facilitate the formation of a superconducting percolation network. We also discuss the useful clues that we gathered about the locations of Cu dopants that are responsible for superconductivity.

Spin-orbit coupling enhanced superconductivity in Bi-rich compounds ABi₃ (A = Sr and Ba)

Recently, Bi-based compounds have attracted attentions because of the strong spin-orbit coupling (SOC). In this work, we figured out the role of SOC in ABi₃ (A = Sr and Ba) by theoretical investigation of the band structures, phonon properties, and electron-phonon coupling. Without SOC, strong Fermi surface nesting leads to phonon instabilities in ABi₃. SOC suppresses the nesting and stabilizes the structure. Moreover, without SOC the calculation largely underestimates the superconducting transition temperatures (T_c), while with SOC the calculated T_c are very close to those determined by measurements on single crystal samples. The SOC enhanced superconductivity in ABi₃ is due to not only the SOC induced phonon softening, but also the SOC related increase of electron-phonon coupling matrix elements. ABi₃ can be potential platforms to construct heterostructure of superconductor/topological insulator to realize topological superconductivity.

Pyridine intercalated Bi2Se3 heterostructures: controlling the topologically protected states

We use ab initio simulations to investigate the incorporation of pyridine molecules (C5H5N) in the van der Waals (vdW) gaps of Bi2Se3. The intercalated pyridine molecules increase the separation distance between the Bi2Se3 quintuple layers (QLs), suppressing the parity inversion of the electronic states at the Γ-point. We find that (i) the intercalated region becomes a trivial insulator. By combining the pristine Bi2Se3 region with the one intercalated by the molecules (py-Bi2Se3), we have a trivial/topological heterojunction (py-Bi2Se3/Bi2Se3) characterized by the presence of topologically protected metallic states at the interfacial region. Next, (ii) we apply an external compressive pressure to the system, and the results are a decrease of the separation distance between the QLs intercalated by pyridine molecules, and the metallic states are shifted toward the bulk region, turning the system back to the insulator. Our findings indicate that, through the intercalation of pyridine molecules in Bi2Se3 [(i)], we may have a number of topologically protected metallic channels embedded in (py-Bi2Se3) m /(Bi2Se3) n heterostructures/superlattices, in addition, through suitable tuning of the external pressure [(ii)], we can control its topological properties, turning on and off the topologically protected metallic states in (py-Bi2Se3)m /(Bi2Se3)n.

Tuning the Fermi level with topological phase transition by internal strain in a topological insulator Bi2Se3 thin film

In a three-dimensional topological insulator Bi2Se3, a stress control for band gap manipulation was predicted but no systematic investigation has been performed yet due to the requirement of large external stress. We report herein on the strain-dependent results for Bi2Se3 films of various thicknesses that are grown via a self-organized ordering process. Using small angle X-ray scattering and Raman spectroscopy, the changes of d-spacings in the crystal structure and phonon vibration shifts resulted from stress are clearly observed when the film thickness is below ten quintuple layers. From the UV photoemission/inverse photoemission spectroscopy (UPS/IPES) results and ab initio calculations, significant changes of the Fermi level and band gap were observed. The deformed band structure also exhibits a Van Hove singularity at specific energies in the UV absorption experiment and ab initio calculations. Our results, including the synthesis of a strained ultrathin topological insulator, suggest a new direction for electronic and spintronic applications for the future.

Intercalation in two-dimensional transition metal chalcogenides

We review various exfoliation methods and extensive tuning of chemical and physical properties for 2D layered nanomaterials based on intercalation chemistry.

Electronic structure, low-temperature transport and thermodynamic properties of polymorphic β-As2Te3

The first-order lattice distortion undergone by β-As₂Te₃ around 200 K results in a cycling effect on its transport properties.

Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals

Three-dimensional (3D) Dirac semimetals, which possess 3D linear dispersion in the electronic structure as a bulk analogue of graphene, have lately generated widespread interest in both materials science and condensed matter physics. Recently, crystalline Cd3As2 has been proposed and proved to be a 3D Dirac semimetal that can survive in the atmosphere. Here, by using point contact spectroscopy measurements, we observe exotic superconductivity around the point contact region on the surface of Cd3As2 crystals. The zero-bias conductance peak (ZBCP) and double conductance peaks (DCPs) symmetric around zero bias suggest p-wave-like unconventional superconductivity. Considering the topological properties of 3D Dirac semimetals, our findings may indicate that Cd3As2 crystals under certain conditions could be topological superconductors, which are predicted to support Majorana zero modes or gapless Majorana edge/surface modes in the boundary depending on the dimensionality of the material.

Topological phase transition in quasi-one dimensional organic conductors

We explore topological phase transition, which involves the energy spectra of field-induced spin-density-wave (FISDW) states in quasi-one dimensional (Q1D) organic conductors, using an extended Su-Schrieffer-Heeger (SSH) model. We show that, in presence of half magnetic-flux FISDW state, the system exhibits topologically nontrivial phases, which can be characterized by a nonzero Chern number. The nontrivial evolution of the bulk bands with chemical potential in a topological phase transition is discussed. We show that the system can have a similar phase diagram which is discussed in the Haldane's model. We suggest that the topological feature should be tested experimentally in this organic system. These studies enrich the theoretical research on topologically nontrivial phases in the Q1D lattice system as compared to the Haldane topological phase appearing in the two-dimensional lattices.

Topologically protected surface states in a centrosymmetric superconductor β-PdBi2

The topological aspects of electrons in solids can emerge in real materials, as represented by topological insulators. In theory, they show a variety of new magneto-electric phenomena, and especially the ones hosting superconductivity are strongly desired as candidates for topological superconductors. While efforts have been made to develop possible topological superconductors by introducing carriers into topological insulators, those exhibiting indisputable superconductivity free from inhomogeneity are very few. Here we report on the observation of topologically protected surface states in a centrosymmetric layered superconductor, β-PdBi₂, by utilizing spin- and angle-resolved photoemission spectroscopy. Besides the bulk bands, several surface bands are clearly observed with symmetrically allowed in-plane spin polarizations, some of which crossing the Fermi level. These surface states are precisely evaluated to be topological, based on the Z₂ invariant analysis in analogy to three-dimensional strong topological insulators. β-PdBi₂ may offer a solid stage to investigate the topological aspect in the superconducting condensate.

Materials possessing topologically non-trivial electronic surface states are predicted to host exotic Majorana fermion excitations in the superconducting state. Here, the authors demonstrate the existence of topologically-protected surface states in the centrosymmetric layered superconductor β-PdBi2.

Ultrasensitive nonlinear absorption response of large-size topological insulator and application in low-threshold bulk pulsed lasers

Dirac-like topological insulators have attracted strong interest in optoelectronic application because of their unusual and startling properties. Here we report for the first time that the pure topological insulator Bi₂Te₃ exhibited a naturally ultrasensitive nonlinear absorption response to photoexcitation. The Bi₂Te₃ sheets with lateral size up to a few micrometers showed extremely low saturation absorption intensities of only 1.1 W/cm² at 1.0 and 1.3 μm, respectively. Benefiting from this sensitive response, a Q-switching pulsed laser was achieved in a 1.0 μm Nd:YVO₄ laser where the threshold absorbed pump power was only 31 mW. This is the lowest threshold in Q-switched solid-state bulk lasers to the best of our knowledge. A pulse duration of 97 ns was observed with an average power of 26.1 mW. A Q-switched laser at 1.3 μm was also realized with a pulse duration as short as 93 ns. Moreover, the mode locking operation was demonstrated. These results strongly exhibit that Bi₂Te₃ is a promising optical device for constructing broadband, miniature and integrated high-energy pulsed laser systems with low power consumption. Our work clearly points out a significantly potential avenue for the development of two-dimensional-material-based broadband ultrasensitive photodetector and other optoelectronic devices.

Emergent surface superconductivity in the topological insulator Sb2Te3

Surfaces of three-dimensional topological insulators have emerged as one of the most remarkable states of condensed quantum matter where exotic electronic phases of Dirac particles should arise. Here we report on superconductivity in the topological insulator Sb2Te3 with transition to zero resistance induced through a minor tuning of growth chemistry that depletes bulk conduction channels. The depletion shifts Fermi energy towards the Dirac point as witnessed by a factor of 300 reduction of bulk carrier density and by the largest carrier mobility (≳25,000 cm(2) V(-1) s(-1)) found in any topological material. Direct evidence from transport, the unprecedentedly large diamagnetic screening, and the presence of ∼25 meV gaps detected by scanning tunnelling spectroscopy reveal the superconducting condensate to emerge first in surface puddles, with the onset of global phase coherence at ∼9 K. The rich structure of this state lends itself to manipulation via growth conditions and the material parameters such as Fermi velocity and mean free path.

Observation of correlated spin-orbit order in a strongly anisotropic quantum wire system

Quantum wires with spin-orbit coupling provide a unique opportunity to simultaneously control the coupling strength and the screened Coulomb interactions where new exotic phases of matter can be explored. Here we report on the observation of an exotic spin-orbit density wave in Pb-atomic wires on Si(557) surfaces by mapping out the evolution of the modulated spin-texture at various conditions with spin- and angle-resolved photoelectron spectroscopy. The results are independently quantified by surface transport measurements. The spin polarization, coherence length, spin dephasing rate and the associated quasiparticle gap decrease simultaneously as the screened Coulomb interaction decreases with increasing excess coverage, providing a new mechanism for generating and manipulating a spin-orbit entanglement effect via electronic interaction. Despite clear evidence of spontaneous spin-rotation symmetry breaking and modulation of spin-momentum structure as a function of excess coverage, the average spin polarization over the Brillouin zone vanishes, indicating that time-reversal symmetry is intact as theoretically predicted.

A Roadmap for Controlled Production of Topological Insulator Nanostructures and Thin Films

The group V-VI chalcogenide semiconductors (Bi2 Se3 , Bi2 Te3 , and Sb2 Te3 ) have long been known as thermoelectric materials. Recently, they have been once more generating interest because Bi2 Se3 , Bi2 Te3 and Sb2 Te3 have been crowned as 3D topological insulators (TIs), which have insulating bulk gaps and metallic Dirac surface states. One big challenge in the study of TIs is the lack of high-quality materials with few defects and insulating bulk states. To manifest the topological surface states, it is critical to suppress the contribution from the bulk carriers. Controlled production of TI nanostructures that have a large surface-to-volume ratio is an efficient way to reduce the bulk conductance and to significantly enhance the topological surface conduction. In this review article, the recent progress on the preparation of TI nanostructures is highlighted. Basic production methods for TI nanostructures are introduced in detail. Furthermore, several specific production approaches to reduce the residual bulk carriers from defects are summarized. Finally, the progress and the prospects of the production of TI-based heterostructures, which hold promise in both fundamental study and novel applications are discussed.

Superconductivity in the surface states of a Bi2X3 topological insulator: effects of a realistic model

Superconductivity in the topological surface states is essential to both the surface spectrum of bulk superconducting state and the proximity-induced superconductivity of Bi2X3 (X is Se or Te) topological insulators. While previous theories were mostly based on simplified models for the bulk topological insulator and the surface states, the accumulating experiments stimulate us to make an analysis using realistic model for the normal state electronic structures, incorporating terms responsible for particle–hole asymmetry and hexagonal warping. An effective low-energy model for the topological surface states is derived first. Then we identify all the bulk time-reversal-invariant superconducting pairings in the topological insulator that can open a gap in the topological surface states. Many more pairings are found to be able to gap the topological surface states as compared to conclusions based on simplified models. The number of proximity-induced pairing channels in the topological surface states increases by one as a result of the hexagonal warping term, but is not changed by the particle–hole asymmetry term.

Effect of pressure on superconductivity in the indium-doped topological crystalline insulator SnTe

We report on the impact of hydrostatic pressure on the superconductivity of optimally (indium)-doped SnTe which is established to be derived from a topological crystalline insulating phase. Single crystals of Sn(1-x)In(x)Te were synthesized by a modified Bridgman method that exhibited maximum superconducting Tc of 4.4 K for x = 0.5. Hydrostatic pressure up to 2.5 GPa was applied on the crystals of Sn0.5In0.5Te, and electrical resistivity as a function of temperature and pressure was measured. We observed a decrease in the onset superconducting transition temperature from 4.4 K to 2.8 K on increasing pressure from ambient to 2.5 GPa. The normal state resistivity also decreased abruptly by an order of magnitude at 0.5 GPa but for higher pressures, it decreased marginally. From onset, offset and zero resistivity values, dTc/dP of ∼ -0.6 K GPa(-1) was confirmed. The low temperature normal state resistivity followed T(2) dependence suggesting Fermi liquid behaviour both for ambient and high pressure data. This increase in metallic characteristics accompanied by normal state Fermi liquid behaviour is in accordance with a 'dome structure' for Tc variation with varying carrier concentration.

Topological RPdBi half-Heusler semimetals: A new family of noncentrosymmetric magnetic superconductors

We report superconductivity and magnetism in a new family of topological semimetals, the ternary half-Heusler compound RPdBi (R: rare earth). In this series, tuning of the rare earth f-electron component allows for simultaneous control of both lattice density via lanthanide contraction and the strength of magnetic interaction via de Gennes scaling, allowing for a unique tuning of the normal-state band inversion strength, superconducting pairing, and magnetically ordered ground states. Antiferromagnetism with ordering vector (½,½,½) occurs below a Néel temperature that scales with de Gennes factor dG, whereas a superconducting transition is simultaneously supressed with increasing dG. With superconductivity appearing in a system with noncentrosymmetric crystallographic symmetry, the possibility of spin-triplet Cooper pairing with nontrivial topology analogous to that predicted for the normal-state electronic structure provides a unique and rich opportunity to realize both predicted and new exotic excitations in topological materials.

Effective low-energy theory for superconducting topological insulators

Candidate pairings of superconducting topological insulators support interesting surface Andreev bound states (SABSs) known as Majorana fermions. As these materials are described by a two-orbital Bernevig-Hughes-Zhang type model, a general understanding of the low-energy physics such as the possible kinds of SABSs are difficult. By virtue of an analogy between a topological insulator and a time reversal invariant topological superconductor, we propose a simple and intuitive method of constructing the low-energy effective models for superconducting topological insulators like CuxBi2Se3. Depending on the value of the chemical potential and for experimentally relevant model parameters, the low-energy properties of these superconductors are shown to be determined by one copy or two copies of single-orbital effective models. If the effective pairing potential shows sign reversal upon reflection by the surface, one Kramers' pair or two Kramers' pairs of SABSs are expected to appear. Explicit analytical calculations in terms of the effective low energy model reproduce the dispersions of the numerically confirmed two pairs of SABSs for a commonly studied pairing.

Electron-phonon coupling and its implication for the superconducting topological insulators

The recent observation of superconductivity in doped topological insulators has sparked a flurry of interest due to the prospect of realizing the long-sought topological superconductors. Yet the understanding of underlying pairing mechanism in these systems is far from complete. Here we investigate this problem by providing robust first-principles calculations of the role of electron-phonon coupling for the superconducting pairing in the prime candidate Cu_xBi₂Se₃. Our results show that electron-phonon scattering process in this system is dominated by zone center and boundary optical modes, with coexistence of phonon stiffening and softening. While the calculated electron-phonon coupling constant λ suggests that T_c from electron-phonon coupling is 2 orders smaller than the ones reported on bulk inhomogeneous samples, suggesting that superconductivity may not come from pure electron-phonon coupling. We discuss the possible enhancement of superconducting transition temperature by local inhomogeneity introduced by doping.

Triplet superconductivity in 3D Dirac semi-metal due to exchange interaction

Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi-metal. Investigation of the order parameters and energies of these states at zero temperature in a wide range of values of chemical potential μ, the effective electron-electron coupling constant λ and Debye energy TD demonstrates that when the exchange interaction is neglected the singlet always prevails, however, in significant portions of the (μ, λ, TD) parameter space the energy difference is very small. This means that interactions that are small, but discriminate between the spin singlet and the spin triplet, are important in order to determine the nature of the superconducting order there. The best candidate for such an interaction in the materials under consideration is the exchange (the Stoner term) characterized by constant λex. We show that at values of λex, much smaller than ones creating Stoner instability to ferromagnetism λex ∼ 1, the triplet pairing becomes energetically favored over the singlet ones. The 3D quantum critical point at μ = 0 is considered in detail. This can be realized experimentally in optically trapped cold atom systems.

Two-dimensional layered chalcogenides: from rational synthesis to property control via orbital occupation and electron filling

Electron occupation of orbitals in two-dimensional (2D) layered materials controls the magnitude and anisotropy of the interatomic electron transfer and exerts a key influence on the chemical bonding modes of 2D layered lattices. Therefore, their orbital occupations are believed to be responsible for massive variations of the physical and chemical properties from electrocatalysis and energy storage, to charge density waves, superconductivity, spin-orbit coupling, and valleytronics. Especially in nanoscale structures such as nanoribbons, nanoplates, and nanoflakes, 2D layered materials provide opportunities to exploit new quantum phenomena. In this Account, we report our recent progress in the rational design and chemical, electrochemical, and electrical modulations of the physical and chemical properties of layered nanomaterials via modification of the electron occupation in their electronic structures. Here, we start with the growth and fabrication of a group of layered chalcogenides with varied orbital occupation (from 4d/5d electron configuration to 5p/6p electron configuration). The growth techniques include bottom-up methods, such as vapor-liquid-solid growth and vapor-solid growth, and top-down methods, such as mechanical exfoliation with tape and AFM tip scanning. Next, we demonstrate the experimental strategies for the tuning of the chemical potential (orbital occupation tuned with electron filling) and the resulting modulation of the electronic states of layered materials, such as electric-double-layer gating, electrochemical intercalation, and chemical intercalation with molecule and zerovalence metal species. Since the properties of layered chalcogenides are normally dominated by the specific band structure around which the chemical potential is sitting, their desired electronic states and properties can be modulated in a large range, showing unique phenomena including quantum electronic transport and extraordinary optical transmittance. As the most important part of this Account, we further demonstrate some representative examples for the tuning of catalytic, optical, electronic, and spintronic properties of 2D layered chalcogenides, where one can see not only edge-state induced enhancement of catalysis, quantum Aharonov-Bohm interference of the topological surface states, intercalation modulated extraordinary transmittance, and surface plasmonics but also external gating induced superconductivity and spin-coupled valley photocurrent. Since our findings reflect the critical influences of the electron filling of orbital occupation to the properties in 2D layered chalcogenides, we thus last highlight the importance and the prospective of orbital occupation in 2D layered materials for further exploring potential functionalized applications.

BaCu2Se2 based compounds as promising thermoelectric materials

The thermoelectric properties of Na doped BaCu₂Se₂ were studied. The electrical conductivity of BaCu₂Se₂ was increased by 2 orders of magnitude through Na doping at the Ba sites, combined with a surprisingly low thermal conductivity; a ZT of 1.0 has been obtained for Ba_0.925Na_0.075Cu₂Se₂ at 773 K.

Physical and chemical tuning of two-dimensional transition metal dichalcogenides

The development of two-dimensional (2D) materials has been experiencing a renaissance since the adventure of graphene. Layered transition metal dichalcogenides (TMDs) are now playing increasingly important roles in both fundamental studies and technological applications due to their wide range of material properties from semiconductors, metals to superconductors. However, a material with fixed properties may not exhibit versatile applications. Due to the unique crystal structures, the physical and chemical properties of 2D TMDs can be effectively tuned through different strategies such as reducing dimensions, intercalation, heterostructure, alloying, and gating. With the flexible tuning of properties 2D TMDs become attractive candidates for a variety of applications including electronics, optoelectronics, catalysis, and energy.

Topological crystalline insulator nanostructures

Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators such as Bi₂Se₃ and Bi₂Te₃, topological crystalline insulators also possess surface states with exotic electronic properties such as spin-momentum locking and Dirac dispersion. Experimentally verified topological crystalline insulators to date are SnTe, Pb₁-xSnxSe, and Pb₁-xSnxTe. Because topological protection comes from the crystal symmetry, magnetic impurities or in-plane magnetic fields are not expected to open a gap in the surface states in topological crystalline insulators. Additionally, because they have a cubic structure instead of a layered structure, branched structures or strong coupling with other materials for large proximity effects are possible, which are difficult with layered Bi₂Se₃ and Bi₂Te₃. Thus, additional fundamental phenomena inaccessible in three-dimensional topological insulators can be pursued. In this review, topological crystalline insulator SnTe nanostructures will be discussed. For comparison, experimental results based on SnTe thin films will be covered. Surface state properties of topological crystalline insulators will be discussed briefly.

Superconductivity in strong spin orbital coupling compound Sb₂Se₃

Recently, A₂B₃ type strong spin orbital coupling compounds such as Bi₂Te₃, Bi₂Se₃ and Sb₂Te₃ were theoretically predicated to be topological insulators and demonstrated through experimental efforts. The counterpart compound Sb₂Se₃ on the other hand was found to be topological trivial, but further theoretical studies indicated that the pressure might induce Sb₂Se₃ into a topological nontrivial state. Here, we report on the discovery of superconductivity in Sb₂Se₃ single crystal induced via pressure. Our experiments indicated that Sb₂Se₃ became superconductive at high pressures above 10 GPa proceeded by a pressure induced insulator to metal like transition at ~3 GPa which should be related to the topological quantum transition. The superconducting transition temperature (T_C) increased to around 8.0 K with pressure up to 40 GPa while it keeps ambient structure. High pressure Raman revealed that new modes appeared around 10 GPa and 20 GPa, respectively, which correspond to occurrence of superconductivity and to the change of T_C slop as the function of high pressure in conjunction with the evolutions of structural parameters at high pressures.

Scanning tunneling microscopy studies of topological insulators

Scanning tunneling microscopy (STM), with surface sensitivity, is an ideal tool to probe the intriguing properties of the surface state of topological insulators (TIs) and topological crystalline insulators (TCIs). We summarize the recent progress on those topological phases revealed by STM studies. STM observations have directly confirmed the existence of the topological surface states and clearly revealed their novel properties. We also discuss STM work on magnetic doped TIs, topological superconductors and crystalline symmetry-protected surface states in TCIs. The studies have greatly promoted our understanding of the exotic properties of the new topological phases, as well as put forward new challenges. STM will continue to play an important role in this rapidly growing field from the point view of both fundamental physics and applications.

Topological transport and atomic tunnelling-clustering dynamics for aged Cu-doped Bi2Te3 crystals

Enhancing the transport contribution of surface states in topological insulators is vital if they are to be incorporated into practical devices. Such efforts have been limited by the defect behaviour of Bi₂Te₃ (Se₃) topological materials, where the subtle bulk carrier from intrinsic defects is dominant over the surface electrons. Compensating such defect carriers is unexpectedly achieved in (Cu_0.1Bi_0.9)₂Te_3.06 crystals. Here we report the suppression of the bulk conductance of the material by four orders of magnitude by intense ageing. The weak antilocalization analysis, Shubnikov–de Haas oscillations and scanning tunnelling spectroscopy corroborate the transport of the topological surface states. Scanning tunnelling microscopy reveals that Cu atoms are initially inside the quintuple layers and migrate to the layer gaps to form Cu clusters during the ageing. In combination with first-principles calculations, an atomic tunnelling–clustering picture across a diffusion barrier of 0.57 eV is proposed.

Enhancing the transport properties of surface states in topological insulators is vital if they are to be incorporated into practical devices. Towards this end, Chen et al. study the transport in aged (Cu_0.1Bi_0.9)₂Te_3.06, where the ageing process suppresses bulk conductance by up to four orders of magnitude.

Absence of a proximity effect for a thin-films of a Bi2Se3 topological insulator grown on top of a Bi2Sr2CaCu2O(8+δ) cuprate superconductor

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.

Dirac and Weyl superconductors in three dimensions

We introduce the concept of three-dimensional Dirac (Weyl) superconductors (SC), which have protected bulk fourfold (twofold) nodal points and surface Majorana arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontrivial. Breaking mirror symmetry may gap Dirac nodes producing a topological SC. Each Dirac node evolves to a nodal ring when inversion-gauge symmetry is broken, whereas it splits into a pair of Weyl nodes when, and only when, time-reversal symmetry is broken.

Weak antilocalization effect and noncentrosymmetric superconductivity in a topologically nontrivial semimetal LuPdBi

A large number of half-Heusler compounds have been recently proposed as three-dimensional (3D) topological insulators (TIs) with tunable physical properties. However, no transport measurements associated with the topological surface states have been observed in these half-Heusler candidates due to the dominating contribution from bulk electrical conductance. Here we show that, by reducing the mobility of bulk carriers, a two-dimensional (2D) weak antilocalization (WAL) effect, one of the hallmarks of topological surface states, was experimentally revealed from the tilted magnetic field dependence of magnetoconductance in a topologically nontrivial semimetal LuPdBi. Besides the observation of a 2D WAL effect, a superconducting transition was revealed at T_c ~ 1.7 K in the same bulk LuPdBi. Quantitative analysis within the framework of a generalized BCS theory leads to the conclusion that the noncentrosymmetric superconductivity of LuPdBi is fully gapped with a possibly unconventional pairing character. The co-existence of superconductivity and the transport signature of topological surface states in the same bulk alloy suggests that LuPdBi represents a very promising candidate as a topological superconductor.

Emergence of decoupled surface transport channels in bulk insulating Bi(2)Se(3) thin films

In ideal topological insulator (TI) films the bulk state, which is supposed to be insulating, should not provide any electric coupling between the two metallic surfaces. However, transport studies on existing TI films show that the topological states on opposite surfaces are electrically tied to each other at thicknesses far greater than the direct coupling limit where the surface wave functions overlap. Here, we show that as the conducting bulk channels are suppressed, the parasitic coupling effect diminishes, and the decoupled surface channels emerge as expected for ideal TIs. In Bi(2)Se(3) thin films with fully suppressed bulk states, the two surfaces, which are directly coupled below ∼10  QL, become gradually isolated with increasing thickness and are completely decoupled beyond ∼20  QL. On such a platform, it is now feasible to implement transport devices whose functionality relies on accessing the individual surface layers without any deleterious coupling effects.

Turning a band insulator into an exotic superconductor

Understanding exotic, non-s-wave-like states of Cooper pairs is important and may lead to new superconductors with higher critical temperatures and novel properties. Their existence is known to be possible but has always been thought to be associated with non-traditional mechanisms of superconductivity where electronic correlations play an important role. Here we use a first principles linear response calculation to show that in doped Bi₂Se₃ an unconventional p-wave-like state can be favoured via a conventional phonon-mediated mechanism, as driven by an unusual, almost singular behaviour of the electron–phonon interaction at long wavelengths. This may provide a new platform for our understanding of superconductivity phenomena in doped band insulators.

Most superconductors that exhibit exotic pairing symmetries are derived from host materials that are Mott insulators. Xiangang Wan and Sergey Savrasov show that it may be possible to realize an exotic p-wave superconductor in doped Bi₂Se₃, which is a topological band insulator.

Superconductivity in topological insulator Sb2Te3 induced by pressure

Topological superconductivity is one of most fascinating properties of topological quantum matters that was theoretically proposed and can support Majorana Fermions at the edge state. Superconductivity was previously realized in a Cu-intercalated Bi₂Se₃ topological compound or a Bi₂Te₃ topological compound at high pressure. Here we report the discovery of superconductivity in the topological compound Sb₂Te₃ when pressure was applied. The crystal structure analysis results reveal that superconductivity at a low-pressure range occurs at the ambient phase. The Hall coefficient measurements indicate the change of p-type carriers at a low-pressure range within the ambient phase, into n-type at higher pressures, showing intimate relation to superconducting transition temperature. The first principle calculations based on experimental measurements of the crystal lattice show that Sb₂Te₃ retains its Dirac surface states within the low-pressure ambient phase where superconductivity was observed, which indicates a strong relationship between superconductivity and topology nature.

Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases

We study superconducting states in the presence of spin-orbital coupling and Zeeman field. It is found that a phase transition from a Fulde-Ferrell-Larkin-Ovchinnikov state to the topological superconducting state occurs upon increasing the spin-orbital coupling. The nature of this topological phase transition and its critical property are investigated numerically. Physical properties of the topological superconducting phase are also explored. Moreover, the local density of states is calculated, through which the topological feature may be tested experimentally.

Pressure controlled transition into a self-induced topological superconducting surface state

Ab-initio calculations show a pressure induced trivial-nontrivial-trivial topological phase transition in the normal state of 1T-TiSe2. The pressure range in which the nontrivial phase emerges overlaps with that of the superconducting ground state. Thus, topological superconductivity can be induced in protected surface states by the proximity effect of superconducting bulk states. This kind of self-induced topological surface superconductivity is promising for a realization of Majorana fermions due to the absence of lattice and chemical potential mismatches. For appropriate electron doping, the formation of the topological superconducting surface state in 1T-TiSe2 becomes accessible to experiments as it can be controlled by pressure.

Evidence for topologically protected surface states and a superconducting phase in [Tl4](Tl(1-x)Sn(x))Te3 using photoemission, specific heat, and magnetization measurements, and density functional theory

We report the discovery of surface states in the perovskite superconductor [Tl4]TlTe3 (Tl5Te3) and its nonsuperconducting tin-doped derivative [Tl4](Tl0.4Sn0.6)Te3 as observed by angle-resolved photoemission spectroscopy. Density functional theory calculations predict that the surface states are protected by a Z2 topology of the bulk band structure. Specific heat and magnetization measurements show that Tl5Te3 has a superconducting volume fraction in excess of 95%. Thus Tl5Te3 is an ideal material in which to study the interplay of bulk band topology and superconductivity.

The family of topological phases in condensed matter†

The discovery of topological insulators and superconductors is an important advance in condensed matter physics. Topological phases reflect global properties of the quantum states in materials, and the boundary states are the characteristic of the materials. Such phases constitute a new branch in condensed matter physics. Here a historic development is briefly introduced, and the known family of phases in condensed matter are summarized.