Session T10: Topological Insulators and Superconductors

S-TI-S (Superconductor-Topological Insulator-Superconductor) Josephson junction networks: a platform for exploring and exploiting Majorana fermions for quantum information processing

One of the proposed approaches to realize a quantum computer is to make use of exotic Majorana fermion modes that can exist in hybrid systems which intertwine superconductivity and topological order.  The goal is to take advantage of the delocalization of quantum information and the non-Abelian statistics of the Majorana states to avoid dephasing and minimize error corrections in what is known as topologically-protected quantum computing.  In this talk, I will update our progress on the development of a potential platform for nucleating and manipulating Majorana fermions in multiply-connected networks of lateral Josephson junctions fabricated by depositing superconductor electrodes onto the surface of topological insulators.  In a magnetic field, Majorana fermions are localized in the cores of Josephson vortices at locations in the junction where the phase difference is an odd multiple of π, and they can be moved by applying fields, currents, and voltages to perform quantum operations.  Electronic transport measurements on Nb-Bi₂Se₃-Nb devices exhibit anomalous features consistent with a 4π-periodic sin(φ/2)-component in the Josephson current-phase relation consistent with this picture, evidence for entry features that indicate the presence of localized Majorana states, and bimodal critical current distributions that reveal the parity degree of freedom and the presence of a finite parity lifetime. We are now exploring circuits for imaging, manipulating, fusing, and braiding these exotic excitations and developing schemes for reading out the parity of the Majorana pairs that encodes the quantum information.

 

In collaboration with Guang Yue, Jessica Montone, Gilbert Arias, Drew Wild, Smitha Vishveshwara, and Seongshik Oh (Rutgers).   

Asymmetric Fraunhofer Spectra in a Bi2Se3 Josephson Junction

Josephson junctions with topological insulators as their weak link (S–TI–S junctions) are predicted to host Majorana fermions. But the details of S–TI–S current-phase relations and their interplay with magnetic fields are not completely understood. We fabricate a Bi₂Se₃ junction with NbTi leads and measure Fraunhofer patterns of the junction with applied in-plane fields. We observe Faunhofer patterns with aperiodic node spacings. These asymmetries appear even at zero parallel field and for temperatures up to 1 K. The anomalous features are compared to asymmetric Fraunhofer patterns expected for finite Cooper pair momentum shifts as well as geometric effects, withthe conclusion that geometric effect can dominate. These results are important for differentiating geometrical phase shifts from those caused by Cooper pair momentum shifting, Majorana mode signatures, or other unconventional superconducting behavior.   

Contact transparency for proximity induced superconductivity in 2D topological insulators for qubit fabrication

Proximity induced superconductivity in Bi_xSb_2-xTe₃  using s-wave superconductors is a promising route to developing Majorana based qubits as this hybrid system will behave as a spinless superconductor. The bismuth antimony telluride (BST) has no bulk carriers so a gap in the induced superconductivity would provide a platform for long lived Majorana parity qubits. The strength of the induced superconductivity is strongly dependent on the contact transparency between the TI and the superconductor. We have developed an analytic solution for normal state current flow from the superconducting metal for two geometries, circular and rectangular. Modeling the current flow into the 2D topological material we obtain the junction conductance and contact transparency. The devices are arrays of niobium islands in contact with the BST that produce arrays of Josephson junctions with supercurrents flowing in the proximitized BST. The experimental verification of induced superconductivity is obtained by measuring the differential conductance of the array which exhibits a finite two dimensional supercurrent. Optimizing contacts should lead to stronger proximity induced superconductivity in the BST surface state.     

Emergent Moiré Pattern from Substrate Strain in Heterostructure of PdTe2/Bi2Se3

Topological superconductivity is a highly sought-after phenomena in condensed matter due to the possibility of such novel electronic states hosting massless Majorana fermions. One avenue to realize topological superconductivity is inducing superconductivity (SC) in a topological insulator (TI) via proximity effect with a s-wave superconductor. Via the method of Molecular Beam Epitaxy (MBE), growing ultra-thin heterostructures to proximitize superconductivity with topological surface states has become much easier while also being much more useful in device applications. This method, however, involves substantial interplay between the substrate and growth, which can lead to unique phenomena such as Moiré patterns. Here we report the growth of Type-II Dirac semimetal and superconductor PdTe2 on the TI Bi2Se3. We observe a Moiré pattern whose periodicity is larger than that caused by a lattice mismatch between the conventional lattices. The period of the Moiré pattern decreases with each additional layer grown. This indicates that the periodicity of the substrate causes significant strain to the crystal and a thickness dependent lattice expansion.   

Proximity-induced Superconductivity in Scalable Topological Insulator/Graphene/Gallium heterostructures

Proximity-induced superconductivity in topological insulator (TI)/superconductor (SC) heterostructures is a potential platform to host Majorana zero modes. In this work, we synthesize and study high-quality, large area (Bi,Sb)₂Te₃/graphene(Gr)/2L-Ga heterostructures combining confinement heteroepitaxy (Briggs et al.  Nat. Mater. 19, 637–643 (2020)) and molecular beam epitaxy. This synthetic approach results in atomically sharp interfaces and the growth of the TI film preserves the superconductivity of our two-layer Ga film extremely well with a transition temperature of T_c ~ 4 K. We fabricated lithography-free van der Waals tunnel junctions using thin hexagonal Boron Nitride as tunnel barrier and performed transport tunneling spectroscopy on TI/Gr/Ga heterostructures. The tunneling spectra exhibit temperature and magnetic field dependences associated with two superconducting gaps. One gap agrees with the SC gap of the 2L-Ga. We attribute the second gap to proximity-induced superconductivity in the Dirac surface state of the TI film. In 5QL TI/Gr/Ga films, the induced gap is approximately 0.2 meV, which is about 40% of the SC gap in 2L-Ga. In addition, we observe discrete tunneling conductance jump corresponding to the addition of a single vortex when a magnetic field is applied. Our results open up new avenues for developing epitaxial two-dimensional systems for Majorana braiding and topological quantum computation.   

Quantum interference on a topological insulator surface

Recently, high-quality thin films of cadmium arsenide (Cd₃As₂) have emerged as a promising platform for the observation of quantum transport phenomena and the realization of new topological states.  Electronic quantum interference is a key ingredient in several approaches for topological quantum information processing.  Here, we report on two distinct quantum interference phenomena, namely an Aharonov–Bohm (AB)-like effect and Fabry-Perot reflections, in nanoscale p-n junctions fabricated on thin films of Cd₃As₂, which are in a topological insulator-like state.  Conductance oscillations at small magnetic fields are AB-like.  We discuss their origins and connection to the junction regions.  Concurrently, conductance oscillations that are periodic with gate voltage can also be observed.  We discuss these oscillations in terms of the collimating effect of the junctions.      

Searching for ideal topological superconductors in Pb-Sn-In-Te system

The discovery of 3D topological insulator  materials and topological superconductor  open  up a new research field in the condensed matter physics.  In order to search for the topological superconductor, we have grown a large number of the single crystals of  Pb-system ( Pb-Sn-In-Te) topological crystalline insulator  and their topological superconductor .  We have measured the physical properties on these single crystals by various techniques. We have studied the effect of crystal growth condition, impurity and composition on the bulk electrical conductivity of these single crystals. We try to find out which composition and crystal growth condition is the best for the ideal topological insulator,  topological crystalline insulator and  topological superconductor.  We have got the bulk topological superconductor  with T_c=5K.   

Superconducting proximity effect in YB6/SmB6 bilayer thin films

Topological superconductivity has been predicted to arise in a topological insulator (TI) in contact with a trivial superconductor by virtue of proximity effect, harboring Majorana excitations [1]. The topological Kondo insulator SmB₆ is an ideal candidate to explore such TI-based quantum phenomena due to its robust insulating bulk properties as well as the conducting surface states [2]. In this work, we study the superconducting proximity effect using bilayer thin films consisting of SmB₆ and superconducting YB₆ due to their excellent lattice match. The superconducting properties of YB₆ have been reported to be strongly dependent on the stoichiometry [3] with the maximum T_c observed in boron deficient samples. We have grown high quality thin films of SmB₆ and YB₆ by cosputtering method in an ultrahigh-vacuum-compatible chamber. The growth parameters have been optimized through microstructural characterizations and magneto-transport measurements. The induced superconductivity in the SmB₆ thin films has been studied via proximity electron tunneling spectroscopy.

[1] L. Fu & C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008).

[2] M. Dzero et al., Annu. Rev. Condens. Matter Phys. 7, 249 (2016); W. K. Park et al., Proc. Natl. Acad. Sci. U.S.A. 113, 6599 (2016).

[3] N. Sluchanko et al., Phys. Rev. B. 96, 144501 (2017); S. Lee et al., Nature 570, 344–348 (2019).   

Soft-point-contact spectroscopy of the topological nodal-line semimetal candidate SnxNbSe2−δ

Topological superconductors have attracted great interest because of the application for topological quantum computing. Topological superconductivity is induced by an odd parity pairing state [1]. Such a state can be realized in noncentrosymmetric superconductors due to parity mixing. Noncentrostymmetric ABSe₂ (A = Pb/Sn and B = Nb/Ta) compounds are predicted to be promising topological superconductor candidates [2]. We have reported superconductivity with possible odd parity contribution to the gap function in Sn_xNbSe_2−δ with the same structure as ABSe₂ [3]. Here, we employed soft-point-contact spectroscopy of Sn_xNbSe_2−δ with T_c∼13K, which is relatively higher in the known topological superconductor candidates. Extracted magnitude of the superconducting gap of Sn_xNbSe_2−δ from our results using the Blonder, Tinkham and Klapwijk (BTK) model [4] is inconsistent with the weak-coupling BCS theory. We will discuss the evolution of the superconducting gap with temperature and magnetic field to understand the superconducting gap structure of Sn_xNbSe_2−δ .

[1].M.Sato et al,Rep. Prog. Phys. 80 076501(2017)

[2]. P.J. Chen, et al, Phys. Rev. B 94, 165148 (2016)

[3].Riffat Munir et al, J. Phys. Condens. Matter 33, 23LT01(2021)

[4]. G.E. Blonder, et al, Phys. Rev.B 25,7, 4515(1982)   

Theory for conventional superconductivity at the surface of a Weyl semimetal

Recent experiments have seen intrinsic surface superconductivity in Weyl semimetals and thus, posed the question of whether the unusual Fermi arc states can support superconductivity without any proximity effect from the bulk. A conclusive answer is hindered by the absence of a well-defined surface Hamiltonian since the Fermi arcs merge with the bulk states at their end points. We circumvent this issue by adopting an alternate, Green's functions-based approach tailored to a layering model from which arbitrary Fermi arcs can be obtained by tuning phenomenological parameters. We find that Fermi arcs, indeed, can support a standard Cooper instability, and their leakage into the bulk has a negligible effect on the nature of the superconducting state if the bulk Weyl nodes are undoped. In the undoped limit, within mean-field theory, we find a finite critical temperature on the surface while the bulk critical temperature is zero, thus realizing a peculiar situation where the surface of a system orders while the bulk is disordered even though the latter has higher dimensionality.    

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We identify time-reversal symmetry breaking mixed parity superconducting states that feature eight Majorana corner modes in properly cleaved three-dimensional cubic crystals. As we show,  when an odd-parity isotropic p-wave pairing coexists with cubic symmetry preserving even-parity octupolar d_x²-y² +i d_3z²-r² pairing, the gapless surface Majorana modes of the former get localized at the eight corners, thus yielding an intrinsic third-order topological superconductor (TOTSC). A cousin d_xy +i d_3z²-r² pairing also accommodating eight corner Majorana modes, by virtue of breaking the cubic symmetry, in contrast, yields an extrinsic  TOTSC. We identify doped octupolar (topological or trivial) Dirac insulator as the suitable platform to sustain such unconventional superconductors. In particular, our analysis suggests that the doped octupolar Dirac insulator does not need to be topological to accommodate TOTSC. Furthermore, a simple intraunit cell pairing is energetically most favorable topological  pairing in this system. Finally, we argue that the proposed TOTSC can be experimentally realizable in NaCl, Ti₄XTe₃, with X=Pb, Sn, and other structurally similar compounds under high pressure.   

Density functional Bogoliubov-de Gennes calculations for a topological superconductor

The possibility to combine topological electronic band structures and superconductivity (SC) opens new pathways towards engineering exotic quantum matter. Proximity induced superconductivity in the topological surface state of topological insulators (TIs) offers the possibility to realize a chiral p-wave superconductor. Such a superconductor is an exotic state of matter which supports non-Abelian anyons and is of great interest for Majorana-based quantum computing applications [1]. Material-specific insights into the microscopic details of such superconductor/TI interfaces are of great interest and an indispensable ingredient in the challenging materials optimization problem.

Here we first introduce the recent Bogoliubov de-Gennes (BdG) extension to the all electron full potential relativistic Korringa-Kohn-Rostoker (KKR) Green function code JuKKR [2,3]. This KKR-BdG method allows a description of inhomogeneous superconductors on the basis of density functional theory. We apply this method to the s-wave superconductor Nb and study its 110 surface [2]. We then turn to the investigation of the proximity effect in Nb/TI interfaces and discuss the induced superconductivity in the topological surface state of this SC/TI heterostructure.

[1] Masatoshi Sato and Yoichi Ando 2017 Rep. Prog. Phys. 80 076501 

[2] Philipp Rüßmann and Stefan Blügel, Density functional Bogoliubov-de Gennes analysis of superconducting Nb and Nb(110) surfaces. arXiv:2110.01713 (2021)

[3] https://jukkr.fz-juelich.de   

Higher-Order Topological Phases in Point-Group Symmetric Superconductors

The search of platforms hosting Majorana zero modes is one of the central issues to achieving topological qubits. One of the newest venues explored to this end is higher-order topological superconductivity. In this talk, we consider a point-group symmetric quantum anomalous Hall system with proximity-induced s-wave superconductivity, that is well-known to host chiral/helical Majorana edge states. We find that as we tune the parameters of chemical potential and superconducting pairing magnitude, higher-order topological Majorana states arise at the corners of the system protected by the underlying rotational point-group symmetry.  We further discuss a method to probe the stability and transport properties of these emergent corner states so as to provide a connection with experimental realizations. Our results point to a parallel path to engineer and manipulate Majorana fermions in topological superconductors with point-group symmetries.