Time-reversal Invariant Topological Superconductivity Research Articles

Topological phases of strongly interacting time-reversal invariant topological superconducting chains under a magnetic field

Topological phases of strongly interacting time-reversal invariant topological superconducting chains under a magnetic field

Three-dimensional time reversal invariant topological superconductivity in doped chiral topological semimetals

Chiral topological semimetals host multifold degenerate band crossing points under the protection of crystalline symmetries. In this paper, we suggest that the recently discovered chiral topological semimetals in space group 198, parts of which are superconducting upon doping, can be new candidates of time reversal invariant topological superconductors. By investigating the Fermi surfaces around the band crossing points that carry nonzero Chern numbers, we clarify how the nontrivial topology of chiral topological semimetals affects their superconducting state and show the existence of topological superconductivity in $s_\pm$-wave pairing with surface Majorana fermions. We further demonstrate that the topological superconductivity is favored by the inter-unit-cell phonon-mediated electron-electron interaction.

Time-reversal invariant topological superconductivity in planar Josephson bijunction

We consider a Josephson bijunction consisting of a thin $SIS$ $\pi$-Josephson junction sandwiched between two-dimensional semiconducting layers with strong Rashba spin-orbit interaction. Each of these layers forms an $SNS$ junction due to proximity-induced superconductivity. The $SIS$ junction is assumed to be thin enough such that the two Rashba layers are tunnel-coupled. We show that, by tuning external gates, this system can be controllably brought into a time-reversal invariant topological superconducting phase with a Kramers pair of Majorana bound states being localized at the end of the normal region for a large parameter phase space. In particular, in the strong spin-orbit interaction limit, the topological phase can be accessed already in the regime of small tunneling amplitudes.

Topological superconductivity from transverse optical phonons in oxide heterostructures

A topological superconductor features at its boundaries and vortices Majorana fermions, which are potentially applicable for topological quantum computations. The scarcity of the known experimentally verified physical systems with topological superconductivity, time-reversal invariant ones in particular, is giving rise to a strong demand for identifying new candidate materials. In this research, we study a heterostructure consisting of a transition metal oxide two-dimensional electron gas (2DEG) sandwiched by insulators near the paraelectric (PE) / ferroelectric (FE) phase transition. Its relevant characteristics is the combination of the transition metal spin-orbit coupling and the soft odd-parity phonons arising from the ferroelectric fluctuation; it gives rise to the fluctuating Rashba effect, which can mediate the pairing interaction for time-reversal invariant topological superconductivity. As the PE / FE phase transition can be driven by applying strain on the heterostructure, this system provides a tunable electron-phonon coupling. Through the first-principle calculations on the (001) [BaOsO3][BaTiO3]4, we find such electron-phonon coupling to be strong over a wide range of applied tensile bi-axial strain in the monolayer BaOsO3 sandwiched between the (001) BaTiO3, hence qualifying it as a good candidate material. Furthermore, the stability of topological superconductivity in this material is enhanced by its orbital physics that gives rise to the anisotropic dispersion.

Proximity induced time-reversal topological superconductivity in Bi2Se3 films without phase tuning

Many proposals to generate a time-reversal invariant topological superconducting phase are based on imposing a $\pi$ phase difference between the superconducting leads proximitizing a nanostructure. We show that this phase can be induced on a thin film of a topological insulator like Bi$_2$Se$_3$ in proximity to a single s-wave superconductor. In our analysis we take into account the parity degree of freedom of the electronic states which is not included in effective Dirac-like surface theories. We find that the topological phase can be reached when the induced interparity pairing dominates over the intraparity one. Application of an electric field perpendicular to the film extends the range of parameters where the topological phase occurs.

Singlet s± -wave pairing in quasi-one-dimensional ACr3As3(A=K,Rb,Cs) superconductors

The recent discovery of quasi-one-dimensional Chromium-based superconductivity has generated much excitement. We study in this work the superconducting instabilities of a representative compound, the newly synthesized KCr$_3$As$_3$ superconductor. Based on inputs from density functional theory calculations, we first construct an effective multi-orbital tight-binding Hamiltonian to model its low-energy band structure. We then employ standard random-phase approximation calculations to investigate the superconducting instabilities of the resultant multi-orbital Hubbard model. We find various pairing symmetries in the phase diagram in different interaction parameter regimes, including the triplet $f$-wave, $p_z$-wave and singlet $s^\pm$-wave pairings. We argue that the singlet $s^\pm$-wave pairing, which emerges at intermediate interaction strength, is realized in this material. This singlet pairing is driven by spin-density wave fluctuations enhanced by Fermi-surface nesting. We point out that phase-sensitive measurement can distinguish the $s$-wave pairing in KCr$_3$As$_3$ from the $p_z$-wave previously proposed for a related compound K$_2$Cr$_3$As$_3$. The $s^{\pm}$-wave pairing in KCr$_3$As$_3$ shall also exhibit a subgap spin resonance mode near the nesting vector, which can be tested by inelastic neutron scattering measurements. Another intriguing property of the $s^\pm$-pairing is that it can induce time-reversal invariant topological superconductivity in a semiconductor wire with large Rashba spin-orbit coupling via proximity effect. Our study shall be of general relevance to all superconductors in the family of ACr$_3$As$_3$ (A=K, Rb, Cs).

Strong antisymmetric spin–orbit coupling and superconducting properties: the case of noncentrosymmetric LaPtSi

In this work we aim to analyze the effect of a strong antisymmetric spin–orbit coupling (ASOC) on the superconductivity of noncentrosymmetric LaPtSi. We study the energy gap structure of polycrystalline LaPtSi by using magnetic penetration depth measurements down to 0.02Tc. We observed a dirty s-wave behavior, which provides compelling evidence that the spin-singlet component of the mixed pairing state is highly dominant. This is consistent with previous results in the sense that the mere presence of a strong ASOC does not lead to unconventional behaviors. Our result also downplays LaPtSi as a good candidate for realizing time-reversal invariant topological superconductivity.

Fractional Spin and Josephson Effect in Time-Reversal-Invariant Topological Superconductors.

Time-reversal-invariant topological superconducting (TRITOPS) wires are known to host a fractional spin ℏ/4 at their ends. We investigate how this fractional spin affects the Josephson current in a TRITOPS-quantum dot-TRITOPS Josephson junction, describing the wire in a model that can be tuned between a topological and a nontopological phase. We compute the equilibrium Josephson current of the full model by continuous-time MonteCarlo simulations and interpret the results within an effective low-energy theory. We show that in the topological phase, the 0-to-π transition is quenched via formation of a spin singlet from the quantum-dot spin and the fractional spins associated with the two adjacent topological superconductors.

High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity

We study possible applications of high critical temperature nodal superconductors for the search for Majorana bound states in the DIII class. We propose a microscopic analysis of the proximity effect induced by d-wave superconductors on a semiconductor wire with strong spin-orbit coupling. We characterize the induced superconductivity on the wire employing a numerical self-consistent tight-binding Bogoliubov-de Gennes approach, and analytical considerations on the Green's function. The order parameter induced on the wire, the pair correlation function, and the renormalization of the Fermi points are analyzed in detail, as well as the topological phase diagram in the case of weak coupling. We highlight optimal Hamiltonian parameters to access the nontrivial topological phase which could display time-reversal invariant Majorana doublets at the boundaries of the wire.

Interaction-driven topological superconductivity in one dimension

We study one-dimensional topological superconductivity in the presence of time-reversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zero-energy Majorana bound states at each of its ends. We present a general simple model which is driven into this topological phase in the presence of repulsive electron-electron interactions. We further propose two experimental setups and show that they realize this model at low energies. The first setup is a narrow two-dimensional topological insulator partially covered by a conventional s-wave superconductor, and the second is a semiconductor wire in proximity to an s-wave superconductor. These systems can therefore be used to realize and probe the time-reversal invariant topological superconducting phase. The effect of interactions is studied using both a mean-field approach and a renormalization group analysis.

Theory of time-reversal topological superconductivity in double Rashba wires: symmetries of Cooper pairs and Andreev bound states

We study the system of double Rashba wires brought into proximity to an s-wave superconductor. Time-reversal invariant topological superconductivity is realized if the interwire pairing, corresponding to a crossed Andreev reflection, dominates over the standard intrawire pairing. We classify the symmetry of the Cooper pairs focusing on four degrees of freedom, i. e., frequency, spin, spatial parity inside wires, and spatial parity between wires. The presence of the spatial parity between wires is a unique feature of this model. The magnitude of the odd-frequency pairing is strongly enhanced in the topological state irrespective of spatial parities. We also explore the properties of junctions occurring in such double-wire systems. If one section of the junction is in a topological state and the other is in a trivial state, the energy dispersion of the Andreev bound states is proportional to similar to +/- sin phi, where phi denotes the macroscopic phase difference between the two sections. This behavior can be intuitively explained by the couplings of a Kramers pair of Majorana fermions and a spin-singlet s-wave Cooper pair and can also be understood by analyzing an effective continuum model of the s + p/s-wave superconductor hybrid system.

Time-Reversal Invariant Topological Superconductivity in Quasi-One-Dimensional Structures

It is shown that a time-reversal invariant topological superconductivity can be realized in a quasi-onedimensional structure, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when s-wave intra-wire and d-wave inter-wire pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. The time-reversal topological superconductor belongs to DIII class of symmetry with a Z2 invariant.

Topological superconductivity and the fractional Josephson effect in quasi-one dimensional wires on a plane

A time-reversal invariant topological superconductivity is suggested to be realized in a quasi-one dimensional structure on a plane, which is fabricated by filling the superconducting materials into the periodic channel of dielectric matrices like zeolite and asbestos under high pressure. The topological superconducting phase sets up in the presence of large spin-orbit interactions when intra-wire s-wave and inter-wire d-wave pairings take place. Kramers pairs of Majorana bound states emerge at the edges of each wire. We analyze effects of Zeeman magnetic field on Majorana zero-energy states. In-plane magnetic field was shown to make asymmetric the energy dispersion, nevertheless Majorana fermions survive due to protection of a particle-hole symmetry. Tunneling of Majorana quasi-particle from the end of one wire to the nearest-neighboring one yields edge fractional Josephson current with $4\pi$-periodicity.

Time-reversal-invariant topological superconductivity inn-doped BiH

Intrinsic and symmetry protected topological states have attracted lots of interest in condensed matter physics recently. In particular, time reversal symmetry protected fermion topological insulators have been theoretically predicted and experimentally verified. However despite considerable experimental and theoretical works, definitive evidence for time reversal invariant topological superconductivity is still lacking. Here we propose that upon electron doping the hydrogenated single bilayer Bi, namely BiH, will exhibit time reversal invariant topological superconductivity. If confirmed experimentally this material will constitute the first example of TRI topological superconductor.

Time-reversal-invariant topological superconductivity induced by repulsive interactions in quantum wires

The authors show that repulsive interactions in a Rashba wire coupled to a conventional superconductor can lead to time-reversal invariant topological superconductivity. Such state supports Majorana bound states in the absence of magnetic field.

Topological superconducting phase in the vicinity of ferromagnetic phases

Using functional renormalization group method, we study the favorable condition for electronic correlation driven time reversal invariant topological superconductivity in symmetry class DIII. For non-centrosymmetric systems we argue that the proximity to ferromagnetic (or small wavevector magnetic) instability can be used as a guideline for the search of this type of superconductivity. This is analogous to the appearance of singlet unconventional superconductivity in the neighborhood of antiferromagnetic instability. We show three concrete examples where ferromagnetic-like fluctuation leads to topological pairing.

Helical Dirac-Majorana interferometer in a superconductor/topological insulator sandwich structure

In the heterostructure composed of a topological insulator sandwiched by two $s$-wave superconductors, the time reversal invariant topological superconducting phase, possessing helical Majorana edge modes, is found to exist when the two $s$-wave superconductors form a Josephson junction with a $\ensuremath{\pi}$ phase shift. Based on such a heterostructure, a helical Dirac-Majorana interferometer is proposed to directly measure a unique transport signature of the helical Majorana modes. Furthermore, we envision how our proposal can be realized on the basis of existing materials such as Bi${}_{2}$Se${}_{3}$ or Bi${}_{2}$Te${}_{3}$ thin films.