Chiral Superconductor Research Articles

First-order superconducting phase transition in a chiralp+ipsystem

We use large-scale Monte Carlo computations to study the phase transitions of a two-component chiral p-wave superconductor in zero external magnetic field. We find a first order phase transition from the normal state to a chiral superconducting state, due to interplay between vortices and domain walls.

A Review of Electronic Transport in Superconducting Sr2RuO4 Junctions

We review electronic transport in superconducting junctions with Sr2RuO4. Transport measurements provide evidence for chiral domain walls and, therefore, chiral superconductivity in superconducting Sr2RuO4, but so far, the symmetry of the underlying superconducting state remains inconclusive. Further studies involving density of states measurements and spin-polarised transport in local/non-local Sr2RuO4 junctions with magnetic materials could lead to fundamental discoveries and a better understanding of the superconducting state.

Nematicity Arising from a Chiral Superconducting Ground State in Magic-Angle Twisted Bilayer Graphene under In-Plane Magnetic Fields.

Recent measurements of the resistivity in magic-angle twisted bilayer graphene near the superconducting transition temperature show twofold anisotropy, or nematicity, when changing the direction of an in-plane magnetic field [Cao etal., Science 372, 264 (2021)SCIEAS0036-807510.1126/science.abc2836]. This was interpreted as strong evidence for exotic nematic superconductivity instead of the widely proposed chiral superconductivity. Counterintuitively, we demonstrate that in two-dimensional chiral superconductors the in-plane magnetic field can hybridize the two chiral superconducting order parameters to induce a phase that shows nematicity in the transport response. Its paraconductivity is modulated as cos(2θ_{B}), with θ_{B} being the direction of the in-plane magnetic field, consistent with experiment in twisted bilayer graphene. We therefore suggest that the nematic response reported by Cao etal. does not rule out a chiral superconducting ground state.

Disorder-induced currents as signatures of chiral superconductivity

Chiral superconductors are expected to carry a spontaneous, chiral, and perpetual current along the sample edge. However, despite the availability of several candidate materials, such a current has not been observed in experiments. In this paper, we suggest an alternative probe in the form of impurity-induced chiral currents. We first demonstrate that a single nonmagnetic impurity induces an encircling chiral current. Its direction depends on the chirality of the order parameter and the sign of the impurity potential. Building on this observation, we consider the case of multiple impurities, e.g., realized as adatoms deposited on the surface of a candidate chiral superconductor. We contrast the responses that are obtained in two cases: (a) when the impurities are all identical in sign and (b) when the impurities have mixed positive and negative signs. The former leads to coherent currents within the sample, arising from the fusion of individual current loops. The latter produces loops of random chirality that lead to incoherent local currents. These two scenarios can be distinguished by measuring the induced magnetic field using recent probes such as diamond nitrogen-vacancy (NV) centers. We argue that impurity-induced currents may be easier to observe than edge currents, as they can be tuned by varying impurity strength, concentration, and correlations. We demonstrate these results using a toy model for ${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$ superconductivity on a square lattice. We develop an improved scheme for Bogoliubov--de Gennes simulations in which both the order parameter and the magnetic field are determined self-consistently.

Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure.

We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel Floquet topological quantum phase transitions driving the system into a myriad of exotic Majorana-carrying Floquet topological superconducting phases. Our theory establishes a new paradigm for realizing Floquet chiral topological superconductivity in solid-state systems, which should be experimentally directly accessible.

Nodeless superconductivity in the kagome metal CsV3Sb5

The recently discovered kagome metal series AV3Sb5 (A=K, Rb, Cs) exhibits topologically nontrivial band structures, chiral charge order and superconductivity, presenting a unique platform for realizing exotic electronic states. The nature of the superconducting state and the corresponding pairing symmetry are key questions that demand experimental clarification. Here, using a technique based on the tunneling diode oscillator, the magnetic penetration depth Δλ(T) of CsV3Sb5 was measured down to 0.07 K. A clear exponential behavior in Δλ(T) with marked deviations from a T or T2 temperature dependence was observed at low temperatures, indicating an absence of nodal quasiparticles. Temperature dependence of the superfluid density and electronic specific heat can be described by two-gap s-wave superconductivity, consistent with the presence of multiple Fermi surfaces in CsV3Sb5. These results evidence nodeless superconductivity in CsV3Sb5 under ambient pressure, and constrain the allowed pairing symmetry.

Skyrmion control of Majorana states in planar Josephson junctions

Planar Josephson junctions provide a versatile platform, alternative to the nanowire-based geometry, for the generation of the Majorana bound states, due to the additional phase tunability of the topological superconductivity. The proximity induction of chiral magnetism and superconductivity in a two-dimensional electron gas showed remarkable promise to manipulate topological superconductivity. Here, we consider a Josephson junction involving a skyrmion crystal and show that the chiral magnetism of the skyrmions can create and control the Majorana bound states without the requirement of an intrinsic Rashba spin-orbit coupling. Interestingly, the Majorana bound states in our geometry are realized robustly at zero phase difference at the junction. The skyrmion radius, being externally tunable by a magnetic field or a magnetic anisotropy, brings a unique control feature for the Majorana bound states.

Shear modulus anomaly of unconventional superconductors in a symmetry breaking field

Using Ginzburg-Landau formalism, we theoretically study the isothermal shear modulus anomaly of an unconventional superconductor with a two-component order parameter, where the superconducting transition is split by a symmetry-breaking field. Experimental signatures are proposed for both chiral and nematic superconductors. Particularly striking is the vanishing of ${C}_{66}$ across the lower transition to a nematic superconducting state. Our findings can guide future experiments and shed new light on materials such as ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ and ${M}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$.

Chiral topological superconducting state with Chern number C = −2 in Pb3Bi/Ge(111)

Materials realization of chiral topological superconductivity is a crucial condition for observing and manipulating Majorana fermions in condensed matter physics. Here we develop a tight-binding description of Pb$_3$Bi/Ge(111), identified recently as an appealing candidate system for realizing chiral $p$-wave topological superconductivity [Nat. Phys. 15, 796 (2019)]. We first show that our phenomenological model can capture the two main features of the electronic band structures obtained from first-principles calculations, namely, the giant Rashba splitting and type-II van Hove singularity. Next, when the $s$-wave superconducting property of the parent Pb system is explicitly considered, we find the alloyed system can be tuned into a chiral topological superconductor with Chern number $\mathcal{C} = -2$, resulting from the synergistic effect of a sufficiently strong Zeeman field and the inherently large Rashba spin-orbit coupling. The nontrivial topology with $\mathcal{C} = -2$ is further shown to be detectable as two chiral Majorana edge modes propagating along the same direction of the system with proper boundaries. We finally discuss the physically realistic conditions to establish the predicted topological superconductivity and observe the corresponding Majorana edge modes, including the influence of the superconducting gap, Land\'{e} $g$-factor, and critical magnetic field. The present study provides useful guides in searching for effective $p$-wave superconductivity and Majorana fermions in two-dimensional or related interfacial systems.

Competing electronic orders on a heavily doped honeycomb lattice with enhanced exchange coupling

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally.

Robust gapless superconductivity in 4Hb−TaS2

The superconducting TMD 4Hb-TaS$_2$ consists of alternating layers of H and T structures, which in their bulk form are metallic and Mott-insulating, respectively. Recently, this compound has been proposed as a candidate chiral superconductor, due to an observed enhancement of the muon spin relaxation at $T_c$. 4Hb-TaS$_2$ also exhibits a puzzling $T$-linear specific heat at low temperatures, which is unlikely to be caused by disorder. Elucidating the origin of this behavior is an essential step in discerning the true nature of the superconducting ground state. Here, we propose a simple model that attributes the $T$-linear specific heat to the emergence of a robust multi-band gapless superconducting state. We show that an extended regime of gapless superconductivity naturally appears when the pair-breaking scattering rate on distinct Fermi-surface pockets differs significantly, and the pairing interaction is predominantly intra-pocket. Using a tight-binding model derived from first-principle calculations, we show that the pair-breaking scattering rate promoted by slow magnetic fluctuations on the T layers, which arise from proximity to a Mott transition, can be significantly different in the various H-layer dominated Fermi pockets depending on their hybridization with T-layer states. Thus, our results suggest that the ground state of 4Hb-TaS$_2$ consists of Fermi pockets displaying gapless superconductivity, which are shunted by superconducting Fermi pockets that are nearly decoupled from the T-layers.

Anomalous normal fluid response in a chiral superconductor UTe2

Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe2 with surface normal fluid response. The microwave surface impedance of the UTe2 crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe2 can be a new platform to study exotic topological excitations in higher dimension.

Chiral singlet superconductivity in the weakly correlated metal LaPt3P

Chiral superconductors are novel topological materials with finite angular momentum Cooper pairs circulating around a unique chiral axis, thereby spontaneously breaking time-reversal symmetry. They are rather scarce and usually feature triplet pairing: a canonical example is the chiral p-wave state realized in the A-phase of superfluid He3. Chiral triplet superconductors are, however, topologically fragile with the corresponding gapless boundary modes only weakly protected against symmetry-preserving perturbations in contrast to their singlet counterparts. Using muon spin relaxation measurements, here we report that the weakly correlated pnictide compound LaPt3P has the two key features of a chiral superconductor: spontaneous magnetic fields inside the superconducting state indicating broken time-reversal symmetry and low temperature linear behaviour in the superfluid density indicating line nodes in the order parameter. Using symmetry analysis, first principles band structure calculation and mean-field theory, we unambiguously establish that the superconducting ground state of LaPt3P is a chiral d-wave singlet.

Anomalous viscosity of a chiral two-orbital superconductor in tight-binding model

We study the linear response of the deformation potential of a chiral two-orbital superconductor Sr $$_2$$ RuO $$_4$$ to the applied strain. This response rises due to the strain-induced modified interatomic distances. In the linear response theory, the deformation potential–deformation potential correlation function defines the full complex frequency-dependent viscosity tensor. We calculate the anti-symmetric part of this tensor, the phonon Hall viscosity, to consider the static and dynamical Hall responses. The static phonon Hall static enables us to distinguish the different topological phases of Sr $$_2$$ RuO $$_4$$ . We focus on two regimes: (a) the phonon Hall viscosity due to the changes in the hopping energies of the tight-binding Hamiltonian and is termed the normal phonon Hall viscosity and (b) the phonon Hall viscosity due to the variation in the amplitudes of the order parameter of the superconducting state that causes an anomalous momentum transport coefficient and is analogous to the one-dimensional odd isotropic part of the viscosity tensor of an incompressible fluid in two dimension space. In both cases, the tetragonal crystal symmetry which corresponds to the isotropy in the system plays an important role. We also investigate the effect of the crystal symmetry on the stability of the nontrivial topological phase.

On stability of fermionic superconducting current in cosmic string

Recently, the chiral superconductivity of the cosmic string in the axion model has gathered attention. The superconductive nature can alter the standard understanding of the cosmology of the axion model. For example, a string loop with a sizable super-conducting current can become a stable configuration, which is called a Vorton. The superconductive nature can also affect the cosmological evolution of the string network. In this paper, we study the stability of the superconducting current in the string. We find the superconductivity is indeed stable for a straight string or infinitely small string core size, even if the carrier particles are unstable in the vacuum. However we also find that the carrier particle decays in a curved string in typical axion models, if the carrier particles are unstable in the vacuum. Accordingly, the lifetime of the Vorton is not far from that of the carrier particle in the vacuum.

Chiral topological superconductivity in Josephson junctions

We consider a heterostructure of semiconductor layers sandwiched between two superconductors, forming a two-dimensional Josephson junction. Applying a Zeeman field perpendicular to the junction can render a topological superconducting phase with chiral Majorana edge mode. We show that the phase difference between two superconductors can efficiently reduce the magnetic field required to achieve the chiral topological superconductivity, providing an experimentally feasible setup to realize chiral Majorana edge modes. We also construct a lattice Hamiltonian of the setup to demonstrate the chiral Majorana edge mode and the Majorana bound state localized in vortices.

Vortex-line topology in iron-based superconductors with and without second-order topology

The band topology of a superconductor is known to have profound impact on the existence of Majorana zero modes in vortices. As iron-based superconductors with band inversion and $s_{\pm}$-wave pairing can give rise to time-reversal invariant second-order topological superconductivity, manifested by the presence of helical Majorana hinge states in three dimensions, we are motivated to investigate the interplay between the second-order topology and the vortex lines in both weak- and strong-Zeeman-field regimes. In the weak-Zeeman-field regime, we find that vortex lines far away from the hinges are topologically nontrivial in the weakly doped regime, regardless of whether the second-order topology is present or not. However, when the superconductor falls into the second-order topological phase and a topological vortex line is moved close to the helical Majorana hinge states, we find that their hybridization will trivialize the vortex line and transfer robust Majorana zero modes to the hinges. Furthermore, when the Zeeman field is large enough, we find that the helical Majorana hinge states are changed into chiral Majorana hinge modes and thus a chiral second-order topological superconducting phase is realized. In this regime, the vortex lines are always topologically trivial, no matter how far away they are from the chiral Majorana hinge modes. By incorporating a realistic assumption of inhomogeneous superconductivity, our findings can explain the recent experimental observation of the peculiar coexistence and evolution of topologically nontrivial and trivial vortex lines in iron-based superconductors.

Light-induced topological superconductivity via Floquet interaction engineering

We propose a mechanism for light-induced unconventional superconductivity in a two-valley semiconductor with a massive Dirac type band structure. The superconducting phase results from the out-of-equilibrium excitation of carriers in the presence of Coulomb repulsion and is stabilized by coupling the driven semiconductor to a bosonic or fermionic thermal bath. We consider a circularly-polarized light pump and show that by controlling the detuning of the pump frequency relative to the band gap, different types of chiral superconductivity would be induced. The emergence of novel superconducting states, such as the chiral $p$-wave pairing, results from the Floquet engineering of the interaction. This is realized by modifying the form of the Coulomb interaction by projecting it into the states that are resonant with the pump frequency. We show that the resulting unconventional pairing in our system can host topologically protected chiral bound states. We discuss a promising experimental platform to realize our proposal and detect the signatures of the emergent superconducting state.

Analog of Gravitational Anomaly in Topological Chiral Superconductors

It is known that the contribution of torsion to the equation for the chiral Weyl fermions can be equivalently considered in terms of the axial $U(1)$ gauge field. In this scenario the gravitational field transforms to the $U(1)$ gauge field. Here we show that in chiral superconductors the opposite scenario takes place: the electromagnetic $U(1)$ field serves as the spin connection for the Bogoliubov fermionic quasiparticles. As a result the electromagnetic field gives rise to the gravitational anomaly, which contains the extra factor $1/3$ in the corresponding Adler-Bell-Jackiw equation as compared with the conventional chiral anomaly. We also consider the gravitational anomaly produced in neutral Weyl superfluids by the analog of the gravitational instanton, the process of creation and annihilation of the 3D topological objects -- hopfions. The gravitational instanton leads to creation of the chiral charge.

Nonlinear electric response of chiral topological superconductors

We investigate, in the non-equilibrium Keldysh frame, a topological resistor–capacitor (RC) circuit consisting of a quantum dot coupled to a Majorana edge mode formed around a chiral topological superconductor. We implement both the adiabatic approximation and the numerical exact calculations to find out the unique non-equilibrium features of the electric response of the dissipative Majorana channel. First, the dependence of the dissipation on the frequency Ω of the ac driving on the dot is found to be greatly different whether the time-dependent dot level crosses the Fermi level or not during the driving. In the latter case, the relaxation resistance R q, the measure of the dissipation, obeys R q ∝ Ω2 for small frequencies, and in the former case, R q ∝ Ω−1/3 diverges as Ω → 0. In the former case, a universal scaling law for the dissipative part of the ac power is observed and attributed to the δ-peak in the dot density of states due to a uncoupled dot Majorana mode at the dot resonance condition. We compare the ac power, current, and the relaxation resistance between Majorana and trivial Dirac channels and clarify the Majorana nature in the dissipation.