Wave Superconductor Research Articles

Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene

We study electronic ordering instabilities of twisted bilayer graphene with $n=2$ electrons per supercell, where correlated insulator state and superconductivity are recently observed. Motivated by the Fermi surface nesting and the proximity to Van Hove singularity, we introduce a hot-spot model to study the effect of various electron interactions systematically. Using renormalization group method, we find $d$/$p$-wave superconductivity and charge/spin density wave emerge as the two types of leading instabilities driven by Coulomb repulsion. The density wave state has a gapped energy spectrum at $n=2$ and yields a single doubly-degenerate pocket upon doping to $n>2$. The intertwinement of density wave and superconductivity and the quasiparticle spectrum in the density wave state are consistent with experimental observations.

Electrically controlled crossover between 2π and 4π Josephson effects through topologically confined channels in silicene

We propose a tunable topological Josephson junction in silicene where electrostatic gates could switch between a trivial and a topological junction. These aspects are a consequence of a tunable phase transition of the topologically confined valley-chiral states from a spin-degenerate to a spin-helical regime. We calculate the Andreev bound states in such a junction analytically using a low-energy approximation to the tight-binding model of silicene in proximity to s-wave superconductors as well as numerically in the short- and long-junction regime and in the presence of intervalley scattering. Combining topologically trivial and non-trivial regions, we show how intervalley scattering can be effectively switched on and off within the Josephson junction. This constitutes a topological Josephson junction with an electrically tunable quasiparticle poisoning source.

Superconductivity arising from layer differentiation in multilayer cuprates

In order to theoretically identify the factors governing superconductivity in multi-layer cuprates, a three-layer Hubbard model is studied with the two-particle self-consistent (TPSC) approach so as to incorporate electron correlations. The linearized Eliashberg equation is then solved for the gap function in a matrix form to resolve the role of outer CuO$_2$ planes (OPs) and inner plane (IP). We show that OPs dominate IP in the $d_{x^{2}-y^{2}}$-wave superconductivity, while IP dominates in the antiferromagnetism. This comes from an electron correlation effect in that the correlation makes the doping rates different between OPs and IP (i.e., a self-doping effect), which occurs in intermediate and strong correlation regimes. Namely, the antiferromagnetic fluctuations in IP are stronger due to a stronger electron correlation, which simultaneously reduces the quasiparticle density of states in IP with a suppressed $d_{x^{2}-y^{2}}$-wave superconductivity. Intriguingly, while the off-diagonal (inter-layer) elements in the gap function matrix are tiny, {\it inter-layer pair scattering} processes are in fact at work in enhancing the superconducting transition temperature $T_{\text{c}}$ through the inter-layer Green's functions. This actually causes the trilayer system to have higher $T_{\text{c}}$ than the single-layer in a weak- and intermediate-coupling regimes. This picture holds for a range of the on-site Hubbard repulsion $U$ that contains those estimated for the cuprates. The present result is qualitatively consistent with nuclear magnetic resonance experiments in multi-layer cuprates superconductors.

Fermi-Liquid Approach for Superconducting Kondo Problems.

We present a Fermi liquid approach to superconducting Kondo problems applicable when the Kondo temperature is large compared to the superconducting gap. To illustrate the theory, we study the current-phase relation and the Andreev level spectrum for an Anderson impurity between two s-wave superconductors. In the particle-hole symmetric Kondo limit, we find a 4π periodic Andreev spectrum. The 4π periodicity persists under a small voltage bias which however causes an asymmetric distortion of Andreev levels. The latter distinguishes the present 4π effect from the one in topological Majorana junctions.

Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method

The long-studied Hubbard model is one of the simplest models of copper-oxide superconductors. However, the connection between the model and the experimental phase diagram is still under debate, in particular regarding the existence and extent of the $d$-wave superconducting phase. Recent rapid progress in improving the accuracy of numerical solvers has opened a way to answer this question reliably. Here, we study the hole-doping concentration ($\delta$) dependence of the Hubbard model in the ground states on a square lattice at strong coupling $U/t=10$, for the on-site interaction $U$ and the transfer $t$, using a variational Monte Carlo method. The method, which combines tensor network and Lanczos methods on top of Pfaffian wave functions, reveals a rich phase diagram, in which many orders compete severely and degenerate within the energy range of 0.01$t$. We have identified distinct phases including a uniform $d$-wave superconducting phase for $0.17\lesssim \delta \lesssim0.22$ and a stripe charge/spin ordered phase for $\delta\lesssim0.17$ with the stripe period depending on $\delta$, together with presumable spatially coexisting antiferromagnetic and stripe order for $\delta\lesssim0.07$ and coexisting stripe and $d$-wave superconductivity for $0.07\lesssim\delta\lesssim0.17$. The present, improved method revealed a wider region of a charge uniform superconducting phase than the previous studies and shows a qualitative similarity to the phase diagram of the cuprate superconductors. The superconducting order parameter is largest at doping of around $\delta=0.17$ in the ground state, which undergoes phase transitions from an inhomogeneous to a uniform state.

Impurity Effects in Nodal Extendeds- and Nodelessd-Wave Superconductors: Gap Symmetry of BiS2-Based Layered Superconductors

In BiS$_2$-based layered superconductors,the existence of gap nodes on Fermi-surface curves has been suggested from angle-resolved photoemission spectroscopy measurements, whereas the conventional $s$-wave gap has been proposed from measurements of superfluid density and thermal conductivity. To reconcile these two distinct experimental results of the gap node, we investigate nonmagnetic impurity effects in the superconductor with a disconnected pocketlike Fermi-surface structure. Then, we claim that the seemingly contradictory situation concerning the gap node is resolved by a concept of dirty nodal extended $s$-wave superconductivity. Provided that it is unnecessary to consider the nodes of the gap, at first glance, the conventional $s$-wave gap seems to be a unique solution, but in the pocketlike Fermi-surface topology, a nontrivial possibility of a nodeless $d$-wave superconductor is pointed out. To clarify the gap symmetry, we propose to perform experiments on nuclear magnetic relaxation rate $T_{1}^{-1}$ in BiS$_2$-based layered superconductors.

Band-Renormalization Effect on Superconductivity and Antiferromagnetism in Two-Dimensional t–J Model

The coexistence or exclusivity of \(d_{x^{2} - y^{2}}\)-wave superconducting (d-SC) and antiferromagnetic (AF) orders and instability toward phase separation (PS) are reconsidered for the square-la...

Influence of electron-phonon coupling on the low-temperature phases of metallic single-wall carbon nanotubes

We investigate the effect of electron-phonon coupling on low temperature phases in metallic single-wall carbon nanotubes. We obtain low-temperature phase diagrams of armchair and zigzag type nanotubes with screened interactions with a weak-coupling renormalization group approach. In the absence of electron-phonon coupling, two types of nanotubes have similar phase diagrams. A $D$-Mott phase or $d$-wave superconductivity appears when the on-site interaction is dominant, while a charge-density wave or an excitonic insulator phase emerges when the nearest neighbor interaction becomes comparable to the on-site interaction. The electron-phonon coupling, treated by a two-cutoff scaling scheme, leads to different behavior in two types of nanotubes. For strong electron-phonon interactions, phonon softening is induced and a Peierls insulator phase appears in armchair nanotubes. We find that this softening of phonons may occur for any intraband scattering phonon mode. On the other hand, the effect of electron-phonon coupling is negligible for zigzag nanotubes. The distinct behavior of armchair and zigzag nanotubes against lattice distortion is explained by analysis of the renormalization group equations.

Interplay between charge, magnetic, and superconducting order in a Kondo lattice with attractive Hubbard interaction

We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion $s$-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation between $s$-wave superconductivity and incommensurate spin-density waves (SDWs). At half filling, we find an intriguing phase where the magnetic ordering of the $f$-electrons lifts the degeneracy between the charge density wave (CDW) state and the superconducting state, leading to a strong suppression of superconductivity. In addition, the system may also become a half metal in this parameter regime. Away from half filling, the CDWs vanish and are replaced by superconductivity combined with incommensurate SDWs up to moderate Kondo couplings to the $f$-electrons. We find that both CDWs as well as superconductivity enhance magnetic ordering due to the suppression of Kondo screening.

Strain-induced superconducting pair density wave states in graphene

Graphene is known to be nonsuperconducting. However, surprising superconductivity is recently discovered in a flat band in a twisted bilayer graphene. Here, we show that superconductivity can be more easily realized in topological flat bands induced by strain in graphene through periodic ripples. Specifically, it is shown that by including correlation effects, the chiral $d$-wave superconductivity can be stabilized under strain even for slightly doped graphene. The chiral $d$-wave superconductivity generally coexists with charge density waves (CDW) and pair density waves (PDW) of the same period. Remarkably, a pure PDW state with doubled period that coexists with the CDW state is found to emerge at a finite-temperature region under reasonable strain strength. The emergent PDW state is shown to be superconducting with nonvanishing superfluid density, and it realizes the long-sought-after superconducting states with nonvanishing center-of-mass momentum for Cooper pairs.

High-Temperature Majorana Corner States.

Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an s_{±}-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.

Coexistence of superconductivity and magnetism in CaK(Fe1−xNix)4As4 as probed by 57Fe Mössbauer spectroscopy

Temperature dependent $^{57}$Fe M\"ossbauer spectroscopy and specific heat measurements for CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$ with $x$ = 0, 0.017, 0.033, and 0.049 are presented. No magnetic hyperfine field (e.g. no static magnetic order) down to 5.5 K was detected for $x$ = 0 and 0.017 in agreement with the absence of any additional feature below superconducting transition temperature, $T_c$, in the specific heat data. The evolution of magnetic hyperfine field with temperature was studied for $x$ = 0.033 and 0.049. The long-range magnetic order in these two compounds coexists with superconductivity. The magnetic hyperfine field, $B_{hf}$, (ordered magnetic moment) below $T_c$ in CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$ is continuously suppressed with the developing superconducting order parameter. The $B_{hf}(T)$ data for CaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$, and CaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$ can be described reasonably well by Machida's model for coexistence of itinerant spin density wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. {\bf 50}, 2195 (1981)]. We demonstrate directly that superconductivity suppresses the spin density wave order parameter if the conditions are right, in agreement with the theoretical analysis.

Induced energy gap in finite-sized superconductor/ferromagnet hybrids

We theoretically study self-consistent proximity effects in finite-sized systems consisting of ferromagnet ($\rm F$) layers coupled to an $s$-wave superconductor ($\rm S$). We consider both $\rm SF_1F_2$ and $\rm SH$ nanostructures, where the $\rm F_1 F_2$ bilayers are uniformly magnetized, and the ferromagnetic $\rm H$ layer possesses a helical magnetization profile. We find that when the $\rm F_1 F_2$ layers are weakly ferromagnetic, a hard gap can emerge when the relative magnetization directions are rotated from parallel to antiparallel. Moreover, the gap is most prominent when the thicknesses of $\rm F_1$ and $\rm F_2$ satisfy $\rm d_{F1}\leq d_{F2}$, respectively. For the $\rm SH$ configuration, increasing the spatial rotation period of the exchange field can enhance the induced hard gap. Our investigations reveal that the origin of these findings can be correlated with the propagation of quasiparticles with wavevectors directed along the interface. To further clarify the source of the induced energy gap, we also examine the spatial and energy resolved density of states, as well as the spin-singlet, and spin-triplet superconducting correlations, using experimentally accessible parameter values. Our findings can be beneficial for designing magnetic hybrid structures where a tunable superconducting hard gap is needed.

Local impedance on a rough surface of a chiral p -wave superconductor

We develop a self-consistent approach for calculating the local impedance at a rough surface of a chiral $p$-wave superconductor. Using the quasiclassical Eilenberger-Larkin-Ovchinnikov formalism, we numerically find the pair potential, pairing functions, and the surface density of states taking into account diffusive electronic scattering at the surface. The obtained solutions are then employed for studying the local complex conductivity and surface impedance in the broad range of microwave frequencies (ranging from subgap to above-gap values). We identify anomalous features of the surface impedance caused by generation of odd-frequency superconductivity at the surface. The results are compared with experimental data for Sr$_2$RuO$_4$ and provide a microscopic explanation of the phenomenological two-fluid model suggested earlier to explain anomalous features of the microwave response in this material.

Majorana fermions in semiconducting nanowire and Fulde–Ferrell superconductor hybrid structures

The novel idea that spin-orbit coupling (SOC) and $s$-wave pairing can lead to induced $p$-wave pairing at strong magnetic limit has stimulated widespread interests in the whole community for the searching of Majorana Fermions (MFs), a self-hermitian particle, in semiconductor-superconductor hybrid structures. However, this system has several inherent limitations that prohibit the realization and identification of MFs with the major advances of semiconductor nanotechnology. We show that these limitations can be resolved by replacing the $s$-wave superconductor with type-II Fulde-Ferrell (FF) superconductor, in which the Cooper pair center-of-mass momentum plays the role of renormalizing the in-plane Zeeman field and chemical potential. As a result, the MFs can be realized for semiconductor nanowires with small Land\'e $g$ factor and high carrier density. The SOC strength directly influences the topological boundary, thus the topological phase transition and associated MFs can be engineered by an external electric field. Almost all the semiconductor nanowires can be used to realize MFs in this new platform. In particular, we find that InP nanowire, in some aspects, is more suitable for the realization of MFs than InAs and InSb nanowires. This new platform therefore can integrate the advances of semiconductor nanotechnology to the realization and identification of MFs in this hybrid structure.

Self-energies and quasiparticle scattering interference

The cuprate high-temperature superconductors are known to host a wide array of effects due to interactions and disorder. In this work, we look at some of the consequences of these effects which can be visualized by scanning tunneling spectroscopy. These interaction and disorder effects can be incorporated into a mean-field description by means of a self-energy appearing in the Green's function. We first examine the quasiparticle scattering interference spectra in the superconducting state at optimal doping as temperature is increased. Assuming agreement with angle-resolved photoemission experiments which suggest that the scattering rate depends on temperature, resulting in the filling of the $d$-wave gap, we find that the peaks predicted by the octet model become progressively smeared as temperature is increased. When the scattering rate is of the same order of magnitude as the superconducting gap, the spectral function shows Fermi-arc-like patterns, while the power spectrum of the local density of states shows the destruction of the octet-model peaks. We next consider the normal state properties of the optimally-doped cuprates. We model this by adding a marginal Fermi liquid self-energy to the normal-state propagator, and consider the dependence of the QPI spectra on frequency, temperature, and doping. We demonstrate that the MFL self-energy leads to a smearing of the caustics appearing in the normal-state QPI power spectrum as either temperature or frequency is increased at fixed doping. The smearing is found to be more prominent in the MFL case than in an ordinary Fermi liquid. We also consider the case of a marginal Fermi liquid with a strongly momentum-dependent self-energy which gives rise to a visible "nodal-antinodal" dichotomy at the normal state, and discuss how the spectra as seen in ARPES and STS differ from both an isotropic metal and a broadened $d$-wave superconductor.

DC-Current Induced Domain Wall in a Chiral p-Wave Superconductor

We study theoretically the impact of an applied DC-current on a mesoscopic chiral $p$-wave superconductor. Performing quasiclassical calculations on a two-dimensional system, with an external magnetic flux to generate a DC current, we show that the current can trigger a transition to a state with a domain wall between regions of different chiralities. The system shows an hysteretic behavior, as different domain wall configurations are possible for a given current. This domain wall creation mechanism can give new insights on recent experiments observing anomalous current variations in Sr${}_2$RuO${}_4$ junctions.

Superconducting and normal-state properties of the noncentrosymmetric superconductor Re3Ta

We systematically investigate the normal and superconducting properties of noncentrosymmetric ${\mathrm{Re}}_{6}\mathrm{Zr}$ using magnetization, heat capacity, and electrical resistivity measurements. Resistivity measurements indicate ${\mathrm{Re}}_{6}\mathrm{Zr}$ has poor metallic behavior and is dominated by disorder. ${\mathrm{Re}}_{6}\mathrm{Zr}$ undergoes a superconducting transition at ${T}_{\mathrm{c}}=\left(6.75\ifmmode\pm\else\textpm\fi{}0.05\right)$ K. Magnetization measurements give a lower critical field, ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}1}=\left(10.3\ifmmode\pm\else\textpm\fi{}0.1\right)$ mT. The Werthamer-Helfand-Hohenberg model is used to approximate the upper critical field ${\ensuremath{\mu}}_{0}{H}_{\mathrm{c}2}=\left(11.2\ifmmode\pm\else\textpm\fi{}0.2\right)\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, which is close to the Pauli limiting field of 12.35 T and which could indicate singlet-triplet mixing. However, low-temperature specific-heat data suggest that ${\mathrm{Re}}_{6}\mathrm{Zr}$ is an isotropic, fully gapped $s$-wave superconductor with enhanced electron-phonon coupling. Unusual flux pinning resulting in a peak effect is observed in the magnetization data, indicating an unconventional vortex state.

Nonequilibrium condensation process of a holographic p -wave superconductor

We study the nonequilibrium condensation process of a holographic $p$-wave superconductor model, which is described by Einstein-Maxwell theory coupled with the charged complex vector field in asymptotic anti-de Sitter (AdS) spacetime. By solving the gravitational dynamics in the asymptotic AdS spacetime numerically, we obtain the full time dependent solution of the system, and observe a dynamical process from the perturbed Reissner-Nordstr\om-AdS black hole to the anisotropic black hole with vector hair when the initial black hole temperature is smaller than the critical temperature ${T}_{c}$. By holography, this nonlinear dynamical process is then dual to the phase transition process from a normal state to a $p$-wave superconducting state on the boundary theory. We also investigate the time evolution of the superconducting condensate operator and horizon area.

Study of the superconducting order parameter in the two-dimensional negative- U Hubbard model by grand-canonical twist-averaged boundary conditions

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the $s$-wave superconducting order parameter and the pairing correlations for the negative-$U$ Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs is much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of $|U|/t$ and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behaviour of the superconducting phase, by means of a suitably chosen Jastrow factor including long-range density-density correlations.