Wave Superconductor Research Articles

Quantized Majorana pump in semiconductor-superconductor heterostructures

We propose a quantized Majorana pump (QMP) in semiconductor-superconductor heterostructures. The pump consists of a Majorana nanowire, i.e., a Rashba wire in proximity to an $s$-wave superconductor and in a magnetic field, and two ferromagnetic leads. When the orientation of the magnetic field is rotated by $2\ensuremath{\pi}$, an elementary charge $e$ is transferred between two leads. The number of the pumped charge in a cycle is related to the winding number of the Andreev reflection amplitude. In the topologically trivial phase without Majorana zero mode (MZM), the pumped charge decreases rapidly to zero. More importantly, the pump works at zero bias and provides a more effective way to distinguish MZMs from trivial partially separated Andreev bound states. Therefore, this QMP provides not only a smoking-gun signature of MZMs, but also an ideal platform to realize topological single-electron pumps with the potential for realizing novel current standards in electrical metrology.

Landau-Fermi liquidness and $$s$$-wave superconducting properties of pressurized gray phosphorus

We investigate the physical properties of compressed gray phosphorus through density functional plus dynamical mean-field theory, showing self-doping and s-wave electronic structure reconstruction. At commensurate electron density, the 3p spectrum is shown to be almost unaffected by electronic correlations, however upon self-doping largely the normal and superconducting states. These findings provide a microscopic understanding of pressure-induced hole carrier superconductivity on the normal state coherence of s-wave superconductors with well-defined Bogoliubov quasiparticles at low temperatures. Upon internal thermalization, the s-wave superconducting state loses its phase coherence.

Comment on "Surface Pair-Density-Wave Superconducting and Superfluid States".

The claim in Barkman et al [Physical Review Letters {\bf 122}, 165302 (2019)] that pair-density wave (PDW) superconductivity in magnetic field is more stable near surface than in bulk, is not supported by microscopic theory.

Emergence of charge loop current in the geometrically frustrated Hubbard model: A functional renormalization group study

Spontaneous current orders due to odd-parity order parameters attract increasing attention in various strongly correlated metals. Here, we discover a novel spin-fluctuation-driven charge loop current (cLC) mechanism based on the functional renormalization group (fRG) theory. The present mechanism leads to the ferro-cLC order in a simple frustrated chain Hubbard model. The cLC appears between the antiferromagnetic and $d$-wave superconducting ($d$SC) phases. While the microscopic origin of the cLC has a close similarity to that of the $d$SC, the cLC transition temperature $T_{\rm cLC}$ can be higher than the $d$SC one for wide parameter range. Furthermore, we reveal that the ferro cLC order is driven by the strong enhancement of the forward scatterings $g_2$ and $g_4$ owing to the two dimensionality based on the $g$-ology language. The present study indicates that the cLC can emerge in metals near the magnetic criticality with geometrical frustration

Van Der Waals Heterostructures Based on Atomically‐Thin Superconductors

AbstractVan der Waals heterostructures (vdWHs) allow the assembly of high‐crystalline 2D materials in order to explore dimensionality effects in strongly correlated systems and the emergence of potential new physical scenarios. In this work, the feasibility of integrating 2D materials in‐between 2D superconductors is illustrated. In particular, the fabrication and electrical characterization of vertical vdWHs based on air‐unstable atomically‐thin transition metal dichalcogenides formed by NbSe2/TaS2/NbSe2 stacks, with TaS2 being the insulator 1T‐TaS2 or the metal 2H‐TaS2, is presented. Phase transitions as 1T‐TaS2 charge density wave and NbSe2 superconductivity are detected. An enhancement of the vdWH resistance due to Andreev reflections is observed below the superconducting transition temperature of the NbSe2 flakes. Moreover, in the NbSe2 superconducting state, the field and temperature dependence of the normalized conductance is analyzed within the Dynes’ model and the overall behavior is consistent with the Bardeen–Cooper–Schrieffer theory. This vdWH approach can be extended to other 2D materials, such as 2D magnets or topological insulators, with the aim of exploring the new emergent properties that may arise from such combinations.

High-temperature superconductivity in SrB3C3 and BaB3C3 predicted from first-principles anisotropic Migdal-Eliashberg theory

Very recently, carbon-boron clathrate $\mathrm{Sr}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$ has been successfully synthesized, in which carbon and boron atoms form $s{p}^{3}$-bonded truncated octahedral cages. Interestingly, the $s{p}^{3}$-hybridized $\ensuremath{\sigma}$-bonding bands are partially occupied. This may drive $\mathrm{Sr}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$ into a superconducting state, like boron-doped diamond. By means of density functional first-principles calculations and Wannier interpolation technique, we have investigated the electron-phonon coupling and phonon-mediated superconductivity in $\mathrm{Sr}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$. Our calculations reveal that there exists strong coupling between $s{p}^{3}$-hybridized $\ensuremath{\sigma}$-bonding bands and boron-associated ${E}_{g}$ phonon modes. Based on the Migdal-Eliashberg theory, we self-consistently solve the anisotropic Eliashberg equations. It is found that $\mathrm{Sr}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$ is a single-gap superconductor, with superconducting transition temperature being 40 K. The anisotropic ratio of superconducting energy gap is computed to be 32.8%. Further replacing Sr with Ba, the transition temperature can be boosted to 43 K in $\mathrm{Ba}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$ due to phonon softening. These findings suggest that $\mathrm{Sr}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$ and $\mathrm{Ba}{\mathrm{B}}_{3}{\mathrm{C}}_{3}$ are phonon-mediated high-temperature anisotropic $s$-wave superconductors.

Yu-Shiba-Rusinov states and ordering of magnetic impurities near the boundary of a superconducting nanowire

We theoretically study the spectrum induced by one and two magnetic impurities near the boundary of a one-dimensional nanowire in proximity to a conventional $s$-wave superconductor and extract the ground state magnetic configuration. We show that the energies of the subgap states, supported by the magnetic impurities, are strongly affected by the boundary for distances less than the superconducting coherence length. In particular, when the impurity is moved towards the boundary, multiple quantum phase transitions periodically occur in which the parity of the superconducting condensate oscillates between even and odd. We find that the magnetic ground state configuration of two magnetic impurities depends not only on the distance between them but also explicitly on their distance away from the boundary of the nanowire. As a consequence, the magnetic ground state can switch from ferromagnetic to antiferromagnetic while keeping the inter-impurity distance unaltered by simultaneously moving both impurities away from the boundary. The ground state magnetic configuration of two impurities is found analytically in the weak coupling regime and exactly for an arbitrary impurity coupling strength using numerical tight-binding simulations.

Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections

Majorana corner modes appearing in two-dimensional second-order topological superconductors have great potential applications for fault-tolerant topological quantum computations. We demonstrate that in the presence of an in-plane magentic field two-dimensional ($s+p$)-wave superconductors host Majorana corner modes, whose location can be manipulated by the direction of the magnetic field. In addition, we discuss the effects of edge imperfections on the Majorana corner modes. We describe how different edge shapes and edge disorder affect the number and controllability of the Majorana corner modes, which is of relevance for the implementation of topological quantum computations. We also discuss tunneling spectroscopy in the presence of the Majorana corner modes, where a lead-wire is attached to the corner of the noncentrosymmetric superconductor. The zero-bias differential conductance shows a distinct periodicity with respect to the direction of the magnetic field, which demonstrates the excellent controllability of the Majorana corner modes in this setup. Our results lay down the theoretical groundwork for observing and tuning Majoran corner modes in experiments on ($s+p$)-wave superconductors.

Topological anomalous skin effect in Weyl superconductors

We show that a Weyl superconductor can absorb light via a novel surface-to-bulk mechanism, which we dub the topological anomalous skin effect. This occurs even in the absence of disorder for a single-band superconductor, and is facilitated by the topological splitting of the Hilbert space into bulk and chiral surface Majorana states. In the clean limit, the effect manifests as a characteristic absorption peak due to surface-bulk transitions. We also consider the effects of bulk disorder, using the Keldysh response theory. For weak disorder, the bulk response is reminiscent of the Mattis-Bardeen result for $s$-wave superconductors, with strongly suppressed spectral weight below twice the pairing energy, despite the presence of gapless Weyl points. For stronger disorder, the bulk response becomes more Drude-like and the $p$-wave features disappear. We show that the surface-bulk signal survives when combined with the bulk in the presence of weak disorder. The topological anomalous skin effect can therefore serve as a fingerprint for Weyl superconductivity. We also compute the Meissner response in the slab geometry, incorporating the effect of the surface states.

Kondo effect in a hybrid superconductor–quantum-dot–superconductor junction with proximity-inducedp-wave pairing states

We study the transport of a hybrid superconductor--quantum-dot--superconductor junction, dominated by the interplay between the Kondo effect and the proximity-induced $p$-wave pairing states. Each superconductor lead is fabricated with a semiconductor with Rashba spin-orbit coupling (RSOC) and the combination of an $s$-wave superconductor and a ferromagnet. The RSOC breaks the SU(2) spin-rotation symmetry and creates the spin-triplet pairing components under the proximity-induced superconducting pairing interaction. Different from the s-wave pairing case, the Kondo screening of the dot spin involves the orbital angular momentum conserved transitions between the $p$-wave pairing states. The Zeeman field inherent from the ferromagnet removes the spin degeneracy of the quasiparticles excited in the triplet states. As a result, the spin-induced Yu-Shiba-Rusinov (YSR) state exhibits Zeeman-dependent splitting behaviors, and the splitting of the YSR state leads to the 0-$\ensuremath{\pi}$ phase transition when the ground state is a Kondo singlet. The temperature-dependent magnetic susceptibility indicates that the dot spin should be partially screened due to the breaking of time-reversal symmetry.

Pairing symmetry of an intermediate valence superconductor CeIr3 investigated using μSR measurements

We have investigated the bulk and microscopic properties of the rhombohedral intermediate valence superconductor ${\mathrm{CeIr}}_{3}$ by employing magnetization, heat capacity, and muon spin rotation and relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements. The magnetic susceptibility indicates bulk superconductivity below ${T}_{\mathrm{C}}=3.1\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Heat capacity data also reveal a bulk superconducting transition at 3.1 K with a second weak anomaly near 1.6 K. Zero-field $\ensuremath{\mu}\mathrm{SR}$ data show no strong evidence of broken time-reversal symmetry but support the presence of spin fluctuations below ${T}_{\mathrm{C}}$. Transverse-field $\ensuremath{\mu}\mathrm{SR}$ measurements suggest a fully gapped, isotropic, $s$-wave superconductivity with $2\mathrm{\ensuremath{\Delta}}(0)/{k}_{\mathrm{B}}{T}_{\mathrm{C}}=3.76(3)$, very close to 3.53, the Bardeen-Cooper-Schrieffer gap value for weak-coupling superconductors. From the temperature variation of the magnetic penetration depth, we have also determined the London penetration depth ${\ensuremath{\lambda}}_{\mathrm{L}}(0)=435(2)\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, the carrier effective-mass enhancement ${m}^{*}=1.69(1){m}_{\mathrm{e}}$, and the superconducting carrier density ${n}_{\mathrm{s}}=2.5(1)\ifmmode\times\else\texttimes\fi{}{10}^{27}$ carriers ${\mathrm{m}}^{\ensuremath{-}3}$. The fact that ${\mathrm{LaIr}}_{3}$, with no $4f$ electrons, and ${\mathrm{CeIr}}_{3}$ with $4{f}^{n}$ electrons where $n\ensuremath{\le}1$ (Ce ion in a valence fluctuating state), both exhibit the same $s$-wave gap symmetry indicates that the $\mathrm{Ir}\text{\ensuremath{-}}d$ band governs the physics of these two compounds near the Fermi level, which is in agreement with previous band structure calculations.

Anderson disorder-induced nontrivial topological phase transitions in two-dimensional topological superconductors

We numerically investigate the quantum phase transitions induced by Anderson disorder in a topological superconductor (TSC), which is composed of a quantum anomalous Hall insulator (QAHI) and a proximity coupled $s$-wave superconductor (SC). From the transport phenomena presented, we deduce that with the increase of Anderson disorder strength, the topological quantum phase changes from Chern number $\mathcal{N}=0$ to $\mathcal{N}=1$ and finally to $\mathcal{N}=2$. Then we use the effective-medium theory to verify our numerical results and conclude that the phase transitions should ascribe to the negative correction of topological mass.

Fate of Majorana zero modes, exact location of critical states, and unconventional real-complex transition in non-Hermitian quasiperiodic lattices

We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic topological phase boundary is verified by calculating the energy gap closing point and the topological invariant. Furthermore, we investigate the localized properties of this model, revealing that the topological phase transition is accompanied with the Anderson localization phase transition, and a wide critical phase emerges with amplitude increments of the non-Hermitian quasiperiodic potentials. Finally, we numerically uncover a non-conventional real-complex transition of the energy spectrum, which is different from the conventional $\mathcal{PT}$ symmetric transition.

Fate of the Hebel-Slichter peak in superconductors with strong antiferromagnetic fluctuations

We show that magnetic fluctuations can destroy the Hebel-Slichter peak in conventional superconductors. The Hebel-Slichter peak has previously been expected to survive even in the presence of strong electronic interactions. However, we show that antiferromagnetic fluctuations suppress the peak at $\bf{q}=0$ in the imaginary part of the magnetic susceptibility, $\chi_{+-}''\left(\bf{q},\omega\right)$, which causes the Hebel-Slichter peak. This is of general interest as in many materials superconductivity is found near a magnetically ordered phase, and the absence of a Hebel-Slichter peak is taken as evidence of unconventional superconductivity in these systems. For example, no Hebel-Slichter peak is observed in the $\kappa$-(BEDT-TTF)$_2X$ organic superconductors but heat capacity measurements have been taken to indicate $s$-wave superconductivity. If antiferromagnetic fluctuations destroy the putative Hebel-Slichter peak in organic superconductors then the peak should be restored by applying a pressure, which is known to suppress antiferromagnetic correlations in these materials.

Dynamical torque from Shiba states ins-wave superconductors

Magnetic impurities inserted in a $s$-wave superconductor give rise to spin-polarized in-gap states called Shiba states. We study the back-action of these induced states on the dynamics of the classical moments. We show that the Shiba state pertains to both reactive and dissipative torques acting on the precessing classical spin that can be detected through ferromagnetic resonance measurements. Moreover, we highlight the influence of the bulk states as well as the effect of the finite linewidth of the Shiba state on the magnetization dynamics. Finally, we demonstrate that the torques are a direct measure of the even and odd frequency triplet pairings generated by the dynamics of the magnetic impurity. Our approach offers non-invasive alternative to the STM techniques used to probe the Shiba states.

Half-integer quantized charge pumping induced by a Majorana fermion

We investigate the adiabatic topological charge pumping in a topological superconductor utilizing a quantum anomalous Hall insulator proximity coupled to an $s$-wave superconductor. We show that topological pumping is characterized by the appearance of protected Majorana edge states during the course of a pumping cycle. In a topological superconductor with a single Majorana edge state, the Majorana state will be pushed into the electrode in a cycle. This leads to a half-integer quantized pumped charge, because a Majorana fermion can be viewed as half of a fermion. The half-integer quantized charge pumping would serve as a fingerprint of a Majorana fermion.

Formation and detection of Majorana modes in quantum spin Hall trenches

We propose a novel realization for a topologically superconducting phase hosting Majorana zero modes on the basis of quantum spin Hall systems. Remarkably, our proposal is completely free of ferromagnets. Instead, we confine helical edge states around a narrow defect line of finite length in a two-dimensional topological insulator. We demonstrate the formation of a new topological regime, hosting protected Majorana modes in the presence of $s$-wave superconductivity and Zeeman coupling. Interestingly, when the system is weakly tunnel coupled to helical edge state reservoirs, a particular transport signature is associated with the presence of a non-Abelian Majorana zero mode.

Dynamics of a quantum phase transition in the Aubry-André-Harper model with p -wave superconductivity

We investigate the nonequilibrium dynamics of the one-dimension Aubry-Andr\'e-Harper model with $p$-wave superconductivity by changing the potential strength with slow and sudden quench. Firstly, we study the slow quench dynamics from the localized phase to the critical phase by linearly decreasing the potential strength $V$. The localization length is finite and its scaling obeys the Kibble-Zurek mechanism. The results show that the second-order phase transition line shares the same critical exponent $z\ensuremath{\nu}$, giving the correlation length $\ensuremath{\nu}=1$ and dynamical exponent $z=1.373\ifmmode\pm\else\textpm\fi{}0.023$, which are different from the Aubry-Andr\'e model. Secondly, we also study the sudden quench dynamics between three different phases: localized phase, critical phase, and extended phase. In the limit of $V=0$ and $V=\ensuremath{\infty}$, we analytically study the sudden quench dynamics via the Loschmidt echo. The results suggest that, if the initial state and the post-quench Hamiltonian are in different phases, the Loschmidt echo vanishes at some time intervals. Furthermore, we found that, if the initial value is in the critical phase, the direction of quenching is the same as one of the two limits mentioned before, and similar behaviors will occur.

Charge and spin transport through a normal lead coupled to an s -wave superconductor and a Majorana zero mode

Zero-bias charge conductance peak (ZBCCP) is a significant symbol of Majorana zero modes (MZMs). The proximity effect of $s$-wave superconductor is usually demanded in the fabrication of MZMs. So in transport experiments, the system is inevitably coupled to the $s$-wave superconductor. Here we study how the ZBCCP is affected by coupling of the $s$-wave superconductor. The results show that the ZBCCP could be changed into a zero-bias valley due to the coupling of $s$-wave superconductor, although the conductance at the zero bias still keeps a quantized value $2{e}^{2}/h$. So it does not mean no MZM exists when no ZBCCP is experimentally observed. In addition, the spin transport is investigated. Four reflection processes (the normal reflection, spin-flip reflection, normal Andreev reflection, and equal-spin Andreev reflection) usually occur. The reflection coefficients are strongly dependent on the spin direction of the incident electron, and they may be symmetrical or Fano resonance shapes. But the spin conductance always shows a zero-bias peak with the height $e/2\ensuremath{\pi}$ regardless of the direction of the spin bias and the coupling strength of the $s$-wave superconductor. So measuring spin transport properties could be a more reliable method to judge the existence of MZMs.

Chiral p -wave superconductivity in a twisted array of proximitized quantum wires

A superconductor with ${p}_{x}+i{p}_{y}$ order has long fascinated the physics community because vortex defects in such a system host Majorana zero modes. Here, we propose a simple construction of a chiral superconductor using proximitized quantum wires and twist angle engineering as basic ingredients. A weakly coupled parallel array of these wires forms a gapless $p$-wave superconductor. Two such arrays, stacked on top of one another with a twist angle close to ${90}^{\ensuremath{\circ}}$, spontaneously break time reversal symmetry and produce a robust, fully gapped ${p}_{x}+i{p}_{y}$ superconductor. We map out the topological phases of this setup, demonstrate the existence of Majorana zero modes in vortices, and discuss prospects for experimental realization.