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Register a new userMechanism of skyrmion condensation and pairing for twisted bi-layer graphene
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When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity ($sigma^f_{xy}$) controls the degeneracy of topologically protected, fermion zero-modes, localized on hedgehogs, and the overlap between zero-mode eigenfunctions or t Hooft vertex determines the nature of pairing. We demonstrate the quantum-disordered, flavor Hall insulators with $sigma^f_{xy}= 2 N$ lead to different types of charge $2 N e^-$ superconductivity. Some implications for the competition among flavor Hall insulators, the charge $2e^-$ paired states in BCS and pair-density-wave channels, and the composite, charge $4e^-$ superconductors for twisted bilayer graphene are outlined.
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In certain unconventional superconductors with sizable electronic correlations, the availability of closely competing pairing channels leads to characteristic soft collective fluctuations of the order parameters, which leave fingerprints in many observables and allow to scrutinize the phase competition. Superconducting layered materials, where electron-electron interactions are enhanced with decreasing thickness, are promising candidates to display these correlation effects. For example, while bulk NbSe2 is essentially a conventional superconductor, recent experiments in the thin-film regime have shown evidence of competing unconventional nematic pairing. In this work, we report the existence of a soft collective mode in single-layer NbSe2, observed as a characteristic resonance excitation in high resolution tunneling spectra. This resonance is observed along with higher harmonics, its frequency is anticorrelated with the local superconducting gap, and its amplitude gradually vanishes by increasing the temperature and upon applying a magnetic field up to the critical values (TC and HC2), which sets an unambiguous link to the superconducting state. Aided by a microscopic model, we interpret this resonance as a collective Leggett mode that represents the fluctuation towards a proximate f-wave triplet state, due to subleading attraction in the triplet channel. Our findings demonstrate the fundamental role of correlations in superconducting 2D transition metal dichalcogenides, opening a path towards unconventional superconductivity in simple, scalable and transferable 2D superconductors.
Identifying the microscopic mechanism for superconductivity in magic-angle twisted bilayer graphene (MATBG) is an outstanding open problem. While MATBG exhibits a rich phase-diagram, driven partly by the strong interactions relative to the electronic bandwidth, its single-particle properties are unique and likely play an important role in some of the phenomenological complexity. Some of the salient features include an electronic bandwidth smaller than the characteristic phonon bandwidth and a non-trivial structure of the underlying Bloch wavefunctions. We perform a theoretical study of the cooperative effects due to phonons and plasmons on pairing in order to disentangle the distinct role played by these modes on superconductivity. We consider a variant of MATBG with an enlarged number of fermion flavors, $N gg 1$, where the study of pairing instabilities reduces to the conventional (weak-coupling) Eliashberg framework. In particular, we show that certain umklapp processes involving mini-optical phonon modes, which arise physically as a result of the folding of the original acoustic branch of graphene due to the moire superlattice structure, contribute significantly towards enhancing pairing. We also investigate the role played by the dynamics of the screened Coulomb interaction on pairing, which leads to an enhancement in a narrow window of fillings, and study the effect of external screening due to a metallic gate on superconductivity. At strong coupling the dynamical pairing interaction leaves a spectral mark in the single particle tunneling density of states. We thus predict such features will appear at specific frequencies of the umklapp phonons corresponding to the sound velocity of graphene times an integer multiple of the Brillouin zone size.
We uncover an edge geometric phase mechanism to realize the second-order topological insulators and topological superconductors (SCs), and predict realistic materials for the realization. The theory is built on a novel result shown here that the nontrivial pseudospin textures of edge states in a class of two-dimensional (2D) topological insulators give rise to the geometric phases defined on the edge, for which the effective edge mass domain walls are obtained across corners when external magnetic field or superconductivity is considered, and the Dirac or Majorana Kramers corner modes are resulted. Remarkably, with this mechanism we predict the Majorana Kramers corner modes by fabricating 2D topological insulator on only a uniform and conventional $s$-wave SC, in sharp contrast to the previous proposals which applies unconventional SC pairing or SC $pi$-junction. We find that Au/GaAs(111) can be a realistic material candidate for realizing such Majorana Kramers corner modes.
We investigate the interplay of magnetic fluctuations and Cooper pairing in twisted bilayer graphene from a purely microscopic model within a large-scale tight-binding approach resolving the AA ngstrom scale. For local onsite repulsive interactions and using the random-phase approximation for spin fluctuations, we derive a microscopic effective pairing interaction that we use for self-consistent solutions of the Bogoliubov-de-Gennes equations of superconductivity. We study the predominant pairing types as function of interaction strength, temperature and band filling. For large regions of this parameter space, we find chiral $d$-wave pairing regimes, spontaneously breaking time-reversal symmetry, separated by magnetic instabilities at integer band fillings. Interestingly, the $d$-wave pairing is strongly concentrated in the AA regions of the moire unit cell and exhibits phase windings of integer multiples of $2pi$ around these superconducting islands, i.e. pinned vortices. The spontaneous circulating current creates a distinctive magnetic field pattern. This signature of the chiral pairing should be measurable by state-of-the-art experimental techniques.
Since the proposal of monopole Cooper pairing in Ref. [1], considerable research efforts have been dedicated to the study of Copper pair order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces. In the current work, we propose a new type of topologically obstructed Cooper pairing, which we call Euler obstructed Cooper pairing. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterized by nonzero Euler numbers; such Fermi surfaces can exist in the $PT$-protected spinless-Dirac/nodal-line semimetals with negligible spin-orbit coupling, where $PT$ is the space-time inversion symmetry. An Euler obstructed pairing channel must have pairing nodes on the pairing-relevant Fermi surfaces, and the total winding number of the pairing nodes is determined by the sum or difference of the Euler numbers on the Fermi surfaces. In particular, we find that when the normal state is nonmagnetic and the pairing is weak, a sufficiently-dominant Euler obstructed pairing channel with zero total momentum leads to nodal superconductivity. If the Fermi surface splitting is small, the resultant nodal superconductor hosts hinge Majorana zero modes, featuring the first class of higher-order nodal superconductivity originating from the topologically obstructed Cooper pairing. The possible dominance of the Euler obstructed pairing channel near the superconducting transition and the robustness of the hinge Majorana zero modes against disorder are explicitly demonstrated using effective or tight-binding models.
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