Thin sheets deposited on a substrate and interfaces of correlated materials offer a plethora of routes towards the realization of exotic phases of matter. In these systems, inversion symmetry is broken which strongly affects the properties of possible instabilities -- in particular in the superconducting channel. By combining symmetry and energetic arguments, we derive general and experimentally accessible selection rules for Cooper instabilities in noncentrosymmetric systems which yield necessary and sufficient conditions for spontaneous time-reversal-symmetry breaking at the superconducting transition and constrain the orientation of the triplet vector. We discuss in detail the implications for various different materials. For instance, we conclude that the pairing state in thin layers of Sr$_2$RuO$_4$ must, as opposed to its bulk superconducting state, preserve time-reversal symmetry with its triplet vector being parallel to the plane of the system. All pairing states of this system allowed by the selection rules are predicted to display topological Majorana modes at dislocations or at the edge of the system. Applying our results to the LaAlO$_3$/SrTiO$_3$ heterostructures, we find that while the condensates of the (001) and (110) oriented interfaces must be time-reversal symmetric, spontaneous time-reversal-symmetry breaking can only occur for the less studied (111) interface. We also discuss the consequences for thin layers of URu$_2$Si$_2$ and UPt$_3$ as well as for single-layer FeSe. On a more general level, our considerations might serve as a design principle in the search for time-reversal-symmetry-breaking superconductivity in the absence of external magnetic fields.
We suggest that an inhomogeneous (non-zero momentum) paired phase can appear in the absence of an external magnetic field in the system with a predominant interband pairing and with separate Fermi-surface sheets. The Fermi wave vector mismatch which appears in such situation can be compensated by nonzero center-of-mass momentum of the Cooper pairs, what can lead to a spontaneous appearance of the Fulde-Ferrell type of superconducting state. The idea is examined using a tight-binding model which emulates the hole-like and the electron-like bands of iron based superconductor. The state can appea…
Finite-momentum superconducting states due to odd-frequency Cooper pairing correlations
Graduate School of Science, Hokkaido University（北海道大学大学院理学研究科）；RIKEN Center for Emergent Matter Science（理化学研究所新兴物质科学中心）；Department of Applied Physics, Hokkaido University（北海道大学应用物理系）
We report experimental evidence for charged boson states in a solid without Cooper pairing, based on attaching two free carriers to an exciton in a semiconducting system. Theoretical calculations show that this type of complex is stable in bilayer systems next to a parallel metal layer. Our experimental measurements on structures made using two different materials show a new spectral line at the predicted energy, if and only if all the required conditions for this complex are fulfilled, including a parallel metal layer that significantly screens the repulsive interaction between the like-charg…
Strong nodeless pairing on separate electron Fermi surface sheets in (Tl, K)Fe$_{1.78}$Se$_2$ probed by ARPES
我们对Tl $_{0.63}$ K $_{0.37}$ Fe $_{1.78}$ Se $_2$超导体（$T_c=29$ K）进行了高分辨角分辨光电子能谱研究。我们证明了在M $(π, 0)$点处存在两个类电子带，它们以相似的费米波矢穿过费米能级，形成近似圆形的类电子费米表面口袋。我们在这些费米面上观察到一个接近各向同性的$\sim$ 8.5 meV超导带隙（$Δ/k_BT_c\sim 7$）。我们对布里渊区中心周围能带结构的分析揭示了两个额外的类电子费米面：一个非常小的费米面和一个较大的费米面，其$k_F$与M处的FS口袋相当。有趣的是，SC间隙的幅度为$\sim$ 8毫电子伏也开发沿后者FS。我们的观测结果与s波强耦合的情况是一致的。
The superconductor FeSe is of intense interest thanks to its unusual non-magnetic nematic state and potential for high temperature superconductivity. But its Cooper pairing mechanism has not been determined. Here we use Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the bands surrounding the $Γ= (0,0)$ and $X=(π/ a_{Fe}, 0)$ points of FeSe, and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless, and exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing …
The Cooper pairing and phase coherence are two fundamental aspects of superconductivity. Due to breaking time reversal symmetry, magnetic impurities are detrimental to superconductivity, yet microscopically how they affect the pairing strength and phase coherence in a real material is less understood. Recently we observed a robust zero-energy bound state at an interstitial Fe impurity (IFI) in superconducting Fe1+x(Te,Se), signifying intense impurity scattering. Here we report a comprehensive study, using scanning tunnelling microscopy/spectroscopy (STM/S) technique, of the global effects of I…
Understanding the nature of Cooper pairs is essential to describe the properties of superconductors. The original proposal of Bardeen, Cooper, and Schrieffer (BCS) was based on electrons pairing with same energy and zero center-of-mass momentum. With the advent of new superconductors, different forms of pairing have been discussed. In particular, Cooper pairs with finite center-of-mass momentum have received large interest. Along with such finite-momentum pairs, pairing of electrons at different energies is also central to understanding some superconductors. Here, we investigate the interplay …
Superconductivity in Dirac electrons has recently been proposed as a new platform between novel concepts in high-energy and condensed matter physics. It has been proposed that supersymmetry and exotic quasiparticles, both of which remain elusive in particle physics, may be realized as emergent particles in superconducting Dirac electron systems. Using artificially fabricated topological insulator-superconductor heterostructures, we present direct spectroscopic evidence for the existence of Cooper pairing in a half Dirac gas 2D topological superconductor. Our studies reveal that superconductivi…
Scanning tunneling spectroscopy (STS) and angle-resolved photoemission spectroscopy (ARPES) have been investigated on single crystal samples of KFe2As2. A van Hove singularity (vHs) has been directly observed just a few meV below the Fermi level E_F of superconducting KFe2As2, which locates in the middle of the principle axes of the first Brillouin zone. The majority of the density-of-states at E_F, mainly contributed by the proximity effect of the saddle point to E_F, is non-gapped in the superconducting state. Our observation of nodal behavior of the momentum area close to the vHs points, wh…
We investigate phonon-mediated Cooper pairing in flat electronic band systems by solving the full-bandwidth multiband Eliashberg equations for superconductivity in magic angle twisted bilayer graphene using a realistic tight-binding model. We find that Cooper pairing away from the Fermi level contributes decisively to superconductivity by enhancing the critical temperature and ensures a robust finite superfluid density. We show that this pairing yields particle-hole asymmetric superconducting domes in the temperature-gating phase diagram and gives rise to distinct spectroscopic signatures in t…
Conventional Cooper pairing arises from attractive interaction of electrons in the metallic bands. Recent experiment on Co-doped LiFeAs shows superconductivity in the insulating valence band, which is evolved from a metallic hole band upon doping. Here we examine this phenomenon by studying superconductivity in a three-orbital Hamiltonian relevant to the doped LiFeAs. We show explicitly that Cooper pairing of the insulating hole band requires a finite pairing interaction strength. For strong coupling, the superconductivity in the hole band is robust against the sink of the hole band below the …
Since the proposal of monopole Cooper pairing in [Phys. Rev. Lett. 120, 067003 (2018)], considerable research efforts have been dedicated to the study of Cooper pairing order parameters constrained (or obstructed) by the nontrivial normal-state band topology at Fermi surfaces in 3D systems. In the current work, we generalize the topologically obstructed pairings between Chern states (like the monopole Cooper pairing) by proposing Euler obstructed Cooper pairing in 3D systems. The Euler obstructed Cooper pairing widely exists between two Fermi surfaces with nontrivial band topology characterize…
We show that Cooper pairing can occur intrinsically away from the Fermi surface in $j=3/2$ superconductors with strong spin-orbit coupling and equally curved bands in the normal state. In contrast to conventional pairing between spin-$1/2$ electrons, we derive that pairing can happen between inter-band electrons having different magnetic quantum numbers, for instance, $m_j=1/2$ and $m_j=3/2$. Such superconducting correlations manifest themselves by a pair of indirect gap-like structures at finite excitation energies. An observable signature of this exotic pairing is the emergence of a pair of …
We study the temperature-dependent electronic B1g Raman response of a slightly under-doped single crystal HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ with a superconducting critical temperature Tc=122 K. Our main finding is that the superconducting pair-breaking peak is associated with a dip on its higher-energy side, disappearing together at Tc. This result hints at an unconventional pairing mechanism, whereas spectral weight lost in the dip is transferred to the pair-breaking peak at lower energies. This conclusion is supported by cellular dynamical mean-field theory on the Hubbard model, which is able to…
We explore the possibility that the ionic electron polarizabilities of the oxygen ions in the cuprates and the bismutates and the polarizabilities of As and Se ions in the iron pnictides contribute to charge carrier pairing leading to high Tc superconductivity. Using the fact that the ionic polarization response to a change in the electric field is practically instantaneous we find, that the inter carrier electrostatic potential is attractive in a limited distance range. This potential is used to calculate quantum mechanically the cooper-like pairing energy and wavefunction and the gap energy …
We discuss odd-frequency Cooper pairs appearing in two-band superconductors by solving the Gor'kov equation analytically. We introduce the equal-time $s$-wave pair potentials as realized in MgB$_2$ and iron pnictides. Although the order parameter symmetry is conventional, the band degree of freedom enriches the symmetry variety of pairing correlations. The hybridization and the asymmetry between the two conduction bands induce odd-frequency pairs as a subdominant pairing correlation in the uniform ground state. To study the magnetic response of odd-frequency Cooper pairs, we analyze the Meissn…
We study the two-dimensional Hubbard model with the Rashba type spin-orbit coupling within and beyond the mean-field theory. The antiferromagnetic ground state for the model at half-filling and the Cooper pairing induced by antiferromagnetic spin fluctuations near half-filling are examined based on the random-phase approximation. We show that the antiferromagnetic order is suppressed and the magnetic susceptibility turns out to be anisotropic in the presence of the spin-orbit coupling. Energy spectrums of transverse spin fluctuations are obtained and the effective interactions between holes me…
The dielectric function method (DFM), which uses a non-adiabatic approach to calculate the critical temperatures for superconductivity, has been quite successful in describing superconductors at low carrier densities. This regime of carrier densities causes other theories, such as BCS and Migdal-Eliashberg theory, to violate their assumption of a small Debye window. We investigate the application of DFM to the linear dispersion of single layer graphene. We derive the gap equation of DFM for a Dirac cone and calculate the critical temperature as a function of carrier density. This is done using…
Ionic-Bond-Driven Atom-Bridged Room-Temperature Cooper Pairing in Cuprates and Nickelates: a Theoretical Framework Supported by 32 Experimental Evidences
Peking University（北京大学）；Beijing Technology and Business University（北京工商大学）
We develop the realistic minimal electronic model for recently discovered BiS$_2$ superconductors including the spin-orbit coupling based on a first-principles band structure calculations. Due to strong spin-orbit coupling, characteristic for the Bi-based systems, the tight-binding low-energy model necessarily includes $p_x$, $p_y$, and $p_z$ orbitals. We analyze a potential Cooper-pairing instability from purely repulsive interaction for the moderate electronic correlations using the so-called leading angular harmonics approximation (LAHA). For small and intermediate doping concentrations we …
High temperature superconducting materials have been known since the pioneering work of Bednorz and Mueller in 1986. While the microscopic mechanism responsible for high Tc superconductivity is still debated, most materials showing high Tc contain highly electronic polarizable ions, suggesting that the mechanism driving high Tc superconductivity can be related to the ion electronic polarizability in high Tc materials. Here we show that a free charge carrier polarizes the ions surrounding it and the total electrical potential generated by the charge carrier itself and the polarized ions becomes…
Unconventional superconductivity often arises from Cooper pairing between neighboring atomic sites, stipulating a characteristic pairing symmetry in the reciprocal space. The twisted bilayer graphene (TBG) presents a new setting where superconductivity emerges on the flat bands whose Wannier wavefunctions spread over many graphene unit cells, forming the so-called Moiré pattern. To unravel how Wannier states form Cooper pairs, we study the interplay between electronic, structural, and pairing instabilities in TBG. For comparisons, we also study graphene on boron-nitride (GBN) possessing a diff…
Non-equilibrium Enhancement of Cooper Pairing in Cold Fermion Systems
本文类比Eliashberg [G. M. Eliashberg，在“非平衡超导性”中，由D. N. Langenberg和A. I. Larkin（North-Holland，New York，1986）]关于微波对超导性的增强。通过由于与玻色子浴的热接触和/或蒸发冷却引起的热损失平衡的费米子的光学激发使得能够存在稳定的非平衡态。这种状态表现为准粒子谱向更高能量的移动，这种效应有效地提高了配对转变温度。作为一个例子，我们计算了有效的增强库珀配对和超流性的正常和超流相的混合物的Rb和Li在小偏离平衡的限制。有人认为，在实验中所希望的效果并不限于这样的小扰动和有效的配对温度的提高可能是相当大的。
We study the topological properties of superconductors with paired $j=\frac{3}{2}$ quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop…
The orbital multiplicity in multiband superconductors yields orbital differentiation in normal-state properties, and can lead to orbital-selective spin-fluctuation Cooper pairing. This phenomenon has become increasingly pivotal in clarifying the pairing 'enigma' particularly for multiband high-temperature superconductors. In one-unit-cell (1-UC) FeSe/SrTiO3, the thinnest and highest-Tc member of iron-based superconductors, the standard electron-hole Fermi pocket nesting scenario is apparently not applicable since the Gamma-centered hole pockets are absent, so the actual pairing mechanism is th…
Motivated by recent developments in the experimental study of superconducting graphene and transition metal dichalcogenides, we investigate superconductivity of the Kane-Mele (KM) model with short-range attractive interactions on the two-dimensional honeycomb lattice. We show that intra-valley spin-triplet pairing arises from nearest-neighbor (NN) attractive interaction and the intrinsic spin-orbit coupling. We demonstrate this in two independent approaches: We study superconducting instability driven by condensation of Cooperons, which are in-gap bound states of two conduction electrons, with…
