The most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can induce a dramatic transition from a superconducting into an insulating state. An outstanding question is whether the route to insulating behavior proceeds via the direct localization of Cooper pairs or, alternatively, by a two-step process in which the Cooper pairing is first destroyed followed by the standard localization of single electrons. Here we address this question by studying the local superconducting gap of a highly disordered, amorphous, superconductor by means of scanning tunneling spectroscopy. Our measurements reveal that, in the vicinity of the superconductor-insulator transition, the coherence peaks in the one-particle density of states disappear while the superconducting gap remains intact indicating the presence of localized Cooper pairs. Our results provide the first direct evidence that the transition in our system is driven by Cooper pair localization.
For high-Tc superconductors, clarifying the role and origin of the pseudogap is essential for understanding the pairing mechanism. Among the various models describing the pseudogap, the preformed Cooper pair model is a potential candidate. Therefore, we present experimental evidence for the preformed Cooper pair model by studying the pseudogap spectrum observed in the optical conductivity of a Ca10(Pt4As8)(Fe2As2)5 (Tc = 34.6 K) single crystal. We observed a clear pseudogap structure in the optical conductivity and observed its temperature dependence. In the superconducting (SC) state, one SC …
We study conditions for the emergence of the preformed Cooper pairs in materials hosting flat bands. As a particular example, we consider a semimetal, with a pair of three-band crossing points at which a flat band intersects with a Dirac cone, and focus on the s-wave intervalley pairing channel. The nearly dispersionless nature of the flat band at strong attraction between electrons promotes local Cooper pair formation so that the system may be modeled as an array of superconducting grains. Due to dispersive bands, Andreev scattering between the grains gives rise to the global phase-coherent s…
In most superconductors the transition to the superconducting state is driven by the binding of electrons into Cooper-pairs. The condensation of these pairs into a single, phase coherent, quantum state takes place concomitantly with their formation at the transition temperature, $T_c$. A different scenario occurs in some disordered, amorphous, superconductors: Instead of a pairing-driven transition, incoherent Cooper pairs first pre-form above $T_c$, causing the opening of a pseudogap, and then, at $T_c$, condense into the phase coherent superconducting state. Such a two-step scenario implies …
A weird electronic state accompanied with an anomalous superconducting precursor and/or exotic orders, called the pseudogap state, arises prior to a superconducting condensate in underdoped cuprates that are situated near Mott transition. Another way to make the system approach the Mott transition is the variation of bandwidth or correlation strength, which gives a new dimension to exploring this exotic state. Here we report nuclear magnetic resonance (NMR) studies on layered organic superconductors with half-filled bands whose widths are pressure-tuned near the Mott transition. The system sit…
Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while the electron pairing occurs at higher temperature than the long-range phase coherence in the underdoped high-Tc cuprate superconductors. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO3 substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudoga…
We present a theory of superconductivity in magic-angle twisted bilayer graphene and analyze the superconducting phase diagram in presence of the magnetic field. Namely, we consider a model of a granular array hosting localized states, which are hybridized via the delocalized fermions in the inter-grain regions. We study a strong coupling situation when the interactions lead to an incoherent state with preformed Cooper pairs inside the grains. The Andreev scattering among different grains manifests itself through the global phase-coherent superconducting state at lower temperatures. We demonst…
The idea that preformed Cooper pairs could exist in a superconductor above its zero-resistance state has been explored for unconventional, interface, and disordered superconductors, yet direct experimental evidence is lacking. Here, we use scanning tunneling noise spectroscopy to unambiguously show that preformed Cooper pairs exist up to temperatures much higher than the zero-resistance critical temperature $T_{C}$ in the disordered superconductor titanium nitride, by observing a clear enhancement in the shot noise that is equivalent to a change of the effective charge from 1 to 2 electron cha…
Search for Cooper-pair Fluctuations in Severely Underdoped YBCO Films
高$T_C$超导体中赝能隙物理的预成对理论预言了低掺杂铜氧化物中$ab$平面超流分数$ρ_S$在低温下的非解析$T$依赖性。我们报道了在严重欠掺杂的YBa $_2$ Cu $_3$ O $_{6+x}$和Y $_{0.8}$ Ca $_{0.2}$ Ba $_2$ Cu $_3$ O $_{6+x}$薄膜上的$ρ_S(T)$的高精度测量。在低$T$时，$ρ_S$看起来更像$1 - T^2$而不是$1 - T^{3/2}$，与理论不符。
We study anomalous mesoscopic transport effects at the onset of the superconducting transition focusing on the observed large Nernst-Ettinghausen signal in disordered thin films. In the vicinity of the transition, as the Ginzburg-Landau coherence length of preformed Cooper pairs diverges, short-range mesoscopic fluctuations are equivalent to local fluctuations of the critical temperature. As a result, the dynamical susceptibility function of pair propagation acquires a singular mesoscopic component, and consequently, superconducting correlations give rise to enhanced mesoscopic fluctuations of…
We demonstrate the rise-and-fall of multiple pseudogaps in the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover in two-band fermionic systems having different pairing strengths in the deep band and in the shallow band. The striking features of this phenomenon are an unusual many-body screening of pseudogap state and the importance of pair-exchange couplings, which induces multiple pseudogap formation in the two bands. The multi-band configuration suppresses pairing fluctuations and the pseudogap opening in the strongly-interacting shallow band at small pair-exchange cou…
Recent scanning tunnelling microscopy experiments in NbN thin disordered superconducting films found an emergent inhomogeneity at the scale of tens of nanometers. This inhomogeneity is mirrored by an apparent dimensional crossover in the paraconductivity measured in transport above the superconducting critical temperature $T_c$. This behavior was interpreted in terms of an anomalous diffusion of fluctuating Cooper pairs, that display a {\em quasi-confinement} (i.e., a slowing down of their diffusive dynamics) on length scales shorter than the inhomogeneity identified by tunnelling experiments.…
FeSe is argued as a superconductor in the Bardeen-Cooper-Schrieffer Bose-Einstein-condensation crossover regime where the superconducting-gap size and the superconducting transition temperature Tc are comparable to the Fermi energy. In this regime, vortex bound states should be well quantized and the preformed pairs above Tc may yield a pseudogap in the quasiparticle-excitation spectrum. We performed spectroscopic-imaging scanning tunneling microscopy to search for these features. We found Friedel-like oscillations near the vortex, which manifest the quantized levels, whereas the pseudogap was…
In two-dimensional Dirac semimetals, Cooper pairing instability occurs only when the attractive interaction strength $|u|$ is larger than some critical value $|u_{c}|$ because the density of states vanishes at Dirac points. Disorders enhance the low-energy density of states but meanwhile shorten the lifetime of fermions, which tend to promote and suppress superconductivity, respectively. To determine which of the two competing effects wins, we study the interplay of Cooper pairing interaction and disorder scattering by means of renormalization group method. We consider three types of disorders…
The physics of the crossover between weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein-condensate (BEC) limits gives a unified framework of quantum bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature $T_{\rm c}=8.5$ K has been found to be deep inside the BCS-BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe below $T…
We discuss whether a simple theory of superconducting stripes coupled by Josephson tunneling can describe a metallic transport, once the coherent tunneling of pairs is suppressed by the magnetic field. For a clean system, the conclusion we reached is negative: the excitation spectrum of preformed pairs consists of Landau levels, and once the magnetic field exceeds a critical value, the transport becomes insulating. As a speculation, we suggest that a Bose metal can exist in disordered systems provided that the disorder is strong enough to localize some pairs. Then the coupling between propagat…
By solving the Bogoliubov-de Gennes equations for a $d$-wave superconductor, we explore how the interplay between disorder and the orbital depairing of an external magnetic field influences the superconductor-metal transition of the hole-overdoped cuprates. For highly disordered systems, we find granular Cooper paring to persist above the critical field where the superfluid stiffness goes to zero. We also show that because the vortices are attracted to regions where the superconducting pairing is already weak, the Caroli-de Gennes-Matricon zero-bias peak in the local density of states at the v…
Majorana Fermions and Odd-frequency Cooper Pairs in a Nano Wire
我们讨论了马约拉纳费米子和奇频库珀对之间的强关系，出现在一个无序的正常（N）纳米线连接到一个拓扑非平凡的超导（S）的。超导纳米线结中的输运性质表现出与无序度无关的普遍行为：NS结中的量子化零偏压微分电导（2 e ^{2}/h）和SNS结中约瑟夫森效应的分数电流-相位（J-φ）关系J \propto \sin（φ/2）。这种行为与奇宇称自旋三重态超导体的反常邻近效应完全相同。我们发现，奇频库珀对支持普遍的输运性质。奇频率对存在于马约拉纳费米子所在的地方。
Cooper Pair Insulator phase induced in amorphous Pb$_0.9$Bi$_0.1$ thin films
在一些强无序薄膜系统的超导-绝缘体相变附近出现了库珀对绝缘体（CPI）相。最近的许多研究集中在驱动潜在的库珀对本地化的机制。我们目前的数据显示，CPI相的发展，在非晶Pb $_{0.9}$ Bi $_{0.1}$膜沉积到纳米多孔阳极氧化铝表面上，正如它已被证明为发展的a-Bi膜。这一结果证实了CPI相由于衬底的结构而出现的断言。它支持的图片，纳米薄膜厚度的变化引起的基板驱动本地化。此外，这意味着CPI相可以在可以沉积到该表面上的任何超导材料中被诱导。
It is now well known that the properties of the disordered s wave superconductors can deviate significantly from the prediction of standard Bardeen-Cooper-Schrieffer (BCS) theory. By measuring the temperature dependence of the resonance frequency, $f_0$, of microwave resonators made from disordered NbTiN and TiN thin films, at low temperatures, below half of the superconducting critical temperature, $T_c$, Driessen et al. \cite{driessen2012PRL} demonstrated that $f_0$ vanishes faster than predicted from the BCS theory. Here, we report on the temperature dependence of $f_0$ of microwave resonat…
