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We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields (B), of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, Bc2. Our higher disorder samples undergo a B-induced transition into a strongly insulating state, which terminates at higher Bs forming an insulating peak. We demonstrate that the B terminating this peak coincides with Bc2 of the lower disorder samples. Additionally we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime.
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Ultrathin amorphous Bi films, patterned with a nano-honeycomb array of holes, can exhibit an insulating phase with transport dominated by the incoherent motion of Cooper pairs of electrons between localized states. Here we show that the magnetoresistance of this Cooper pair insulator phase is positive and grows exponentially with decreasing temperature, for temperatures well below the pair formation temperature. It peaks at a field estimated to be sufficient to break the pairs and then decreases monotonically into a regime in which the film resistance assumes the temperature dependence appropriate for weakly localized single electron transport. We discuss how these results support proposals that the large MR peaks in other unpatterned, ultrathin film systems disclose a Cooper Pair Insulator phase and provide new insight into the Cooper pair localization.
The advent of quantum optical techniques based on superconducting circuits has opened new regimes in the study of the non-linear interaction of light with matter. Of particular interest has been the creation of non-classical states of light, which are essential for continuous-variable quantum information processing, and could enable quantum-enhanced measurement sensitivity. Here we demonstrate a device consisting of a superconducting artificial atom, the Cooper pair transistor, embedded in a superconducting microwave cavity that may offer a path toward simple, continual production of non-classical photons. By applying a dc voltage to the atom, we use the ac Josephson effect to inject photons into the cavity. The backaction of the photons on single-Cooper-pair tunneling events results in a new regime of simultaneous quantum coherent transport of Cooper pairs and microwave photons. This single-pair Josephson laser offers great potential for the production of amplitude-squeezed photon states and a rich environment for the study of the quantum dynamics of nonlinear systems.
The interplay of charge orders with superconductivity in underdoped cuprates at high magnetic fields ($H$) is an open question, and even the value of the upper critical field ($H_{c2}$), a measure of the strength of superconductivity, has been the subject of a long-term debate. We combined three complementary transport techniques on underdoped La$_{1.8-x}$Eu$_{0.2}$Sr$_{x}$CuO$_{4}$ with a striped charge order and a low $H=0$ transition temperature $T_{c}^{0}$, to establish the $T-H$ phase diagram and reveal the ground states in CuO$_2$ planes: a superconductor, a wide regime of superconducting phase fluctuations (i.e. a vortex liquid), and a high-field normal state. The relatively high $H_{c2}$ is consistent with the opening of a superconducting gap above $T_{c}^{0}$, but only at $Tsim (2$-$3)T_{c}^{0}$, an order of magnitude below the pseudogap temperature. Within the vortex liquid, an unanticipated, insulatinglike region, but with strong superconducting correlations, begins to emerge already at $Tlesssim T_{c}^{0}$. The results suggest that the presence of stripes plays a crucial role in the freezing of Cooper pairs in this novel state. Our findings provide a fresh perspective on the pairing strength in underdoped cuprates, and introduce a new avenue for exploring the interplay of various orders.
Unusual transport properties of superconducting (SC) materials, such as the under doped cuprates, low dimensional superconductors in strong magnetic fields, and insulating films near the Insulator Superconductor Transition (IST), have been attributed to the formation of inhomogeneous phases. Difficulty correlating the behaviors with observations of the inhomogeneities make these connections uncertain. Of primary interest here are proposals that insulating films near the IST, which show an activated resistance and giant positive magnetoresistance, contain islands of Cooper Pairs (CPs). Here we present evidence that these types of inhomogeneities are essential to such an insulating phase in amorphous Bi (a-Bi) films deposited on substrates patterned with nanometer-sized holes. The patterning induces film thickness variations, and corresponding coupling constant variations, that transform the composition of the insulator from localized electrons to CPs. Analyses near the thickness-tuned ISTs of films on nine different substrates show that weak links between SC islands dominate the transport. In particular, the ISTs all occur when the link resistance approaches the resistance quantum for pairs. These observations lead to a detailed picture of CPs localized by spatial variations of the superconducting coupling constant.
We present investigations of the superconductor to insulator transition (SIT) of uniform a-Bi films using a technique sensitive to Cooper pair phase coherence. The films are perforated with a nanohoneycomb array of holes to form a multiply connected geometry and subjected to a perpendicular magnetic field. Film magnetoresistances on the superconducting side of the SIT oscillate with a period dictated by the superconducting flux quantum and the areal hole density. The oscillations disappear close to the SIT critical point to leave a monotonically rising magnetoresistance that persists in the insulating phase. These observations indicate that the Cooper pair phase coherence length, which is infinite in the superconducting phase, collapses to a value less than the interhole spacing at this SIT. This behavior is inconsistent with the gradual reduction of the phase coherence length expected for a bosonic, phase fluctuation driven SIT. This result starkly contrasts with previous observations of oscillations persisting in the insulating phase of other films implying that there must be at least two distinct classes of disorder tuned SITs.
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