Atomic-scale visualization of electronic fluid flow

Liu, Xiaolong; Chong, Yi Xue; Sharma, Rahul; Davis, J. C.

doi:10.1038/s41563-021-01077-1

Cited by 15 publications

(18 citation statements)

References 28 publications

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“…An experimental observation of the secondary gaps by means of conventional tunneling spectroscopy [31][32][33][34][35] seems challenging due to the small gap widths. However, the recent progress in scanning tunneling spectroscopy techniques due to functionalized superconducting tips [36][37][38] could help to resolve in principle features down to the μeV scale. Another possible access to the gap structure is via multiple Andreev reflection experiments [39][40][41][42][43].…”

Section: Discussionmentioning

confidence: 99%

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

et al. 2022

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The energy levels of a quasicontinuous spectrum in mesoscopic systems fluctuate in positions and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we investigate mesoscopic fluctuations of a secondary gap that appears in the quasiclassical spectrum of a chaotic cavity coupled to one or more superconductors. Utilizing a random matrix model, we compute numerically the energies of Andreev levels and access the distribution of the gap widths. We mostly concentrate on the universal regime E Th, with E Th being the Thouless energy of the cavity and being the superconducting gap. We find that the distribution is determined by an intermediate energy scale g with the value between the level spacing in the cavity δ s and the quasiclassical value of the gap E g . From our numerics we extrapolate the first two cumulants of the gap distribution in the limit of large level and channel number. We find that the scaled distribution in this regime is the Tracy-Widom distribution: the same as found by Vavilov et al. [Phys. Rev. Lett. 86, 874 (2001)] for the distribution of the minigap edge in the opposite limit E Th . This leads us to the conclusion that the distribution found is a universal property of chaotic proximity systems at the edge of a continuous spectrum in agreement with the known random matrix models featuring a square root singularity in the density of states.

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Section: Discussionmentioning

confidence: 99%

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

et al. 2022

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“…The typical electrontunneling signature of the UTe2 superconducting energy-gap is exemplified in Fig. 3a [26][27][28][29] ; this has most recently been demonstrated in the development of electronic fluid flow visualization 29…”

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confidence: 83%

“…This can be visualized using either normal-insulator-superconductor (NIS) tunneling 20,21,22 , or superconductor-insulator-superconductor (SIS) tunneling from superconductive STM tips 17,23,29 whose gap energy is known a priori. Here we execute the second technique for UTe2 studies.…”

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Detection of a Pair Density Wave State in UTe2

Carroll

Wang

et al. 2022

Preprint

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Although UTe2 is a very promising candidate material to embody bulk topological superconductivity, its superconductive order-parameter ∆(k) remains unknown. Many diverse forms for ∆(k) are physically possible because, in uranium-based heavy fermion materials, strongly hybridized flat bands of composite fermions generate highly complex interactions. Moreover, in such materials intertwined density waves of spin (SDW), charge (CDW) and pairs (PDW) may interpose, with the latter state exhibiting spatially modulating, superconductive order-parameter ∆(r), electron pair density and pairing energy gap. Hence, the newly discovered CDW state in UTe2 motivates the exciting prospect that a PDW state may exist in this material. To search for a PDW in UTe2, we visualize the pairing energy-gap with μV-scale energy-resolution made possible by superconductive STM tips at subkelvin temperatures. We detect three PDWs, each with peak-peak gap modulations circa 10 μeV and at incommensurate wavevectors P_(i=1,2,3) that are indistinguishable from the wavevectors Q_(i=1,2,3) of the prevenient CDW. Concurrent visualization of the UTe2 superconductive PDWs and the non-superconductive CDWs reveals that every Pi: Qi pair is registered to each other spatially, but with a relative phase δϕ≈π. From these observations, and given UTe2 as a spin-triplet superconductor, the PDW state detected here should be a spin-triplet pair density wave. While such states do exist in superfluid 3He, for superconductors they are unprecedented.

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“…The existence and phenomenology of PDW states are fundamental issues within the challenge to understand cuprate correlated superconductivity ( 1 – 4 ). Their definitive characteristic is a periodically modulating electron-pair density which can now be visualized directly at the atomic scale, by using scanned Josephson tunneling microscopy ( 5 – 9 ) (SJTM). This new capability allows one to explore both the microscopic electronic structure of the cuprate pair density wave (PDW) state and the interactions between it and the other electronic orders.…”

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confidence: 99%

“…Using such an approach, excellent success has been achieved in understanding the induced order parameters, the most prominent of which are the induced charge density wave (CDW) states with order parameters ( 2 , 3 )

and

. However, to fully understand the PDW of cuprates, one is not limited to studying such secondary or induced states, because SJTM imaging can give direct access ( 5 – 9 ) to the primary electron-pair orders. The structure and intertwining between PDW and DSC states are described by a subset of terms from the overall GLW free energy density

where only the lowest order coupling terms are considered and the gradient terms are ignored.…”

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confidence: 99%

Identification of a nematic pair density wave state in Bi ₂ Sr ₂ CaCu ₂ O _8+x

Chen

Ren

Kennedy

et al. 2022

Proc. Natl. Acad. Sci. U.S.A.

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Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d -wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. Here, we use SJTM to visualize the interplay of PDW and DSC states in Bi 2 Sr 2 CaCu 2 O 8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al. , Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi 2 Sr 2 CaCu 2 O 8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

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Atomic-scale visualization of electronic fluid flow

Cited by 15 publications

References 28 publications

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

Detection of a Pair Density Wave State in UTe2

Identification of a nematic pair density wave state in Bi ₂ Sr ₂ CaCu ₂ O _8+x

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Atomic-scale visualization of electronic fluid flow

Cited by 15 publications

References 28 publications

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

Detection of a Pair Density Wave State in UTe2

Identification of a nematic pair density wave state in Bi 2 Sr 2 CaCu 2 O 8+x

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Identification of a nematic pair density wave state in Bi ₂ Sr ₂ CaCu ₂ O _8+x