MILLIKELVIN VISUALISATION OF TOPOLOGICAL ORDER

Project Information

mVITO

Grant agreement ID: 788932

DOI

10.3030/788932

Project closed

EC signature date 24 August 2018

Start date 1 January 2019

End date 30 April 2025

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 3 499 176,00

EU contribution

€ 3 499 176,00

Coordinated by

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom

Periodic Reporting for period 4 - mVITO (MILLIKELVIN VISUALISATION OF TOPOLOGICAL ORDER)

Reporting period: 2023-07-01 to 2025-04-30

Summary of the context and overall objectives of the project

Macroscopic quantum states of matter, such as correlated and topological superconductors, topological ferromagnetic and Kondo insulators, quantum monopole and spin liquids, and electron liquid crystals are now at the forefront of physics research. But these exotic forms of quantum matter have proven very difficult to discover, explore and understand - one reason being the lack of instrumentation designed specifically to deal with their novel measurement challenges. To address this issue, we develop and utilize a suite of novel quantum microscopes with different capabilities for direct visualization of quantum matter.


The significance of such research is that macroscopic quantum mechanics now plays a key role in science, and is anticipated to soon become central to 21th century quantum information technology. Discovery, exploration, understanding and application of macroscopic quantum matter is central to achieving that target.


Our overall objectives are thus to invent, develop and apply novel quantum microscopes for direct visualization and quantitative understanding of electronic and magnetic quantum matter.
Specific foci include the search for and exploration of bulk topologic superconductors, understanding of topological ferromagnetic & Kondo insulators, exploration of quantum monopole & spin liquids, and identification of novel electronic liquid crystal states.


The ultimate goal is discovery and communication of the new science revealed by our instruments, in the clearest and simplest appropriate format, to those who can use the knowledge to benefit society.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The overall mVITO research program yielded the following results:

Energy Gap Modulations of PDW State
We discovered strong Δ(r) modulations in Bi2Sr2CaCu2O8+δ twith eight-unit-cell periodicity revealing a PDW in Bi2Sr2CaCu2O8+δ.
Nature 580, 657 (2020)

Atomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity
We modeled eight-unit-cell periodic, pair density wave (PDW) plus d-wave superconductivity (DSC) consistent with experiments Bi2Sr2CaCu2O8.
PNAS 117, 14804 (2020).

Severe Dirac Mass Gap Suppression in Sb2Te3-based Quantum Anomalous Hall Materials =
Landau-level spectroscopic imaging= reveals why anomalous Hall effect in Sb2Te3-based FMTI materials is limited to temperatures below the energy scale 100 μeV (or ∼1 K).
Nano Lett 20, 8001-8007 (2020)

Multi-Atom Quasiparticle Scattering Interference for Superconductor Energy-Gap Symmetry Determination
We developed generalization of QPI approach with multiple impurity atoms, and demonstrate its utility.
Quantum Materials 6, 7 (2021).

Discovery of an Electron-Pair Density Wave State in a Transition-Metal Dichalcogenide
Scanned Josephson-tunnelling microscopy (SJTM) reveals a PDW state in TMD NbSe2.
Science 372, 1447 (2021)

Atomic-scale Visualization of Electronic Fluid Flow
We invented a electronic fluid flow visualization technique & visualized flow patterns in an electronic fluid.
Nature Materials 20, 1480 (2021)

Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase
We demonstrated scattering interference signature indicating that a pure PDW state occurs in the cuprate pseudogap phase.
Nature Comm. 12, 6087 (2021)

On the Electron Pairing Mechanism of Copper-Oxide High Temperature Superconductivity
We discovered that charge-transfer superexchange is the electron-pairing mechanism in hole-doped cuprate superconductors.
Proc. Nat. Acad. Sci. 119, 2207449119 (2022).

Identification of a Nematic Pair Density Wave State in Bi2Sr2CaCu2O8+x
Sanned Josephson tunnelling microscopy (SJTM) reveals interplay of PDW and superconductive (DSC) states in Bi2Sr2CaCu2O8+x discovering Q=0 nematic PDW state with Ising domains.
Proc. Nat. Acad. Sci. 119, 2206481119 (2022)

Interplay of hidden orbital order and superconductivity in CeCoIn5
Sublattice-resolved QPI visualization in the superconducting Kondo material CeCoIn5 revealed two orthogonal QPI patterns centered at impurity atoms segregated by sublattice - and thus hidden orbital order .
Nature Comm. 14, 2984 (2023)

Discovery of Orbital Ordering in Bi2Sr2CaCu2O8+x
We introduced sublattice resolved E(r) imaging techniques to CuO2 studies and discovered powerful intra-unit-cell rotational symmetry breaking of E(r), with energy-level splitting 50 meV scale, thus orbital ordering.
Nature Materials 23, 492 (2024)

Visualizing the atomic-scale origin of metallic behaviour in Kondo insulators
We discovered nanometer-scale “puddles” of metallic conduction electrons in the topological Kondo insulator samarium hexaboride (SmB6), implying that its three-dimensional quantum oscillations arise from Kondo-lattice defects.

Science 379, 1214 (2023)

Detection of a Pair Density Wave State in UTe2
Within mVITO, we visualized the Ute2 pairing energy-gap and detected three PDWs, that are indistinguishable from the wavevectors of the prevenient CDW. This PDW state is evidently a topological spin-triplet pair density wave.
Nature 618, 921 (2023)

Pair Wavefunction Symmetry in UTe2 from Zero-Energy Surface State Visualization
We discover a zero-energy Andreev conductance maximum at the (0-11) crystal termination categorizing UTe2 as the odd-parity non-chiral B3u state.
Science 388, 938-944 (2025)

Odd-Parity Quasiparticle Interference in the Superconductive Surface State of UTe2
We visualize quasiparticle interference patterns of its QSB, consistent with bulk Δ(k) exhibiting B3u symmetry.
Nature Physics , 2025.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Progress beyond the state of the art includesd:

Imaging the energy gap modulations of the cuprate pair-density-wave state Nature 571, 234 (2020) has been an outstanding challenge in physics sicn about 2014 .

Discovery of Pair Density Wave State on a Transition Metal Dichalcogenide, Science 372, 1447 (2021) opend a vast new area of research into electron-pair crystals in TMD materials.

Visualizing the atomic-scale origin of metallic behavior in Kondo insulators, Harris Pirie, E. Mascot, C. E. Matt, Yu Liu, Pengcheng Chen, M. H. Hamidian, Shanta Saha, X. Wang,
Science 379, 1214 (2023) solves a long standing mystery on how an insulator could support quantum oscillations.

Detection of a Pair Density Wave State in UTe2, Nature 618, 921 (2023) is the first and only known spin-triplet topological pair density wave state.

Pair Wave Function Symmetry in UTe2 from Zero-Energy Surface State Visualization. Science 388, 938 (2025) is a profound breakthrough in the capability to detect intrinsic topological superconductivity.

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