This project develops theory leveraging the unique understanding of 1D electrons in order to

design superconductors where electron pairing from repulsive interactions is understood, and the critical temperature for the onset of superconductivity could be increased based on accurate theory

design 1D nanowires that are effectively superconducting, and would be so at high temperatures

understand pairing from repulsive electrons in existing unconventionally superconducting (USC) materials that are build from 1D structures (Bechgaard and Fabre salts, Sr-ladder compounds, K₂Cr₃As₃)

translating the mechanism to stabilize superconductivity from 1D to 2D materials, such as doped graphene

Method-wise, these aims will be achieved by combining parallel DMRG numerics with analytical approaches. This project is funded by an ERC Starting Grant from the European Union's Horizon 2020 research and innovation programme under grant agreement No 758935.

Background

In condensed matter physics superconducting (SC) materials are of great fundamental and technological interest. In a superconductor, electrons show correlated motion, as opposed to their effectively independent behaviour in a conventional metal - we speak of electron pairing. When the phases of macroscopically many of these pairs become coherent at low enough temperature, they exhibit off-diagonal long range order (ODLRO). This allows for lossless transport of current and energy, which crucially is protected by a SC gap.

The unconventionally superconducting (USC) materials are especially important to condensed matter physics then. As in them pairing results from repulsive electron-electron interactions, they can work at much higher temperatures than conventionally SC materials (where phonon-mediated pairing is just a few Kelvin strong). But no matter which USC material is studied - whether the high-T_c materials, or the organic Bechgaard and Fabre salts (the first materials discovered to be USC) - their fundamental electron pairing mechanism is uniformly very difficult to understand. This prevents theory from guiding any deliberate and systematic increase of critical temperatures for superconductivity in USC materials.

In this context, one-dimensional (1D) electrons have two unique advantages over higher-dimensional ones: in 1D, electron interactions are effectively the strongest, crucial to stability against thermal pair-breaking. And the theory of 1D electrons has a major edge, as it can solve and understand models of USC materials which in higher spatial dimensions remain unsolved, or admit solutions only under strong approximations not widely accepted. The drawback that so far has prevented 1D materials to be used as superconductors are the strong quantum and thermal fluctuations in 1D systems that prevent macroscopic phase coherence of pairs, and thus suppress superconductivity.

This project is based on eliminating this drawback of 1D electron systems via several different mechanisms, each corresponding to concrete physical set-ups. The systems thus enlarged are no longer strictly one-dimensional, but remain in some ways dominated by their original 1D character. The novel theory framework this project is developing will make it possible to gain qualitative and quantitative understanding of both existing and new to-be-proposed USC devices and materials. This understanding will be significantly beyond that currently available for e.g. fully 2D or 3D models and materials, and allow to systematically improve key properties like the critical temperature for superconductivity based on well-controlled and accurate theory.