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Charge orders, Magnetism and Pairings in High Temperature Superconductors

Periodic Reporting for period 4 - CHAMPAGNE (Charge orders, Magnetism and Pairings in High Temperature Superconductors)

Reporting period: 2021-02-01 to 2021-07-31

For nearly thirty years, the search for a room-temperature superconductor has focused on exotic materials known as cuprates, obtained by doping a parent Mott insulator, and which can carry currents without losing energy as heat at temperatures up to 164 Kelvin. Conventionally three main players were identified as being crucial i) the Mott insulating phase, ii) the anti-ferromagnetic order and iii) the superconducting (SC) phase. Recently a body of experimental probes suggested the presence of a fourth forgotten player, charge ordering-, as a direct competitor for superconductivity. In this project we propose that the relationship between charge ordering and superconductivity is more intimate than previously thought and is protected by an emerging SU(2) symmetry relating the two. The beauty of our theory resides in that it can be encapsulated in one simple and universal "gap equation", which in contrast to strong coupling approaches used up to now, can easily be connected to experiments. In the first part of this work, we will refine the theoretical model in order to shape it for comparison with experiments and consistently test the SU(2) symmetry. In the second part of the work, we will search for the experimental signatures of our theory through a back and forth interaction with experimental groups.
In the first 30 months of the project, we have refined the theoretical concepts with the idea of "droplets" or phase separation, the idea of topological defects, or Skyrmions, coming from a description in terms of an effective O(3) non linear sigma model. Lastly, we recently introduced a new concept, of entangled preformed pairs in both the particle-particle and particle-hole channel, which will enable us strengthen the theoretical foundations of the concepts of droplets and topological defects. We have then re-formulated the idea to introduce the concept of fractionalisation of a charge-two boson, or " fractionalisation of a Pair Density Wave (PDW) which enables us to describe many aspects of the formation of the Pseudo-gap state. The phenomenology associated to this new state of matter is very close to the one of the SU(2) emergent symmetry, both being described by a non linear sigma model. Lastly, we introduce the novel idea that the strange metal phase of the cuprates could be the host of a pack of charge two bosons, which would considerably affect the transport properties and could explain the linear in T resistivity over a wide regime in temperature.
We have developed a consistent theory for the SU(2) emergent symmetry in the under-doped region of the cuprates. We have tested it through various experiments, investigating Inelastic Neutron Scattering, evolution of the pseudo-gap with doping, and most interestingly we made predictions concerning the presence of collective modes of spin zero and charge 2 which would be the signature of the emergent symmetry. The idea of emergent symmetry is interesting and produces strong phenomenology, but to go further we need to strengthen its microscopic basis. That is why we introduced a new concept of two kinds of preformed pairs, in the particle-particle and particle-hole channels, which gets entangled at T*. This is a very new direction for the physics of cuprates, motivated by the very recent observation of a precursor gap in the charge channel ( Raman Scattering on Hg1223) of the same size and variation with doping of the long observed precursor gap in the Cooper pairing channel. The idea of entangled preformed pairs will maybe be able to capture this fascinating competition between the two pairings. The new theory doesn't require an exact SU(2) symmetric ground state, but still is described in terms of a similar O(3) non linear sigma model. The introduction of a new concept, of fractionalized Pair Density Wave in order to explain the formation of a pseudo-gap gives a new viewpoint to this very old mystery of condensed matter physics. This new viewpoint led to the idea that preformed charge two bosons might be present in the strange metal phase, giving rise to anomalous transport and in particular to a linear in T resistivity.

This work has led to 19 publications in peer reviewed scientific journals and one preprint, to three papers disseminating to a general audience, and to an intense dissemination through participation as an invited speaker to 25 international workshops and conferences, four talks to general audiences and the organisation of two workshops.
Phase diagram in a magnetic field from the SU(2) emergent symmetry