Exploring Quantum Criticality and Quantum Oscillations in High-Temperature Superconductors
Spin structure factor as a function of wave vector and frequency for certain parameters. See, Ref. 1.
Sudip Chakravarty
In the past year I have focused on quantum criticality in general, as well as quantum oscillations, and non-Fermi liquid aspects of conductivity in high-temperature superconductors.
Continuous phase transitions in the ground states of matter signify quantum critical points, where fluctuations diverge. It is a widely discussed topic in modern condensed matter physics. One might ask, "What about quantum critical lines or surfaces?" Although quantum critical points have been known for some time, it is remarkable that these simple extensions of the concept are hardly studied. We introduced a simple but exactly-solved model and explored it in some detail. This model was introduced earlier by myself and my former students and has numerous exciting properties, including multiple Majorana zero modes at the end of the one-dimensional chain.
The quantum phase transitions in this model have intriguing topological properties. I cannot overemphasize the fact that subtle effects related to quantum fluctuations require an exact solution of the proposed model. We have computed the spin-spin correlation function and extracted the correlation length, and identified the crossover regimes. We constructed the quantum critical fans along the critical lines. In addition, we also constructed the finite temperature dynamic structure factors. We hope this model will become experimentally realizable in the future, and our results could stimulate studies in many similar models.
Quantum oscillations in high temperature superconductors shed important light on this topic. I show that there is rigorous justification of quantum oscillations as in a Fermi liquid for cuprates. Oscillation frequencies are identical to the non-interacting problem. Thus, quantum oscillations protect the Fermi liquid and are in turn protected by it. This is not to imply that other properties of the cuprates could not exhibit non-Fermi liquid behavior, for example, angle resolved photoemission spectroscopy.
An interesting concept in condensed matter physics is Planckian dissipation, in particular its manifestation in a remarkable phenomenology of superfluid density as a function of superconducting transition temperature. The concept was introduced for $ab$-plane properties. However, when suitably interpreted, it can also be applicable to the incoherent c-axis resistivity, which has not been adequately addressed previously. In this paper I do precisely this explaining the experimental observations.
Quantum critical points, lines and surfaces, H. Yu and S. Chakravarty, Phys. Rev. B 107, 045124 (2023).
Quantum critical fans from critical lines at zero temperature, H. Yu and S. Chakravarty, Phys. Rev. B 108, 155143 (2023).
Planckian dissipation and c-axis superfluid density in cuprate superconductors, S. Chakravarty, arXiv:2306.13235
A theorem of Kohn applied to quantum oscillations in Cuprates, S. Chakravarty, arXiv:2307.04919