Speaker
Description
The engineering of exotic ordered states in two-dimensional itinerant electron systems is a matter central to the field of quantum materials, from the viewpoints of both fundamental physics and applications. Ordinary Van Hove singularities (VHSs), logarithmic divergences in the density of states arising from quadratic saddle points in a material’s dispersion, have long been known to induce strong correlations when situated at the Fermi level [1,2]; more recently, particular attention has been given to higher-order VHSs, whose power-law divergences (arising from higher-order saddle points in the dispersion) may further dramatically alter the adopted ordered state [3]. These strongly correlated phenomena are ideally studied using renormalization-group methods; however, such approaches have rarely been used to investigate how the phase diagram changes as the order of a VHS is tuned, or when the VHS is moved away from the Fermi level. Here, using the truncated-unity functional renormalization group (TUFRG), we perform an analysis of the square-lattice Hubbard model at weak coupling, in which varying a third-nearest-neighbour hopping ($t_3$) tunes the order of its VHSs. We also analyse the system using the parquet renormalization group in a patch scheme – comparing its results to those of TUFRG provides insights into the reliability of patch methods. We first pin the VHSs to the Fermi level and vary the hopping parameters, finding a rich landscape of phases that vary gradually but non-trivially with $t_3$. We then show that the system is much more sensitive to the energetic position of the VHSs, with some phases disappearing on perturbing very slightly from Van Hove filling. We conclude with some remarks on the implications our results have for the design of correlated two-dimensional materials.
References:
[1] A. Steppke, L. Zhao, M. E. Barber, T. Scaffidi, F. Jerzembeck, H. Rosner et al., Science 355, eaaf9398 (2017).
[2] G. Li, A. Luican, J. M. B. Lopes dos Santos, A. H. Castro Neto, A. Reina, J. Kong et al., Nature Phys. 6, 109 (2010).
[3] L. Classen and J. J. Betouras, Annu. Rev. Condens. Matter Phys. 16, 229 (2025).
| Affiliation | School of Physics and Astronomy, University of St Andrews |
|---|---|
| Career status | Postdoc |