 |
Center for Nonlinear Studies |
Strain engineering has emerged in recent years as a promising way to access novel topological phases. When low-lying excitations obey Dirac or Weyl dispersions, non-uniform strain can lead to artificial pseudo-magnetic fields, which, in contrast to actual magnetic fields, preserve the time-reversal symmetry. I show that one of the most dramatic consequences arises in gapless superconductors. Unlike the case of actual applied magnetic fields, strained gapless superconductors exhibit Landau quantization under applied strain [1]. A similar picture emerges in the presence of slowly-varying doping gradients. I focus on the resulting flat “zeroth” Landau level band of zero energy which manifests the most striking properties. I elucidate the nature of these unusual zero-energy excitations together with their topological properties. To gain a more complete picture, I also discuss strained three-dimensional odd-parity superconductors, which exhibit emergent real-space Majorana fermions. In all cases, I examine the stability of the highly-degenerate ground state with respect to interactions and discuss leading many-body instabilities [2].
The Sachdev-Ye-Kitaev (SYK) model in various incarnations has garnered much attention in recent years from high-energy and condensed-matter communities alike. In the latter case, it has been proposed as a simple, solvable system capable of reproducing non-Fermi liquid phenomenology. In spite of a wealth of esoteric theoretical results, few studies have focused on immediate realizations of this model and their signatures in experiment. Here, I consider a recent proposal for such a simple physical realization of the SYK model in the zeroth-Landau-level sector of an irregularly-shaped graphene flake. I study the charge transport signatures of the non-Fermi liquid state of such a quantum dot coupled to non-interacting leads. I show that the properties of this setup depend essentially on the ratio p between the number of transverse modes in the lead and the number of the fermion degrees of freedom N on the SYK dot. This ratio can be tuned via the magnetic field applied to the dot. The proposed setup gives access to the non-trivial conformal-invariant regime associated with the SYK model as well as a more conventional Fermi-liquid regime via tuning the field. I discuss the scaling behavior of the predicted conductance in both non-Fermi liquid and Fermi-liquid regimes respectively. I also describe the out-of-equilibrium current-bias characteristics and the various crossovers between the limiting behaviors [3].
[1] Emilian M. Nica and Marcel Franz, “Landau levels from neutral Bogoliubov particles in twodimensional nodal superconductors under strain and doping gradients,” Phys, Rev. B 97, 024520 (2018).
[2] Emilian M. Nica and Onur Erten, “Interacting Majorana fermions in strained nodal superconductors”, arXiv:1902.06759.
[3] Oguzhan Can, Emilian M. Nica, and Marcel Franz, “Charge transport in graphene-based mesoscopic realizations of Sachdev-Ye-Kitaev models”, Phys. Rev. B 99, 045419 (2019).
Host: Qimiao Si