Frontiers in Synthetic Moiré Quantum Matter Proceedings of a Workshop (2022) / Chapter Skim
Currently Skimming:
7 Topological Superconductivity in Twisted Cuprate Double Layers
7 Topological Superconductivity in Twisted Cuprate Double Layers
Pages 72-83
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 72... ...
. ENGINEERING A BILAYER TOPOLOGICAL SUPERCONDUCTOR The basic idea behind his approach, Franz explained, is to engineer a high-Tc cuprate bilayer into a topological superconductor.
|
From page 73... ...
is a complex phase between the two order parameters. It is known, Franz said, that this is a fully gapped topological superconductor with protected chiral edge modes and it exhibits spontaneously broken time-reversal symmetry.
|
From page 74... ...
"What I'm proposing here to take two such monolayers and assemble them into a bilayer with a twist to realize this topological superconductor." THEORETICAL UNDERPINNINGS After explaining his goal of using two monolayers of Bi2Sr2CaCu2O8+δ with a twist of about 45 degrees to create a topological superconductor, Franz sketched out the theoretical calculations that indicate that it should work. He began by ex plaining topological superconductivity and, specifically, what it means to add the two order parameters with a complex phase.
|
From page 75... ...
"This is the origin of the fully gapped superconductor that can occur in this way." Having offered that background, Franz described in qualitative terms the results he has derived about what happens when two single layers of Bi2Sr2CaCu2O8+δ are stacked on top of each other with a twist. For small twist angles below a certain critical angle, it is energetically favorable for the two order parameters to add with just real coefficients, as in the first of the two superpositions he described, and in this case, "nothing very interesting happens." The resulting order parameter looks like the order parameter of the original two-layer d-wave superconductor with point nodes in the momentum space that are shifted a bit by that twisting.
|
From page 76... ...
Thus in the region around 45 degrees that stretches from θc– to θc+, there is time reversal symmetry breaking and topological superconductivity. This is the range, Franz said, "that I'm so excited about and that is the subject of this talk." Taking into account how the order parameters vary with temperature, Franz produced a phase diagram showing at what temperatures and twist angles the bilayer materials would be a topological superconductor.
|
From page 77... ...
Starting with a standard Hamiltonian for a d-wave superconductor, he briefly described some calculations that allowed him to plot the phase at which the free energy of the superconductor was a minimum as a function of the twist angle. The resulting plot matched up very closely with the plot he had calculated from Ginzburg-Landau theory, but in this case the microscopic theory gave him something additional: the size of the excitation gap in the twisted bilayer structure.
|
From page 78... ...
First, he showed a series of commensurate moiré patterns that progressively approximated a 45-degree angle, which is whether things are most interesting, he said. Then he showed a series of Fermi surfaces, first for the untwisted bilayer and then for three twisted bilayers with increasing twist angles.
|
From page 79... ...
According to the authors, as the twist angle is increased up to around 10 degrees, the Dirac cones from the individual layers collide, and because they have the same chirality and are protected by time reversal symmetry, they cannot gap out within a non-interacting model, so instead, at some magic angle, they form a quadratic band crossing. Time reversal symmetry does not allow the formation of isolated flat bands as happens in graphene, Franz explained, but the equivalent of the magic angle in graphene is the angle at which the quadratic band crossing forms, and the authors argue that although interactions are perturbatively irrelevant at the Dirac point, they become relevant at the quadratic band crossing.
|
From page 80... ...
There are also two-dimensional examples where Majorana fermions occur in the core of a superconducting vortex. This situation may arise when there is a topological insulator interfaced with an ordinary superconductor, and that interface forms a kind of topological superconductor that supports Majo rana zero modes in individual vortices.
|
From page 81... ...
Franz's has team has analyzed such a superconductor theoretically using the same sorts of calculations they used to examine the bilayer BSCCO materials, and the calculated phase diagrams show large portions that contain the desired px + ipy superconducting phase with spontaneously broken time reversal symmetry. Furthermore, the calculations show that this type of superconductor would harbor an isolated Majorana zero mode in the vortex (Tummuru et al.
|
From page 82... ...
2021b. "Probing Time Reversal Symmetry Breaking Topological Superconductivity in Twisted Double Layer Copper Oxides with Polar Kerr Effect." Physical Review Letters 127(15)
|
From page 83... ...
2020. "Magic Angles and Current-Induced Topology in Twisted Nodal Superconductors." arXiv 2012:07860v1.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.