## Symposium X: Frontiers of Materials Research

##### December 06, 2019

** Alessandra Lanzara, University of California, Berkeley, and Lawrence Berkeley National Laboratory**

*Engineering Two-Dimensional Heterostructures with a Twist** *

Written by Arthur L. Robinson

The past few years have seen exciting new opportunities emerging from simply stacking and/or twisting together atom-thick layers of the same or different materials. The lattice mismatch or rotational misalignment introduced by such stacking gives rise to long-range Moiré patterns that lead to modification of the electronic band structure, which in turn gives rise to the appearance of unexpected properties, such as Mott-like behavior and superconductivity, even in weakly interacting systems such as graphene.

In her Thursday Symposium X presentation, Alessandra Lanzara of the University of California, Berkeley, and the Lawrence Berkeley National Laboratory described recent investigations by her group on twisted and strained graphene and transition metal dichalcogenide (TMD) heterostructures as a function of twisting angle and gating. Using angle-resolved photoemission spectroscopy, the group studied the effect of such misalignments on the electronic structure of these materials, yielding insight on the key parameters that lead to the onset of strong correlation and novel behavior in these materials.

Lanzara opened her talk by introducing the importance of topology as an essential theoretical tool in understanding the properties of materials. Until recently, thinking about transitions in crystalline solids has been based on order parameters related to symmetry breaking and correlations. Topology has now joined these as an organizing principle of matter. In general, topological properties are those that are preserved under continuous deformation. For example, in a topological insulator there is no sharp phase transition, but the insulator property is preserved as the electronic band structure is continuously deformed.

With the addition of topology, said Lanzara, it is now possible to describe the various states of materials now on a single diagram with a correlation energy on one axis and the spin–orbit coupling on the other. Close to the origin, conventional metals and insulators are well described by band theory. As the correlations increase, Mott insulators come to the fore, whereas topological insulators and semimetals come to the fore when spin–orbit coupling increases. But the future may lie in the panoply of exotic behaviors like Weyl insulators that arise as both correlations and spin–orbit coupling grow.

“What new cooperative phenomena and particles will occur when you bring together correlation, spin orbit coupling, and topology?” Lanzara asked next. Taking a hint from physicist Richard Feynman’s famed questions about two-dimensional pages, the question became “What would the properties of materials be if we could really arrange the atoms the way we want them?” But how would one go about exploring this immense space? One way to arrange atoms is by means of heterostructures consisting of stacks of materials with different properties with relevant aspects being dimensionality, coupling to the lattice, order (spin, charge, orbitals, and Cooper pairs in superconductors), and electrostatic doping. Outcomes of building these structures include emergent phenomena at interfaces, such as ferromagnetism, superconductivity, and metal-to-insulator transitions.

From here Lanzara rapidly reviewed some considerations, such as electron screening, and methods for controlling the electronic structure in the context of searching for new phenomena. In particular, her group found that twisting the layers in the heterostructure provided a new level of band-structure control. In fact, when Lanzara was being introduced as the speaker for this Symposium X, the MC used the term twist-tronics.

After discussing engineering of topology and strong correlation, including local inversion-symmetry breaking in the heterostructure layers that gives rise to spin–orbit coupling, Lanzara turned toward the possibility of an even larger phase space for materials design, moving from periodic crystals with both long- and short-range order, to quasiperiodic crystals with order but are not periodic, to Floquet crystals that are periodic in time, and ending with amorphous materials with no long-range order but perhaps some short-range order. After asking if amorphous systems can be used for materials engineering, she reported some early results on the amorphous topological insulator Bi_{2}Se_{3}. One task was to find a replacement for the momentum quantum numbers (k_{x}, k_{y}, k_{z}) in crystals. The group was thinking of an (average) bulk Hamiltonian as spherically symmetric in k-space, resulting in a wavefunction parameterized by k^{2} and the angles q and f in a spherical coordinate system.

Lanzara summed up her presentation by declaring that two-dimensional heterostructures constitute an incredible, highly tunable platform for exploring correlation, symmetry breaking, and topology. The electronic structure of two-dimensional van der Waals materials is extremely easy to modify, including effects such as symmetry breaking to induce gap opening and renormalization effects due to screening, and spin–orbit coupling and other many-body interactions. But questions still ripe for investigation include: Can we design new types of many-body topological properties and new particles? And what new phases can result from the interplay between them?

*Symposium X—Frontiers of Materials Research features lectures aimed at a broad audience to provide meeting attendees with an overview of leading-edge topics.*