Perfect and Controllable Nesting in Minimally Twisted Bilayer Graphene

Abstract

Parallel ("nested") regions of a Fermi surface (FS) drive instabilities of the electron fluid, for example the spin density wave in elemental chromium. In one-dimensional materials, the FS is trivially fully nested (a single nesting vector connects two "Fermi dots"), while in higher dimensions only a fraction of the FS consists of parallel sheets. We demonstrate that the tiny angle regime of twist bilayer graphene (TBLG) possess a phase, accessible by interlayer bias, in which the FS consists entirely of nestable "Fermi lines": the first example of a completely nested FS in a 2d material. This nested phase is found both in the ideal as well as relaxed structure of the twist bilayer. We demonstrate excellent agreement with recent STM images of topological states in this material and elucidate the connection between these and the underlying Fermiology. We show that the geometry of the "Fermi lines" network is controllable by the strength of the applied interlayer bias, and thus that TBLG offers unprecedented access to the physics of FS nesting in 2d materials. 1 arXiv:1908.08318v1 [cond-mat.mtrl-sci] 22 Aug 2019 of the FS consists of nested sheets) and notoriously difficult to control 10,11 . In contrast, the nesting exhibited by the twist bilayer is both complete (100% nested) and, as we show, can be fully controlled by tuning of the interlayer bias.This "nesting phase" of the twist bilayer is found in a large regime of angle-field space and is, remarkably, found both for the ideal twist geometry as well as the structural dislocation network that it reconstructs to at tiny angles 12-14 . The finding of a robust moiré-induced 2d "Fermi line" analogy of the 1d "Fermi dot" topology, controllable via bias, both offers unprecedented access to the physics of FS nesting, as well as highlighting the remarkable electronic structures that can be created by moiré geometries and their structural dislocation networks in 2d materials. II. RESULTS A. ModelThe physics of the tiny angle regime of the twist bilayer is an essentially multiscale problem involving both the lattice constant of graphene -the scale at which atomic relaxation 2 FIG. 1: Fully nested Fermiology in the graphene twist bilayer and the corresponding dislocation network (θ = 0.51 • , E = 90 mV/Å). Below ∼ 1 • twist bilayer graphene relaxes into an ordered network of dislocations, with the smoothly varying stacking order of the ideal twist geometry (a) becoming series of sharp AB and BA domains (b), each separated by pure shear partial dislocations with high von Mises strain (J 2 ) (c,d). Pseudo-magnetic fields of the order of 40 T are induced in the AB and BA regions with alternating sign between the latter (e,f). In the density of states (DOS) the zero mode is substantially broadened, with the valley region shifting upwards in energy (g).However, while atomic relaxation induces dramatic changes to the Fermiology in the zero mode region (l,m), in the valley region a remarkably stable Fermi topology of fully nested Fermi lines is seen (nesting vector indicated by...

Perfect one-dimensional chiral states in biased twisted bilayer graphene

“…The modes along different directions are never hybridized, and therefore all these states serve as independent perfect 1D channels over the whole TBG. The result is consistent with a recent work which predicts the perfect nesting of the Fermi surface in the biased TBG 19 .…”

“…The different planes are not hybridized with each other, giving nearly straight Fermi lines at the fixed energy. Such straight Fermi surfaces were also reported in the recent paper 19 . In the largest bias ∆ = 400 meV, we notice some flat levels appear in the upper part of the energy window independently from the dispersive 1D states, (e.g., three horizontal lines in 50 meV < |E| < 100 meV for θ = 0.3 • ), which can be interpreted as pseudo-Landau levels of the fictitious gauge field 17 .…”

“…This is natural because the AB and BA regions (where the energy band is gapped out) significantly expand under the lattice relaxation, and the wave amplitude must be confined to the narrow boundary region. 19,20 The similar, zigzag-shaped wave func-tion was also reported in a recent work 19 . Interestingly, we see that the relaxed TBG's wave function in Fig.…”

“…The real TBG is not a simple stack of rigid graphene layers as assumed in the previous section, but it has a spontaneous lattice relaxation and resulting AB/BA domain formation [31][32][33]35,[45][46][47][48][49][50][51][52][53] . Such a structural deformation modifies the electronic band structure 19,20,35,44,50,[52][53][54] . Here we calculate the energy band structures in the presence of the lattice strain using the tight-binding method 50 .…”

“…In this paper, we theoretically study the electronic structure of small-angle TBG with a large interlayer bias (i.e., potential asymmetry between the top and bottom layers), and demonstrate the formation of perfect onedimensional (1D) states within well-defined energy windows on either side of zero energy. The effect of the interlayer bias on TBG was investigated in the previous theoretical works [14][15][16][17][18][19][20][21] , and it was found that a large enough bias gives rise to a network of topological channels on the domain boundaries between AB and BA stacking regions 15,[17][18][19][20][21] . There the electronic states at AB and BA regions are locally gapped out by the interlayer bias 22 , and two topological modes per spin and per valley necessarily appear on each AB-BA boundary [23][24][25][26][27][28][29] , reflecting that the two regions have different quantized values of single-valley Hall conductivity, ±e 2 /h.…”