A central feature of many van der Waals (vdW) supplies is the power to exactly control their cost doping, nn, and electric displacement discipline, DD, utilizing prime and backside gates. For gadgets composed of just a few layers, it is commonly assumed that DD causes the layer-by-layer potential to drop linearly throughout the structure. Here, we present that this assumption fails for a broad class of crystalline and moiré vdW structures based mostly on Bernal- or rhombohedral-stacked multilayer graphene. We discover that the digital properties at the Fermi stage are largely dictated by special layer-polarized states arising at Bernal-stacked crystal faces, which sometimes coexist in the same band with layer-delocalized states. We uncover a novel mechanism by which the layer-delocalized states fully display the layer-polarized states from the bias applied to the distant gate. This screening mechanism results in an unusual scenario the place voltages on either gate dope the band as expected, but the band dispersion and associated digital properties remain primarily (and sometimes completely) governed by the gate nearer to the layer-polarized states.

Our outcomes reveal a novel electronic mechanism underlying the atypical single-gate--managed transport traits observed across many flat-band graphitic constructions, and iTagPro features provide key theoretical insights essential for accurately modeling these programs. Dual-gated two-dimensional (2D) van der Waals (vdW) machine buildings offer unprecedented tunability, enabling simultaneous in situ control of the cost density and perpendicular displacement subject. 0) at bigger |D||D|. Fig. 1b, corresponding to a twisted bilayer-trilayer graphene gadget. 4.9 V corresponds to a transition from an unpolarized metallic phase to a metallic phase with full isospin degeneracy breaking. In distinction, other options of the maps in Figs. A key microscopic feature of these graphene-primarily based techniques is the presence of robust layer- and sublattice-polarized states at the K and K’ points of the monolayer Brillouin zone, arising from the local AB (Bernal) stacking arrangement between neighboring graphene sheets away from any twisted interface. The schematic in Fig. 1c shows the case of TDBG, formed by twisting two Bernal bilayers.

0, iTagPro features making up a layer-polarized "pocket" that coexists with extra delocalized states inside a single band (Fig. 1d). The gate-tracking behavior then generally arises from a combination of two effects: (i) the layer-polarized pocket (on layer 1 in Fig. 1c) predominantly controls the onset of symmetry-breaking phases as a consequence of its high density of states, and (ii) the delocalized states screen the layer-polarized pocket from the potential applied to the distant gate (the highest gate in Fig. 1c). The interplay of these two results naturally results in single-gate tracking of the symmetry-breaking boundary, as seen in Figs. In this paper, we analyze the gate-tracking mechanism to delineate its microscopic origins, examine its ubiquity in moiré graphene structures, and assess its robustness. We begin by clarifying the pivotal function of layer-polarized states in shaping the band construction of Bernal-terminated multilayer techniques. D plane, revealing a novel mechanism by which the delocalized states display the layer-polarized states.

Finally, we apply this framework to TDBG, performing numerical mean-field simulations which will then be in comparison with experiment observations, ItagPro for instance in Fig. 1a. Although we give attention to TDBG for readability, our theory establishes a basic mechanism that applies to any multilayer techniques with Bernal stacking as a component of its structure, ItagPro together with rhombohedral multilayer graphene and twisted bilayer-trilayer graphene. Appropriately generalized, our principle also needs to apply to any layered system that includes completely polarized states, similar to twisted bilayer transition metallic dichalcogenides. We begin by reviewing the properties of 2D graphene multilayer methods that characteristic a Bernal stacked interface. A2 interlayer tunneling is critical. This arrangement yields a state at the K point that is totally polarized to the bottom layer, even when other states away from the K point are not bound to the surface. The layer-polarized state on the A1A1 orbital is an actual layer and sublattice polarized eigenstate of Eq. K point, states retain sturdy layer polarization, forming a well-outlined pocket of layer-polarized states.

The peculiarity of moiré methods featuring Bernal interfaces that distinguishes them from normal Bernal bilayer graphene is that this pocket exists within a nicely-outlined flat moiré band. As we'll present, this excessive density-of-states pocket controls symmetry breaking, and responds primarily to the proximal gate because of its layer polarization. For example the role of the layer-polarized pocket, we now study its influence on the band structure of TDBG. Delta U are treated as theoretical parameters; later, we'll join them to experimentally tunable gate expenses. 0 contour reveals that this excessive-DOS area coincides with the layer-polarized state being exactly on the Fermi level. 0 contour, shown in Figs. 0 (Fig. 2b) your complete band (not simply the pocket) is strongly polarized to the underside of the structure, leading to a quenching of the layer-polarized pocket dispersion. In the standard strategy (i.e., retaining solely the first term in Eq. Crucially, the true potentials deviate from the typical outcome not solely in magnitude, but in addition in the signal of the power distinction, suggesting a risk for non-trivial state renormalization with external displacement discipline. These expressions can be understood as follows. Next, we relate the gate-projected compressibilities in Eq. 0, the contour tilts towards the DD axis. 1 it's tuned equally by both gates following the naive picture often utilized to 2D stacks. We now apply the above mechanism to real techniques and connect to experimental observations. Zero for most symmetry-breaking phase boundaries.