Tunning the tilt of a Dirac cone by atomic manipulations: application to 8Pmmn borophene

Abstract

We decipher the microscopic mechanism of the formation of tilt in the two-dimensional Dirac cone of 8P mmn borophene sheet. With the aid of ab initio calculations, we identify relevant low-energy degrees of freedom on the 8P mmn lattice and find that these atomic orbitals reside on an effective honeycomb lattice (inner sites), while the high-energy degrees of freedom reside on the rest of the 8P mmn lattice (ridge sites). Local chemical bonds formed between the low-and high-energy sublattices provide the required off-diagonal coupling between the two sectors. Elimination of high-energy ridge sites gives rise to a remarkably large effective further neighbor hoppings on the coarse grained (honeycomb) lattice of inner sites that determine the location and tilt of the Dirac cone. This insight based on real space renormalization of the 8P mmn lattice enables us to design atomic scale substitutions that can lead to desired change in the tilt of the Dirac cone. We furthermore encode the process of renormalization into an effective tight-binding model on a parent honeycomb lattice that facilitates numerical modeling of various effects such as disorder/interactions/symmetry-breaking for tilted Dirac cone fermions of 8P mmn structure. The tilt parameters determine a spacetime metric, and therefore the ability to vary the tilt over distances much larger than the atomic separations opens up a paradigm for fabricating arbitrary solid-state spacetimes.

Circuit realization of tilted Dirac cone: A platform for fabrication of curved spacetime geometry on a chip

“…We will show how the "square root" of the resulting Klein-Gordon equation is equivalent to a theory of tilted Dirac fermions. The same tilted Dirac theory emerges in both electron theory of 8P mmn borophene [27]. This suggests that the resulting Dirac theory is a property of the underlying lattice.…”

“…Honeycomb lattice circuit model: Inspired by our coarse grained [28,29] fermionic model introduced in Ref. [27], in Fig. 1 we consider a LC circuit based on the periodic honeycomb lattice.…”

“…Every site is grounded by a capacitance C 0 . The inductance connection enriches the graph structure of a simple honeycomb lattice similar to an effective fermionic hopping model [2], where the further neighbor connections set the location [30] and tilt [27] of the Dirac cone. The honeycomb lattice is composed of two Bravis sublattices A and B [10].…”

Hawking radiation on the lattice as universal (Floquet) quench dynamics

“…These results now pave the way for exploring the Hawking effect in other quantum many-body systems, such as for example interacting spin chains (both analytically in integrable models, and numerically using e.g. matrix product state simulations), 2D materials with tilted Dirac cones [36][37][38], and cold-atom or trapped ion experiments. region of the horizon, and x < 0 is the 'inside' region.…”

Kinetic theory of tilted Dirac cone materials

“…The remarkable fact is that, the above metric that emerges as the long-distance behavior of certain lattices or certain graphs, is independent of what excitation is being propagated on the lattice/graph. The circuit realization of the above metric [18] on a honeycomb graph is obtained by coarse-graining of the 8P mmn lattice [19].…”