Communications Physics

Table 1 Atomic and renormalized hoppings (in eV) for borophene and carbon-substituted borophene.

From: Tunning the tilt of the Dirac cone by atomic manipulations in 8Pmmn borophene

(atomic)	t₃₆	t₆₅	t₅₃	t₈₁	t₃₈	t₃₇	t₇₂	t₇₈
pure borophene B₈	2.09	−2.66	2.09	2.09	−1.87	−1.87	−1.87	−2.54
B₆C₂-I-[C2&C3]	1.93	−2.52	1.96	1.92	−1.52	−1.52	−1.55	−2.34
B₆C₂-R-[C5&C6]	2.14	−2.33	2.12	2.15	−2.23	−2.21	−2.20	−2.43

(renormalized)	t	t^p	t^x	\(\tilde{t}\)	\(\bar{t}\)	ζ_y	k_D/k_Y	\({\zeta }_{y}^{{{{{{{{\rm{DFT}}}}}}}}}\)
pure borophene B₈	−2.21	−2.36	−1.07	−1.99	−2.51	0.46	0.48	0.49
B₆C₂-[C2&C3]	−2.37	−1.75	−0.95	−1.62	−2.05	0.36	0.66	0.47
B₆C₂-R-[C5&C6]	−2.05	−2.49	−1.09	−2.24	−2.85	0.59	0.32	0.66

(top) ab initio hopping matrix elements (in eV) for borophene and C-doped borophene obtained from Wannier functions. Conventions for labeling of the hopping matrix elements are given in Fig. 2a. (bottom) Renormalized parameters of Fig. 2c. ζ_y is the tilt parameter and k_D/k_Y quantifies the location of Dirac node.

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