Supporting Information

Variable Electronic Properties of Lateral Phosphorene-

Graphene Heterostructures

Xiaoqing Tian, Lin Liu, Yu Du,* Juan Gu, Jian-bin Xu,* and Boris I. Yakobson*

1. Electronic properties of the heterostructures of 15-APNR/16-AGNR

(a) (b)

Figure S1. (a) Band structure and (b) DOS of the heterostructure of 15-APNR/16-AGNR

The relaxed heterostructure of 15-APNR/16-AGNR has a width of 4.5 nm. 15-APNR and 16-

AGNR are connected by robust chemical bonds. The length of P-C bond is 1.86Å at this interface,

which is the same to that of 15-APNR/15-AGNR. Heterostructure of 15-APNR/16-AGNR has a

band gap of 0.66 eV as shown in Figure S1(a). Its corresponding density of states (DOS) is shown

in Figure S1(b). Based on the DOS, the VBM and CBM are mainly contributed from the 15-

APNR and 16-AGNR respectively. This is confirmed by the charge distribution of HOMO and

LUMO orbitals ( see Figure S3g, h). The mh* and me

* are 0.28 and 0.37 times m0 calculated by Eq

(1). The mh* is smaller than me

*. According to the Drude model, the mobility of hole carriers will

be 1.32 times that of electron carriers. The charge transfer is the same as that of heterostructure of

15-APNR/15-AGNR. The calculated Φw is 4.47 eV which is comparable to pristine monolayer

graphene’s theoretical value of 4.48 eV and experimental value 4.6 eV. The Φws of 2-APNR/2-

AGNR, 4-APNR/4-AGNR, 7-APNR/7-AGNR, 16-APNR/15-AGNR and 16-APNR/16-AGNR

are 4.80, 4.84, 4.50, 4.42 and 4.45 eV, respectively. The corresponding band gaps are 1.53, 1.55,

0.93, 0.63 and 0.65 eV, respectively. Thus the work function can be modulated by the width and

constituents of the heterostructures. The larger the band gap the larger the work function.

Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics.This journal is © the Owner Societies 2015

2. Two-dimensional stripes of phosphorene/graphene

(a) (b)

(c)

(d) (e)

(f)

Figure S2. Optimized structures of periodic two-dimensional stripes of (a) 15-APNR/15-AGNR, (b) 15-

APNR/16-AGNR and (c) 24-APNR/24-AGNR. Band structures of periodic two-dimensional stripes of (d) 15-

APNR/16-AGNR, (e) 15-APNR/16-AGNR and (f) 24-APNR/24-AGNR. In (a), (b) and (c), the blue lines denote

the boundary of the supercells and the supercells are extended along both the X and Y directions.

The electronic properties of infinitely periodic stripes of APNRs/AGNRs are also

investigated. The optimized structures are shown in Figure S2(a)-2(c). The supercells

are periodicly extended along both the X and Y directions. The widths of periodic

stripes of 15-APNR/15-AGNR, 15-APNR/16-AGNR and 24-APNR/24-AGNR within

the supercells are 4.3, 4.4 and 6.8 nm, respectively. The band gaps of these periodic

stripes are 0.4, 0.48 and 0.31 eV, respectively (see Figure S2(d)-f). These values are

smaller than corresponding isolated APNRs/AGNRs terminated with hydrogen atoms

due to the interactions between the boundaries of stripes. These differences of band

gaps are attributed to the interactions between supercells. For all the periodic stripes

investigated, the band structures exhibits the parabolic energy-momentum dispersion

near the Fermi level, which indicate the semiconducting characteristics. The mh*s of

15-APNR/15-AGNR, 15-APNR/16-AGNR and 24-APNR/24-AGNR are 0.33, 0.42

and 0.28 m0 respectively. The me*s of 15-APNR/15-AGNR, 15-APNR/16-AGNR and

24-APNR/24-AGNR are 0.30, 0.49 and 0.26 m0 respectively. These values are larger

than those of corresponding one dimensional heterostructures with H terminated. This

indicates that interactions between the boundaries of stripes can increase the carriers’

effective masses.

3. Scheme and illustration of tight-binding ladder model

(a) (b)

Figure S3. Schemes of tight binding ladder model with inter-edge hopping parameters (a) t = 0 (b) t ≠0.

The Hamilton for this tight-binding ladder model [1] is

(1)

01 1

2 20

0 020 0

2

lika ika

r

U t t tH e e

t tUt

Where t1 and t2 are he hopping integrals along the left and right edges, respectively.

εl and εr are the on-site energies of left and right edges. The hopping integral between

two edges is t0. εl and εr are the on-site energies of left and right edges respectively.

The tranverse Eext will cause the additional potential energy difference of the two

edges U, which is defined as U=eEext(dP/κP+dG/κG), where κP and κG are the dielectric

constants for APNRs and AGNRs, respectively. dP and dG are the widths of APNRs

and AGNRs respectively.

The eigenvalues of this Hamilton are

(2)2 20

( ) ( ) 1( ) [ ( ) ( ) ] 42 2

l rl r

E k E kE k E k E k U t

Where El(k)=εl-2t1coska and Er(k)=εr-2t2coska.

For one-dimensional materials, the two edges could be thought as their “surfaces”.

The band gap is the order of the energy split of the two surface states.

4. Effects of H doping on the electronic properties of the heterostructure of APNRs/AGNR

Figure S4. Adsorption sites for H monomer on the heterostrucutures of APNR/AGNR. There is totally NP+NG

sites, which corresponding to NP+NG configurations.

Table S1 Adsorption energy (Ead) of H monomer on the phosphorene side of 15-APNR/15-AGNR.

Site 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ead 1.29 1.56 1.55 1.57 1.58 1.58 1.59 1.59 1.59 1.60 1.58 1.60 1.76 1.41 1.80

Table S2 Adsorption energy (Ead) of H monomer on the graphene side of 15-APNR/15-AGNR.

Site 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Ead 1.84 1.30 1.10 1.05 1.05 0.93 0.93 1.00 0.95 0.95 1.01 1.04 0.78 1.14 1.63

For H monomer adsorption on the heterostrucuture of 15-APNR/15-AGNR, totally thirty

configurations are considered as shown in Figure S4. The calculated adsorption energies are

shown in Tables S1 and S2. The two most stable configurations of H monomer doped 15-

APNR/15-AGNR are shown in Figures 3 (a) and 3(b) of main text respectively. The highest

adsorption energies indicate that the boundary between graphene and phosphorene is more

chemically active.

(a)

(b)

(c)

(d) (e)

(f)

Figure S5. Calculated structures and DOS of H dimmer doped 15-APNR/16-AGNR with three configurations. (a)

H dimmer adsorbed on both planes of the heterostrucuture. (b) H dimmer adsorbed on graphene part of the

heterostrucuture. (c) H dimmer adsorbed on graphene part of the heterostrucuture. (d) DOS of configuration a. (e)

DOS of configuration b. (f) DOS of configuration c.

The calculated structures of H dimmer doped 15-APNR/16-AGNR with three configurations

are shown in Fig. S5 (a), 5(b) and 5(c). For configuration a, it has a band gap of 0.2 eV as shown

in Figure S 5(d). For configuration b, it has a band gap of 0.37 eV as shown in Figure S 5(e). For

both configurations a and b, the band gap is smaller than that of the undoped heterostrucuture of

15-APNR/16-AGNR (0.66 eV). H doping effects will raise up the VBM of 15-APNR/16-AGNR

and the band gap is reduced. For configuration c, the H doping will inject excessive electron

carriers into APNR and raise up the Fermi level. The Fermi level is 0.23 eV above the CBM, so

the heterostructure is heavily doped and exhibits the metallic characteristics. Thus the H doping

effects can be configuration-dependent.

References 1 K. Dolui, C. Das Pemmaraju and S. Sanvito, ACS Nano,2012, 6, 4823-4834.