Microsoft Word - APL-Ribbon_junctions_20070328-Text_with_Figures-ARXIV.doc
Molecular circuits based on graphene nano-ribbon junctions 
Zhiping Xu† 
Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China 
Graphene nano-ribbons junctions based electronic devices are proposed in this Letter. Non-
equilibrium Green’s function calculations show that nano-ribbon junctions tailored from 
single layer graphene with different edge shape and width can act as metal/semiconductor 
junctions and quantum dots can be implemented. In virtue of the possibilities of patterning 
monolayer graphene down to atomic precision, these structures, quite different from the 
previously reported two-dimensional bulk graphene or carbon nanotube devices, are 
expected to be used as the building blocks of the future nano-electronics. 
Keyword: graphene nano-ribbon, electronic transport, metal/semiconductor junction, quantum dot 
                                                 
† Email: xuzhiping@gmail.com 
Nano-electronics, or molecular electronics have been proposed as the alternative to silicon in 
future technical applications1 and have attracted great interests recently. In virtue of their unique 
structures and various functions, these nanostructures possess intriguing electromagnetic, 
mechanical and optical features. Especially, carbon based nanostructure, such as fullerene, graphene 
and carbon nanotubes are the most interesting structures because of their rich variety of excellent 
physical properties. For instance, anomalous quantum hall effects (QHE) and massless Dirac 
electronic behavior have been discovered in the graphene systems2, 3, and these discovery has 
sparked lots of investigations on this unique two-dimensional material. Tailored from monolayer 
graphene, graphene ribbon (GNR) with finite width has been shown to hold unusual electronic 
properties4, depending on their edge shape and width. In more details, ribbons with zigzag edges 
(ZGNRs) possess spin-polarized peculiar edges states and spin-polarized electronic state provides 
half-metallicity under transverse electric field and has great potential in the application as 
spintronics5. In contrast, the armchair edged ribbons (AGNR) can be either metallic or 
semiconducting depending on their width6, AGNR with width Na (named as NaAGNR in the 
conventional nomenclature) has been shown to be metallic only if Na = 3k + 2 and semiconducting 
otherwise, where k is an integer. 
From the experimental point of view, the fascinating feature of the ribbons is that the 
graphene material can be easily patterned using standard micro- or nano-electronics lithography 
methods. Unlike the carbon nanotubes or other low-dimensional nanostructures, the GNRs with 
intricate sub-micrometer structures can now be fabricated7, 8, 9, and it is believed that a combination 
of standard lithographic and chemical methods will help to pattern the graphene with atomic 
precision down to the molecular level. The high mobility μ = 2.7 m2/V.s, large elastic mean free 
path le = 600nm and phase coherence lengths lφ= 1.1 μm observed7 in the epitaxial graphene 
patterned suggest the use of pure GNR structures as the building blocks of the nanoscale confined 
and coherent electronic circuits. To realize the components such as field transistors9 and coulomb 
blockade devices, experimentally controllable metal/semiconductor junctions and quantum dots will 
be essential. As proposed by Chico et al.10, 11, these can be achieved by jointing different carbon 
nanotubes. However, the fabrication and control of the nanostructure of graphene ribbons are much 
more convenient than introducing pentagon-heptagon defects in carbon nanotubes as discussed, 
therefore it is interesting to investigate the possibilities of ribbon junction based nano-circuits. 
To this end, we have proposed several kinds of the GNRs based electronic devices in this 
Letter. We show that, by controlling the tailoring process of GNRs with different edge shape and 
width, the metal/semiconductor junctions and quantum dots can be easily implemented 
experimentally. To validate this, electronic transport calculation using the non-equilibrium Green’s 
function method have been carried out following Landauer’s approach12. The electronic structure of 
the graphene lattice is described using the nearest-neighbour π-orbital tight-binding model and the 
hopping parameter Vppπ = 2.75 eV is used. This simple topological model gives quantitative results 
comparing with the LDA results except for the gap opening at small width as the consequence of 
the length changing of σ bonds6. By solving the Green’s function, the conductance was finally 
calculated as G = G0Tr[ΓLGRΓRGA] and the density of state is expressed as D = –ImTr[GR]/π11, 
where G0 = 2e2/h is the unit quanta of conductance including the spin degeneracy, GR(A) is the 
retarded (advanced) Green’s function of the conductor and ΓL(R) is the spectral density describing 
the coupling between the left (right) lead and the conductor. In our model, the leads are represented 
using semi-infinite graphene ribbons attached to the conductor region, with the same shape and 
width. 
First of all we investigate straight metal/semiconducting junction 11AGNR/10AGNR. The 
structure of the junction is considered by simply patching two different straight ribbons together, 
leave a width mismatching at the interface. The result shown in Fig. 1 indicates a gap Eg = 0.93 eV 
near the Fermi energy and the imperfection at the interface induces a deviation of conductance from 
the step-like curve of the perfect ribbon. However, the van Hove singularities which are the 
characteristics of 1D system remain. 
To examine the detailed electronic structure of the junction, a spatial-resolved localized 
density of states (LDOS) analysis is helpful. We have grouped the atoms into slices according to 
their distance from the interface. Each 4.26 Å long slice (a unit cell of the perfect AGNR) in the 
10AGNR, 11AGNR and interface part contain 20, 22 and 21 atoms respectively. The LDOS 
averaged at different slices are plotted in Fig. 1. From the semiconducting 10AGNR side we find 
the LDOS is distorted near the interface and gap state appears through the contact with metallic 
11AGNR. However at slices far from the interface, at slice 3 for example, the perfect 
semiconduting behavior is mostly recovered. At the scattering interface the van Hove singularities 
have been smoothed and 1D metallic structure gradually emerges as the distance from interface 
increases from the 11AGNR side. The arising of gap state near the interface characterizes the metal-
semiconductor junction and suggests the possibilities of building Schottky devices. 
Furthermore, L-shape GNR junctions with different orientations can be constructed. For 
instance, the LDOS of 8ZGNR/15AGNR junction with a π/6 joint is analysized in Fig. 2. As 
expected, the edge state of the 8ZGNR spreads into the semiconducting 15AGNR side. Because of 
the ZGNR possess spin-polarized structure, so this half-metal/semiconducting junction inspires 
interests in the spin-transport devices. 
Beside of the metal/semiconductor junction, the semiconductor/semiconductor junctions 
have also been investigated and defect states in gap appear at the interface. Moreover in the 
ZGNR/ZGNR junctions, zero-conductance dips13 near Fermi energy have been observed, caused by 
the complete backward scattering. 
The metal-semiconductor junction also suggests quantum dot devices through combing two 
of them together. We now consider the junction 12AGNR/11AGNR/12AGNR. In this structure a 
central metallic ribbon is sandwiched by two semiconductor barriers where quantized states can be 
formed. Our calculation results depicted in Fig. 3 show two sharp DOS peaks inside the gap of 
semiconducting 12AGNR containing 7 unit cells, with energy E1,2 = 0.2025 and -0.2025 eV. As 
seen from the spatial-resolved LDOS at E = 0.2025, the bounded state is localized inside the 
11AGNR region. The structure of the quantum levels can be further tuned by changing the length of 
11AGNR. From our calculation, as it changes from 1 to 8 unit cells, the energy spacing between the 
nearest peaks around Fermi energy, i.e. ΔE = E1-E2, gradually decreases from 0.785 eV to 0.385 eV 
and their DOS becomes higher and sharper. 
We have also observed quantized edge states within the 10AGNR/7ZGNR/10AGNR 
junctions through introducing two π/6 joints. The results are shown in Fig. 3 where we can found 7 
LDOS peaks inside the zero-conductance gap. The quantized states with E = -0.3525, -0.1625, - 
0.05, 0, 0.05, 0.1625 and 0.3525 correspond to different LDOS patterns (see Fig. 4 for E = 0.3525). 
The higher the energy, the more nodes of the bounded standing wave have. The electron wave 
quantized pattern depends on the structure of the central region. 
In conclusion, we have proposed nano-electronic circuits based on graphene nano-ribbon 
junctions. Through tailoring GNRs into junctions of different edge shape and width, we can 
implement metal/semiconductor junctions and quantum dots in principle. In virtue of the possibility 
of molecular level patterning based on lithography and chemical methods, these devices are 
expected to be fabricated easier in comparison with other structures such as the single molecule or 
carbon nanotubes junctions, and are expected to find great applications in the large-scale integrated 
nano-circuits in future. 
The work is supported by the National Science Foundation of China through Grants 
10172051, 10252001, and 10332020 and the Hong Kong Research Grant Council (NSFC/RGC N 
HKU 764/05 and HKU 7012/04P). ZX also thanks Prof. Wenhui Duan, Dr. Tao Zhou and Dr. 
Haiyun Qian from the Department of Physics in Tsinghua University for their help on the 
calculation. 
1N. J. Tao, Nature Nanotechnology 1 173 (2006). 
2K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. 
Dubonos and A. A. Firsov, Nature 438, 197 (2005). 
3Y. Zhang, Y. Tan, H. L. Stormer and P. Kim, Nature 438, 201 (2005). 
4Y. Kobayashi, K. Fukui, T. Enoki, K. Kusakabe and Y. Kaburagi, Phys. Rev. B 71, 193406 (2005). 
5Y. Son, M. L. Cohen and S. G. Louie, Nature 444, 347 (2006). 
6Y. Son, M. L. Cohen and S. G. Louie, Phys. Rev. Lett. 97, 216803 (2006). 
7C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. 
Marchenkov, E. H. Conrad, P. N. First and W. A. de Heer, Science 312, 119 (2006). 
8S. Liu, F. Zhou, A. Jin, H. Yang, Y. Ma, H. Li, C. Gu, L. Lu, B. Jiang, Q. Zheng, S. Wang and L. 
Peng, Acta Physica Sinica 54, 4251 (2005). 
9Z. Chen, Y. Lin, M. Rooks and P. Avouris, http://arvix.org/abs/cond-mat/0701599, (2007). 
10L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie and M. L. Cohen, Phys. Rev. Lett. 76, 971 
(1996). 
11L. Chico, M. P. Lopez Sancho and M. C. Munoz, Phys. Rev. Lett. 81, 1278 (1998). 
12J. Lu, J. Wu, W. Duan, F. Liu, B. Zhu and B. Gu, Phys. Rev. Lett. 90, 156601 (2003). 
13K. Wakabayashi, Phys. Rev. B 64, 125428 (2001).
FIG. 1. The metal/semiconducting junction 11AGNR/10AGNR: (Top) Conductance and DOS of 
the whole system. (Bottom) LDOS at slices near the interface. Slice n (n = 1, 2 and 3) represents the 
n-th nearest slice to the interface and the vertical scale of DOS is 0.2. 
FIG. 2. Spatial-resolved LDOS in metal/semiconducting junction 8ZGNR/15AGNR, the vertical 
scale of DOS is 0.2. 
FIG. 3. Quantum dot structure based on 12AGNR/11AGNR/12AGNR junction: (Top) Conductance 
and DOS at low bias, where two isolated sharp peaks appear inside the gap; (Bottom) Spatial-
resolved LDOS at E = 0.2025 eV, the grey dot represents the ionic site and the radius of circle 
around it corresponds to the value of LDOS. 
FIG. 4. Quantum dot structure based on 10AGNR/7ZGNR/10AGNR junction: (Top) Conductance 
and DOS; (Bottom) Spatial-resolved LDOS at E = 0.3525 eV. 
Figure 1 
Figure 2 
Figure 3 
Figure 4

  Graphene nano-ribbons junctions based electronic devices are proposed in this
Letter. Non-equilibrium Green function calculations show that nano-ribbon
junctions tailored from single layer graphene with different edge shape and
width can act as metal-semiconductor junctions and quantum dots can be
implemented. In virtue of the possibilities of patterning monolayer graphene
down to atomic precision, these structures, quite different from the previously
reported two-dimensional bulk graphene or carbon nanotube devices, are expected
to be used as the building blocks of the future nano-electronics.

Microsoft Word - APL-Ribbon_junctions_20070328-Text_with_Figures-ARXIV.doc
Molecular circuits based on graphene nano-ribbon junctions 
Zhiping Xu† 
Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China 
Graphene nano-ribbons junctions based electronic devices are proposed in this Letter. Non-
equilibrium Green’s function calculations show that nano-ribbon junctions tailored from 
single layer graphene with different edge shape and width can act as metal/semiconductor 
junctions and quantum dots can be implemented. In virtue of the possibilities of patterning 
monolayer graphene down to atomic precision, these structures, quite different from the 
previously reported two-dimensional bulk graphene or carbon nanotube devices, are 
expected to be used as the building blocks of the future nano-electronics. 
Keyword: graphene nano-ribbon, electronic transport, metal/semiconductor junction, quantum dot 
                                                 
† Email: xuzhiping@gmail.com 
Nano-electronics, or molecular electronics have been proposed as the alternative to silicon in 
future technical applications1 and have attracted great interests recently. In virtue of their unique 
structures and various functions, these nanostructures possess intriguing electromagnetic, 
mechanical and optical features. Especially, carbon based nanostructure, such as fullerene, graphene 
and carbon nanotubes are the most interesting structures because of their rich variety of excellent 
physical properties. For instance, anomalous quantum hall effects (QHE) and massless Dirac 
electronic behavior have been discovered in the graphene systems2, 3, and these discovery has 
sparked lots of investigations on this unique two-dimensional material. Tailored from monolayer 
graphene, graphene ribbon (GNR) with finite width has been shown to hold unusual electronic 
properties4, depending on their edge shape and width. In more details, ribbons with zigzag edges 
(ZGNRs) possess spin-polarized peculiar edges states and spin-polarized electronic state provides 
half-metallicity under transverse electric field and has great potential in the application as 
spintronics5. In contrast, the armchair edged ribbons (AGNR) can be either metallic or 
semiconducting depending on their width6, AGNR with width Na (named as NaAGNR in the 
conventional nomenclature) has been shown to be metallic only if Na = 3k + 2 and semiconducting 
otherwise, where k is an integer. 
From the experimental point of view, the fascinating feature of the ribbons is that the 
graphene material can be easily patterned using standard micro- or nano-electronics lithography 
methods. Unlike the carbon nanotubes or other low-dimensional nanostructures, the GNRs with 
intricate sub-micrometer structures can now be fabricated7, 8, 9, and it is believed that a combination 
of standard lithographic and chemical methods will help to pattern the graphene with atomic 
precision down to the molecular level. The high mobility μ = 2.7 m2/V.s, large elastic mean free 
path le = 600nm and phase coherence lengths lφ= 1.1 μm observed7 in the epitaxial graphene 
patterned suggest the use of pure GNR structures as the building blocks of the nanoscale confined 
and coherent electronic circuits. To realize the components such as field transistors9 and coulomb 
blockade devices, experimentally controllable metal/semiconductor junctions and quantum dots will 
be essential. As proposed by Chico et al.10, 11, these can be achieved by jointing different carbon 
nanotubes. However, the fabrication and control of the nanostructure of graphene ribbons are much 
more convenient than introducing pentagon-heptagon defects in carbon nanotubes as discussed, 
therefore it is interesting to investigate the possibilities of ribbon junction based nano-circuits. 
To this end, we have proposed several kinds of the GNRs based electronic devices in this 
Letter. We show that, by controlling the tailoring process of GNRs with different edge shape and 
width, the metal/semiconductor junctions and quantum dots can be easily implemented 
experimentally. To validate this, electronic transport calculation using the non-equilibrium Green’s 
function method have been carried out following Landauer’s approach12. The electronic structure of 
the graphene lattice is described using the nearest-neighbour π-orbital tight-binding model and the 
hopping parameter Vppπ = 2.75 eV is used. This simple topological model gives quantitative results 
comparing with the LDA results except for the gap opening at small width as the consequence of 
the length changing of σ bonds6. By solving the Green’s function, the conductance was finally 
calculated as G = G0Tr[ΓLGRΓRGA] and the density of state is expressed as D = –ImTr[GR]/π11, 
where G0 = 2e2/h is the unit quanta of conductance including the spin degeneracy, GR(A) is the 
retarded (advanced) Green’s function of the conductor and ΓL(R) is the spectral density describing 
the coupling between the left (right) lead and the conductor. In our model, the leads are represented 
using semi-infinite graphene ribbons attached to the conductor region, with the same shape and 
width. 
First of all we investigate straight metal/semiconducting junction 11AGNR/10AGNR. The 
structure of the junction is considered by simply patching two different straight ribbons together, 
leave a width mismatching at the interface. The result shown in Fig. 1 indicates a gap Eg = 0.93 eV 
near the Fermi energy and the imperfection at the interface induces a deviation of conductance from 
the step-like curve of the perfect ribbon. However, the van Hove singularities which are the 
characteristics of 1D system remain. 
To examine the detailed electronic structure of the junction, a spatial-resolved localized 
density of states (LDOS) analysis is helpful. We have grouped the atoms into slices according to 
their distance from the interface. Each 4.26 Å long slice (a unit cell of the perfect AGNR) in the 
10AGNR, 11AGNR and interface part contain 20, 22 and 21 atoms respectively. The LDOS 
averaged at different slices are plotted in Fig. 1. From the semiconducting 10AGNR side we find 
the LDOS is distorted near the interface and gap state appears through the contact with metallic 
11AGNR. However at slices far from the interface, at slice 3 for example, the perfect 
semiconduting behavior is mostly recovered. At the scattering interface the van Hove singularities 
have been smoothed and 1D metallic structure gradually emerges as the distance from interface 
increases from the 11AGNR side. The arising of gap state near the interface characterizes the metal-
semiconductor junction and suggests the possibilities of building Schottky devices. 
Furthermore, L-shape GNR junctions with different orientations can be constructed. For 
instance, the LDOS of 8ZGNR/15AGNR junction with a π/6 joint is analysized in Fig. 2. As 
expected, the edge state of the 8ZGNR spreads into the semiconducting 15AGNR side. Because of 
the ZGNR possess spin-polarized structure, so this half-metal/semiconducting junction inspires 
interests in the spin-transport devices. 
Beside of the metal/semiconductor junction, the semiconductor/semiconductor junctions 
have also been investigated and defect states in gap appear at the interface. Moreover in the 
ZGNR/ZGNR junctions, zero-conductance dips13 near Fermi energy have been observed, caused by 
the complete backward scattering. 
The metal-semiconductor junction also suggests quantum dot devices through combing two 
of them together. We now consider the junction 12AGNR/11AGNR/12AGNR. In this structure a 
central metallic ribbon is sandwiched by two semiconductor barriers where quantized states can be 
formed. Our calculation results depicted in Fig. 3 show two sharp DOS peaks inside the gap of 
semiconducting 12AGNR containing 7 unit cells, with energy E1,2 = 0.2025 and -0.2025 eV. As 
seen from the spatial-resolved LDOS at E = 0.2025, the bounded state is localized inside the 
11AGNR region. The structure of the quantum levels can be further tuned by changing the length of 
11AGNR. From our calculation, as it changes from 1 to 8 unit cells, the energy spacing between the 
nearest peaks around Fermi energy, i.e. ΔE = E1-E2, gradually decreases from 0.785 eV to 0.385 eV 
and their DOS becomes higher and sharper. 
We have also observed quantized edge states within the 10AGNR/7ZGNR/10AGNR 
junctions through introducing two π/6 joints. The results are shown in Fig. 3 where we can found 7 
LDOS peaks inside the zero-conductance gap. The quantized states with E = -0.3525, -0.1625, - 
0.05, 0, 0.05, 0.1625 and 0.3525 correspond to different LDOS patterns (see Fig. 4 for E = 0.3525). 
The higher the energy, the more nodes of the bounded standing wave have. The electron wave 
quantized pattern depends on the structure of the central region. 
In conclusion, we have proposed nano-electronic circuits based on graphene nano-ribbon 
junctions. Through tailoring GNRs into junctions of different edge shape and width, we can 
implement metal/semiconductor junctions and quantum dots in principle. In virtue of the possibility 
of molecular level patterning based on lithography and chemical methods, these devices are 
expected to be fabricated easier in comparison with other structures such as the single molecule or 
carbon nanotubes junctions, and are expected to find great applications in the large-scale integrated 
nano-circuits in future. 
The work is supported by the National Science Foundation of China through Grants 
10172051, 10252001, and 10332020 and the Hong Kong Research Grant Council (NSFC/RGC N 
HKU 764/05 and HKU 7012/04P). ZX also thanks Prof. Wenhui Duan, Dr. Tao Zhou and Dr. 
Haiyun Qian from the Department of Physics in Tsinghua University for their help on the 
calculation. 
1N. J. Tao, Nature Nanotechnology 1 173 (2006). 
2K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. 
Dubonos and A. A. Firsov, Nature 438, 197 (2005). 
3Y. Zhang, Y. Tan, H. L. Stormer and P. Kim, Nature 438, 201 (2005). 
4Y. Kobayashi, K. Fukui, T. Enoki, K. Kusakabe and Y. Kaburagi, Phys. Rev. B 71, 193406 (2005). 
5Y. Son, M. L. Cohen and S. G. Louie, Nature 444, 347 (2006). 
6Y. Son, M. L. Cohen and S. G. Louie, Phys. Rev. Lett. 97, 216803 (2006). 
7C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. 
Marchenkov, E. H. Conrad, P. N. First and W. A. de Heer, Science 312, 119 (2006). 
8S. Liu, F. Zhou, A. Jin, H. Yang, Y. Ma, H. Li, C. Gu, L. Lu, B. Jiang, Q. Zheng, S. Wang and L. 
Peng, Acta Physica Sinica 54, 4251 (2005). 
9Z. Chen, Y. Lin, M. Rooks and P. Avouris, http://arvix.org/abs/cond-mat/0701599, (2007). 
10L. Chico, V. H. Crespi, L. X. Benedict, S. G. Louie and M. L. Cohen, Phys. Rev. Lett. 76, 971 
(1996). 
11L. Chico, M. P. Lopez Sancho and M. C. Munoz, Phys. Rev. Lett. 81, 1278 (1998). 
12J. Lu, J. Wu, W. Duan, F. Liu, B. Zhu and B. Gu, Phys. Rev. Lett. 90, 156601 (2003). 
13K. Wakabayashi, Phys. Rev. B 64, 125428 (2001).
FIG. 1. The metal/semiconducting junction 11AGNR/10AGNR: (Top) Conductance and DOS of 
the whole system. (Bottom) LDOS at slices near the interface. Slice n (n = 1, 2 and 3) represents the 
n-th nearest slice to the interface and the vertical scale of DOS is 0.2. 
FIG. 2. Spatial-resolved LDOS in metal/semiconducting junction 8ZGNR/15AGNR, the vertical 
scale of DOS is 0.2. 
FIG. 3. Quantum dot structure based on 12AGNR/11AGNR/12AGNR junction: (Top) Conductance 
and DOS at low bias, where two isolated sharp peaks appear inside the gap; (Bottom) Spatial-
resolved LDOS at E = 0.2025 eV, the grey dot represents the ionic site and the radius of circle 
around it corresponds to the value of LDOS. 
FIG. 4. Quantum dot structure based on 10AGNR/7ZGNR/10AGNR junction: (Top) Conductance 
and DOS; (Bottom) Spatial-resolved LDOS at E = 0.3525 eV. 
Figure 1 
Figure 2 
Figure 3 
Figure 4
