Gate Voltage-Modulated Conductance in Zigzag Graphene Nanoribbon Junctions

Li, Ming; Feng, Zhi-Bo; Zhao, Zheng-Yin

doi:https://doi.org/10.1155/2023/6463744

Advances in Condensed Matter Physics

On this page

Abstract Introduction Model Results and Discussion Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 6463744 | https://doi.org/10.1155/2023/6463744

Gate Voltage-Modulated Conductance in Zigzag Graphene Nanoribbon Junctions

Ming Li,¹Zhi-Bo Feng,¹and Zheng-Yin Zhao¹

Academic Editor: Shobhit K. Patel

Received18 Feb 2023

Revised15 Apr 2023

Accepted28 Jul 2023

Published25 Aug 2023

Abstract

Using the Green’s function method, we study the modulation of the conductance in zigzag graphene nanoribbon (ZGNR) junctions by the gate voltages. As long as the difference between the gate voltages applied on the left and right ZGNRs (ΔV) remains unchanged, the conductance profiles for different cases are exactly the same, except to a displacement along E_F-axis. It is found that the transmission of electrons from the upper/lower edge state of the left ZGNR to the lower/upper edge state of the right ZGNR is forbidden, therefore, the width of the conductance gap increases first and then decreases as |ΔV| increases. The upper/lower edge states and conduction/valence subbands of ZGNR under higher/lower gate voltage (V_H/V_L) determine step positions of the conductance when E_F >V_H/E_F < V_L. But when V_L ≤ E_F ≤ V_H, the conductance profile is mainly determined by the upper and lower edge states, a few lowest conduction subbands/topmost valence subbands of ZGNR under lower/higher gate voltage. These results are helpful to the exploration and application of a new kind of field effect transistor based on ZGNR junctions.

1. Introduction

Graphene has excellent electrical, optical, and thermal properties, and has been considered as a perspective base for the postsilicon electronics since the successful fabrication in experiment [1–4]. Around the Dirac points, the band structure of graphene presents a linear dispersion, and the quasiparticles obey the massless Dirac equation and relativistic-like behaviors appear [3–7]. If graphene is patterned into graphene nanoribbon (GNR), interesting properties emerge [8]. For example, the edge states are found in graphene nanostructures with zigzag edge [4, 9–15]. In fact, many interesting phenomena in graphene and other novel two dimensional honeycomb lattice materials are in nature associated with the edge states [4, 9, 15–20], e.g., the valley-filtered transport [10, 21–23] and magnetism [11–13].

Furthermore, by interconnecting two semi-infinite GNRs with different widths, a GNR junction can be obtained [17, 23]. The conductance of metal–semiconductor GNR junctions, which is the key elements in all-graphene circuits, has attracted extensive research recently [24–26]. Due to the mismatch between conducting channels in the left and right GNRs, a traveling carrier is strongly scattered at the junction interface and a finite junction conductance is induced [17, 23, 27, 28]. Therefore, the junction conductance strongly depends on the geometry of the junction interface [24].

Experimentally, the Fermi level (E_F) in the GNR can be above or below the Dirac points by tuning the gate voltage, then the global or local charge carriers can be easily tuned from electron like to hole like and vice versa [1, 4, 5, 29, 30]. Moreover, the transport of topological edge states can be manipulated by adjusting the gate voltage embedding on the surface of two-dimensional topological insulator systems [31], and the spin polarization [32], spin inversion [33], and valley polarization [34] in silicene nanoribbons can also be manipulated by the gate voltage.

However, to the best of our knowledge, modulation of the electronic and transport properties of zigzag graphene nanoribbon (ZGNR) junctions by the gate voltages applied on the left and right ZGNRs (V_gL and V_gR, with ΔV = V_gL−V_gR) has not been studied, which is crucial for designing all-graphene junctions and circuits [35]. Thus in this paper, to explore how the gate voltage affects the conductance channels (the edge states, the conduction, and valence subbands) and the mode matching between the left and right ZGNRs, we study how the conductance of the ZGNR junction depends on the gate voltage applied on the left and right ZGNRs. The G–E_F curves in all cases can be clarified from the energy band structures of the left and right ZGNRs. For V_gL = 0 (V_gR = 0), the G profiles for opposite V_gR (V_gL) are symmetric to each other with respect to E_F = 0, and they move further away from each other with increasing |ΔV|. For a given ΔV, the G profiles for different V_gL or V_gR are identical, except to a displacement along E_F-axis. The transmission probability of electrons from the upper/lower edge state of the left ZGNR to the lower/upper edge state of the right ZGNR is found to be 0. As a result, the width of the conductance gap increases first and then decreases with increasing |ΔV|.

The rest of the paper is organized as follows. In Section 2, the Green’s function method, the tight-binding model, and the geometrical structure of the ZGNR junction are introduced in brief. In Section 3, the dependance of the conductance of the ZGNR junction on the gate voltages applied on the left and right ZGNRs is studied and analyzed in detail. Finally, conclusions are given in Section 4.

2. Theory and Model

Figure 1 shows the geometry of the zigzag ZGNR junction connecting the left and right leads (semi-infinite ZGNR). From the top to down, atoms in a unit cell are labeled as 1, 2, …, N_L/N_R. Here N_L/N_R denotes the width of the left/right ZGNR.

The Hamiltonian for the ZGNR junction reads [5, 36–39]

Here t = 2.75 eV is the transfer energy of the nearest neighbor hopping, <ij> represents the nearest neighbors, α denotes the spin index, and E_F is the gate voltage applied on the ZGNR.

The conductance of the ZGNR junction can be calculated from the Landauer–Büttiker formula [40, 41],

Here is the unit quanta of conductance considering the spin degeneracy [26]. is the retarded Green function [42, 43]. is the self-energy, is the line width function, and is the surface Green function of the left/right semi-infinite ZGNR [44–47].

3. Results and Discussion

In this section, assuming N_L = 40 and N_R = 20, the dependance of the conductance of the ZGNR junction on the gate voltages applied on the left and right ZGNRs is studied and analyzed in detail. The G–E_F curves are clearly clarified by analyzing the energy band structures of the left and right ZGNRs. First, the conductance of the ZGNR junction for V_gR = 0 and different V_gL are explored. Second, for V_gL = 0, how G depends on V_gR is analyzed. Next, assuming V_gL = −V_gR = V_g, the variation of G as a function of V_g is considered. Finally, for a given ΔV, the G profiles of the ZGNR junction under different V_gL or V_gR are compared.

3.1. Conductance of the ZGNR Junction for V_gR = 0 and Different V_gL

In Figures 2(a)–2(d) and 3(a)–3(d), we show G versus E_F in the ZGNR junction for V_gR = 0 and V_gL = 0, 0.018, ±0.4, ±0.8, 0.8964, and 1.2 eV, and the corresponding energy band structures of ZGNRs.

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

When V_gR = 0, the G profile for V_gL = V_g is symmetric to that for V_gL = −V_g with respect to E_F = 0, i.e., , because the conduction and valecne subbands are just reversed when the sign of the gate voltage applied on the left ZGNR is reversed. With the increase of |V_gL|, the profile of moves further away from that of , and G decreases as a whole, because the energy mismatch of the conducting channels increases.

For V_gL > 0 (V_gL < 0) and E_F > V_gL (E_F < V_gL), G decreases with the increase of |V_gL| as a whole, and step positions of G are determined by the upper (lower) edge state and conduction (valence) subbands of ZGNR under higher (lower) gate voltage. For V_gL > 0 (V_gL < 0) and E_F < 0 (E_F > 0), G for different V_gL are in proximity to that of V_gL = 0, especially for a lower |E_F|, since step positions of G are mainly determined by the lower (upper) edge states and the valence (conduction) subbands of ZGNR under lower (higher) gate voltage. When V_gL = V_gR, step positions of G are just decided by the subbands of the right narrower ZGNR.

When 0.018 ≤ |V_gL| ≤0.8964 eV and V_gL > 0 (V_gL < 0), there is a conductance gap at the positive (negative) direction of E_F-axis. By increasing |V_gL|, the width of the conductance gap increases first and then decreases. These originate from that the transmission of electrons from the upper/lower edge state of the left ZGNR to the lower/upper edge state of the right ZGNR is forbidden. In fact, when the zigzag-chain number N is even (here N_L = 40 and N_R = 20), the electron transport in the ZGNR should satisfy the pseudoparity conservation and the valley valve effect appears [10, 46, 48], so electrons of the lower/upper edge state in the left ZGNR cannot transmit to the upper/lower edge sate in the right ZGNR.

When V_gL = 0.018 eV, the profile of G is almost the same as that of V_gL = 0, but G decreases abruptly to 0 at E_F = 0.018 eV, then increases rapidly to a 1·G₀ plateau at E_F = 0 eV. With further increasing V_gL, the conduction gap begins to form and the width of conduction gap increases. This is determined by the lower edge state of ZGNR under higher gate voltage and lower edge state of ZGNR under lower gate voltage.

When V_gL = 0.4 eV, with the decrease of E_F, G decreases to a 1·G₀ plateau at E_F = 0.7 eV, and decreases to a 0 plateau at E_F = 0.4 eV, which is determined by the conduction subbands and the upper and lower edge states of ZGNR under higher gate voltage. Then G increases to a 0.5·G₀ plateau at E_F = 0.1 eV, which is determined by the topmost valence subband of ZGNR under higher gate voltage. So the conductance gap is in the E_F interval [0.1, 0.4 eV], rather than [0, 0.4 eV], which is determined by the topmost valence subband and lower edge state of ZGNR under higher gate voltage. Finally, G shows a dip at E_F = 0 and increases step by step as E_F decreases, which is determined by the lower edge state and valence subbands of ZGNR under lower gate voltage.

When V_gL = 0.8 eV, with the decrease of E_F, G decreases to a 0.5·G₀ plateau at E_F = 0.8 eV. Then G decreases to a 0 plateau at E_F = 0.59 eV, and increases to a 0.8·G₀ plateau at E_F = 0.5 eV, which is determined by the lowest conduction subband of ZGNR under lower gate voltage and topmost valence subband of ZGNR under higher gate voltage. So the conductance gap is in the E_F interval [0.5, 0.59 eV], rather than [0, 0.8 eV].

When V_gL = 0.8964 eV, the edge position of the lowest conduction subband of ZGNR under lower gate voltage just coincides with that of the topmost valence subband of ZGNR under higher gate voltage, so G decreases to 0 and increases rapidly to a 0.8·G₀ plateau at E_F = 0.59 eV with the decrease of E_F. Therefore, the conduction gap begins to disappear, rather than lies in the E_F interval [0, 0.8964 eV]. With further increasing V_gL, there is no conduction gap.

When V_gL = 1.2 eV, with the decrease of E_F, G increases to a 1.4·G₀ plateau at E_F = 0.91 eV, and decreases to a 0.9·G₀ plateau at E_F = 0.59 eV. This is also determined by the topmost valence subband of ZGNR under higher gate voltage and the lowest conduction subband of ZGNR under lower gate voltage.

3.2. Conductance of the ZGNR Junction for V_gL = 0 and Different V_gR

In Figures 4(a)–4(d) and 5(a)–5(d), we show G versus E_F in the ZGNR junction for V_gL = 0 and V_gR = 0, 0.018, ±0.4, ±0.8, 0.8964, and 1.2 eV, and the corresponding energy band structures of ZGNRs.

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

Here the G profiles for V_gL = 0 and different V_gR can be discussed similarly as that in Section 3.1 for V_gR = 0 and different V_gL, and the G profiles are found to be the same. For example, the G profiles for V_gR = 0 and V_gL = −0.8, −0.4, 0.4, and 0.8 shown in Figure 2(a) are the same to that for V_gL = 0 and V_gR = 0.8, 0.4, −0.4, and −0.8 shown in Figure 4(a), respectively. By comparing the G profiles for the above cases, it is found that as long as the difference between the gate voltages applied on the left and right ZGNRs (ΔV) remains unchanged, the conductance profiles for different cases are exactly the same, except to a displacement along E_F-axis. This general rule and detailed reasons will be further discussed in Section 3.4.

3.3. Conductance of the ZGNR Junction for V_gL = −V_gR

Figure 6 shows G versus E_F in the ZGNR junction for V_gL = −V_gR = V_g = 0.009, ±0.4, 0.4482, and 0.8 eV and Figures 7(a1–a4) and 7(b1–b4) show the corresponding energy band structures of ZGNRs.

The G profile for V_gL = −V_gR = V_g is symmetric to that for V_gL = −V_gR = −V_g with respect to E_F = 0, i.e., , because the conduction and valence subbands are just reversed when the sign of the gate voltage applied on the left/right ZGNR is reversed. With the increase of |V_g|, the profile of moves further away from that of , and G decreases as a whole, because the energy mismatch of the conducting channels increases.

For V_g > 0 (V_g < 0) and E_F > V_g (E_F < V_g), step positions of G are determined by the upper (lower) edge states and conduction (valence) subbands of ZGNR under higher (lower) gate voltage. For V_g > 0 (V_g < 0) and E_F < −V_g (E_F > −V_g), step positions of G are mainly determined by the lower (upper) edge states and the valence (conduction) subbands of ZGNR under lower (higher) gate voltage.

When 0.009 ≤ |V_g| ≤ 0.4482 eV and V_g > 0 (V_g < 0), there is a conductance gap at the positive (negative) direction of E_F-axis. With the increase of |V_g|, the width of the conductance gap first increases and then decreases. As discussed above, these originate from that the transmission of electrons from the upper/lower edge state of the left ZGNR to the lower/upper edge state of the right ZGNR is forbidden as a result of the pseudoparity conservation and the valley valve effect [10, 46, 48]. Here the G profiles are the same to that for 0.018 ≤ |V_gL| ≤ 0.8964 eV and V_gR = 0, because ΔV in the above two cases is the same.

When V_g = 0.009 eV, the profile of G is almost the same as that of V_g = 0, but G decreases abruptly to 0 around E_F = 0.009 eV, then increases rapidly to a 1·G₀ plateau at E_F = −0.009 eV, namely, the 1·G₀ plateau shows a conductance dip to 0 at E_F = 0. With further increasing V_g, the conduction gap begins to form and the width of conduction gap increases. This is determined by the lower edge state of ZGNR under higher gate voltage and upper edge state of ZGNR under lower gate voltage. Here the G profiles are the same to that for V_gL = 0.18 eV and V_gR = 0, because ΔV in the above two cases is the same.

When V_g = 0.4 eV, with the decrease of E_F, G decreases to a 1·G₀ plateau at E_F = 0.7 eV, and decreases to a 0.5·G₀ plateau at E_F = 0.4 eV, which is determined by the conduction subbands and the upper and lower edge states of ZGNR under higher gate voltage. Then G decreases slowly to a 0 plateau at E_F = 0.2 eV, and increases to a 0.8·G₀ plateau at E_F = 0.1 eV, which is determined by the lowest conduction subband of ZGNR under lower gate voltage and the topmost valence subband of ZGNR under higher gate voltage. So the conductance gap is in the E_F interval [0.1, 0.2 eV], rather than [0, 0.4 eV]. Finally, G shows a dip and increases to a 1·G₀ plateau at E_F = −0.4 eV, then increases step by step with the decrease of E_F. This is determined by the upper and lower edge states and valence subbands of ZGNR under lower gate voltage. Here the G profiles are the same to that for V_gL = 0.8 eV and V_gR = 0, because ΔV in the above two cases is the same.

When V_g = 0.4482 eV, the edge position of the lowest conduction subband of ZGNR under lower gate voltage just coincides with that of the topmost valence subband of ZGNR under higher gate voltage, so G decreases to 0 and increases rapidly to a 0.9·G₀ plateau at E_F = 0.15 eV with the decrease of E_F. Therefore, the conduction gap begins to disappear, rather than lies in the E_F interval [0, 0.4482 eV]. As |V_g| increases, there is no conduction gap. Here the G profiles are the same to that for V_gL = 0.8964 eV and V_gR = 0, because ΔV in the above two cases is the same.

When V_g = 0.8 eV, with the decrease of E_F, G increases to a 1.5·G₀ plateau at E_F = 0.48 eV, and increases to a 2.25·G₀ plateau at E_F = 0.27 eV. This is determined by the topmost two valence subbands of ZGNR under higher gate voltage. When −0.233≤E_F ≤ 0.27 eV, G is determined by the upper edge state, a few lowest conduction subbands of ZGNR under lower gate voltage and a few topmost valence subbands of ZGNR under higher gate voltage. Finally, G decreases to a 0.9·G₀ plateau at E_F = −0.233 eV, which is determined by the lowest conduction subband of ZGNR under lower gate voltage.

3.4. Conductance of the ZGNR Junction for V_gL−V_gR = ΔV ()

In this Section 3.4, the G profiles of the ZGNR junction for the same ΔV but different V_gL or V_gR are compared. Taking ΔV = 0.8 eV as an example, the G profiles of the ZGNR junction for different V_gL or V_gR are demonstrated in Figure 8. The G profiles for the same ΔV are exactly the same, i.e., for any V_g. If V_g > 0 (V_g < 0), the G profile for V_gL can be obtained by translating that for V_gL−V_g by |V_g| along the positive (negative) direction of E_F-axis. In fact, the gate voltage applied on the ZGNR will shift the position of the energy subbands (conducting channels), the transmission coefficient of electrons or holes from one channel in the left ZGNR to that of the right one is just determined by the relative positions of the above conducting channels.

Therefore, as long as the difference between the gate voltages applied on the left and right ZGNRs (ΔV) remains unchanged, the conductance profiles for different cases are exactly the same, except to a displacement along E_F-axis. Moreover, as discussed above, the width of the conductance gap increases first and then decreases as |ΔV| increases.

These results are helpful to the exploration and application of a new kind of field effect transistor (FET) based on ZGNR junctions, in which the conducting channels involved in the transmission of electrons or holes are controlled by the gate voltage, and their functions are similar to those of semiconductor FETs.

4. Conclusion

In summary, by adjusting the gate voltages applied on the left and right ZGNRs, the conductance of the ZGNR junction is studied. The G–E_F curves for all cases can be clarified from the energy band structures of the left and right ZGNRs. When V_gL = 0 (V_gR = 0), the G profiles for opposite V_gR (V_gL) are symmetric to each other with respect to E_F = 0, and they move further away from each other with the increase of |ΔV|. For a given ΔV, the G profiles for different V_gL or V_gR are exactly the same, except to a displacement along the positive or negative direction of E_F-axis. Because the transmission of electrons from the upper/lower edge state of the left ZGNR to the lower/upper edge state of the right ZGNR is not allowed, the width of the conductance gap increases first and then decreases as |ΔV| increases. The width of the conduction gap is mainly determined by the upper and lower edge states, a few lowest conduction subbands of ZGNR under lower gate voltage and a few topmost valence subbands of ZGNR under higher gate voltage. Step positions of G are determined by the upper edge state and conduction subbands of ZGNR under higher gate voltage (E_F) when E_F > V_H, and by the lower edge state and the valence subbands of ZGNR under lower gate voltage (V_L) when E_F < V_L. These results are helpful to the exploration and application of graphene-based FETs.

Data Availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was supported by the Scientific Research Innovation Team of the Xuchang University (grant no. 2022CXTD005) and the “316” Project Plan of the Xuchang University.

References

K. S. Novoselov, A. K. Geim, S. V. Morozov et al., “Electric field effect in atomically thin carbon films,” Science, vol. 306, no. 5696, pp. 666–669, 2004.
View at: Publisher Site | Google Scholar
K. S. Novoselov, A. K. Geim, S. V. Morozov et al., “Two-dimensional gas of massless Dirac fermions in graphene,” Nature, vol. 438, pp. 197–200, 2005.
View at: Publisher Site | Google Scholar
Y. Xing, J. Wang, and Q.-F. Sun, “Focusing of electron flow in a bipolar graphene ribbon with different chiralities,” Physical Review B, vol. 81, Article ID 165425, 2010.
View at: Publisher Site | Google Scholar
Y. Xing, Q.-F. Sun, and J. Wang, “Nernst and Seebeck effects in a graphene nanoribbon,” Physical Review B, vol. 80, no. 23, Article ID 235411, 2009.
View at: Publisher Site | Google Scholar
W. Long, Q.-F. Sun, and J. Wang, “Disorder-induced enhancement of transport through graphene p−n junctions,” Physical Review Letters, vol. 101, no. 16, Article ID 166806, 2008.
View at: Publisher Site | Google Scholar
J. C. Slonczewski and P. R. Weiss, “Band structure of graphite,” Physical Review, vol. 109, no. 2, pp. 272–279, 1958.
View at: Publisher Site | Google Scholar
A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Reviews of Modern Physics, vol. 81, no. 1, pp. 109–162, 2009.
View at: Publisher Site | Google Scholar
A. Saffarzadeh and M. Ghorbani Asl, “Spin currents and magnetoresistance of graphene-based magnetic junctions,” The European Physical Journal B, vol. 67, pp. 239–244, 2009.
View at: Publisher Site | Google Scholar
K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, “Edge state in graphene ribbons: nanometer size effect and edge shape dependence,” Physical Review B, vol. 54, no. 24, pp. 17954–17961, 1996.
View at: Publisher Site | Google Scholar
A. Rycerz, J. Tworzydło, and C. W. J. Beenakker, “Valley filter and valley valve in graphene,” Nature Physics, vol. 3, pp. 172–175, 2007.
View at: Publisher Site | Google Scholar
J. Fernández-Rossier and J. J. Palacios, “Magnetism in graphene nanoislands,” Physical Review Letters, vol. 99, no. 17, Article ID 177204, 2007.
View at: Publisher Site | Google Scholar
L. Pisani, J. A. Chan, B. Montanari, and N. M. Harrison, “Electronic structure and magnetic properties of graphitic ribbons,” Physical Review B, vol. 75, no. 6, Article ID 064418, 2007.
View at: Publisher Site | Google Scholar
O. Hod, V. Barone, and G. E. Scuseria, “Half-metallic graphene nanodots: a comprehensive first-principles theoretical study,” Physical Review B, vol. 77, no. 3, Article ID 035411, 2008.
View at: Publisher Site | Google Scholar
C. Wang, Y. Zou, J. Song, and Y.-X. Li, “Andreev reflection in a Y-shaped graphene–superconductor device,” Physical Review B, vol. 98, no. 3, Article ID 035403, 2018.
View at: Publisher Site | Google Scholar
Z. Z. Zhang, Z. H. Wu, K. Chang, and F. M. Peeters, “Resonant tunneling through S- and U-shaped graphene nanoribbons,” Nanotechnology, vol. 20, no. 41, Article ID 415203, 2009.
View at: Publisher Site | Google Scholar
L. Jiang, Y. Zheng, C. Yi, H. Li, and T. Lü, “Analytical study of edge states in a semi-infinite graphene nanoribbon,” Physical Review B, vol. 80, no. 15, Article ID 155454, 2009.
View at: Publisher Site | Google Scholar
H. Li, L. Wang, and Y. Zheng, “Suppressed conductance in a metallic graphene nanojunction,” Journal of Applied Physics, vol. 105, no. 1, Article ID 013703, 2009.
View at: Publisher Site | Google Scholar
S.-G. Cheng, J. Zhou, H. Jiang, and Q.-F. Sun, “The valley filter efficiency of monolayer graphene and bilayer graphene line defect model,” New Journal of Physics, vol. 18, Article ID 103024, 2016.
View at: Publisher Site | Google Scholar
S.-G. Cheng, R.-Z. Zhang, J. Zhou, H. Jiang, and Q.-F. Sun, “Perfect valley filter based on a topological phase in a disordered Sb monolayer heterostructure,” Physical Review B, vol. 97, no. 8, Article ID 085420, 2018.
View at: Publisher Site | Google Scholar
X.-T. An, J. Xiao, M. W.-Y. Tu, H. Yu, V. I. Fal’ko, and W. Yao, “Realization of valley and spin pumps by scattering at nonmagnetic disorders,” Physical Review Letters, vol. 118, no. 9, Article ID 096602, 2017.
View at: Publisher Site | Google Scholar
V. Hung-Nguyen, S. Dechamps, P. Dollfus, and J.-C. Charlier, “Valley filtering and electronic optics using polycrystalline graphene,” Physical Review Letters, vol. 117, no. 24, Article ID 247702, 2016.
View at: Publisher Site | Google Scholar
M. Ezawa, “Valley-polarized metals and quantum anomalous hall effect in silicene,” Physical Review Letters, vol. 109, no. 5, Article ID 055502, 2012.
View at: Publisher Site | Google Scholar
M. Li, Z.-L. Cai, Z.-B. Feng, and Z.-Y. Zhao, “Valley-resolved transport in zigzag graphene nanoribbon junctions,” Communications in Theoretical Physics, vol. 73, no. 11, Article ID 115701, 2021.
View at: Publisher Site | Google Scholar
S. Hong, Y. Yoon, and J. Guo, “Metal-semiconductor junction of graphene nanoribbons,” Applied Physics Letters, vol. 92, no. 8, Article ID 083107, 2008.
View at: Publisher Site | Google Scholar
T. C. Li and S.-P. Lu, “Quantum conductance of graphene nanoribbons with edge defects,” Physical Review B, vol. 77, no. 8, Article ID 085408, 2008.
View at: Publisher Site | Google Scholar
Z. Xu, Q.-S. Zheng, and G. Chen, “Elementary building blocks of graphene–nanoribbon-based electronic devices,” Applied Physics Letters, vol. 90, no. 22, Article ID 223115, 2007.
View at: Publisher Site | Google Scholar
Y. Wu and P. A. Childs, “Conductance of graphene nanoribbon junctions and the tight binding model,” Nanoscale Research Letters, vol. 6, Article ID 62, 2011.
View at: Publisher Site | Google Scholar
L. Ming, H. Hongpei, Z.-B. Feng, and Z. Zhengyin, “Conductance of armchair silicene nanoribbon junctions,” Physica E: Low-Dimensional Systems and Nanostructures, vol. 111, pp. 172–178, 2019.
View at: Publisher Site | Google Scholar
J. R. Williams, L. Dicarlo, and C. M. Marcus, “Quantum hall effect in a gate-controlled p–n junction of graphene,” Science, vol. 317, no. 5838, pp. 638–641, 2007.
View at: Publisher Site | Google Scholar
A. F. Young and P. Kim, “Quantum interference and Klein tunnelling in graphene heterojunctions,” Nature Physics, vol. 5, pp. 222–226, 2009.
View at: Publisher Site | Google Scholar
H.-H. Fu, J.-H. Gao, and K.-L. Yao, “Topological field-effect quantum transistors in HgTe nanoribbons,” Nanotechnology, vol. 25, no. 22, Article ID 225201, 2014.
View at: Publisher Site | Google Scholar
N. Pournaghavi, M. Esmaeilzadeh, A. Abrishamifar, and S. Ahmadi, “Extrinsic Rashba spin–orbit coupling effect on silicene spin polarized field effect transistors,” Journal of Physics: Condensed Matter, vol. 29, no. 14, Article ID 145501, 2017.
View at: Publisher Site | Google Scholar
B. Rzeszotarski and B. Szafran, “Electron spin inversion in gated silicene nanoribbons,” Physical Review B, vol. 98, no. 7, Article ID 075417, 2018.
View at: Publisher Site | Google Scholar
H. Tian, C. D. Ren, B. Zhou et al., “Controllable valley polarization using silicene double line defects due to rashba spin–orbit coupling,” Nanoscale Research Letters, vol. 14, Article ID 350, 2019.
View at: Publisher Site | Google Scholar
L. Wang, “Thermopower and thermoconductance properties of zigzag edged graphene nanoribbon based thermoelectric module,” Physics Letters A, vol. 377, no. 21-22, pp. 1486–1490, 2013.
View at: Publisher Site | Google Scholar
D. N. Sheng, L. Sheng, and Z. Y. Weng, “Quantum hall effect in graphene: disorder effect and phase diagram,” Physical Review B, vol. 73, no. 23, Article ID 233406, 2006.
View at: Publisher Site | Google Scholar
Z. Qiao and J. Wang, “A variant transfer matrix method suitable for transport through multi-probe systems,” Nanotechnology, vol. 18, no. 43, Article ID 435402, 2007.
View at: Publisher Site | Google Scholar
J. Li and S.-Q. Shen, “Disorder effects in the quantum Hall effect of graphene p−n junctions,” Physical Review B, vol. 78, no. 20, Article ID 205308, 2008.
View at: Publisher Site | Google Scholar
C. W. J. Beenakker, “Colloquium: Andreev reflection and Klein tunneling in graphene,” Reviews of Modern Physics, vol. 80, no. 4, pp. 1337–1354, 2008.
View at: Publisher Site | Google Scholar
S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, Cambridge, England, 1995.
Y.-T. Zhang, F. Zhai, Z. Qiao, and Q.-F. Sun, “Spin-polarized edge modes and snake states in HgTe/CdTe quantum wells under an antisymmetric magnetic field,” Physical Review B, vol. 86, no. 12, Article ID 121403, 2012.
View at: Publisher Site | Google Scholar
X.-T. An, Y.-Y. Zhang, J.-J. Liu, and S.-S. Li, “Spin–polarized current induced by a local exchange field in a silicene nanoribbon,” New Journal of Physics, vol. 14, Article ID 083039, 2012.
View at: Publisher Site | Google Scholar
W. Ren, Z. Qiao, J. Wang, Q. Sun, and H. Guo, “Universal spin-hall conductance fluctuations in two dimensions,” Physical Review Letters, vol. 97, no. 6, Article ID 066603, 2006.
View at: Publisher Site | Google Scholar
D. H. Lee and J. D. Joannopoulos, “Simple scheme for surface-band calculations. II. The green’s function,” Physical Review B, vol. 23, no. 10, pp. 4997–5004, 1981.
View at: Publisher Site | Google Scholar
M. P. Lopez-Sancho, J. M. Lopez-Sancho, J. M. L. Sancho, and J. Rubio, “Highly convergent schemes for the calculation of bulk and surface Green functions,” Journal of Physics F: Metal Physics, vol. 15, no. 4, Article ID 851, 1985.
View at: Publisher Site | Google Scholar
B. Zhou, B. Zhou, X. Chen, W. Liao, and G. Zhou, “Symmetry-dependent spin-charge transport and thermopower through a ZSiNR-based FM/normal/FM junction,” Journal of Physics: Condensed Matter, vol. 27, no. 46, Article ID 465301, 2015.
View at: Publisher Site | Google Scholar
B. Zhou, B. Zhou, Y. Yao, G. Zhou, and M. Hu, “Spin-dependent Seebeck effects in a graphene superlattice p–n junction with different shapes,” Journal of Physics: Condensed Matter, vol. 29, Article ID 405303, 2017.
View at: Publisher Site | Google Scholar
M. Li, Z.-B. Feng, and Z.-Y. Zhao, “Symmetry and magnetization effect on the selective spin–valley polarized transport through the ferromagnetic-normal-ferromagnetic ZSiNR junction,” Physica E: Low-Dimensional Systems and Nanostructures, vol. 151, Article ID 115729, 2023.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2023 Ming Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

111

Downloads

210

Citations

Advances in Condensed Matter Physics

Gate Voltage-Modulated Conductance in Zigzag Graphene Nanoribbon Junctions

Abstract

1. Introduction

2. Theory and Model

3. Results and Discussion

3.1. Conductance of the ZGNR Junction for VgR = 0 and Different VgL

3.2. Conductance of the ZGNR Junction for VgL = 0 and Different VgR

3.3. Conductance of the ZGNR Junction for VgL = −VgR

3.4. Conductance of the ZGNR Junction for VgL−VgR = ΔV ()

4. Conclusion

Data Availability

Conflicts of Interest

Acknowledgments

References

Copyright

3.1. Conductance of the ZGNR Junction for V_gR = 0 and Different V_gL

3.2. Conductance of the ZGNR Junction for V_gL = 0 and Different V_gR

3.3. Conductance of the ZGNR Junction for V_gL = −V_gR

3.4. Conductance of the ZGNR Junction for V_gL−V_gR = ΔV ()