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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 5 — Mar. 1, 2010
  • pp: 4066–4073
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Negative photoconductivity induced by surface plasmon polaritons in Ag nanowire macrobundles

Jia-Lin Sun, Wei Zhang, Jia-Lin Zhu, and Yang Bao  »View Author Affiliations


Optics Express, Vol. 18, Issue 5, pp. 4066-4073 (2010)
http://dx.doi.org/10.1364/OE.18.004066


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Abstract

We study experimentally and theoretically the transport properties of Ag nanowire macrobundles in the presence of light irradiation. We have observed significant negative photoconductivity induced by the interaction between electrons and the excited surface plasmon polaritons (SPPs). As temperature T increases from 77 K to 304 K, the dark resistivity ρd without light irradiation increases linearly with T, and the resistivity change Δρ due to light irradiation decreases nonlinearly with increasing T. The current change |ΔI| due to light irradiation, which is proportional to the laser intensity, also decreases nonlinearly with increasing T. We explain well the experimental results using our proposed model with a new scattering channel due to the interaction between electrons and SPPs. Both our experimental and theoretical results reveal the novel phenomena due to the combination of photonics and electronics properties of Ag nanowires and they will be useful for scientific research, and technical applications.

© 2010 OSA

1. Introduction

Nanoplasmonics has arisen considerable interest recently due to its promising applications in nano-optics, electronics and biosensors etc [1

1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

]. One of the basic excitations in the relevant systems is the surface plasmon polariton (SPP), i.e., the collective oscillation of the electromagnetic field and electrons propagating along a metal-dielectric surface. It has the ability of strong confinement and control of energy in a nanoscale near metal nanostructures. In theses nanostructures, there are several elemental excitations of different natures, for instance, plasmon, exciton, soliton etc.. The interaction among theses excitations in nanoscale is of fundamental interest and leads to novel phenomena [2

2. W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006). [CrossRef] [PubMed]

4

4. K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, “Resonant Plasmon-Soliton Interaction,” arXiv: 0806.2183.

].

In this work we experimentally and theoretically explore the photoconductivity due to the interaction between SPPs and electrons on the surface of AgNWs. We should note that the heating effects may also have contribution to the photoconductivity. Fortunately, the characteristic time scales for the heating process and SPP-electron scattering process are quite different, which makes them distinguishable. Our results clearly show that the photo-induced SPPs have an appreciable influence on transportation of electrons in AgNWs.

2. Experimental details

In experiments, the length of the nanowire should be much larger than the diameter of the illuminating light spot to avoid possible influence on transport behavior of the metal nanowire caused by two electrodes and their interfaces. On the other hand, in order to generate strong photo-induced SPPs on the surface of the nanowire, its diameter is usually much less than μm scale. According to above-mentioned analysis, we have fabricated a macrolong pure metal Ag nanowire bundle (AgNWB) and measured the transport properties on a macroscopic circuit. Figure 1(a)
Fig. 1 (a) Photograph of as-fabricated AgNWB located between two conductive silver paint electrodes. (b) SEM image of the AgNWB. (c) TEM image of the ultrasonically dispersed AgNWs. (d) Schematic measurement setup for photoconductivity of the AgNWB.
shows an AgNWB of length about 8.0 mm and width about 300 μm, which was fabricated [17

17. J. Xu, J. L. Sun, and J. L. Zhu, “Thermo- and photoinduced voltages in Ag heterodimensional junctions,” Appl. Phys. Lett. 91(16), 161107 (2007). [CrossRef]

] by an improved solid-state ionics method. The two ends of the macrobundle were connected with conductive silver paint electrodes, and fixed to an insulating substrate. The microstructure of the macrobundle, comprising numerous AgNWs aligned in the same direction, is clearly shown in the scanning electron microscopy (SEM) image in Fig. 1(b). In Fig. 1(c), the transmission electron microscopy (TEM) image shows that the diameters of AgNWs in the macrobundle range from 30 to 90 nm.

After the fabrication of the AgNWB, we studied the influence of SPP-electron interaction on the transport behavior under continuous and pulsed laser field. We placed the sample in a cryostat at a vacuum about 10−3 Pa to control its temperature and to prevent it from being affected by air [shown in Fig. 1(d)]. An optical chopper is used for periodically interrupting a 532 nm monochromatic light beam from a semiconductor laser. The transmission coefficient of the quartz glass window of the cryostat at a wavelength of 532 nm is about 90%. In order to avoid generation of the photo-induced voltage, the laser spot is located near the geometric center of the AgNWB [17

17. J. Xu, J. L. Sun, and J. L. Zhu, “Thermo- and photoinduced voltages in Ag heterodimensional junctions,” Appl. Phys. Lett. 91(16), 161107 (2007). [CrossRef]

]. The laser spot diameter on the sample is about 4.0 mm.

3. The experimental results

The I-V characteristics [shown in Fig. 2(a)
Fig. 2 (a) I-V characteristics of the AgNWB without light irradiation at 304 K (red line) and 77 K (blue line). (b) Dark resistance (without light irradiation) Rd of the AgNWB as a function of temperature. (c) Dynamic response of negative photoconductivity at 304 K when the AgNWB was irradiated (on/off circles) by 142.3 mW continuous laser under a bias voltage of 0.1 V. (d) and (e) are dynamic responses of negative photoconductivity at 304 K and 77 K, respectively, when the AgNWB was irradiated by 142.3 mW pulsed light (the pulse duty factor is about 6%) under a bias voltage of 0.1 V. (f) The absolute values of the photo-induced current change |ΔI| (pink line) and |ΔI| -1/4 (green line) as a function of temperature.
] of the AgNWB without light irradiation were recorded by a SourceMeter (Keithley 2400) at 304 K (red line) and 77 K (blue line), respectively. The results show the ohmic contacts between Ag electrode and AgNWB. The temperature dependence of dark resistance Rd of the sample measured in the temperature range 77 K to 304 K is displayed in Fig. 2(b). It clearly shows a linear relationship between the dark resistance Rd and sample temperature T.

To avoid possible influence on negative photoconductivity of the AgNWB caused by the Joule heating and the SPP-induced heating processes, we studied the conductive properties of the AgNWB under small bias voltage of 0.1 V and pulsed laser field with small pulse duty factor. Thus the dynamic responses of negative photoconductivity for the AgNWB illuminated by pulsed light were studied in the temperature range 304 K to 77 K. As an example, Fig. 2(d) and Fig. 2(e) show the dynamic responses at 304 K and 77 K, respectively. Figure 2(e) clearly shows that the dark current Id maintains a constant 4.542 mA at 77 K, while it is 3.216 mA with small fluctuation at 304 K during 5 seconds as seen in Fig. 2(d). When the light was turned on, a significant decrease in current of the AgNWB was observed too. By comparing Figs. 2(c), 2(d) and 2(e), one sees that the fast process of SPP-electron scattering gives most contribution to current change in the case with short characteristic time scale. The current change |ΔI| due to the illumination as a function of temperature is shown in Fig. 2(f) (pink line). Based on the above experimental results, we may have a linear relationship between the |ΔI|-1/4 and temperature [see Fig. 2(f), green line]. Furthermore from all the data shown in Fig. 2, one sees that during temperature increasing, the dark resistivity ρd of the AgNWB increases and the photo-induced resistivity change Δρ decreases. This is due to the particular natures of the SPP-electron interaction and phonon-electron interaction as will be discussed in more details later. The ratio of resistivity change Δρ/ρdhas been plotted as a function of temperature in Fig. 3(a)
Fig. 3 (a) The ratio of photo-induced resistivity change Δρ / ρd of the AgNWB as a function of temperature. (b) The absolute values of the change of the photo-induced current |ΔI| of the AgNWB as a function of laser power P at 77 K (blue line) and 304 K (red line) under a bias voltage of 0.1 V.
. The photo-inducedΔρ/ρddecreases as the temperature increases from 77 K to 304 K, and there is a nonlinear relationship between theΔρ/ρdand temperature. The monotonically linear increases of the current change |ΔI| with laser power were observed both at 77 K and 304 K as shown in [Fig. 3(b)]. The results indicate that the SPP-electron interactions are more sensitive to laser power at lower temperature. This transmission behavior of the AgNWB can be ascribed to the SPP-electron interaction on the surface of the AgNWs. We also observed a weak dependence on the angle of excitation, which is due to the fact that the nanowires in the macrobundle are not strictly parallel to each other, as seen in SEM image Fig. 1(b).

4. The theoretical analyses

We propose a model to explain the experimental observations. From Drude theory and Matthiessen's rule, the resistivity isρ=ρ1+ρ2+ρ3, where ρ1+ρ2ρdis the dark resistivity in the absence of irradiation and ρ3 is the correction due to the interaction between electrons and SPPs excited by external light. ρ1=m/ne2τ1is the bulk resistivity. The bulk resistivity due to the scattering between electrons and impurities and phonons has a linear relation with temperature. ρ 2 is the resistivity due to surface scattering. ρ2ρ1l1/D [18

18. W. Steinhögl, G. Schindler, G. Steinlesberger, and M. Engelhardt, “Size-dependent resistivity of metallic wires in the mesoscopic range,” Phys. Rev. B 66(7), 075414 (2002). [CrossRef]

], l1=νFτ1, the bulk mean free path, νF Fermi velocity and D the radius of the nanowire. ρ 2 is temperature independent due to the cancellation of the temperature dependence of ρ 1 and l 1. Overall we have ρd=m/ne2τ0A+BT, where τ0 is the relaxation time of an electron in metal nanowires in the absence of irradiation, which includes the effects from scattering of electrons with impurities, phonons and surfaces.

In the presence of irradiation (with frequencyω, wavelength 532 nm), additional scattering channel is generated due to the interaction between electrons and excited SPPs. The external laser field excites SPPs due to the surface roughness as seen in Fig. 1(c) [19

19. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]

]. The resistivity due to the interaction between electrons and SPPs has the form
ρ3=mne2τ3λmD,
(1)
whereτ3 is the scattering time andλmthe field penetration length. Based on the experimental observation that the correction to the current due to SPPs is small (a few percent), the main contribution to the SPP induced resistance is from the first order perturbation with term AP^ (or Er^) involved, where A(E) is the electromagnetic potential (field) for SPP field and P^ (r^) is the electron momentum (coordinate) operator. Thus the scattering rate of electrons near Fermi surface in the SPP-induced channel is W=1/τ3E2l02 (l0 the mean free path) [20

20. J. Shi and X. C. Xie, “Radiation-induced “zero-resistance state” and the photon-assisted transport,” Phys. Rev. Lett. 91(8), 086801 (2003). [CrossRef] [PubMed]

]. Thus we have1/τ3Pl02, where PE2is the laser power. For lower temperature with longer relaxations timeτ0 (longer mean free pathl0), there is bigger probability for electrons scattered by SPPs before it scatters with other degree of freedoms (phonons for instance). Therefore we obtainρd1/τ0, ΔρPl02λm/D, and the formula for current

I=I0+ΔI1/ρdγPl02ρd2λmD.
(2)

The accurate value of γ depends on the electronic structure, the surface roughness, the SPP distribution, etc. The calculation ofγ is beyond the scope of this paper and will be discussed in the future. Yet, our theoretical analysis reveals the basic physical picture and leads to a few important results. First, SPP-electron interaction leads to another scattering channel and results in the decrease of current. As temperature increases, ρdincreases and Δρ=ρ3 decreases as observed in our experiments. Second, the SPP-induced resistance has weak dependence on the laser frequency and vanishes when the radius of nanowire D is very large, which are consistent with our experimental observations (not shown in this paper). Third, our theory shows that ΔIρd4(A+BT)4 (sinceρd1/l0). Figure 2(f) shows a nice linear relation between |ΔI|1/4and T. Furthermore, from the fitting of the curve (green line) in Fig. 2(f), we haveB/A=0.0020, which agrees very well with the value from dark resistanceRd=A+BT, B/A=0.0021, as obtained from Fig. 2(b). Fourth, ΔI=k(T)P, as also seen in Fig. 3(b). Moreover our theory points out that

l0(T=77K)l0(T=304K)=[k(T=77K)k(T=304K)]1/4.
(3)

From the slop for ΔIversus P in Fig. 3(b), we have l0(T = 77 K) / l0(T = 304 K) = 1.49, which is consistent with l0(T = 77 K) / l0(T = 304 K) = ρd (T = 304 K) / ρd (T = 77 K) = 1.41 from Fig. 2(b). Our theory

5. Discussion and conclusion

In summary, considerable negative photoconductivity has been observed experimentally and demonstrated for macroscopic length AgNWB. The theoretical investigation clearly shows that the photo-induced SPPs have a notable influence on transportation of electrons in AgNWB. SPP-electron interaction leads to another scattering channel and the decrease of current. We expect that the photoconductive behavior will be more pronounced if AgNWs have smaller dimensions and higher surface-to-volume ratio. Our experimental and theoretical studies have shed new light on the novel phenomena from combination of photonic and electronic properties of AgNWBs. Their unusual photoelectrical properties will be useful for scientific research and technical applications, such as a high sensitivity photoconductor.

Acknowledgments

This work was supported by the National Natural Science Foundations of China (No. 10711120167, 10744004, 10874020, 10774085 and 10974108), MOST Program (No. 2006CB0L0601) of China and a grant of the China Academy of Engineering and Physics.

References and Links

1.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]

2.

W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006). [CrossRef] [PubMed]

3.

M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008). [CrossRef] [PubMed]

4.

K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, “Resonant Plasmon-Soliton Interaction,” arXiv: 0806.2183.

5.

S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef] [PubMed]

6.

K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997). [CrossRef]

7.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]

8.

M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. St, and J Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008). [CrossRef]

9.

P. P. Pompa, L. Martiradonna, A. D. Torre, F. D. Sala, L. Manna, M. De Vittorio, F. Calabi, R. Cingolani, and R. Rinaldi, “Metal-enhanced fluorescence of colloidal nanocrystals with nanoscale control,” Nat. Nanotechnol. 1(2), 126–130 (2006). [CrossRef]

10.

Z. Gueroui and A. Libchaber, “Single-molecule measurements of gold-quenched quantum dots,” Phys. Rev. Lett. 93(16), 166108 (2004). [CrossRef] [PubMed]

11.

Y. Wu, J. Xiang, C. Yang, W. Lu, and C. M. Lieber, “Single-crystal metallic nanowires and metal/semiconductor nanowire heterostructures,” Nature 430(6995), 61–65 (2004). [CrossRef] [PubMed]

12.

N. A. Melosh, A. Boukai, F. Diana, B. Gerardot, A. Badolato, P. M. Petroff, and J. R. Heath, “Ultrahigh-density nanowire lattices and circuits,” Science 300(5616), 112–115 (2003). [CrossRef] [PubMed]

13.

P. A. Smith, C. D. Nordquist, T. N. Jackson, T. S. Mayer, B. R. Martin, J. Mbindyo, and T. E. Mallouk, “Electric-Field Assisted Assembly and Alignment of Metallic Nanowires,” Appl. Phys. Lett. 77(9), 1399–1401 (2000). [CrossRef]

14.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90(8), 3825–3830 (2001). [CrossRef]

15.

M. N. Ou, S. R. Harutyunyan, S. J. Lai, C. D. Chen, T. J. Yang, and Y. Y. Chen, “Thermal and electrical transport properties of a single nickel nanowire,” Phys. Status Solidi 244(12), 4512–4517 (2007) (b). [CrossRef]

16.

B. H. Hong, S. C. Bae, C. W. Lee, S. Jeong, and K. S. Kim, “Ultrathin single-crystalline silver nanowire arrays formed in an ambient solution phase,” Science 294(5541), 348–351 (2001). [CrossRef] [PubMed]

17.

J. Xu, J. L. Sun, and J. L. Zhu, “Thermo- and photoinduced voltages in Ag heterodimensional junctions,” Appl. Phys. Lett. 91(16), 161107 (2007). [CrossRef]

18.

W. Steinhögl, G. Schindler, G. Steinlesberger, and M. Engelhardt, “Size-dependent resistivity of metallic wires in the mesoscopic range,” Phys. Rev. B 66(7), 075414 (2002). [CrossRef]

19.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]

20.

J. Shi and X. C. Xie, “Radiation-induced “zero-resistance state” and the photon-assisted transport,” Phys. Rev. Lett. 91(8), 086801 (2003). [CrossRef] [PubMed]

OCIS Codes
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(160.4236) Materials : Nanomaterials

ToC Category:
Optics at Surfaces

History
Original Manuscript: January 4, 2010
Revised Manuscript: February 2, 2010
Manuscript Accepted: February 4, 2010
Published: February 16, 2010

Citation
Jia-Lin Sun, Wei Zhang, Jia-Lin Zhu, and Yang Bao, "Negative photoconductivity induced by surface plasmon polaritons in Ag nanowire macrobundles," Opt. Express 18, 4066-4073 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-5-4066


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References

  1. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006). [CrossRef] [PubMed]
  2. W. Zhang, A. O. Govorov, and G. W. Bryant, “Semiconductor-metal nanoparticle molecules: hybrid excitons and the nonlinear fano effect,” Phys. Rev. Lett. 97(14), 146804 (2006). [CrossRef] [PubMed]
  3. M. Kroner, A. O. Govorov, S. Remi, B. Biedermann, S. Seidl, A. Badolato, P. M. Petroff, W. Zhang, R. Barbour, B. D. Gerardot, R. J. Warburton, and K. Karrai, “The nonlinear Fano effect,” Nature 451(7176), 311–314 (2008). [CrossRef] [PubMed]
  4. K. Y. Bliokh, Y. P. Bliokh, and A. Ferrando, “Resonant Plasmon-Soliton Interaction,” arXiv: 0806.2183.
  5. S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef] [PubMed]
  6. K. Kneipp, Y. Wang, H. Kneipp, L. T. Perelman, I. Itzkan, R. R. Dasari, and M. S. Feld, “Single Molecule Detection Using Surface-Enhanced Raman Scattering (SERS),” Phys. Rev. Lett. 78(9), 1667–1670 (1997). [CrossRef]
  7. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95(25), 257403 (2005). [CrossRef] [PubMed]
  8. M. A. Schmidt, L. N. Prill Sempere, H. K. Tyagi, C. G. Poulton, P. St. J. Russell, “Waveguiding and plasmon resonances in two-dimensional photonic lattices of gold and silver nanowires,” Phys. Rev. B 77(3), 033417 (2008). [CrossRef]
  9. P. P. Pompa, L. Martiradonna, A. D. Torre, F. D. Sala, L. Manna, M. De Vittorio, F. Calabi, R. Cingolani, and R. Rinaldi, “Metal-enhanced fluorescence of colloidal nanocrystals with nanoscale control,” Nat. Nanotechnol. 1(2), 126–130 (2006). [CrossRef]
  10. Z. Gueroui and A. Libchaber, “Single-molecule measurements of gold-quenched quantum dots,” Phys. Rev. Lett. 93(16), 166108 (2004). [CrossRef] [PubMed]
  11. Y. Wu, J. Xiang, C. Yang, W. Lu, and C. M. Lieber, “Single-crystal metallic nanowires and metal/semiconductor nanowire heterostructures,” Nature 430(6995), 61–65 (2004). [CrossRef] [PubMed]
  12. N. A. Melosh, A. Boukai, F. Diana, B. Gerardot, A. Badolato, P. M. Petroff, and J. R. Heath, “Ultrahigh-density nanowire lattices and circuits,” Science 300(5616), 112–115 (2003). [CrossRef] [PubMed]
  13. P. A. Smith, C. D. Nordquist, T. N. Jackson, T. S. Mayer, B. R. Martin, J. Mbindyo, and T. E. Mallouk, “Electric-Field Assisted Assembly and Alignment of Metallic Nanowires,” Appl. Phys. Lett. 77(9), 1399–1401 (2000). [CrossRef]
  14. G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, “Optical properties of Ag and Au nanowire gratings,” J. Appl. Phys. 90(8), 3825–3830 (2001). [CrossRef]
  15. M. N. Ou, S. R. Harutyunyan, S. J. Lai, C. D. Chen, T. J. Yang, and Y. Y. Chen, “Thermal and electrical transport properties of a single nickel nanowire,” Phys. Status Solidi 244(12), 4512–4517 (2007) (b). [CrossRef]
  16. B. H. Hong, S. C. Bae, C. W. Lee, S. Jeong, and K. S. Kim, “Ultrathin single-crystalline silver nanowire arrays formed in an ambient solution phase,” Science 294(5541), 348–351 (2001). [CrossRef] [PubMed]
  17. J. Xu, J. L. Sun, and J. L. Zhu, “Thermo- and photoinduced voltages in Ag heterodimensional junctions,” Appl. Phys. Lett. 91(16), 161107 (2007). [CrossRef]
  18. W. Steinhögl, G. Schindler, G. Steinlesberger, and M. Engelhardt, “Size-dependent resistivity of metallic wires in the mesoscopic range,” Phys. Rev. B 66(7), 075414 (2002). [CrossRef]
  19. A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408(3-4), 131–314 (2005). [CrossRef]
  20. J. Shi and X. C. Xie, “Radiation-induced “zero-resistance state” and the photon-assisted transport,” Phys. Rev. Lett. 91(8), 086801 (2003). [CrossRef] [PubMed]

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