Single molecular shuttle-junction: Shot noise and decoherence

Abstract

Single molecular shuttle-junction is one kind of nanoscale electromechanical tunneling system. In this junction, a molecular island oscillates depending on its charge occupation, and this charge dependent oscillation leads to modulation of electron tunneling through the molecular island. This paper reviews recent development on the study of current, shot noise and decoherence of electrons in the single molecular shuttle-junction. We will give detailed discussion on this topic using the typical system model, the theory of fully quantum master equation and the Aharonov–Bohm interferometer.

Graphical abstract

Keywords

molecular shuttle-junction / master equation / shot noise / decoherence

References

[1] L. Y. Gorelik, A. Isacsson, M. V. Voinova, B. Kasemo, R. I. Shekhter , and M. Jonson, Shuttle mechanism for charge transfer in coulomb blockade nanostructures, Phys. Rev. Lett.80(20), 4526 (1998)

[2] A. Donarini, T. Novotn’y, and A. P. Jauho, Simple models suffice for the single-dot quantum shuttle, New J. Phys.7(1), 237 (2005)

[3] D. W. Utami, H. S. Goan, C. A. Holmes, and G. J. Milburn, Quantum noise in the electromechanical shuttle: Quantum master equation treatment, Phys. Rev. B74(1), 014303 (2006)

[4] D. Mozyrsky and I. Martin, Quantum classical transition induced by electrical measurement, Phys. Rev. Lett. 89(1), 018301 (2002)

[5] D. Mozyrsky, I. Martin, and M. B. Hastings, Quantumlimited sensitivity of single-electron-transistor-based displacement detectors, Phys. Rev. Lett.92(1), 018303 (2004)

[6] S. Etaki, M. Poot, I. Mahboob, K. Onomitsu, H. Yamaguchi, and H. S. J. Van Der Zant, Motion detection of a micromechanical resonator embedded in a d.c. SQUID, Nat. Phys.4(10), 785 (2008)

[7] M. P. Blencowe and M. N. Wybourne, Sensitivity of a micromechanical displacement detector based on the radio-frequency single-electron transistor,Appl. Phys. Lett.77( 23), 3845 (2000)

[8] J. Twamley, D. W. Utami, H. S. Goan, and G. Milburn, Spin-detection in a quantum electromechanical shuttle system, New J. Phys.8(5), 63 (2006)

[9] D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, Single spin detection by magnetic resonance force microscopy, Nature430(6997), 329 (2004)

[10] A. N. Cleland and M. L. Roukes, A nanometre-scale mechanical electrometer, Nature392, 160 (1998)

[11] H. B. Meerwaldt, G. Labadze, B. H. Schneider, A. Taspinar, Ya. M. Blanter, H. S. J. van der Zant, and G. A. Steele, Probing the charge of a quantum dot with a nanomechanical resonator, Phys. Rev. B86(11), 115454 (2012)

[12] K. Jensen, K. Kim, and A. Zettl, An atomic-resolution nanomechanical mass sensor, Nat. Nanotechnol.3(9), 533 (2008)

[13] J. Koch, F. von Oppen, Y. Oreg, and E. Sela, Thermopower of single-molecule devices, Phys. Rev. B70(19), 195107 (2004)

[14] M. Galperin, K. Saito, A. V. Balatsky, and A. Nitzan, Cooling mechanisms in molecular conduction junctions, Phys. Rev. B80(11), 115427 (2009)

[15] G. Romano, A. Gagliardi, A. Pecchia, and A. Di Carlo, Heating and cooling mechanisms in single-molecule junctions, Phys. Rev. B81(11), 115438 (2010)

[16] G. Schulze, K. J. Franke, A. Gagliardi, G. Romano, C. S. Lin, A. L. Rosa, T. A. Niehaus, Th. Frauenheim, A. Di Carlo, A. Pecchia, and J. I. Pascual, Resonant electron heating and molecular phonon cooling in single C₆₀ junctions, Phys. Rev. Lett.100(13), 136801 (2008)

[17] P. C. E. Stamp and C. Zhang, Theory of Bloch delocalization and quantum diffusion of heavy particles in insulators, Phys. Rev. Lett.66(14), 1902 (1991)

[18] C. Zhang and Y. Takahashi, Dynamical conductivity of a two-layered structure with electron acoustic phonon coupling, J. Phys.: Condens. Matter5(28), 5009 (1993)

[19] A. Nocera, C. A. Perroni, V. Marigliano Ramaglia, and V. Cataudella, Stochastic dynamics for a single vibrational mode in molecular junctions, Phys. Rev. B83(11), 115420 (2011)

[20] A. Metelmann and T. Brandes, Adiabaticity in semiclassical nanoelectromechanical systems, Phys. Rev. B84(15), 155455 (2011)

[21] T. Koch, J. Loos, A. Alvermann, and H. Fehske, Nonequilibrium transport through molecular junctions in the quantum regime, Phys. Rev. B84(12), 125131 (2011)

[22] R. C. Monreal, F. Flores, and A. Martin-Rodero, Nonequilibrium transport in molecular junctions with strong electron-phonon interactions, Phys. Rev. B82(23), 235412 (2010)

[23] M. Galperin, M. A. Ratner, and A. Nitzan, Inelastic electron tunneling spectroscopy in molecular junctions: Peaks and dips, J. Chem. Phys.121(23), 11965 (2004)

[24] M. Galperin, M. A. Ratner, and A. Nitzan, On the line widths of vibrational features in inelastic electron tunneling spectroscopy, Nano Lett.4(9), 1605 (2004)

[25] L. Mühlbacher and E. Rabani, Real-time path integral approach to nonequilibrium many-body quantum systems, Phys. Rev. Lett.100(17), 176403 (2008)

[26] D. F. Walls and G. J. Milburn, Quantum Optics, New York: Springer-Verlag, 1994, p91

[27] M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge: Cambridge University Press, 1997, page 249

[28] S. A. Gurvitz and Y. S. Prager, Microscopic derivation of rate equations for quantum transport, Phys. Rev. B53(23), 15932 (1996)

[29] D. Boese and H. Schoeller, Influence of nanomechanical properties on single-electron tunneling: A vibrating singleelectron transistor, Europhys. Lett.54(5), 668 (2001)

[30] K. D. McCarthy, N. Prokofev, and M. T. Tuominen, Incoherent dynamics of vibrating single-molecule transistors, Phys. Rev. B67(24), 245415 (2003)

[31] S. Braig and K. Flensberg, Vibrational sidebands and dissipative tunneling in molecular transistors, Phys. Rev. B68(20), 205324 (2003)

[32] J. Koch and F. von Oppen, Franck–Condon blockade and giant fano factors in transport through single molecules, Phys. Rev. Lett.94(20), 206804 (2005)

[33] D. Kast, L. Keche, and J. Ankerhold, Charge transfer through single molecule contacts: How reliable are rate descriptions? Beilstein J. Nanotechnol.2, 416 (2011)

[34] W. Lai, Y. Cao, and Z. Ma, Current–oscillator correlation and Fano factor spectrum of quantum shuttle with finite bias voltage and temperature, J. Phys.: Condens. Matter24(17), 175301 (2012)

[35] W. Lai, Y. Xing, and Z. Ma, Dephasing of electrons in the Aharonov–Bohm interferometer with a single-molecular vibrational junction, J. Phys.: Condens. Matter25(20), 205304 (2013)

[36] T. Novotný, A. Donarini, and A. P. Jauho, Quantum shuttle in phase space, Phys. Rev. Lett.90(25), 256801 (2003)

[37] T. Novotný, A. Donarini, C. Flindt, and A. P. Jauho, Shot noise of a quantum shuttle, Phys. Rev. Lett.92(24), 248302 (2004)

[38] F. Haupt, F. Cavaliere, R. Fazio, and M. Sassetti, Anomalous suppression of the shot noise in a nanoelectromechanical system, Phys. Rev. B74(20), 205328 (2006)

[39] L. Y. Gorelik, S. I. Kulinich, R. I. Shekhter, M. Jonson, and V. M. Vinokur, Mechanically assisted spin-dependent transport of electrons, Phys. Rev. B71(3), 035327 (2005)

[40] R. Q. Wang, B. Wang, and D. Y. Xing, Spin valve effect in a magnetic nanoelectromechanical shuttle, Phys. Rev. Lett. 100(11), 117206 (2008)

[41] D. Fedorets, L. Y. Gorelik, R. I. Shekhter, and M. Jonson, Quantum shuttle phenomena in a nanoelectromechanical single-electron transistor, Phys. Rev. Lett.92(16), 166801 (2004)

[42] S. D. Bennett and A. A. Clerk, Laser-like instabilities in quantum nano-electromechanical systems, Phys. Rev. B74(20), 201301 (2006)

[43] A. D. Armour and A. MacKinnon, Transport via a quantum shuttle, Phys. Rev. B66(3), 035333 (2002)

[44] M. N. Kiselev, K. Kikoin, R. I. Shekhter, and V. M. Vinokur, Kondo shuttling in a nanoelectromechanical single-electron transistor, Phys. Rev. B74(23), 233403 (2006)

[45] J. Mravlje and A. Ramšak, Kondo effect and channel mixing in oscillating molecules, Phys. Rev. B78(23), 235416 (2008)

[46] J. Mravlje and A. Ramšak, Kondo effect in oscillating molecules, Phys. Status Solidi B246(5), 994 (2009)

[47] L. G. G. V. Dias da Silva, and E. Dagotto, Phonon-assisted tunneling and two-channel Kondo physics in molecular junctions, Phys. Rev. B79(15), 155302 (2009)

[48] D. Golež, J. Bonča, and R. Zitko, Vibrational Andreevˇ bound states in magnetic molecules, Phys. Rev. B86(8), 085142 (2012)

[49] J. Koch, M. E. Raikh, and F. von Oppen, Pair tunneling through single molecules, Phys. Rev. Lett.96(5), 056803 (2006)

[50] M. J. Hwang, M. S. Choi, and R. López, Pair tunneling and shot noise through a single molecule in a strong electron phonon coupling regime, Phys. Rev. B 76(16), 165312 (2007)

[51] Z. Ioffe, T. Shamai, A. Ophir, G. Noy, I. Yutsis, K. Kfir, O. Cheshnovsky, and Y. Selzer, Detection of heating in current-carrying molecular junctions by Raman scattering, Nat. Nanotechnol.3(12), 727 (2008)

[52] S. W. Wu, G. V. Nazin, and W. Ho, Intramolecular photon emission from a single molecule in a scanning tunneling microscope, Phys. Rev. B77(20), 205430 (2008)

[53] D. R. Ward, N. J. Halas, J. W. Ciszek, J. M. Tour, Y. Wu, P. Nordlander, and D. Natelson, Simultaneous measurements of electronic conduction and raman response in molecular junctions, Nano Lett.8(3), 919 (2008)

[54] M. Galperin, M. A. Ratner, and A. Nitzan, Raman scattering from nonequilibrium molecular conduction junctions, Nano Lett.9(2), 758 (2009)

[55] M. Galperin, M. A. Ratner, and A. Nitzan, Raman scattering in current-carrying molecular junctions, J. Chem. Phys.130(14), 144109 (2009)

[56] M. Oren, M. Galperin, and A. Nitzan, Raman scattering from molecular conduction junctions: Charge transfer mechanism, Phys. Rev. B85(11), 115435 (2012)

[57] G. L. Eesley and J. R. Smith, Enhanced Raman scattering on metal surfaces, Solid State Commun.31(11), 815 (1979)

[58] J. P. Goudonnet, G. M. Begun, and E. T. Arakawa, Surfaceenhanced raman scattering on silver-coated Teflon sphere substrates, Chem. Phys. Lett.92(2), 197 (1982)

[59] H. Yamada, Y. Yamamoto, and N. Tani, Surface-enhanced raman scattering (SERS) of adsorbed molecules on smooth surfaces of metals and a metal oxide, Chem. Phys. Lett.86(4), 397 (1982)

[60] H. Wetzel, H. Gerischer, and B. Pettinger, Surface-enhanced raman scattering from silver-cyanide and silver-thiocyanate vibrations and the importance of adatoms, Chem. Phys. Lett.80(1), 159 (1981)

[61] P. F. Liao, J. G. Bergman, D. S. Chemla, A. Wokaun, J. Melngailis, A. M. Hawryluk, and N. P. Economou, Surfaceenhanced raman scattering from microlithographic silver particle surfaces, Chem. Phys. Lett.82(2), 355 (1981)

[62] D. A. Weitz, S. Garoff, J. I. Gersten, and A. Nitzan, The enhancement of Raman scattering, resonance Raman scattering, and fluorescence from molecules adsorbed on a rough silver surface, J. Chem. Phys.78(9), 5324 (1983)

[63] C. G. Blatchford, M. Kerker, and D. S. Wang, Surfaceenhanced Raman spectroscopy of water: Iniplications of the electromagnetic model, Chem. Phys. Lett.100(3), 230 (1983)

[64] D. Fedorets, L. Y. Gorelik, R. I. Shekhter, and M. Jonson, Spintronics of a nanoelectromechanical shuttle, Phys. Rev. Lett.95(5), 057203 (2005)

[65] R. I. Shekhter, A. Pulkin, and M. Jonson, Spintronic mechanics of a magnetic nanoshuttle, Phys. Rev. B86(10), 100404 (2012)

[66] S. Datta, W. Tian, S. Hong, R. Reifenberger, J. I. Henderson, and C. P. Kubiak, Current-voltage characteristics of self-assembled monolayers by scanning tunneling microscopy, Phys. Rev. Lett.79(13), 2530 (1997)

[67] C. Kergueris, J. P. Bourgoin, S. Palacin, D. Esteve, C. Urbina, M. Magoga, and C. Joachim, Electron transport through a metal molecule metal junction, Phys. Rev. B59(19), 12505 (1999)

[68] D. Porath, A. Bezryadin, S. de Vries, and C. Dekker , Direct measurement of electrical transport through DNA molecules, Nature403(6770), 635 (2000)

[69] H. Park, J. Park, A. K. L. Lim, E. H. Anderson, A. P. Alivisatos, and P. L. McEuen, Nanomechanical oscillations in a single-C₆₀ transistor, Nature407, 57 (2000)

[70] M. A. Reed, C. Zhou, C. J. Muller, T. P. Burgin, and J. M. Tour, Conductance of a molecular junction, Science278(5336), 252 (1997)

[71] N. B. Zhitenev, H. Meng, and Z. Bao, Conductance of small molecular junctions, Phys. Rev. Lett.88(22), 226801 (2002)

[72] J. H. Schön, H. Meng, and Z. Bao, Self-assembled monolayer organic field-effect transistors, Nature413(6857), 713 (2001)

[73] C. P. Collier, G. Mattersteig, E. W. Wong, Y. Luo, K. Beverly, J. Sampaio, F. M. Raymo, J. F. Stoddart, and J. R. Heath, A [2]catenane-based solid state electronically reconfigurable switch, Science289(5482), 1172 (2000)

[74] J. Chen, M. A. Reed, A. M. Rawlett, and J. M. Tour, Large on-off ratios and negative differential resistance in a molecular electronic device, Science286(5444), 1550 (1999)

[75] X. D. Cui, A. Primak, X. Zarate, J. Tomfohr, O. F. Sankey, A. L. Moore, T. A. Moore, D. Gust, G. Harris, and S. M. Lindsay, Reproducible measurement of single-molecule conductivity, Sience294(5542), 571 (2001)

[76] Z. J. Donhauser, B. A. Mantooth, K. F. Kelly, L. A. Bumm, J. D. Monnell, J. J. Stapleton, A. M. Price, D. L. Rawlett, and J. M. Allara, Tour, and P. S. Weiss, Conductance switching in single molecules through conformational changes, Science292(5525), 2303 (2001)

[77] O. Tal, M. Kiguchi, W. H. A. Thijssen, D. Djukic, C. Untiedt, R. H. M. Smit, and J. M. van Ruitenbeek, Molecular signature of highly conductive metal molecule metal junctions, Phys. Rev. B80(8), 085427 (2009)

[78] A. Bannani, C. Bobisch, and R. Möller, Ballistic electron microscopy of individual molecules, Science315(5820), 1824 (2007)

[79] S. W. Wu, N. Ogawa, and W. Ho, Atomic scale coupling of photons to single-molecule junctions, Science312(5778), 1362 (2006)

[80] L. Venkataraman, J. E. Klare, C. Nuckolls, M. S. Hybertsen, and M. L. Steigerwald, Dependence of single-molecule junction conductance on molecular conformation, Nature442(7105), 904 (2006)

[81] A. Erbe, C. Weiss, W. Zwerger, and R. H. Blick, Nanomechanical resonator shuttling single electrons at radio frequencies, Phys. Rev. Lett.87(9), 096106 (2001)

[82] A. V. Moskalenko, S. N. Gordeev, O. F. Koentjoro, P. R. Raithby, R. W. French, F. Marken, and S. E. Savel’ev, Nanomechanical electron shuttle consisting of a gold nanoparticle embedded within the gap between two gold electrodes, Phys. Rev. B79(24), 241403 (2009)

[83] A. V. Moskalenko, S. N. Gordeev, O. F. Koentjoro, P. R. Raithby, R. W. French, F. Marken, and S. Savel’ev, Fabrication of shuttle-junctions for nanomechanical transfer of electrons, Nanotechnology20(48), 485202 (2009)

[84] M. Galperin, M. A. Ratner, and A. Nitzan, On the line widths of vibrational features in inelastic electron tunneling spectroscopy, Nano Lett.4(9), 1605 (2004)

[85] D. W. Utami, H. S. Goan, and G. J. Milburn, Charge transport in a quantum electromechanical system, Phys. Rev. B70(7), 075303 (2004)

[86] M. Galperin, M. A. Ratner, and A. Nitzan, Molecular transport junctions: Vibrational effects, J. Phys.: Condens. Matter19(10), 103201 (2007)

[87] D. Fedorets, L. Y. Gorelik, R. I. Shekhter, and M. Jonson, Vibrational instability due to coherent tunneling of electrons, Europhys. Lett.58(1), 99 (2002)

[88] A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, Coherence and phase sensitive measurements in a quantum dot, Phys. Rev. Lett.74(20), 4047 (1995)

[89] R. Schuster, E. Buks, M. Heiblum, D. Mahalu, V. Umansky, and H. Shtrikman, Phase measurement in a quantum dot via a double-slit interference experiment, Nature385(6615), 417 (1997)

[90] G. Cernicchiaro, T. Martin, K. Hasselbach, D. Mailly, and A. Benoit, Channel interference in a quasiballistic Aharonov Bohm experiment, Phys. Rev. Lett.79(2), 273 (1997)

[91] V. N. Stavrou and X. Hu, Charge decoherence in laterally coupled quantum dots due to electron–phonon interactions, Phys. Rev. B72(7), 075362 (2005)

[92] A. Grodecka-Grad and J. Förstner, Phonon-assisted decoherence and tunneling in quantum dot molecules, Phys. Status Solidi C8(4), 1125 (2011)

[93] K. Roszak, A. Grodecka, P. Machnikowski, and T. Kuhn, Phonon-induced decoherence for a quantum-dot spin qubit operated by Raman passage, Phys. Rev. B71(19), 195333 (2005)

[94] X. Hu, Two-spin dephasing by electron-phonon interaction in semiconductor double quantum dots, Phys. Rev. B83(16), 165322 (2011)

[95] F. L. Semião, K. Furuya, and G. J. Milburn, Vibrationenhanced quantum transport, New J. Phys.12(8), 083033 (2010)

[96] I. L. Aleiner, N. S. Wingreen, and Y. Meir, Dephasing and the orthogonality catastrophe in tunneling through a quantum dot: The “which path?” interferometer, Phys. Rev. Lett.79(19), 3740 (1997)

[97] M. Heiblum, E. Buks, R. Schuster, D. Mahalu, and V. Umansky, Dephasing in electron interference by a “whichpath” detector, Nature391(6670), 871 (1998)

[98] D. Sprinzak, E. Buks, M. Heiblum, and H. Shtrikman, Controlled dephasing of electrons via a phase sensitive detector, Phys. Rev. Lett.84(25), 5820 (2000)

[99] J. König and Y. Gefen, Coherence and partial coherence in interacting electron systems, Phys. Rev. Lett.86(17), 3855 (2001)

[100] J. König and Y. Gefen, Aharonov Bohm interferometry with interacting quantum dots: Spin configurations, asymmetric interference patterns, bias-voltage-induced Aharonov Bohm oscillations, and symmetries of transport coefficients, Phys. Rev. B65(4), 045316 (2002)

[101] H. Aikawa, K. Kobayashi, A. Sano, S. Katsumoto, and Y. Iye, Observation of “partial coherence” in an Aharonov Bohm interferometer with a quantum dot, Phys. Rev. Lett.92(17), 176802 (2004)

[102] G. Luck Khym and K. Kang, Charge detection in a closedloop Aharonov–Bohm interferometer, Phys. Rev. B74(15), 153309 (2006)

[103] V. Moldoveanu, M. Tolea, and B. Tanatar, Controlled dephasing in single-dot Aharonov–Bohm interferometers, Phys. Rev. B75(4), 045309 (2007)

[104] D. Rohrlich, O. Zarchin, M. Heiblum, D. Mahalu, and V. Umansky, Controlled dephasing of a quantum dot: From coherent to sequential tunneling, Phys. Rev. Lett.98(9), 096803 (2007)

[105] A. D. Armour and M. P. Blencowe, Possibility of an electromechanical which-path interferometer, Phys. Rev. B64(3), 035311 (2001)

[106] A. D. Armour and M. Blencowe, Dephasing and thermal smearing in an electromechanical which-path device, Physica B, 2002, 316 317: 400

[107] C. Joachim, J. K. Gimzewski, and A. Aviram, Electronics using hybrid-molecular and mono-molecular devices, Nature408(6812), 541 (2000)

[108] R. I. Shekhter, Y. Galperin, L. Y. Gorelik, A. Isacsson, and M. Jonson, Shuttling of electrons and Cooper pairs, J. Phys.: Condens. Matter15(12), R441 (2003)

[109] R. I. Shekhter, L. Y. Gorelik, I. V. Krive, M. N. Kiselev, A. V. Parafilo, and M. Jonson, Nanoelectromechanics of shuttle devices, Nanomechanics1, 1 (2013)

[110] M. Galperin, M. A. Ratner, A. Nitzan, and A. Troisi, Nuclear coupling and polarization in molecular transport junctions: Beyond tunneling to function, Science319(5866), 1056 (2008)

[111] M. Esposito, U. Harbola, and S. Mukamel, Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems, Rev. Mod. Phys.81(4), 1665 (2009)

[112] X. Li, J. Luo, Y. Yang, P. Cui, and Y. Yan, Quantum master-equation approach to quantum transport through mesoscopic systems, Phys. Rev. B71(20), 205304 (2005)

[113] C. Timm, Tunneling through molecules and quantum dots: Master-equation approaches, Phys. Rev. B77(19), 195416 (2008)

[114] O. Sauret, D. Feinberg, and T. Martin, Quantum master equations for the superconductor–quantum dot entangler, Phys. Rev. B 70(24), 245313 (2004)

[115] H. B. Sun and G. Milburn, Quantum open-systems approach to current noise in resonant tunneling junctions, Phys. Rev. B59(16), 10748 (1999)

[116] C. Flindt, T. Novotny, and A. P. Jauho, Current noise in a vibrating quantum dot array, Phys. Rev. B70(20), 205334 (2004)

[117] S. A. Gurvitz, D. Mozyrsky, and G. P. Berman, Coherent effects in magnetotransport through Zeeman-split levels, Phys. Rev. B72(20), 205341 (2005)

[118] R. Härtle and M. Thoss, Resonant electron transport in single-molecule junctions: Vibrational excitation, rectification, negative differential resistance, and local cooling, Phys. Rev. B83(11), 115414 (2011)

[119] B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, Quantized conductance of point contacts in a twodimensional electron gas, Phys. Rev. Lett.60(9), 848 (1988)

[120] D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacockt, D. A. Ritchie, and G. A. C. Jones, One-dimensional transport and the quantisation of the ballistic resistance, J. Phys. Chem.21(8), L209 (1988)

[121] D. K. C. Macdonald, Spontaneous fluctuations, Rep. Prog. Phys.12(1), 56 (1949)

[122] C. Flindt, T. Novotny, and A. P. Jauho, Current noise spectrum of a quantum shuttle, Physica E29(1–2), 411 (2005)

[123] C. Flindt, T. Novotny, and A. P. Jauho, Full counting statistics of nano-electromechanical systems, Europhys. Lett.69(3), 475 (2005)

[124] M. Merlo, F. Haupt, F. Cavaliere, and M. Sassetti, SubPoissonian phononic population in a nanoelectromechanical system, New J. Phys.10(2), 023008 (2008)

[125] D. A. Rodrigues, J. Imbers, and A. D. Armour, Quantum dynamics of a resonator driven by a superconducting single-electron transistor: A solid-state analogue of the micromaser, Phys. Rev. Lett.98(6), 067204 (2007)

[126] A. Y. Smirnov, L. G. Mourokh, and N. J. M. Horing, Temperature dependence of electron transport through a quantum shuttle, Phys. Rev. B 69(15), 155310 (2004)

[127] C. Weiss and W. Zwerger, Accuracy of a mechanical singleelectron shuttle, Europhys. Lett.47(1), 97 (1999)

[128] M. Galperin, A. Nitzan, and M. A. Ratner, Resonant inelastic tunneling in molecular junctions, Phys. Rev. B73(4), 045314 (2006)

[129] F. Domínguez, S. Kohler, and G. Platero, Phonon-mediated decoherence in triple quantum dot interferometers, Phys. Rev. B83(23), 235319 (2011)

[130] J. Friedel, The distribution of electrons round impurities in monovalent metals, Philos. Mag.43(337), 153 (1952)

[131] J. M. Ziman, Principles of the Theory of Solids, Cambridge: Cambridge University Press, 2nd Ed., 1972, page 157

[132] G. D. Mahan, Many-Particle Physics, New York: Kluwer Academic/Plenum Publishers, 3rd Ed., 2000, page 195

[133] J. S. Langer and V. Ambegaokar, Friedel sum rule for a system of interacting electrons, Phys. Rev.121(4), 1090 (1961)

[134] A. L. Yeyati and M. Büttiker, Aharonov Bohm oscillations in a mesoscopic ring with a quantum dot, Phys. Rev. B52(20), R14360 (1995)

[135] S. Bandopadhyay and P. S. Deo, Friedel sum rule for a singlechannel quantum wire, Phys. Rev. B68(11), 113301 (2003)

[136] M. Rontani, Friedel sum rule for an interacting multiorbital quantum dot, Phys. Rev. Lett.97(7), 076801 (2006)

[137] P. S. Deo, Nondispersive backscattering in quantum wires, Phys. Rev. B75(23), 235330 (2007)

[138] M. R. Galpin and D. E. Logan, Anderson impurity model in a semiconductor, Phys. Rev. B77(19), 195108 (2008)

[139] B. Rosenow and Y. Gefen, Dephasing by a zero-temperature detector and the Friedel sum rule, Phys. Rev. Lett.108(25), 256805 (2012)

[140] H. M. Pastawskia, L. E. F. Foa Torresa, and E. Medina, Electron–phonon interaction and electronic decoherence in molecular conductors, Chem. Phys.281(23), 257 (2002)

[141] A. Ueda and M. Eto, Resonant tunneling and Fano resonance in quantum dots with electron phonon interaction, Phys. Rev. B73(23), 235353 (2006)

[142] H. W. Lee, Generic transmission zeros and in-phase resonances in time-reversal symmetric single channel transport, Phys. Rev. Lett.82(11), 2358 (1999)

[143] H. Akera, Aharonov–Bohm effect and electron correlation in quantum dots, Phys. Rev. B47(11), 6835 (1993)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg