|
|
Master equation approach to transient quantum transport in nanostructures |
Pei-Yun Yang( ),Wei-Min Zhang( ) |
Department of Physics and Centre for Quantum Information Science, Cheng Kung University, Tainan 70101 |
|
|
Abstract In this review article, we present a non-equilibrium quantum transport theory for transient electron dynamics in nanodevices based on exact Master equation derived with the path integral method in the fermion coherent-state representation. Applying the exact Master equation to nanodevices, we also establish the connection of the reduced density matrix and the transient quantum transport current with the Keldysh nonequilibrium Green functions. The theory enables us to study transient quantum transport in nanostructures with back-reaction effects from the contacts, with non-Markovian dissipation and decoherence being fully taken into account. In applications, we utilize the theory to specific quantum transport systems, a variety of quantum decoherence and quantum transport phenomena involving the non-Markovian memory effect are investigated in both transient and stationary scenarios at arbitrary initial temperatures of the contacts.
|
Keywords
quantum transport
Master equation
open systems
nanostructures
|
Corresponding Author(s):
Pei-Yun Yang,Wei-Min Zhang
|
Issue Date: 25 November 2016
|
|
1 |
M. A. Kastner, Artificial atoms, Phys. Today 46(1), 24 (1993)
https://doi.org/10.1063/1.881393
|
2 |
L. L. Chang, L. Esaki, and R. Tsu, Resonant tunneling in semiconductor double barriers, Appl. Phys. Lett. 24(12), 593 (1974)
https://doi.org/10.1063/1.1655067
|
3 |
T. Ando, A. B. Fowler, and F. Stern, Electronic properties of two-dimensional systems, Rev. Mod. Phys. 54(2), 437 (1982)
https://doi.org/10.1103/RevModPhys.54.437
|
4 |
E. R. Brown, J. R. Soderstrom, C. D. Parker, L. J. Mahoney, K. M. Molvar, and T. C. McGill, Oscillations up to 712 GHz in InAs/AlSb resonant-tunneling diodes, Appl. Phys. Lett. 58(20), 2291 (1991)
https://doi.org/10.1063/1.104902
|
5 |
K. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45(6), 494 (1980)
https://doi.org/10.1103/PhysRevLett.45.494
|
6 |
Y. Imry, Introduction to Mesoscopic Physics, 2nd Ed., Oxford, 2002
|
7 |
M. Büttiker, Scattering theory of current and intensity noise correlations in conductors and wave guides, Phys. Rev. B 46(19), 12485 (1992)
https://doi.org/10.1103/PhysRevB.46.12485
|
8 |
H. Ohnishi, T. Inata, S. Muto, N. Yokoyama, and A. Shibatomi, Selfconsistent analysis of resonant tunneling current, Appl. Phys. Lett. 49(19), 1248 (1986)
https://doi.org/10.1063/1.97428
|
9 |
A. Szafer and A. D. Stone, Theory of quantum conduction through a constriction, Phys. Rev. Lett. 62(3), 300 (1989)
https://doi.org/10.1103/PhysRevLett.62.300
|
10 |
J. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2(3), 407 (1961)
https://doi.org/10.1063/1.1703727
|
11 |
L. P. Kadano and G. Baym, Quantum Statistical Mechanics, New York: Benjamin, 1962
|
12 |
K. C. Chou, Z. B. Su, B. L. Hao, and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rep. 118(1–2), 1 (1985)
https://doi.org/10.1016/0370-1573(85)90136-X
|
13 |
J. Rammer and H. Smith, Quantum field-theoretical methods in transport theory of metals, Rev. Mod. Phys. 58(2), 323 (1986)
https://doi.org/10.1103/RevModPhys.58.323
|
14 |
J. S. Wang, B. K. Agarwalla, H. Li, and J. Thingna, Nonequilibrium Green’s function method for quantum thermal transport, Front. Phys. 9(6), 673 (2014)
https://doi.org/10.1007/s11467-013-0340-x
|
15 |
H. Haug and A. P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Springer Series in Solid-State Sciences Vol. 123, 2008
|
16 |
N. S. Wingreen, A. P. Jauho, and Y. Meir, Tim dependent transport through a mesoscopic structure, Phys. Rev. B 48(11), 8487 (1993)
https://doi.org/10.1103/PhysRevB.48.8487
|
17 |
A. P. Jauho, N. S. Wingreen, and Y. Meir, Time dependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B 50(8), 5528 (1994)
https://doi.org/10.1103/PhysRevB.50.5528
|
18 |
H. Schoeller and G. Schön, Mesoscopic quantum transport: Resonant tunneling in the presence of a strong Coulomb interaction, Phys. Rev. B 50(24), 18436 (1994)
https://doi.org/10.1103/PhysRevB.50.18436
|
19 |
S. A. Gurvitz and Ya. S. Prager, Microscopic derivation of rate equations for quantum transport, Phys. Rev. B 53(23), 15932 (1996)
https://doi.org/10.1103/PhysRevB.53.15932
|
20 |
J. S. Jin, X. Zheng, and Y. J. Yan, Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach, J. Chem. Phys. 128(23), 234703 (2008)
https://doi.org/10.1063/1.2938087
|
21 |
M. W.-Y. Tu and W. M. Zhang, Non-Markovian decoherence theory for a double-dot charge qubit, Phys. Rev. B 78(23), 235311 (2008)
https://doi.org/10.1103/PhysRevB.78.235311
|
22 |
M. W.-Y. Tu, M. T. Lee, and W. M. Zhang, Exact Master equation and non-Markovian decoherence for quantum dot quantum computing, Quantum Inf. Processing 8(6), 631 (2009)
https://doi.org/10.1007/s11128-009-0143-8
|
23 |
J. S. Jin, M. W.-Y. Tu, W. M. Zhang, and Y. J. Yan, Non-equilibrium quantum theory for nanodevices based on the Feynman–Vernon influence functional, New J. Phys. 12(8), 083013 (2010)
https://doi.org/10.1088/1367-2630/12/8/083013
|
24 |
X. Q. Li, Number-resolved Master equation approach to quantum measurement and quantum transport, Front. Phys. 11(4), 110307 (2016)
https://doi.org/10.1007/s11467-016-0539-8
|
25 |
Y. J. Yan, J. S. Jin, R. X. Xu, and X. Zheng, Dissipaton equation of motion approach to open quantum systems, Front. Phys. 11(4), 110306 (2016)
https://doi.org/10.1007/s11467-016-0513-5
|
26 |
S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge: Cambridge University Press, 1995
https://doi.org/10.1017/CBO9780511805776
|
27 |
R. Landauer, Spatial variation of currents and fields due to localized scatterers in metallic conduction, IBM J. Res. Develop. 1(3), 223 (1957)
https://doi.org/10.1147/rd.13.0223
|
28 |
R. Landauer, Electrical resistance of disordered one dimensional lattices, Philos. Mag. 21(172), 863 (1970)
https://doi.org/10.1080/14786437008238472
|
29 |
M. Büttiker, Y. Imry, R. Landauer, and S. Pinhas, Generalized many-channel conductance formula with application to small rings, Phys. Rev. B 31(10), 6207 (1985)
https://doi.org/10.1103/PhysRevB.31.6207
|
30 |
M. Büttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57(14), 1761 (1986)
https://doi.org/10.1103/PhysRevLett.57.1761
|
31 |
Ya. M. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys. Rep. 336(1–2), 1 (2000)
https://doi.org/10.1016/S0370-1573(99)00123-4
|
32 |
M. Büttiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B 38(14), 9375 (1988)
https://doi.org/10.1103/PhysRevB.38.9375
|
33 |
M. Büttiker, Quantized transmission of a saddle-point constriction, Phys. Rev. B 41(11), 7906 (1990)
https://doi.org/10.1103/PhysRevB.41.7906
|
34 |
P. Samuelsson and M. Büttiker, Quantum state tomography with quantum shot noise, Phys. Rev. B 73(4), 041305 (2006)
https://doi.org/10.1103/PhysRevB.73.041305
|
35 |
E. A. Rothstein, O. Entin-Wohlman, and A. Aharony, Noise spectra of a biased quantum dot, Phys. Rev. B 79(7), 075307 (2009)
https://doi.org/10.1103/PhysRevB.79.075307
|
36 |
M. Moskalets and M. Büttiker, Adiabatic quantum pump in the presence of external ac voltages, Phys. Rev. B 69(20), 205316 (2004)
https://doi.org/10.1103/PhysRevB.69.205316
|
37 |
O. Entin-Wohlman, A. Aharony, and Y. Levinson, Adiabatic transport in nanostructures, Phys. Rev. B 65(19), 195411 (2002)
https://doi.org/10.1103/PhysRevB.65.195411
|
38 |
M. Moskalets and M. Büttiker, Time-resolved noise of adiabatic quantum pumps, Phys. Rev. B 75(3), 035315 (2007)
https://doi.org/10.1103/PhysRevB.75.035315
|
39 |
G. D. Mahan, Many Particle Physics, 2nd Ed., New York: Plenum, 1990
https://doi.org/10.1007/978-1-4613-1469-1
|
40 |
L. V. Keldysh, Diagram technique for nonequilibrium processes, Zh. Eksp. Teor. Fiz. 47(4), 1515 (1964) [Sov. Phys. JETP 20(4), 1018 (1965)]
|
41 |
G. Stefanucci and C. O. Almbladh, Time-dependent partition-free approach in resonant tunneling systems, Phys. Rev. B 69(19), 195318 (2004)
https://doi.org/10.1103/PhysRevB.69.195318
|
42 |
M. Cini, Time-dependent approach to electron transport through junctions: General theory and simple applications, Phys. Rev. B 22(12), 5887 (1980)
https://doi.org/10.1103/PhysRevB.22.5887
|
43 |
U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124(6), 1866 (1961)
https://doi.org/10.1103/PhysRev.124.1866
|
44 |
P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109(5), 1492 (1958)
https://doi.org/10.1103/PhysRev.109.1492
|
45 |
C. Caroli, R. Combescot, P. Nozìeres, and D. Saint- James, Direct calculation of the tunneling current, J. Phys. Chem. 4, 916 (1971)
|
46 |
C. Caroli, R. Combescot, P. Nozìeres, and D. Saint- James, A direct calculation of the tunnelling current (II): Free electron description, J. Phys. Chem. 4(16), 2598 (1971)
|
47 |
D. C. Langreth, Linear and Nonlinear Electron Transport in Solids, edited by J. T. Devreese and E. Van Doren, New York: Plenum, 1976
|
48 |
X. Q. Li, J. Luo, Y. G. Yang, P. Cui, and Y. J. Yan, Quantum master-equation approach to quantum transport through mesoscopic systems, Phys. Rev. B 71(20), 205304 (2005)
https://doi.org/10.1103/PhysRevB.71.205304
|
49 |
R. P. Feynman and F. L. Jr Vernon, The theory of a general quantum system interacting with a linear dissipative system, Ann. Phys. 24, 118 (1963)
https://doi.org/10.1016/0003-4916(63)90068-X
|
50 |
W. M. Zhang, D. H. Feng, and R. Gilmore, Coherent states: Theory and some applications, Rev. Mod. Phys. 62(4), 867 (1990)
https://doi.org/10.1103/RevModPhys.62.867
|
51 |
M. W. Y. Tu, W. M. Zhang, and J. S. Jin, Intrinsic coherence dynamics and phase localization in nanoscale Aharonov–Bohm interferometers, Phys. Rev. B 83(11), 115318 (2011)
https://doi.org/10.1103/PhysRevB.83.115318
|
52 |
C. Y. Lin and W. M. Zhang, Single-electron turnstile pumping with high frequencies, Appl. Phys. Lett. 99(7), 072105 (2011)
https://doi.org/10.1063/1.3626585
|
53 |
M. W.-Y. Tu, W. M. Zhang, J. S. Jin, O. Entin- Wohlman, and A. Aharony, Transient quantum transport in double-dot Aharonov–Bohm interferometers, Phys. Rev. B 86(11), 115453 (2012)
https://doi.org/10.1103/PhysRevB.86.115453
|
54 |
M. W.-Y. Tu, W.M. Zhang, J. Jin, O. Entin-Wohlman, and A. Aharony, Transient quantum transport in double-dot Aharonov–Bohm interferometers, Phys. Rev. B 86(11), 115453 (2012)
https://doi.org/10.1103/PhysRevB.86.115453
|
55 |
J. S. Jin, M. W.-Y. Tu, N. E. Wang, and W. M. Zhang, Precision control of charge coherence in parallel double dot systems through spin–orbit interaction, J. Chem. Phys. 139(6), 064706 (2013)
https://doi.org/10.1063/1.4817850
|
56 |
M. W.-Y. Tu, A. Aharony, W. M. Zhang, and O. Entin- Wohlman, Real-time dynamics of spin-dependent transport through a double-quantum-dot Aharonov–Bohm interferometer with spin–orbit interaction, Phys. Rev. B 90(16), 165422 (2014)
https://doi.org/10.1103/PhysRevB.90.165422
|
57 |
P. Y. Yang, C. Y. Lin, and W. M. Zhang, Transient current–current correlations and noise spectra, Phys. Rev. B 89(11), 115411 (2014)
https://doi.org/10.1103/PhysRevB.89.115411
|
58 |
P. Y. Yang, C. Y. Lin, and W. M. Zhang, Master equation approach to transient quantum transport in nanostructures incorporating initial correlations, Phys. Rev. B 92(16), 165403 (2015)
https://doi.org/10.1103/PhysRevB.92.165403
|
59 |
M. W.-Y. Tu, A. Aharony, O. Entin-Wohlman, A. Schiller, and W. M. Zhang, Transient probing of the symmetry and the asymmetry of electron interference, Phys. Rev. B 93(12), 125437 (2016)
https://doi.org/10.1103/PhysRevB.93.125437
|
60 |
J. H. Liu, M. W.-Y. Tu, and W. M. Zhang, Quantum coherence of the molecular states and their corresponding currents in nanoscale Aharonov–Bohm interferometers, Phys. Rev. B 94(4), 045403 (2016)
https://doi.org/10.1103/PhysRevB.94.045403
|
61 |
A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59(1), 1 (1987)
https://doi.org/10.1103/RevModPhys.59.1
|
62 |
R. Landauer, Condensed-matter physics: The noise is the signal, Nature 392(6677), 658 (1998)
https://doi.org/10.1038/33551
|
63 |
C. Beenakker and C. Schonenberger, Quantum shot noise, Phys. Today 56(5), 37 (2003)
https://doi.org/10.1063/1.1583532
|
64 |
T. Gramespacher and M. Büttiker, Quantum shot noise at local tunneling contacts on mesoscopic multiprobe conductors, Phys. Rev. Lett. 81(13), 2763 (1998)
https://doi.org/10.1103/PhysRevLett.81.2763
|
65 |
L. Saminadayar, D. C. Glattli, Y. Jin, and B. Etienne, Observation of the e/3 Fractionally Charged Laughlin Quasiparticle, Phys. Rev. Lett. 79(13), 2526 (1997)
https://doi.org/10.1103/PhysRevLett.79.2526
|
66 |
F. Lefloch, C. Hoffmann, M. Sanquer, and D. Quirion, Doubled full shot noise in quantum coherent superconductor–semiconductor junctions, Phys. Rev. Lett. 90(6), 067002 (2003)
https://doi.org/10.1103/PhysRevLett.90.067002
|
67 |
R. J. Schoelkopf, P. J. Burke, A. A. Kozhevnikov, D. E. Prober, and M. J. Rooks, Frequency dependence of shot noise in a diffusive mesoscopic conductor, Phys. Rev. Lett. 78(17), 3370 (1997)
https://doi.org/10.1103/PhysRevLett.78.3370
|
68 |
R. Deblock, E. Onac, L. Gurevich, and L. P. Kouwenhoven, Detection of quantum noise from an electrically driven two-level system, Science 301(5630), 203 (2003)
https://doi.org/10.1126/science.1084175
|
69 |
E. Onac, F. Balestro, L. H. W. van Beveren, U. Hartmann, Y. V. Nazarov, and L. P. Kouwenhoven, Using a quantum dot as a high-frequency shot noise detector, Phys. Rev. Lett. 96(17), 176601 (2006)
https://doi.org/10.1103/PhysRevLett.96.176601
|
70 |
E. Zakka-Bajjani, J. Ségala, F. Portier, P. Roche, D. C. Glattli, A. Cavanna, and Y. Jin, Experimental test of the high-frequency quantum shot noise theory in a quantum point contact, Phys. Rev. Lett. 99(23), 236803 (2007)
https://doi.org/10.1103/PhysRevLett.99.236803
|
71 |
N. Lambert, R. Aguado, and T. Brandes, Nonequilibrium entanglement and noise in coupled qubits, Phys. Rev. B 75(4), 045340 (2007)
https://doi.org/10.1103/PhysRevB.75.045340
|
72 |
R. Aguado and T. Brandes, Shot noise spectrum of open dissipative quantum two-level systems, Phys. Rev. Lett. 92(20), 206601 (2004)
https://doi.org/10.1103/PhysRevLett.92.206601
|
73 |
B. H. Wu and C. Timm, Noise spectra of ac-driven quantum dots: Floquet master-equation approach, Phys. Rev. B 81(7), 075309 (2010)
https://doi.org/10.1103/PhysRevB.81.075309
|
74 |
H. A. Engel and D. Loss, Asymmetric quantum shot noise in quantum dots, Phys. Rev. Lett. 93(13), 136602 (2004)
https://doi.org/10.1103/PhysRevLett.93.136602
|
75 |
O. Entin-Wohlman, Y. Imry, S. A. Gurvitz, and A. Aharony, Steps and dips in the ac conductance and noise of mesoscopic structures, Phys. Rev. B 75(19), 193308 (2007)
https://doi.org/10.1103/PhysRevB.75.193308
|
76 |
C. P. Orth, D. F. Urban, and A. Komnik, Finite frequency noise properties of the nonequilibrium Anderson impurity model, Phys. Rev. B 86(12), 125324 (2012)
https://doi.org/10.1103/PhysRevB.86.125324
|
77 |
U. Gavish, Y. Levinson, and Y. Imry, Detection of quantum noise, Phys. Rev. B 62(16), 10637 (2000)
https://doi.org/10.1103/PhysRevB.62.R10637
|
78 |
R. Aguado and L. P. Kouwenhoven, Double quantum dots as detectors of high-frequency quantum noise in mesoscopic conductors, Phys. Rev. Lett. 84(9), 1986 (2000)
https://doi.org/10.1103/PhysRevLett.84.1986
|
79 |
P. Billangeon, F. Pierre, R. Deblock, and H. Bouchiat, Out of equilibrium noise in electronic devices: from the classical to the quantum regime, J. Stat. Mech. 1, P01041 (2009)
https://doi.org/10.1088/1742-5468/2009/01/p01041
|
80 |
N. Ubbelohde, C. Fricke, C. Flindt, F. Hohls, and R. J. Haug, Measurement of finite-frequency current statistics in a single-electron transistor, Nat. Commun. 3, 612 (2012)
https://doi.org/10.1038/ncomms1620
|
81 |
A. Zazunov, M. Creux, E. Paladino, A. Crépieux, and T. Martin, Detection of finite-frequency current moments with a dissipative resonant circuit, Phys. Rev. Lett. 99(6), 066601 (2007)
https://doi.org/10.1103/PhysRevLett.99.066601
|
82 |
Z. Feng, J. Maciejko, J. Wang, and H. Guo, Current fluctuations in the transient regime: An exact formulation for mesoscopic systems, Phys. Rev. B 77(7), 075302 (2008)
https://doi.org/10.1103/PhysRevB.77.075302
|
83 |
K. Joho, S. Maier, and A. Komnik, Transient noise spectra in resonant tunneling setups: Exactly solvable models, Phys. Rev. B 86(15), 155304 (2012)
https://doi.org/10.1103/PhysRevB.86.155304
|
84 |
R. Zwanzig, Nonequilibrium Statistical Mechanics, New York: Oxford University Press, 2001
|
85 |
G. F. Mazenlo, Nonequilibrium Statistics Mechanics, Weinheim: Wiley-VCH, 2006
https://doi.org/10.1002/9783527618958
|
86 |
J. Maciejko, J. Wang, and H. Guo, Time-dependent quantum transport far from equilibrium: An exact nonlinear response theory, Phys. Rev. B 74(8), 085324 (2006)
https://doi.org/10.1103/PhysRevB.74.085324
|
87 |
W. Lu, Z. Ji, L. Pfeiffer, K. W. West, and A. J. Rimberg, Real-time detection of electron tunnelling in a quantum dot, Nature 423(6938), 422 (2003)
https://doi.org/10.1038/nature01642
|
88 |
J. Bylander, T. Duty, and P. Delsing, Current measurement by real-time counting of single electrons, Nature 434(7031), 361 (2005)
https://doi.org/10.1038/nature03375
|
89 |
S. Gustavsson, I. Shorubalko, R. Leturcq, S. Schön, and K. Ensslin, Measuring current by counting electrons in a nanowire quantum dot, Appl. Phys. Lett. 92(15), 152101 (2008)
https://doi.org/10.1063/1.2892679
|
90 |
G. Stefanucci, Bound states in ab initio approaches to quantum transport: A time-dependent formulation, Phys. Rev. B 75(19), 195115 (2007)
https://doi.org/10.1103/PhysRevB.75.195115
|
91 |
R. Kubo, S. J. Muyake, and N. Hashitsume, Solid State Physics, edited by H. Ehrenreich and D. Turnbull, New York: Academic, New York, Vol. 17, p. 269 (1965)
|
92 |
C. Cercignani, Theory and Application of the Boltzmann Equation, Edinburgh: Scottish Academic Press, 1975
|
93 |
H. Smith and H. H. Jensen, Transport Phenomena, Oxford: Clarendon, 1989
|
94 |
P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, New York: Oxford University Press, 2002
|
95 |
S. Nakajima, On quantum theory of transport phenomena, Prog. Theor. Phys. 20(6), 948 (1958)
https://doi.org/10.1143/PTP.20.948
|
96 |
R. Zwanzig, Ensemble method in the theory of irreversibility, J. Chem. Phys. 33(5), 1338 (1960)
https://doi.org/10.1063/1.1731409
|
97 |
P. Y. Yang and W. M. Zhang, Exact homogeneous Master equation for open quantum systems incorporating initial correlations, arXiv: 1605.08521 (2016)
|
98 |
H. L. Lai and W. M. Zhang, Non-Markovian decoherence dynamics of Majorana fermions (in preparation)
|
99 |
W. M. Zhang, P. Y. Lo, H. N. Xiong, M. W. Y. Tu, and F. Nori, General non-Markovian dynamics of open quantum systems, Phys. Rev. Lett. 109(17), 170402 (2012)
https://doi.org/10.1103/PhysRevLett.109.170402
|
100 |
X. L. Yin, M. W.-Y. Tu, P. Y. Lo, and W. M. Zhang, Localized state effect in quantum transport (in preparation)
|
101 |
S. P. Giblin, M. Kataoka, J. D. Fletcher, P. See, T. J. B. M. Janssen, J. P. Griffiths, G. A. C. Jones, I. Farrer, and D. A. Ritchie, Towards a quantum representation of the ampere using single electron pumps, Nat. Commun. 3, 930 (2012)
https://doi.org/10.1038/ncomms1935
|
102 |
P. Y. Lo, H. N. Xiong, and W. M. Zhang, Breakdown of Bose–Einstein distribution in photonic crystals, Sci. Rep. 5, 9423 (2015)
https://doi.org/10.1038/srep09423
|
103 |
J. Taylor, H. Guo, and J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B 63(24), 245407 (2001)
https://doi.org/10.1103/PhysRevB.63.245407
|
104 |
P. Pomorski, L. Pastewka, C. Roland, H. Guo, and J. Wang, Capacitance, induced charges, and bound states of biased carbon nanotube systems, Phys. Rev. B 69(11), 115418 (2004)
https://doi.org/10.1103/PhysRevB.69.115418
|
105 |
V. Vettchinkina, A. Kartsev, D. Karlsson, and C. Verdozzi, Interacting fermions in one-dimensional disordered lattices: Exploring localization and transport properties with lattice density-functional theories, Phys. Rev. B 87(11), 115117 (2013)
https://doi.org/10.1103/PhysRevB.87.115117
|
106 |
A. Dhar and D. Sen, Nonequilibrium Greens function formalism and the problem of bound states, Phys. Rev. B 73(8), 085119 (2006)
https://doi.org/10.1103/PhysRevB.73.085119
|
107 |
D. Loss and D. P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57(1), 120 (1998)
https://doi.org/10.1103/PhysRevA.57.120
|
108 |
T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, Coherent manipulation of electronic states in a double quantum dot, Phys. Rev. Lett. 91(22), 226804 (2003)
https://doi.org/10.1103/PhysRevLett.91.226804
|
109 |
J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren, S. De Franceschi, L. M. K. Vandersypen, S. Tarucha, and L. P. Kouwenhoven, Fewelectron quantum dot circuit with integrated charge read out, Phys. Rev. B 67(16), 161308(R) (2003)
|
110 |
J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Manipulation of a single charge in a double quantum dot, Phys. Rev. Lett. 93(18), 186802 (2004)
https://doi.org/10.1103/PhysRevLett.93.186802
|
111 |
J. Gorman, D. G. Hasko, and D. A. Williams, Chargequbit operation of an isolated double quantum dot, Phys. Rev. Lett. 95(9), 090502 (2005)
https://doi.org/10.1103/PhysRevLett.95.090502
|
112 |
A. C. Johnson, J. R. Petta, J. M. Taylor, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Triplet-singlet spin relaxation via nuclei in a double quantum dot, Nature 435(7044), 925 (2005)
https://doi.org/10.1038/nature03815
|
113 |
J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Coherent manipulation of coupled electron spins in semiconductor quantum dots, Science 309(5744), 2180 (2005)
https://doi.org/10.1126/science.1116955
|
114 |
K. D. Petersson, C. G. Smith, D. Anderson, P. Atkinson, G. A. C. Jones, and D. A. Ritchie, Charge and spin state readout of a double quantum dot coupled to a resonator, Nano Lett. 10(8), 2789 (2010)
https://doi.org/10.1021/nl100663w
|
115 |
B. M. Maune, M. G. Borselli, B. Huang, T. D. Ladd, P. W. Deelman, K. S. Holabird, A. A. Kiselev, I. Alvarado- Rodriguez, R. S. Ross, A. E. Schmitz, M. Sokolich, C. A. Watson, M. F. Gyure, and A. T. Hunter, Coherent singlet-triplet oscillations in a silicon-based double quantum dot, Nature 481(7381), 344 (2012)
https://doi.org/10.1038/nature10707
|
116 |
L. Fricke, M. Wulf, B. Kaestner, V. Kashcheyevs, J. Timoshenko, P. Nazarov, F. Hohls, P. Mirovsky, B. Mackrodt, R. Dolata, T. Weimann, K. Pierz, and H. W. Schumacher, Counting statistics for electron capture in a dynamic quantum dot, Phys. Rev. Lett. 110(12), 126803 (2013)
https://doi.org/10.1103/PhysRevLett.110.126803
|
117 |
Z. Shi, C. B. Simmons, D. R. Ward, J. R. Prance, X. Wu, T. S. Koh, J. K. Gamble, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Fast coherent manipulation of three-electron states in a double quantum dot, Nat. Commun. 5, 3020 (2014)
https://doi.org/10.1038/ncomms4020
|
118 |
T. Fujisawa, T. Hayashi, and S. Sasaki, Time-dependent single-electron transport through quantum dots, Rep. Prog. Phys. 69(3), 759 (2006)
https://doi.org/10.1088/0034-4885/69/3/R05
|
119 |
R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys. 79(4), 1217 (2007)
https://doi.org/10.1103/RevModPhys.79.1217
|
120 |
D. Kim, Z. Shi, C. B. Simmons, D. R. Ward, J. R. Prance, T. S. Koh, J. K. Gamble, D. E. Savage, M. G. Lagally, M. Friesen, S. N. Coppersmith, and M. A. Eriksson, Quantum control and process tomography of a semiconductor quantum dot hybrid qubit, Nature 511(7507), 70 (2014)
https://doi.org/10.1038/nature13407
|
121 |
Y. Wu, X. Li, L. M. Duan, D. G. Steel, and D. Gammon, Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot, Phys. Rev. Lett. 96(8), 087402 (2006)
https://doi.org/10.1103/PhysRevLett.96.087402
|
122 |
S. Foletti, H. Bluhm, D. Mahalu, V. Umansky, and A. Yacoby, Universal quantum control of two-electron spin quantum bits using dynamic nuclear polarization, Nat. Phys. 5(12), 903 (2009)
https://doi.org/10.1038/nphys1424
|
123 |
J. Medford, J. Beil, J. M. Taylor, S. D. Bartlett, A. C. Doherty, E. I. Rashba, D. P. DiVincenzo, H. Lu, A. C. Gossard, and C. M. Marcus, Self-consistent measurement and state tomography of an exchange-only spin qubit, Nat. Nanotechnol. 8(9), 654 (2013)
https://doi.org/10.1038/nnano.2013.168
|
124 |
Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in the quantum theory, Phys. Rev. 115(3), 485 (1959)
https://doi.org/10.1103/PhysRev.115.485
|
125 |
A. W. Holleitner, C. R. Decker, H. Qin, K. Eberl, and R. H. Blick, Coherent coupling of two quantum dots embedded in an Aharonov–Bohm interferometer, Phys. Rev. Lett. 87(25), 256802 (2001)
https://doi.org/10.1103/PhysRevLett.87.256802
|
126 |
T. Hatano, M. Stopa, W. Izumida, T. Yamaguchi, T. Ota, and S. Tarucha, Gate-voltage dependence of inter dot coupling and Aharanov–Bohm oscillation in laterally coupled vertical double dot, Physica E 22(1–3), 534 (2004)
https://doi.org/10.1016/j.physe.2003.12.063
|
127 |
M. Sigrist, A. Fuhrer, T. Ihn, K. Ensslin, S. E. Ulloa, W. Wegscheider, and M. Bichler, Magnetic-field-dependent transmission phase of a double-dot system in a quantum ring, Phys. Rev. Lett. 93(6), 066802 (2004)
https://doi.org/10.1103/PhysRevLett.93.066802
|
128 |
D. Loss and E. V. Sukhorukov, Probing entanglement and nonlocality of electrons in a double-dot via transport and noise, Phys. Rev. Lett. 84(5), 1035 (2000)
https://doi.org/10.1103/PhysRevLett.84.1035
|
129 |
K. Kang and S. Y. Cho, Tunable molecular resonances of a double quantum dot Aharonov–Bohm interferometer,J. Phys.: Condens. Matter 16(1), 117 (2004)
https://doi.org/10.1088/0953-8984/16/1/011
|
130 |
T. Kubo, Y. Tokura, T. Hatano, and S. Tarucha, Electron transport through Aharonov–Bohm interferometer with laterally coupled double quantum dots, Phys. Rev. B 74(20), 205310 (2006)
https://doi.org/10.1103/PhysRevB.74.205310
|
131 |
T. Hatano, T. Kubo, Y. Tokura, S. Amaha, S. Teraoka, and S. Tarucha, Aharonov–Bohm oscillations changed by indirect interdot tunneling via electrodes in parallelcoupled vertical double quantum dots, Phys. Rev. Lett. 106(7), 076801 (2011)
https://doi.org/10.1103/PhysRevLett.106.076801
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|