To understand the measured conductance spectra quantitatively, we employ the theory of DCB as explained in Sec. 2.3. We model the impedance of the island substrate contact by an ohmic resistance R in parallel with a capacitance C (see inset of Fig. 5.2a). The external impedance then reads
Zex(ω) = 1/(iωC +R−1), (5.1) and the total impedance is given by Eq. (2.83). The tunneling resistanceRT between STM tip and island is of the order of MΩs to GΩs and thus much larger than the resistance quantumRK =h/e2 '25.8 kΩ, which justies a perturbative calculation in the tunnel coupling. The DC current between the tip and the island reads
I(V) = (−e)[Γtip→isl(V)−Γisl→tip(V)], (5.2) where tunneling rates are given by Eq. (2.75). We calculate the dierential con-ductance as explained in Sec. 2.3.1. In order to compare our calculations with the experimental data, we convolve the theoretical result with the instrumental resolu-tion funcresolu-tion
gm(ε) = 2Θ(Vpp− |ε|)q
Vpp2 −ε2/πVpp2 (5.3) that accounts for the broadening due to the modulation voltage [197, 198]. The resulting dierential conductance is obtained by
Im0 (V) = Z
dεI0(V +ε)gm(ε), (5.4)
whereI0 =dI/dV.
−40 −20 0 20 40
Figure 5.2: Dierential tunnel conductance spectra. Experimental (thick lines) and theoretical (thin lines) results for at Pb islands of various sizes on dierent substrates: a) Cu(111), b) Si(111)-7x7, c) HOPG, d) 1 ML of h-BN on Ni(111), e) 2 MLs of NaCl on Ag(111), and f) 3 MLs of NaCl on Ag(111) (not normalized).
The inset of a shows a schematic of the experiment(1), as well as the corresponding electrical circuit (2) used in b-e. The tipisland junction is characterized by the tunneling resistance RT and the capacitance CT. The islandsubstrate contact is modeled as an ohmic resistor R in parallel with a capacitor C. Extracted values are indicated together with the island areas in b-e. In f, the tip-island junction and the island-substrate contact are both modeled as tunnel barriers [95]. The residual charge on the island is Q0 = 0.064e.
0 500 1000 1500 2000
0.00 0.01 0.02 0.03 0.04 0.05 0.06
1/A(nm−2)
Figure 5.3: Extracted capacitances and resistances. Circles: Pb/Si(111). Squares:
Pb/HOPG. Triangles: Pb/BN/Ni(111) Diamonds: Pb/2 ML NaCl/Ag(111). a) Capacitances as functions of the island area A. b) Resistances as functions of the inverse island area1/A. Solid lines are guides to the eye.
Figures 5.2b-e show calculations of the dierential conductance based on Sec. 2.3.1.
The tting parameters C and R used for the calculations were independently ex-tracted from the experimental data: The charging energyEC, which determines the width of the dierential conductance suppression, is given mainly by C, since the tip-island resistance CT is small, CT . 1 aF C. The resistance R determines the shape of the curves at small voltages (see Fig. 2.5b), and is adjusted so that the theoretical curves best t the experimental data.
The theoretical curves are in good agreement with the experimental data and show a clear dependence of the electrical islandsubstrate contact on the island area.
To further corroborate our analysis, we consider the extracted capacitances and re-sistances as functions of the island size. One would expect that the capacitance (resistance) increases with the (inverse) contact area A. This systematic behavior is conrmed by Fig. 5.3, showing that we indeed are probing the electrical con-tact between the islands and the substrates. For HOPG, BN/Ni(111), and 2 MLs NaCl/Ag(111) the capacitance (resistance) depends approximately linearly on the (inverse) island area. For Si(111), in contrast, a dierent behavior is observed: the capacitance has a clear o-set value for small islands, and the resistance is essentially independent of the island area. This is due to the wetting layer, whose resistance (in parallel) mainly determines the current to the electrical drain contact and whose capacitance does not depend on the island size, giving rise to the o-set at A ' 0. Further studies of the wetting layer have been performed [199]. In addition, it has been shown that the DCB eect on an ultrasmall tunnel junction is formally equiv-alent to tunneling into a disordered 2D conductor [200], as discussed by Altshuler, Aronov and Lee [201].
Finally, we turn to the samples with several insulating MLs between island and
substrate, Figs. 5.2e-f. As additional MLs are introduced, electron transport between island and substrate takes place by tunneling through the insulating layers. The is-lands are then connected both to the tip and the substrate via tunneling barriers, and the orthodox theory of tunneling through a double junction applies (see Sec. 2.2.2 and [92]). According to our analysis, this occurs with three or more MLs of NaCl. In Fig.
5.2e (2 MLs) some deviations between experiment and the theory of DCB are already visible for small islands, and in Fig. 5.2f (3 MLs) we calculated the spectra using the orthodox theory [95]. The gap is associated with the islandsubstrate junction, while the two peaks represent spectral features due to the tipisland junction. The asymmetric gaps in Figs. 5.2e,f are due to the fractional residual charge Q0 on the Pb islands, which shifts the spectra [95]. The controlled addition of single insulating MLs opens an interesting approach to systematic investigations of asymmetric dou-ble junctions, similar to recent works on nano-particles coupled to metallic electrodes [202, 203].
Summary
We have used DCB eects to characterize the electrical contact between metallic nano-islands and their supporting substrates in low-temperature STM measurements.
Our analysis is supported by the systematic area-dependence of the capacitances and resistances. The present work facilitates quantitative investigations of electrical nano-contacts and is important for future studies of the physical and chemical prop-erties of supported nano-structures in relation to superconductivity, magnetism, and catalysis.
Chapter 6 Conclusion
In this thesis we investigated fundamental properties of quantum-coherent ductors. First, we considered the entanglement entropy of two fermionic leads con-nected by a quantum point contact (QPC) with time-dependent transmission, mod-eled by a non-interacting tight-binding chain. We found that, after opening the QPC, the entanglement entropy at zero temperature and zero bias grows logarithmically in time due to quantum uctuations, while at both nite temperature and nite bias the behavior becomes linear for long times. The logarithmic behavior may be inves-tigated by opening and closing the QPC in a periodic manner. For non-interacting particles this result is related to the FCS of transferred charge, and we investigated the convergence properties of the corresponding series expression. Overall we nd that the Gaussian approximation, which only takes the second cumulant of the FCS into account, is valid for a fully open QPC, while at transmissions below unity higher cumulants have to be considered. We then studied clean single-particle excitations (levitons) on top of the Fermi sea produced by applying designed pulses to the leads.
We demonstrated that partitioning a leviton on a half-open QPC produces an en-tanglement increase of log 2. In addition, we have shown that the interference of two levitons at the QPC represents an electronic version of the Hong-Ou-Mandel experiment. We argue that time-bin entanglement between the leads can be created by sending a stream of well separated levitons on a half open QPC.
In the second part, we investigated the electronic waiting time distribution (WTD), which characterizes electronic transport on short time scales. We presented a method to calculate the WTD for tight-binding systems, laying the groundwork for the treat-ment of interacting systems. We calculated the WTD for dierent scatterers and com-pared our results with a scattering approach as well as a master equation approach, nding excellent agreement in both cases. Within the master equation approach, we then investigated how the WTD is aected by an imperfect detection process, as well as the inuence of dephasing, which reduces coherent oscillation in the WTD of a serial double quantum dot (DQD). Finally, we derived the WTD for systems described by non-Markovian master equations, and considered a DQD coupled to a thermal bath. From the WTD we see that the coupling to the bath slows down the
transport through the DQD in most cases and induces dephasing. However, for a strongly dealigned DQD, the bath can supply the energy necessary to overcome the internal barrier between the dots.
Finally, we investigated the dierential conductance of small metallic islands grown on metallic, semimetallic, semiconducting, and partially insulating substrates.
The spectra were obtained by scanning tunneling spectroscopy measurements showed a zero-bias anomaly, whose size and shape depends on the substrate and the size of the islands. We explained the data in terms of dynamical Coulomb blockade, modeling the islandsubstrate interface as an ohmic impedance in parallel with a capacitance.
Our interpretation is supported by the linear dependence of the capacitances on the island area, while the resistances are proportional to the inverse island are.
On the one hand, our results show the power of the tight-binding approach to simulate a wide class of time-dependent physical systems with only few assumptions.
We hope that our results will stimulate further research and serve as a reference point for the treatment of interacting systems. On the other hand, we have demon-strated that the interaction with an environment can have a profound eect on the transport characteristics of nano-scale conductors, which can be important for the in-terpretation of experimental data. Moreover, this interaction may be used as a way to characterize the environment by studying transport properties of an electronic system.
Appendix A
Appendices for Chapter 3
A.1 Time evolution operator
The time evolution operator Uˆ in Eq. (2.18) can be evaluated using a Crank-Nicolson scheme [204]. By discretizing time in small steps of length δt ~/¯t, we can write
U(tˆ +δt)'e−iH(t+δt/2)δt/ˆ ~Uˆ(t), (A.1) assuming that the Hamiltonian, here evaluated at the center of the interval, is roughly constant during the time step. We rewrite this approximation as
eiHˆ(t+δt/2)δt/2~Uˆ(t+δt)'e−iHˆ(t+δt/2)δt/2~Uˆ(t) (A.2) and expand the exponentials on each side to rst order in δt. We then nd the expression
Uˆ(t+δt)' 2~−iH(tˆ +δt/2)δt 2~+iH(tˆ +δt/2)δt
Uˆ(t), (A.3)
which allows us to determine the time evolution operator iteratively in each time step, starting from the initial conditionUˆ(t0) = ˆ1.
A.2 Zero-frequency noise
Here we show that the zero-frequency noise for a periodic process is given by the increase of the second cumulant per period, following Ref. [205]. We rst introduce the current-current correlation function
c(t, t0) = 1
2h{δI(t), δˆ I(tˆ 0)}i, (A.4) where the curly brackets denote the anti-commutator and δI(t) = ˆˆ I(t)− hI(t)ˆ i. For a periodic process, the correlation function shares the periodicity of the process,
c(t+T, t0 +T) =c(t, t0), whereT is the period. The zero-frequency noise is then
To relate the zero-frequency noise to the second cumulant of the FCS, we con-sider the charge Q(t) =ˆ Rt
t0dt0I(tˆ 0) accumulated in one of the leads during the time interval[t0, t]. The second cumulant of the charge uctuation can then be written as C2(t) = h[δQ(t)]ˆ 2i=hQˆ2(t)i − hQ(t)ˆ i2, (A.6) Finally, by averaging over a period and taking the limit t0 → −∞, we nd
1
A leviton and an anti-leviton can be created on a tight-binding chain by ap-plying a time-dependent potential dierence between two sides of the chain. The corresponding Hamiltonian reads where¯tis the tunneling amplitude between neighboring sites and the potential drops between sites number L < M and L+ 1, with M being the number of sites. The time-dependent potential is chosen to be Lorentzian
V(t) = 2~τ
(t−te)2+τ2, (A.10)
with widthτ, centered at t=te.
The Hamiltonian can be brought into an equivalent form by considering a con-tinuum description of the potential
Φ(x, t) = Θ(x0−x)V(t). (A.11)
Here x0 denotes the point along the x-axis where the potential drops, and Θ(x) is the Heaviside step function. The potential can now be removed using a gauge transformation by choosing the gauge potential as
γ(x, t) = Z t
−∞
dt0Φ(x, t0), (A.12) so that the transformed scalar potential Φ0(x, t) = Φ(x, t)−∂tγ(x, t) is zero every-where. This, however, leads to a non-zero vector potential
A0(x, t) = [∂xγ(x, t)]x=−δ(x0−x) Z t
−∞
dt0V(t0)x, (A.13) where x is a unit vector along the x-axis. With this gauge transformation, the potential dierence between the two sides of the chain has been removed. In turn, the presence of a vector potential should be included in the tight-binding Hamiltonian.
This can be accomplished using a Peierls substitution of the tunneling amplitudes [206]
¯t→exp
−i
~ Z
`
A0(x, t)·dx
t,¯ (A.14)
where the integral is evaluated along the line segment ` connecting the two neigh-boring sites. Inserting the vector potential in Eq. (A.13), we see that the tunneling amplitude where the potential drops should be modied as
¯t→eiφ(t)t¯ (A.15)
with the time-dependent phase
φ(t) = 2 arctan
t−te
τ
+π, (A.16)
given in Eq. (3.37).
Appendix B
Appendices for Chapter 4
B.1 Scattering approach to waiting time distribu-tions
For the sake of completeness, we provide here the essential steps in calculating WTDs within scattering theory following Ref. [54]. In this approach, the WTD is calculated in the basis of the scattering states,
ϕk(x) =
eikx+rke−ikx, x < 0
tkeikx, x > xs>0 (B.1) where the interval[0, xs] contains the scatterer with transmission (reection) ampli-tudestk (rk). The dispersion relation is linearized in the transport window[εF, εF+ eV], whereV is the applied voltage, such that
k = ~2k2
2m 'εF +~vFk0. (B.2)
HerevF = ~kF/m is the Fermi velocity, and we have dened k0 =k−kF, which is much smaller than the Fermi momentum,k0 kF.
The momentum interval [kF, kF +eV /~vF] is split into N intervals of size κ = eV /N~vF. The many-body Slater determinant is constructed from the time-dependent single-particle wave functions
φm(x, t) = e−iεFt/~
√2πκ Z κm
κ(m−1)
dk0e−ivFk0tϕkF+k0(x). (B.3) Moreover, we dene the single-particle operator
Qˆτ =
Z x0+vFτ x0
dx|xihx|, (B.4)
where x0 > xs is located on the right side of the scatterer. The matrix elements of Qτ are
[Qτ]m,n =hφm(τ)|Qˆτ|φn(τ)i, (B.5)
which in the limitN → ∞ become
[Qτ]m,n = t∗κmtκn
2πi
1−eivFτ κ(n−m)
n−m , (B.6)
having redenedtkF+κn →tκn. Finally, the ITP is [54]
Π(τ) = det(1−Qτ) (B.7)
from which the WTD follows using Eq. (4.4). We note that only the transmission amplitudetk of the scatterer is required to calculate the WTD.
B.2 Transmission amplitudes for tight-binding sys-tems
Here we calculate the transmission and reection amplitudes in our tight-binding description for a given scatterer withMs sites. To this end, we consider an incoming plane wave that is transmitted across the scatterer with amplitude tk and reected with amplitude rk, cf. Eq. (B.1). The Schrödinger equation for the eigenstates of the tight-binding Hamiltonian, Eq. (4.19), reads
Hˆ|φki=εk|φki. (B.8) We expand the eigenstates on the lattice sites as
|φki= X
α=L,R Mα
X
m=1
ckαm|m, αi+
Ms
X
m=1
ckm|mi, (B.9) where the rst sum runs over the sites in the leads and the second sum over the sites of the scatterer.
We evaluate the Schrödinger equation on the last site of the left lead and on the rst site of the right lead [207]
hML, L|Hˆ|φki=εkckLML =−¯tckL(ML−1)−tLck1,
h1, R|Hˆ|φki=εkckR1 =−¯tckR2−tRckMs, (B.10) assuming that the scatterer is coupled to the left (right) lead with hopping amplitude tL (tR). Similar equations can be formulated for each site of the scatterer, giving us a total of2 +Ms equations. Next, we make the ansatz
ckLm=e−ik(m−1)+rkeik(m−1),
ckRm =tkeik(m−1) (B.11)
for the lead coecients, where the signs of the exponents in the rst line are reversed with respect to Eq. (B.1), because we number the sites in the left lead ascending to
the left (see Fig 2.1). Inserting the ansatz into the 2 +Ms (linear) equations above, we can solve for the amplitudestk and rk.
For the QPC considered in Sec. 4.2.1, Eqs. (B.10) and (B.11) become εk(1 +rk) = −¯t(e−ik+rkeik)−tQPCtk,
εktk=−¯ttkeik−t∗QPC(1 +rk), (B.12) since the leads are directly coupled via the hopping amplitude tQPC. Solving this system of equations, we nd
tk = 2i¯tt∗QPCsink relation εk = −2¯tcosk still approximately holds, we obtain Eqs. (2.33) and (2.36) from Eq. (B.13). The transmission amplitudes in Eqs. (4.22) and (4.25), as well as in Fig. 4.6a are found in a similar way.
B.3 Transition rates in the master equation approach
Here we evaluate the rates entering the master equation approach, starting from our tight-binding model. As shown in Sec. 2.1.1, the Hamiltonian of the leads can be diagonalized by the transformation
|m, αi= We take a generic tunneling Hamiltonian
HˆT =− X
connecting the outermost sites of the leads to theNs sites of the scatterer. Applying the transformation in Eq. (B.15) to the tunneling Hamiltonian then yields
HˆT =− X
with the hopping amplitudes tjαµ =
r 2
Mα+ 1sin(kαj)tαµ. (B.19) If the level of the scatterer is well inside the energy window [−V /2, V /2], the particle transport is unidirectional and the transition rates between the leads and the scatterer are given by
Γαµ(ε) = 2π
Mα
X
j=1
|tjαµ|2δ(ε−εjα). (B.20) From Eq. (B.19) we then get
Γαµ(ε) =4π|tαµ|2 Mα+ 1
Mα
X
j=1
sin2(kαj)δ(ε−εjα)
≈4π|tαµ|2 Mα+ 1
Mα π
Z π 0
dkαsin2(kα)δ(ε−ε(kα)).
(B.21)
Moreover, using Eq. (B.16) and takingMα 1, we nd Γαµ(ε) = 2|tαµ|2
¯t r
1−ε 2¯t
2
. (B.22)
Around the center of the band (ε'0), this gives Γαµ(ε'0)≈ 2|tαµ|2
¯t = 4|tαµ|2 vF
. (B.23)
Bibliography
[1] M. A. Nielsen and I. L. Chuang, Quantum computation and quantum informa-tion. Cambridge Univ. Press, 2001.
[2] I. uti¢, J. Fabian, and S. Das Sarma, Spintronics: Fundamentals and appli-cations, Rev. Mod. Phys., vol. 76, p. 323, 2004.
[3] F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola, Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications, Rev. Mod. Phys., vol. 78, p. 217, 2006.
[4] S. Datta, Electronic Transport in Mesoscopic Systems. Cambridge Univ. Press, 1997.
[5] Y. Imry, Introduction to Mesoscopic Physics. Oxford University Press, 1997.
[6] E. Akkermans and G. Montambaux, Mesoscopic Physics of Electrons and Pho-tons. Cambridge Univ. Press, 2007.
[7] Yu. V. Nazarov and Ya. M. Blanter, Quantum Transport. Cambridge Univ.
Press, 2009.
[8] H. van Houten, B. J. van Wees, and C. W. J. Beenakker, Quantum and classi-cal ballistic transport in constricted two-dimensional electron gases, vol. 83 of Springer Series in Solid-State Sciences, p. 198. Springer, Berlin, 1988.
[9] A. Yacoby, M. Heiblum, V. Umansky, H. Shtrikman, and D. Mahalu, Unex-pected Periodicity in an Electronic Double Slit Interference Experiment, Phys.
Rev. Lett., vol. 73, p. 3149, 1994.
[10] W. Ehrenberg and R. E. Siday, The Refractive Index in Electron Optics and the Principles of Dynamics, Proceedings of the Physical Society B, vol. 62, p. 8, 1949.
[11] Y. Aharonov and D. Bohm, Signicance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev., vol. 115, p. 485, 1959.
[12] M. Büttiker, Y. Imry, and R. Landauer, Josephson behavior in small normal one-dimensional rings, Physics Letters A, vol. 96, p. 365, 1983.
[13] L. P. Lévy, G. Dolan, J. Dunsmuir, and H. Bouchiat, Magnetization of meso-scopic copper rings: Evidence for persistent currents, Phys. Rev. Lett., vol. 64, p. 2074, 1990.
[14] A. C. Bleszynski-Jayich, W. E. Shanks, B. Peaudecerf, E. Ginossar, F. von Oppen, L. Glazman, and J. G. E. Harris, Persistent Currents in Normal Metal Rings, Science, vol. 326, p. 272, 2009.
[15] J. H. Davies, The physics of low-dimensional semiconductors : an introduction.
Cambridge Univ. Press, 1998.
[16] A. Kumar, G. A. Csáthy, M. J. Manfra, L. N. Pfeier, and K. W. West, Nonconventional Odd-Denominator Fractional Quantum Hall States in the Second Landau Level, Phys. Rev. Lett., vol. 105, p. 246808, 2010.
[17] D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F.
Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, One-dimensional transport and the quantisation of the ballistic resistance, J. Phys.
C: Solid State Phys., vol. 21, p. L209, 1988.
[18] 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 two-dimensional electron gas, Phys. Rev. Lett., vol. 60, p. 848, 1988.
[19] H. van Houten and C.W.J. Beenakker, Quantum Point Contacts, Physics Today, vol. 49, p. 22, 1996.
[20] K. v. Klitzing, G. Dorda, and M. Pepper, New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resis-tance, Phys. Rev. Lett., vol. 45, p. 494, 1980.
[21] D. R. Yennie, Integral quantum Hall eect for nonspecialists, Rev. Mod.
Phys., vol. 59, p. 781, 1987.
[22] Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, An electronic Mach-Zehnder interferometer, Nature, vol. 422, no. 6930, p. 415, 2003.
[23] I. Neder, N. Ofek, Y. Chung, M. Heiblum, D. Mahalu, and V. Umansky, In-terference between two indistinguishable electrons from independent sources, Nature, vol. 448, p. 333, 2007.
[24] G. Fève, A. Mahé, J.-M. Berroir, T. Kontos, B. Plaçais, D. C. Glattli, A. Ca-vanna, B. Etienne, and Y. Jin, An On-Demand Coherent Single-Electron Source, Science, vol. 316, p. 1169, 2007.
[25] E. Bocquillon, V. Freulon, J.-M. Berroir, P. Degiovanni, B. Plaçais, A. Ca-vanna, Y. Jin, and G. Fève, Separation of neutral and charge modes in one-dimensional chiral edge channels, Nat. Commun., vol. 4, p. 1839, 2013.
[26] L. S. Levitov and G. B. Lesovik, Charge-distribution in Quantum Shot-noise, JETP Lett., vol. 58, p. 230, 1993.
[27] L. S. Levitov, H. Lee, and G. B. Lesovik, Electron counting statistics and coherent states of electric current, J. Math. Phys., vol. 37, p. 4845, 1996.
[28] J. Keeling, I. Klich, and L. S. Levitov, Minimal Excitation States of Electrons in One-Dimensional Wires, Phys. Rev. Lett., vol. 97, p. 116403, 2006.
[29] J. Dubois, T. Jullien, F. Portier, P. Roche, A. Cavanna, Y. Jin, W. Wegschei-der, P. Roulleau, and D. C. Glattli, Minimal-excitation states for electron quantum optics using levitons, Nature, vol. 502, p. 659, 2013.
[30] T. Jullien, P. Roulleau, B. Roche, A. Cavanna, Y. Jin, and D. C. Glattli, Quantum tomography of an electron, Nature, vol. 514, p. 603, 2014.
[31] C. L. Kane and E. J. Mele, Z2 Topological Order and the Quantum Spin Hall Eect, Phys. Rev. Lett., vol. 95, p. 146802, 2005.
[32] M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum Spin Hall Insulator State in HgTe Quan-tum Wells, Science, vol. 318, p. 766, 2007.
[33] V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P.
Kouwenhoven, Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices, Science, vol. 336, p. 1003, 2012.
[34] S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDon-ald, B. A. Bernevig, and A. Yazdani, Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor, Science, vol. 346, p. 602, 2014.
[35] Ya. M. Blanter and M. Büttiker, Shot noise in mesoscopic conductors, Phys.
Rep., vol. 336, p. 1, 2000.
[36] S. Gustavsson, R. Leturcq, B. Simovic, R. Schleser, T. Ihn, P. Studerus, K.
[36] S. Gustavsson, R. Leturcq, B. Simovic, R. Schleser, T. Ihn, P. Studerus, K.