Momentum noise in a quantum point contact

Abstract

Ballistic elections flowing thiough a constuction can transfei momentum to the lattice and excite a Vibration of a free-standing conductor We show (both numencally and analytically) that the electromechanical noise power P does not vanish on the plateaus of quantized conductance -in contiast to the current noise The dependence of P on the constnction width can be oscillatoiy or stepwise, depending on the geometry The stepwise mcrease amounts to an approximate quantization of momentum noise DOI 10 1103/PhysRevB 66 2413XX PACS number(s) 85 85 +j, 73 23 Ad, 73 50 Td, 73 63 Rt Not long after the discovety of conductance quantization in a balhstic constnction 1 it was predicted that the quantization is noiseless ~ The time dependent current fluctuations should vanish at low tempeiatuies on the plateaus of quantized conductance and they should peak m the tiansition from one plateau to the next The conclusive expenmental venfication of this piediction followed many years latei, 3 delayed by the difficulty of ehmmating extraneous sources of noise The notion of noiseless quantum balhstic tiansport is now well estabhshed 4 The ongm of noiseless transpoit lies in the fact that the eigenvalues T n of the tiansmission matnx pioduct tt^ take only the values 0 01 l on a conductance plateau The cunent noise power at zeio tempeiatuie Ρ/ α Σ,,Γ,,(1 -Τ η ) then vanishes 5 In othei woids, cuirent fluctuations lequire paitially filled scatteimg channels, which are incompatible with a quantized conductanceIn this papei we pomt out that the notion of noiseless quantum balhstic tianspoit does not apply if one consideis momentum transfer mstead of Charge tiansfei Momentum noise cieated by an electucal cunent (socalled electiomechanical noise) has been studied m the tunneling legime 6 and m a diffusive conductor, 7 but not yet in connection with balhstic tiansport Our analysis is based on a recent scatteimg matnx repiesentation of the momentum noise powei P, accoiding to which P depends not only on the ttansmission eigenvalues but also on the eigenvectoi s 8 This makes it possible for the elections to generate noise even m the absence of partially filled scatteimg channelsThe geometiy is shown schematically m Fig l We considei a two-dimensional election gas channel m the x-y plane The width of the channel m the y duection is W and the length in the χ direction is L The channel contams a nanow constnction of length SL-^L and width ciH 7 ·^ W located at a distance L' fiom the left end (We choose x = 0 at the middle of the constnction, so that the channel extends fiom -L'<x<L -L' ) A voltage ydnves a cunent thiough the constnction, excitmg a vibiation of the channel We seek the low-frequency noise powei. , ~ t (D of the fluctuatmg foice 8F(t) = F(t)-F that dnves the vibiationThe noise power is piopottional to the vanance of the momentum ΔΡ(ί) transfened by the electrons to the channel in a long time t We assume that the election gas is deposited on top of a doubly clamped beam extended along the χ axis and free to vibiate m the y duection T...

Quantum theory of electromechanical noise and momentum transfer statistics

“…We conclude by estimatmg the ordei of magmtude of the cumulants of the displacement distnbution P(ß) of a vibiatmg current-canymg wire Foi an oscillatoi with a laige quality factor only the even oidei cumulants ((Q 2k )) are appreciable, given m good approximation by cf Eqs (3 9) and (3 11) The cumulants of tiansfened momentum Δ T 5 have been calculated foi a smgle-channel conductoi with a localized scatteiei in See V At zeio tempeiatuie one has The theoiy presented in this woik is moie than a fiamewoik foi the calculation of highei oidei cumulants in the momentum tiansfer statistics It also piovides foi a foimalism to tieat quantum effects m electiomechanical noise A fiist application, to quantum size effects in a constnction, has been leahzed 21 Othei apphcations, includmg icsonant tunnehng, supeiconductivity, and mteiaction effects, aie envisaged…”

“…The more complex situation of a transverse phonon mode, when the matrices M L,R are no longer diagonal, is treated in Ref. [21].…”

“…The excitation of a phonon mode by conduction electrons is descnbed by the Hamiltoman (21) wheie we have set h= J The phonon mode has anmhilation opeiatoi a, fiequency ü, mass M, and displacement ßu(r), wheie ö = (2Mil)~1 /2 (a + a t ) is the amphtude opeiatoi The electrons have posiüon r ; , momentum p,= -id/dr,, and mass m Elections and phonons aie coupled thiough the ιοη potential V(r) We assume a zeio magnetic field Election-election mteiactions and the inteiactions of elections and phonons with an extemal electiic field have also been omitted…”

CFN Lectures on Functional Nanostructures - Volume 2

“…First, in NEMS one can discuss not only charge noise, but also momentum noise-random fluctuations of momentum transferred from electrons to the crystalline lattice [96][97][98]. Actually, this situation is rather common: In any mesoscopic and macroscopic system, electrons interact with phonons.…”

Statistics of charge fluctuations in chaotic cavities

“…The interpretation of the statistics of these quantities is less intuitive, in general they cannot be characterized by transmission probabilities only. Momentum transfer for example is not quantized in contrast to charge transfer 13 .…”