Effect of partial phase coherence on Aharonov-Bohm oscillations in metal loops

Milliken, F. P.; Washburn, S.; Umbach, C. P.; Laibowitz, R. B.; Webb, Richard A.

doi:10.1103/physrevb.36.4465

Cited by 53 publications

(41 citation statements)

References 28 publications

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“…The same exponent p = −1/2 is observed for the rms amplitude of the AB oscillations in the magnetoconductance of our sample (for V g = +25 V) even though a slightly faster decay is observed above ∼300 mK, as discussed below. Such a value for p is typical for the AB oscillations in diffusive QRs, as reported experimentally in the case of metallic QRs [51,52] and etched graphene QRs [18]. The observed exponent p, and similarity of both temperature dependences, confirm that, when the tip scans on the sides of the QR's arms, the SGM tip-induced perturbation tunes charge-carrier interferences inside the QR [53].…”

Section: Temperature Dependencesupporting

confidence: 73%

Imaging coherent transport in a mesoscopic graphene ring

et al. 2014

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Section: Temperature Dependencesupporting

confidence: 73%

Imaging coherent transport in a mesoscopic graphene ring

et al. 2014

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“…This simple argument is supported by calculations for conductance fluctuations in a loop [46], and the same exponential factor appears in the theory for the oscillatory Cooperon terms discussed above [24,26]. Experimental tests [40] of this surmise about the decay of the oscillations have essentially confirmed it. In two Sb loops, L^ was measured by the conventional method; i.e., it was inferred from the magnetoresistance associated with the Cooperons [23].…”

Section: Decay Of the Fluctuations From Averagingsupporting

confidence: 51%

“…In these samples [see Figure 7 In the case of Aharonov-Bohm oscillations from a single loop wherein L^<L (the distance around the loop), the averaging is more severe. The dominant source of decay in the oscillations is the loss of phase coherence of the carriers whose interference generates the Aharonov-Bohm oscillations [40]. The carriers that do not retain phase coherence until reaching the terminus of the loop do not contribute to Aharonov-Bohm oscillations.…”

Section: Decay Of the Fluctuations From Averagingmentioning

confidence: 99%

Fluctuations in the extrinsic conductivity of disordered metal

Washburn

1988

IBM J. Res. & Dev.

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Random fluctuations of the electrical conductance are ubiquitous in small (typical dimension i ^ 1 urn) metallic samples at low temperatures (typically TsiK=i 0.09 meV). The fluctuations result from the quantum-mechanical interference of the carrier wavefunctions. The superpositions of the wavefunctions depend randomly on the placement of impurities, on magnetic field, and on the current driven tttrough the sample. At length scale L^ (ttie average distance over which the carriers retain phase information), the fluctuations always have amplitude AG =^ e^Jh, and any observations at scale larger than the coherence length yield a decreased amplitude of the fluctuations. Since ttie carrier wavefunctions are not classical, local objects (they extend over regions of size i.), the conductance contains nonlocal temis. For instance, the conductance is not zero far from the classical current paths through the sample and is not symmetric under the reversal of the magnetic field. In this article, the physics of the fluctaiatimis is reviewed, and some of the experiments which illuminate the physics are described.

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“…− , I [3] + = I [4] − , I [4] + = I [5] − , I [6] + = I [1] − . In addition, there are 6 additional equations associated with current conservation at the terminals.…”

Section: Devicesmentioning

confidence: 99%

“…In fact, the experiments of Milliken et al [4] is only the most recent contribution to the understanding of Luttinger liquid transport. Let us begin our discussion by recounting, in a semi-historical manner, some of the major developments in the field.…”

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confidence: 99%

NonlinearI(V) characteristics of Luttinger liquids and gated Hall bars

Renn

Arovas

1995

Phys. Rev. B

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Non-linear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds non-universal power law characteristics of the form I(V ) ∼ V 1/(2g−1) which is valid both in the superfluid phase when I is small and also in the insulator phase when I is large. Mesoscopic voltage fluctuations are also calculated. One finds Var(∆V ) ∼ I 4g−3 . Both the I(V ) characteristic and the voltage fluctuations exhibit universal power law behavior at the superfluid insulator transition whereg = 3 2. The possible application of these results to the non-linear transport properties of gated Hall bars is discussed.PACS numbers: 73.20Dx, 73.20Ht, 72.15Rn Recently there has been considerable interest in the transport properties of the Luttinger liquid [1]. There are many reasons for this including applications to quantum wires, quasi-one dimensional organic conductors In their experiments , the point contact tunneling conductance between two ν = 1/3 fractional quantum Hall edge channels is measured as a function of the point contact gate voltage. One observes transmission resonances whose half-widths scale with temperature as T 2/3 . This is in agreement with Kane and Fisher [5]. Off resonance, the conductance scales as T 4 as was also predicted [5].In fact, the experiments of Milliken et al.[4] is only the most recent contribution to the understanding of Luttinger liquid transport. Let us begin our discussion by recounting, in a semi-historical manner, some of the major developments in the field. We will begin by recalling the work by Apel and Rice [6], who used the Kubo formalism to show that the conductance of a clean quantum wire differed from the usual Landauer result that G = e 2 /h [7]. Instead these authors found that G = ge 2 /h, where g ≡ πhv(∂n/∂µ). This result may be obtained as follows: First consider the current injected into the wire from the left reservoir. This is I + giveswhere I B (I) = I[1]− is the backscattering current. Now I B = 0 for a clean wire, so eq. 1 gives G = I/e(µ 1 − µ 2 ) = ge 2 /h.Another major advance in transport theory was the investigation of the superfluid-insulator transition in uniformly disordered Luttinger liquids by Giamarchi and Schultz [8]. These authors found that an infinitesimal amount of disorder will localize a Luttinger liquid with g < 3 2 . Moreover, they find that, if g > 3 2 , disorder is irrelevant and the Luttinger liquid exhibits superfluid behavior.Further progress was made by Kane and Fisher [5] who investigated a Luttinger wire with a single or double barrier. These authors found that V 2kF , the Fourier coefficient of the potential barrier, is highly relevant if g < 1. Because of this, the conductance of a Luttinger liquid with a single impurity vanishes. The existence of conductance resonances may be crudely understood if one views Luttinger liquids as Wigner crystals with quasi-long range positional order [9]. According to this point of view, the coupling of a CDW to a barrier potential may be described by the...

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Effect of partial phase coherence on Aharonov-Bohm oscillations in metal loops

Cited by 53 publications

References 28 publications

Imaging coherent transport in a mesoscopic graphene ring

Imaging coherent transport in a mesoscopic graphene ring

Fluctuations in the extrinsic conductivity of disordered metal

NonlinearI(V) characteristics of Luttinger liquids and gated Hall bars

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