REVIEW
Comment on "Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations"
Mesoscale and Nanoscale Physics · Submitted 3 Mar 2006 · 6 references
Pith's verdict: A tight, exact U=0 counterexample to JVL's factor-of-two phase; the finite-U step leans on a cited relation, but the core point holds.
T0 · AI review
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Referee report
The paper
The paper claims
A Comment shows that, within the single-level Anderson model, the Aharonov–Bohm transmission phase equals the conductance phase, so a claimed factor-of-two relation has no valid derivation.
The reading
What carries the argument
The central object is the two-lead scattering matrix $S_k$ of the single-level Anderson model, which relates incoming to outgoing lead amplitudes and contains a single overall phase $e^{i\delta_k}$ together with entries proportional to $\sin\delta_k$. The load-bearing identity is $T_{d\sigma}\propto G_{d\sigma}(0)$, the proportionality between the complex transmission amplitude through the dot and the local dot Green's function at the Fermi energy; together with $G\propto\sum_\sigma \mathrm{Im}\,G_{d\sigma}(0)$, it forces the interferometer phase $\delta_{ABI}=\arg T_{d\sigma}$ and the conductance phase $\delta_\sigma$ to coincide. The exact $U=0$ solution exposes the error: the ansatz used by the commented Letter multiplies the scattering matrix by a spurious factor $-C_\sigma=-e^{i\delta_{-\sigma}}$, which has no counterpart in the Schrödinger solution.
Extended reading notes
Core claim
The central claim is that, within the single-level Anderson model, the transmission phase $\delta_{ABI}$ measured through an Aharonov–Bohm interferometer is the same as the scattering phase $\delta_\sigma$ that determines the conductance, not half of it. The paper proves this at $U=0$ by writing the exact two-lead scattering matrix and showing that the commented Letter's modified matrix, which carries an extra factor $-C_\sigma = -e^{i\delta_{-\sigma}}$, contradicts the exact solution. For $U\neq 0$ it invokes the exact local Green's function relation $G \propto \sum_\sigma \mathrm{Im}\,G_{d\sigma}(0) \propto \sum_\sigma \sin^2\delta_\sigma$ and cites the general identity $T_{d\sigma}\propto G_{d\sigma}(0)$ to conclude that $\delta_{ABI} = \arg T_{d\sigma} = \delta_\sigma$. The conclusion is that the Letter's Eq. (4), and with it the prediction $\delta_G = \delta_{ABI}/2$, does not follow from the single-level Anderson model.
Load-bearing premise
For nonzero interaction, the argument assumes that the dot's complex transmission amplitude remains proportional to its local Green's function at the Fermi energy; if that proportionality fails in the Kondo regime, only the non-interacting counterexample would stand.
Editorial extensions
If this is right
- The factor-of-two relation $\delta_G=\delta_{ABI}/2$ cannot be derived from the single-level Anderson model; any calculation within that model must recover $\delta_{ABI}=\delta_G$.
- In the non-interacting limit the exact scattering matrix contradicts the commented Letter's modified matrix, so the claim already fails at $U=0$.
- For $U\neq0$, the identity $T_{d\sigma}\propto G_{d\sigma}(0)$ ties the measured Aharonov–Bohm phase directly to the conductance phase, removing the need for an extra Levinson-type phase.
- The comment shifts the burden of proof: proponents of the factor-of-two relation must supply an explicit derivation of their modified scattering matrix from a well-defined model.
Reading between the lines
- A direct test of the finite-$U$ step would be to compute $T_{d\sigma}$ and $G_{d\sigma}(0)$ in the Kondo regime with a method independent of the cited proportionality; if the phases differ, the factor-of-two relation could reappear even though the $U=0$ counterexample stands.
- The exact $U=0$ scattering matrix provides a clean check for any approximate scheme: an approximation that introduces an extra overall phase factor in the S-matrix can be ruled out immediately.
- The argument is specific to the single-level Anderson model; nothing in the comment rules out an effective factor-of-two emerging from a multi-level dot or from the second branch of the interferometer.
- If the conclusion survives, the experiment becomes a direct measurement of the Kondo scattering phase, which sharpens the interpretation of the observed phase lapse and its connection to the conductance.
Original abstract
Recently, A. Jerez, P. Vitushinsky and M. Lavagna [Phys. Rev. Lett. 95, 127203 (2005)] claimed that the transmission phase through a quantum fot, as measured via the Aharonov-Bohm interferometer, differs from the phase which determines the corresponding conductance. Here we show that this claim is wrong for the single level Anderson model, which is usually used to describe the quantum dot. So far, there exists no derivation of this claim from any explicit theoretical model.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Recently, A. Jerez, P. Vitushinsky and M. Lavagna [Phys. Rev. Lett. 95, 127203 (2005)] claimed that the transmission phase through a quantum fot, as measured via the Aharonov-Bohm interferometer, differs from the phase which determines the corresponding conductance. Here we show that this claim is wrong for the single level Anderson model, which is usually used to describe the quantum dot. So far, there exists no derivation of this claim from any explicit theoretical model.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently, A. Jerez, P. Vitushinsky and M. | background 1.00 | 0.03 | 0.01 | unclear 1.00 |
| s1 | Lavagna [Phys. Rev. Lett. 95, 127203 (2005)] claimed that the transmission phase through a quantum fot, as measured via the Aharonov-Bohm interferometer, differs from the phase which determines the corresponding conductance. | background 1.00 | 0.03 | 0.05 | asserted 0.99 |
| s2 | Here we show that this claim is wrong for the single level Anderson model, which is usually used to describe the quantum dot. | result 0.92 | 0.90 | 0.94 | asserted 1.00 |
| s3 | So far, there exists no derivation of this claim from any explicit theoretical model. | gap 0.98 | 0.19 | 0.06 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
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- P abstract
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References
How the literature uses it
Papers whose main result relates to this one's
States a conflicting result 3 papers
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We show that there is a factor of 2 difference between the phase of the S-matrix responsible for the shift in the AB oscillations, and the one controlling the conductance.
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We argue that this anomalous phase evolution is a universal property that can be found in the high-temperature Kondo phase in the presence of the time-reversal symmetry.
Anomalous Transmission Phase of a Kondo-Correlated Quantum Dot · 1.00
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As a result, we show how there exists a factor of 2 difference between the phase of the S-matrix responsible for the shift in the Aharonov-Bohm (AB) oscillations, and the one controlling the conductance.
Discussion
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