Comment on ``Four-Point Resistance of Individual Single-Wall Carbon Nanotubes'' by Gao et al. PRL 95, 196208 (2005)
We remark on some delicate points that attend the physical meaning of intrinsic device resistance.
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arXiv subjects
Mukunda P. Das
Publications and source records attributed to Mukunda P. Das.
Ballistic transport is dissipative: the why and how
In the ballistic limit, the Landauer conductance steps of a mesoscopic quantum wire have been explained by coherent and dissipationless transmission of individual electrons across a one-dimensional barrier. This leaves untouched the central issue of conduction: a quantum wire, albeit ballistic, has finite resistance and so must dissipate energy. Exactly HOW does the quantum wire shed its excess electrical energy? We show that the answer is provided, uniquely, by many-body quantum kinetics. Not only does this inevitably lead to universal quantization of the conductance, in spite of dissipation; it fully resolves a baffling experimental result in quantum-point-contact noise. The underlying physics rests crucially upon the action of the conservation laws in these open metallic systems.
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Conservation, Dissipation, and Ballistics: Mesoscopic Physics beyond the Landauer-Buettiker Theory
The standard physical model of contemporary mesoscopic noise and transport consists in a phenomenologically based approach, proposed originally by Landauer and since continued and amplified by Buettiker (and others). Throughout all the years of its gestation and growth, it is surprising that the Landauer-Buettiker approach to mesoscopics has matured with scant attention to the conservation properties lying at its roots: that is, at the level of actual microscopic principles. We systematically apply the conserving sum rules for the electron gas to clarify this fundamental issue within the standard phenomenology of mesoscopic conduction. Noise, as observed in quantum point contacts, provides the vital clue.
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Where is the Shot Noise of a Quantum Point Contact?
Reznikov et al. (Phys. Rev. Lett. 75, 3340 (1995)) have presented definitive observations of nonequilibrium noise in a quantum point contact. Especially puzzling is the "anomalous" peak structure of the excess noise measured at constant current; to date it remains unexplained. We show that their experiment directly reveals the deep link between conservation principles in the electron gas and its low-dimensional, mesoscopic behavior. Key to that connection are gauge invariance and the compressibility sum rule. These are central not only to the experiment of Reznikov et al. but to the very nature of all mesoscopic transport.
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Quantum Point Contacts and Beyond: New Results on Mesoscopic Conductance and Fluctuations
We summarize the main results of a microscopically based kinetic theory, applicable to open quantum point contacts (QPCs) driven up to high fields. The governing role of gauge invariance -- and the many-body sum rules for the electron gas -- lead to stringent constraints on both transport and fluctuations. These constraints exert a dominant influence on the observable properties of QPCs and similar open mesoscopic conductors. We illustrate this in the context of certain predictions within purely phenomenological models of mesoscopic transport.
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Mesoscopic Transport: The Electron-Gas Sum Rules in a Driven Quantum Point Contact
The nature of the electron gas is characterized, above all, by its multi-particle correlations. The conserving sum rules for the electron gas have been thoroughly studied for many years, and their centrality to the physics of metallic conduction is widely understood (at least in the many-body community). We review the role of the conserving sum rules in mesoscopic transport, as normative criteria for assessing the conserving status of mesoscopic models. In themselves, the sum rules are specific enough to rule out any such theory if it fails to respect the conservation laws. Of greater interest is the capacity of the compressibility sum rule, in particular, to reveal unexpected fluctuation effects in nonuniform mesoscopic structures.
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Landauer formula without Landauer's assumptions
The Landauer formula for dissipationless conductance lies at the heart of modern electronic transport, yet it remains without a clear microscopic basis. We analyze the Landauer formula microscopically, and give a straightforward quantum kinetic derivation for open systems. Some important experimental implications follow. These lie beyond the Landauer result as popularly received.
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The Landauer Formula: a Magic Mantra Revisited
We review the conceptual structure of the Landauer theory of electron transport in the light of quantum kinetics, the orthodox framework for describing conductance at all scales. In a straightforward analysis, we assess popular claims for a rational link between Landauer theory on the one hand, and orthodox microscopics on the other. The need to explicitly include inelastic (dissipative) carrier relaxation is key to any well-posed microscopic model of open-system mesoscopic transport.
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Transport, Noise, and Conservation in the Electron Gas: How to Build a Credible Mesoscopic Theory
The Boltzmann-Landau-Silin and Landauer-Buettiker-Imry theories of electron transport are shown to be mutually incompatible. The first respects microscopic gauge invariance, electron-hole symmetry, and the conserving sum rules for the correlated electron gas. The second approach does not. That is directly evident in its unphysical compressibility.
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Mesoscopic Transport as Many-Body Physics
We show that a completely orthodox and conserving Landau-Silin approach to current fluctuations in quantum point contacts accounts for the major, and as yet unexplained, peak structures observed in the QPC experiment of Reznikov et al. [Phys. Rev. Lett. 75, 3340 (1995)], for constant values of source-drain current. Those features are absent from corresponding phenomenological predictions and are unanticipated by Landauer-Buettiker theory. The kinetic origin of the Reznikov et al. noise peaks directly manifests the action of the compressibility sum rule in the electron gas. This rule, in turn, is the outworking of microscopic gauge invariance.
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Comment on ``Anomalous crossover between thermal and shot noise in macroscopic diffusive conductors''
Shot noise is not normally evident in bulk solid-state conductors, since it is strongly attenuated by inelastic collisions. The ``anomalous'' emergence of macroscopic shot noise is discussed in G. Gomila and L. Reggiani, Phys. Rev. B 62, 8068 (2000). We remark on the consistency of this linear diffusive model at the large voltages and currents needed to see the effect.
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