Thermal superconductivity

Question

Good day!

Can anyone help me find articles or another information on  topics "Thermal superconductivity". 

I consider that this is not about thermal effects accompanying the electrical superconductivity, but the thermally superconductivity as an independent phenomenon, realized for ultra-pure materials (materials that contain a negligible number of inclusions and defects).

I need information  specialists in the subject. Maybe someone is engaged in thermal superconductivity. For example on model of one-dimensional crystal. Maybe someone has already researched the thermomechanical processes in such systems (infinite thermal conductivity, which can be interpreted as a superconductivity). In fact, the distribution of heat in these systems occurs at a rate close to the speed of sound. This is a super-pure materials.

Thanks in advance!

Comments

As tmschaefer explained, you won't get truly infinite thermal conductivity. But one can apparently achieve it in the limit of infinite length nanotubes; see my answer below.

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I think we should be talking quantum mechanically. Perhaps about materials whose Lieb-Robinson velocity is the speed of light. Are there such materials?

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Not quantum mechanically, only classical mechanics

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Superconductivity is a quantum phenomenon :P

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I search experimental work about breakdown fourier law in 1D structure  like work  "Breakdown of Fourier’s Law in Nanotube Thermal Conductors" by A. Zettl et al. May be you know   work like Zettl's work? 

Answer 1

I am not exactly sure if I understand your question correctly. I will assume that by thermal superconductivity you mean perfect conduction of heat.

This is indeed an interesting question: Are there systems that are analogous to superfluids and superconductors, perfect conductors of particle number and charge,  that are perfect conductors of heat?

I think the answer is no. In superfluids and superconductors there is a spontaneoulsy broken symmetry, and an associated Goldstone boson $\varphi$. Gradients of $\varphi$ defines a superfluid velocity that enters in the hydrodynamic description and describes transport without dissipations. In a superfluid, $v_s=\nabla\varphi/m$ is the superfluid velocity. The equation of motion $\partial_tv_s =-\nabla\mu+\ldots$ shows that an arbitrarily small gradient of the chemical potential will drive a flow. Gradients of $v_s$ do not contribute to the stress tensor, so there is no dissipation. In a superconductor we have the London current $j_s=e^2n/(mc)(\nabla\varphi-A)$, and the equation of motion is $\partial_t(\nabla\varphi)=-\nabla V+\ldots$. The London current does not contribute to Ohmic heating.

So can we find a Goldstone boson that contributes to the energy current, and has an equation of motion of the form $\partial_t(\nabla\varphi)=-\nabla T+\ldots$? I see several difficulties with this: The symmetry would have to be time reparametrization invariance (or Lorentz boosts in the relativistic case). Also, $\nabla T$ does not appear in the effective Lagrangian (which is a $T=0$ object), it would have to arise from integrating out thermal fluctuations (but that will usually lead to dissipative terms, because of fluctuation-dissipation relations). This is not a proof, of course, but at least it shows that it is not obvious how to obtain perfect conductors of heat.

 There are systems that are extremely good conductors of heat:

1) In a typical material small gradients of T do not lead to convection, the heat current is diffusive and proportional to $-\kappa\nabla T$. This is how we measure $\kappa$. In superfluids (like liquid He) small gradients of T drive a new type of convection, involving a flow of the normal component balanced by a backflow of the superfluid. The energy current is not proportional to $-\kappa\nabla T$, so the thermal conductivity appears to be very large. Helium does, however, have a finite thermal conductivity which can be measured by attenuation of first and second sound.

2) There are systems in which the mean free path (of electrons or phonons or other carriers) is larger than the system size. The usual example is nanowires or carbon nanotubes. Transport is ballistic, not diffusive, and a naive measurement of thermal conductivity will give a very large $\kappa$. There is a large amount of literature on this, look for the Landauer formula or the Landauer-Buttiker formalism.

Comments

I have heard several times of the concept of "thermal superconductivity" (As opposed to "electrical superconductivity"). I search article about it. I search article about breakdown fourier law in 1D structure  (nanotube and etc).

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A reference would indeed be useful. Fourier's law is often violated in low-dimensional (d<2) systems (see here for a review). This has nothing to do with superconductivity, but is a consequence of non-ergodicity, fluctuations, etc.

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nice review article!

Answer 2

The following papers discuss indications that in the limit of infinite length of a nanotube, the thermal conductivity may diverge. 

Length Dependence of Carbon Nanotube Thermal Conductivity and the “Problem of Long Waves” by Mingo and Broido (2005)

High Thermal Conductivity of Single Polyethylene Chains Using Molecular Dynamics Simulations by Henry and Chen (2008)

Anomalous thermal conductivity of frustrated Heisenberg spin-chains and ladders by Alvarez and Gros (2002)

Review of Heat Conduction in Nanofluids by Fan and Wang (2011)

Comments

Thank you ( tmschaefer and  Arnold Neumaier ) very much. Especially I search experimental work about breakdown fourier law in 1D structure (nanotube and etc) like work  "Breakdown of Fourier’s Law in Nanotube Thermal Conductors" by C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl. May be you help me find similar articles.

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@sashavak: I can't do the literature search for you. Please go to scholar.google.com and enter the title of the above paper. You'll get information about the paper and a list of over 200 papers citing it. Go through these to find out what you need. 

Such searches are the standard work of all scientists who want to enter a field that is new to them; so you better learn doing it now.

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Thank you for the answer. But I do not mean scientific articles that have a reference to the scientific article Zettl. I mean experimental scientific articles that showed a violation of the  Fourier Law for 1D structures. These scientific articles do not necessarily have a reference to a scientific article Zettl. Maybe you know these scientific articles.

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@sashavak: You can find these papers if they exist by looking at promising papers that cite the paper you know and look into their references. Then repeat the whole procedure with some of the titles (you can also enter authors) that look most promising, and iterate the process. After a while you find in this way everything that has been done in the field, and in particular the things you were looking for. 

Finding the right papers to read is one of the harder parts of research work. You cannot expect that anyone else is doing this work for you. Moreover, the work in searching is not spent in vain as you get to know this way a lot of other information that is relevant for your research - especially in the long run.

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Thank you for the answer.