Friday, May 15, 2009

A new state of quantum matter: the superinsulator

At the weekly COPE science meeting we discussed a Nature paper, Superinsulator and Quantum synchronization, chosen by Andrew Stephenson. It is a great paper. It had been sitting in my big pile of papers to read since it was published 9 months ago. Being "forced" to read it before the meeting and discussing it made me realise just how significant it is. It is not very often that new states of quantum matter are discovered. Some examples (including somewhat contentious ones) are the supersolid, fractional quantum Hall fluids, pseudogap state in cuprates, and non-Fermi liquid states in heavy fermions and cuprates.
My understanding of the superinsulator is the following. It occurs in a two-dimensional array of small superconducting metallic grains which are coupled together by Josephson tunneling. Each grain has a significant charging energy and the phase and Cooper pair number operators are conjugate quantum operators. In the superconducting state there is phase coherence between grains and there are large quantum fluctuations on the Cooper pair number in each grain. Increasing the temperature one can destroy this phase coherence and produce a (conventional) insulating state. I think in the superinsulator state may be viewed as a coherent superposition of number states on each on the grains.

I have a few questions:

The experiments were done on very thin films which can be described by a theory in two spatial dimensions.
Can this state exist in three dimensions?

What is the broken symmetry associated with the superinsulator state?

The experiments were done on very dirty films near a disorder induced quantum phase transition between insulating and superconducting states.
Can the state also be observed in clean systems?

Can one draw a phase diagram with both superconducting and superinsulating phases on it?

In clean two-dimensional superconducting films there is a jump of universal magnitude in the superfluid density at the Kosterlitz-Thouless transition. How does one define the superinsulator density and does it have a universal jump at the transition?


  1. Art Winfree's law of coupled oscillators, which he developed in the late 1960s and applied to biological oscillators (fireflies, heart cells) provides a fundamental explanation. Art never applied his law to physics, but his theory (as further developed by Steve Strogatz, author of Sync) explains phases of matter and their transitions.

    Superconductors are a form of perfect synchrony. Superinsulators are also a form of perfect synchrony--the exact opposite of superconductors. Titanium nitride exhibits both phases. We should look for a fundamental explanation that can explain both phenomena.

    Winfree's law says that oscillating elements organize themselves in certain exact ways. In a two oscillator system, the two exact ways are fully synchronous (e.g. kangaroo legs) or fully antisynchronous (e.g. human legs).

    This is what happens with titanium nitride. The superinsulator version is the antithesis of the superinsulator version. The thin film, which has two spatial dimensions only, limits the organizational choices, which is akin to a two oscillator system. With a thicker film, more organizational choices are available, so the superinsulator state is far less likely to occur. Probably impossible.

    The broken symmetry is probably as follows. In a superconductor, we know that the Cooper pairs have two paired components. The electron orbits are exactly antisynchronous, and the spins are exactly opposed (one up, one down). Notice that they follow Winfree's laws.

    Reasoning from this starting point, I imagine that in a superinsulator, one of the pairings has this case, from antisynchronous to synchronous. Specifically, I suspect that the spins are both up, up, or down down.

    For an explanation of Winfree's law of coupled oscillators, read Steve Strogatz's article in the December 1993 Scientific American, which you can find on Strogatz's Cornell website. And for an explanation of how Winfree's theory is relevant to physics, especially phases of matter and phase transitions, see my dozen or so posts at the Aspen physics website. My posts follow an August 2007 story about Doug Scalapino and superconductivity.

  2. Now let me address some of the main text. Prof. McKenzie mentions supersolids, fqH fluids, the pseudogap state in cuprates, as new and interesting states of quantum matter, all of which I have considered as possible manifestations of Winfree coupled oscillator organization. I believe the pseudogap state in HTS cuprates is explainable by the Winfree/Macksb law of coupled oscillators. Specifically, I believe that phenomenon might be viewed as a defective Cooper pair, in which electrons are paired by antisynchronous orbit, and by antisynchronous spin (like a regular Cooper pair) but with two different dance partners--one partner for orbit, and another partner for spin. Then, this quasi-Cooper pair combines with another quasi-Cooper pair to form a fully coherent 2 by 2 pairing. That is why there is D wave symmetry in HTS, and that is why pseudogaps are a related phenomenon exhibited in the same material.

    For the fractional quantum Hall effect, I note that the fractions themselves correspond with the allowable Winfree patterns. For example, the 1/3, 1/3, 1/3rd pattern is predicted by Winfree as one of only four allowable states for a system of three oscillators.

    For supersolids, I am not certain that they exist, but I think they might. The interesting point for me is that supersolids, as described at Penn State, involve a twist that oscillates around the ring. That periodic oscillation makes me think that Winfree's theory is relevant. But I have not been able to develop that glimmer of a hypothesis any further.

    A few lines below that, Prof. McKenzie addresses superconductors and superinsulators. I agree with him that there is phase coherence between the grains (and within them, of course). To which I would add: as Winfree would predict. I agree also that there are large quantum fluctuations. To which I would add: Those fluctuations might also be called oscillations--coordinated oscillations.

    Turning to the superinsulator phase, Prof. McKenzie says at the end of his post that the superinsulator state may be viewed "as a coherent superposition of number states on each on (sic..should be "of") the grains." I think I agree, though I am not smart enough to know for sure. I like the fact that Prof. McKenzie begins with the word "coherent." I begin there...and then ask myself why would those superpositions be coherent? To that, I tell myself that superpositions are sums of probabilities or waves or oscillations. Which leads me to conclude that his description means coupled oscillations, to use my terminology--but without offering a reason why the oscillations in question would synchronize, or why they would synchronize in a way that is the exact antithesis of the superconductor state. My explanation,I believe, addresses that critical and fundamental question. Moreover, my explanation is the only explanation I know that can explain exact opposites so easily (not to mention its potential for illuminating fractional quantum Hall effects and other states of matter, new or old).

    Again, my primary claim is that Winfree's 1965 era theory of coupled oscillators is the right way to analyze phases of matter and their transitions. In my effort to apply that theory to particular states of matter, I may fumble some details.

  3. A new announcement by Riken, the research institute in Japan, is extremely interesting, providing experimental confirmation of the point I made in the two posts above.

    On April 22, 2010, Riken announced observations about superconductivity in a pnictide (iron based) material. They observed an S +- wave structure that is unique to a material with two types of electrons.

    As I look closely at the picture in the Riken release, I believe it depicts a synchronized complex seiche. I believe it is formed by wave sets A emanating from point A intersecting with wave sets B emanating from point B in the pnictide structure. In a seiche, intersecting waves produce organized oscillations of standing waves. In the Riken picture, there are up dots and down dots, perfectly spaced. This suggests a perfectly organized seiche.

    The Riken news suggests that oscillations within the pnictide couple and synchronize to produce S wave symmetry. Other research with pnictides, showing that the structural angle within a pnictide must be exactly so to produce superconductivity, is consistent.

    Assuming my interpretation of the Riken picture is correct, this is consistent with, and may even prove, my theory that Art Winfree's law of coupled oscillators is the general mechanism behind all types of superconductivity--BCS, cuprate and pnictide. The specific oscillators that couple and synchronize vary. And the specific Winfree pairing pattern that emerges varies, though not very much. BCS and pnictide pairing is 2 way pairing, exactly antisynchronous. And cuprate pairing is 2 by 2, with each twosome exactly antisychronous and the 2 by 2 interaction exactly antisynchronous. In the preferred terms of physicists, S wave for BCS and pnictide, versus D wave for cuprates.

    Art Winfree's coupled oscillator theory appears to be the Ockham's Razor explanation for superconductivity and other phases of matter. Even quantum phase transitions are based on quantum fluctuations...fluctuations being another term for oscillations.