Scientists observe quantum superconductor-metal transition and superconducting glass

April 17, 2014

An article published in Nature Physics on March 30, 2014, presents the results of the first experimental study of graphene-based quantum phase transition of the "superconductor-to-metal" type, i.e. transformation of the system's ground state from superconducting to metallic, upon changing the electron concentration in graphene sheet.

The system is a regular array of tin nanodisks (the radius of each disk is 200 nm) situated on a graphene substrate. Tin becomes a superconductor at temperatures lower than T0 = 3.5 degrees Kelvin. Tin nanodiscs electrically contact with each other due to electronic conductivity through graphene. At temperatures significantly below T0 the state of the nanodisk can be characterized by a single variable - "phase," defined in the period from 0 to 2π. Due to the transfer of Cooper pairs of electrons between nanodiscs, the so-called Josephson junctions are formed, which seek to establish a coherent superconducting state with uniform nanodisk phases across the entire lattice.

Graphene gradually changes the density of conduction electrons by changing the voltage on the electrostatic gate, and thus the strength of Josephson junctions between tin nanodiscs. Phase correlations among nanodiscs are destroyed by thermal fluctuations at temperatures above the critical Tc. At high density of conduction electrons in graphene, the measured value Tc (around 0.5-0.7 K) is in good agreement with the previously developed theory, published in the 2009 article "Theory of proximity-induced superconductivity in graphene," in Solid State Communications.

Upon lowering the electron density of graphene, the energies of Josephson junctions weaken due to increase in the resistance of graphene, and the temperature of transition into coherent state drops sharply to below the minimum temperature of the experiment (60 mK). In other words, the spatial phase coherence between different individual nanodisks is destroyed solely by quantum (independent of temperature) phase fluctuations. As a result, superconductor-to-metal quantum phase transition takes place.

First approach to the theory of such a phase transition have previously been developed in the paper Feigel'man, M.; Larkin A. & Skvortsov, M. "Quantum superconductor-metal transition in a proximity array," Physical Review Letters *86* 1869, (2001).

In the domain of lowest measurable temperatures the resistance of the studied array turns out to be nearly temperature-independent, and, at the same time, it is an exponentially sharp function of voltage on the electric back-gate; this observation has yet to be explained, as no complete theory is capable of describing it at present.

In addition to the above-mentioned superconductor-to-metal transition, the authors discovered the so-called "superconducting glass" state, which is created as a result of disorder and frustration in the Josephson junctions, but nevertheless corresponds to some of the minima of the total energy of the Josephson junctions array. Here, the controlling parameter is the strength of external . Competition of periodic dependency on the magnitude of magnetic flux through the elementary cell of the nanodisk lattice and random dependency on the same parameter (due to mesoscopic fluctuations) leads to a phase diagram of the "re-entrant" type. Namely, the magnitude of the maximum superconducting current that flows through the entire lattice depends non-monotonically upon an external magnetic field; first it decreases (all the way down to zero), and then reappears with the increase of the magnetic field in a certain range of its values.

Explore further: Superconductors that work by themselves: Scientists discover new possibilities in chryoelectronics

More information: "Collapse of superconductivity in a hybrid tin–grapheme Josephson junction array'," Zheng Han, Adrien Allain, Hadi Arjmandi-Tash,Konstantin Tikhonov, Mikhail Feigelman, Benjamin Sacépé,Vincent Bouchiat, published in Nature Physics on March 30, 2014, DOI: 10.1038/NPHYS2929

M.V. Feigel'man, M.A. Skvortsov, K.S. Tikhonov, "Theory of proximity-induced superconductivity in graphene," Solid State Communications, Volume 149, Issues 27–28, July 2009, Pages 1101-1105, ISSN 0038-1098,

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not rated yet Apr 18, 2014
This experiment is much like the serendipitous "experiment" by Christiaan Huygens in 1665 involving two pendulum clocks. The pendula demonstrated an "odd kind of sympathy," as he phrased it in a letter to the Royal Society of London. (The "sympathy" was antisynchronous phases.) He noticed this while he was sick in bed, staring at the wall with the clocks.

Here, the tin nanodisks are like Huygens clocks Their phases become coordinated or coupled, like the pendula phases of Huygen's clocks. The graphene sheet is the medium through which the nanodisks "sympathize" with each other. With Huygen's clocks, the communication medium was the beam from which the two clocks were suspended.

Circa 1967, Art Winfree developed a mathematical theory of coupled periodic oscillators. When they couple, in groupings of any size (not just two), various specific patterns are allowed, but no others. E.g., a group of two may be synchronous (the tin disks) or antisynchronous (the clock pendula).
not rated yet Apr 18, 2014
See also research led by Ivan Bozovic at Brookhaven (PhysOrg April 27, 2011), dealing with high temp (cuprate) superconductivity: "Technique Reveals Quantum Phase Transition..." An excerpt: "One key finding: As the density of mobile charge carriers is increased, their cuprate film transitions from insulating to superconducting...when the film sheet exactly equal to the Planck quantum constant divided by twice the electron charge squared..."

In prior PhysOrg posts, approximately 50 in number going back to 2010, I have proposed a theory of superconductivity, old and new, based on Art Winfree's mathematical theory of coupled periodic oscillators. Winfree's math is the "glue." This tin nanodisk article (low temp superconductivity) and the Bozovic work (high temp cuprate superconductivity) reach similar conclusions. Taken together, Occam's Razor says they provide strong support for my theory. So there is a "complete theory."
not rated yet Apr 19, 2014
Cooper pairs of electrons are bound anti-synchronously, coupled to each other via their two periodic oscillations (spin and orbit 180 degrees out of phase to counterpart). So too were the pendulums on Christiaan Huygens clocks--their periodic oscillations coupled anti-synchronously.

The tin disks in this article are visually similar to Huygens' clocks, but the similarity goes much deeper. Their coherent behavior arises from the same "odd sympathy" : the sympathy of regular periodic oscillations interacting with each other and synchronizing pendula, or phases.

Max Planck's quantum is a regular periodic oscillation. All quanta are periodic oscillations. So, if Winfree's math truly applies to all periodic oscillators (as he said), then it should also apply to physics, even and especially at the quantum level. This tin disk article and the 2011 Brookhaven article cited above both focus on periodic oscillations ("quantum phase fluctuations") and superconductivity, low and high.
not rated yet Apr 21, 2014
How then can Winfree's law explain high temp superconductivity? Suppose that in certain complex lattices, the lattice vibrations might synchronize according to Winfree's law, in one or more Winfree patterns. If so, the lattice vibrations would be precisely coordinated and organized, no longer chaotic and disruptive, below some transition temp. Perhaps the transition temp would be relatively high, because coordinated motion in the lattice would "absorb" heat.

If that were to happen, then electrons attached to the synchronized atoms might pair with counterparts attached to other synchronized atoms because their (now more orderly) oscillations could influence each other more easily. Good signals, no lattice noise. This might lead to two way electron pairing (like the Cooper model) or even 4 way pairing, in a 4 way Winfree pattern. An insulator would then become a superconductor.

Some cuprates and pnictides have complex and interesting lattice structures.

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