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Supersolid In Two Dimensions: Exotic Matter Is a Solid That Flows Like A Liquid

Monday, February 13, 2017 18:17
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A supersolid is an exotic quantum state of matter, which would have both the rigidity of a solid, but also paradoxically be able to flow without resistance. Such a material was first discussed and theoretically predicted almost 50 years ago. The phenomenon would occur in a system composed of particles which are bosons, cooled close to the absolute zero of temperature.

Experimentalists have long searched for a supersolid material, but so far in vain. Solid helium-4 was the prime candidate, and the first reported observation of supersolidity appeared in 2004 (group of Moses Chan), catalysing a flurry of interest. In this case separating the supersolid response from the unusual elastic properties of solid helium, has prevented unambiguous observation.

In a paper published online in Nature Physics this week (6 February 2017) physicists at Royal Holloway and their collaborators report evidence for this new state of matter, realized in two dimensional helium-4; just an atomic layer film of helium-4 on a flat surface. Moreover, in order to account for their observations, they propose that the film goes into a new Schrodinger cat-like quantum state, in which solid and superfluid are quantum entangled. This helps resolve the implied apparent paradox of contradictory properties suggested by “solid” and “superfluid”.

Credit: Royal Holloway 

This work is fundamental science; a new quantum state is found to emerge at low temperatures in a very simple model system. It has strong connections with the work of Michael Kosterlitz and David Thouless, who shared the 2016 Nobel Prize for Physics.

Coincidentally this publication coincides with that of an article “The return of supersolids” in the Institute of Physics professional journal, Physics World (February 2017 issue). This describes two reports, currently on the archive, from groups led by Tilman Esslinger and Wolfgang Ketterle (Nobel Prize 2001) in which a “striped” supersolid phase is engineered in a Bose-Einstein Condensate of cold atoms (rubidium or sodium atoms trapped and cooled in a metastable gas state).

The race to demonstrate supersolidity is hotting up!

For a more technical description of the work at Royal Holloway read on:

A new state of quantum matter, with “intertwined density wave and superfluid order”

Experimentalists in the London Low Temperature Laboratory at Royal Holloway, working in collaboration with Cornell University and theorists in the Hubbard Theory Consortium and Imperial College, report the identification of a new state of quantum matter, with “intertwined density wave and superfluid order”, in Nature Physics.

Solids are rigid. In a crystal the atoms are arranged in a regular lattice structure; we can think of this as a density wave (atom – space – atom – space….). Liquids can flow. A superfluid is a liquid that can flow without resistance through the tiniest of cracks. The first discovered and most famous superfluid is liquid helium-4. Helium-4 is the most abundant isotope of helium, containing two protons and two neutrons in its nucleus. It becomes superfluid upon cooling to a temperature of 2K (-271°C): just two degrees above absolute zero (-273°C). 

Superfluidity is a quantum phenomenon. In quantum physics we describe an object using a wavefunction. We usually think of a wavefunction as describing a microscopic object, such as an atom. Amazingly, in superfluid liquid helium-4 the entire liquid behaves as a single quantum object, described by a single wavefunction. This is quantum mechanics operating on the macroscopic scale. It is triggered by the fact that helium-4 atoms are bosons, a class of particles which are allowed by quantum rules to occupy the same quantum state. And so at low temperatures all the bosons can occupy the lowest energy quantum state. This is known as Bose-Einstein Condensation or BEC.

Almost 50 years ago Anthony Leggett (Nobel Prize 2003) and others wondered whether a solid made of bosons could also be a superfluid. Leggett also discussed how it might be detected. This somewhat mind-blowing idea, that a normally rigid solid could flow without resistance at low enough temperatures, is admittedly hard to grasp. Nevertheless, the natural candidate system to look for such a “supersolid” is the solid phase of helium-4. The already remarkable thing about helium is that it is the only material which remains liquid under its own vapour pressure down to absolute zero; this again is a quantum effect and helium is referred to as a quantum liquid. However helium-4 can be solidified at a pressure of more than 25 atmospheres. 

Solid helium-4 is really interesting because the atoms, even in a perfect crystal, move about their equilibrium positions and can even swap places; we say that the ground state is subject to large quantum fluctuations. There is motion even at absolute zero; this is a quantum solid. Might it even be a superfluid? Unambiguous detection of this supersolidity has proved a huge challenge. It appears, theoretically, that superfluidity might coexist with solidity, and be associated with the frictionless flow of crystalline defects such as vacancies or line defects, called dislocations. Encouragingly, some theorists believe that supersolidity is a robust phenomenon; for example Philip Anderson (Nobel Prize 1977) has written “every pure Bose solid’s ground state is a supersolid”. Other theorists are highly sceptical. The experimental search continues.

The group at Royal Holloway took a different approach, by studying helium-4 in two dimensions. They took an atomically flat surface, that of graphite, and added helium-4 atoms, which are attracted to the surface. At low temperature they cannot escape this surface, and so are confined to a two dimensional world. The number of helium-4 atoms can be adjusted at will, and so it is possible to build a thin film of helium, which grows in atomic layers. In two dimensions the transition of a liquid helium-4 film from normal to superfluid is quite different from what happens in bulk liquid. These ideas were developed by David Thouless and Michael Kosterlitz, who shared the Nobel Prize in Physics in 2016 with Duncan Haldane, in part for this work. Kosterlitz-Thouless superfluidity appears with a sharp jump on cooling {see note}, and indeed this is observed for thin liquid helium-4 films.

At Royal Holloway a helium-4 film was studied that was believed should host a two-dimensional solid, with low density and therefore high quantum motion. The graphite surface is oscillated back a forth (see Figure). At relatively high temperatures, 1K, the film moves with the graphite surface. The signature of superfluidity is the decoupling of the film from the surface, as the temperature is decreased. The system is studied down to ultralow temperatures, all the way from 1.5 K down to 0.002 K. The interesting behaviour occurs in a film consisting of two atomic layers, where the first layer is a high density solid and passive, while all the interesting “action” happens in the second layer, whose density can be adjusted in small steps until a third layer forms. The superfluidity in the second layer strongly depends on the density of that layer, only appears gradually as temperature is decreased, and has its strongest temperature dependence at the lowest temperature. Both these observations are unusual.

In an experimental-theoretical collaboration these observations are accounted for by proposing a new quantum state that possesses both spatial (solid) order and superfluidity. This is a property of the entire layer. It is quite different from the possible coexistence of solid and superfluid proposed for bulk solid helium-4. The new suggestion is that the wave function is a quantum entanglement of these two apparently contradictory types of order. This profoundly alters the symmetry of the quantum state. That means that the Kosterlitz-Thouless topological defects [see note] that control the superfluid transition in two dimensions are not stable. In technical language, we have a non-Abelian superfluid. Moreover, using Feynman’s and Landau’s fundamental ideas on superfluidity we can explain the unusually strong low temperature dependence of the superfluid signature.

More work is required to measure directly the structure of this unusual two-dimensional quantum matter, and to explicitly show that there is a locally well-defined quantum phase. Elsewhere these ideas of entangled different types of order may also play a role, possibly in understanding high temperature superconductors, where magnetic, density wave and superconducting order are all relevant.

Quantum behaviour often appears contrary to our everyday intuition but quantum mechanics works. Schrodinger’s cat can exist in a superposition (quantum entangled state) of “alive” and “dead”. Here the entangled state of “solid” and “superfluid” describes a macroscopic thin film of helium, determines its flow properties, and may help resolve the paradox of “supersolidity”.

Note on KT transition:

The jump arises from the unbinding of topological defects called vortices. A vortex is a quantised eddy in which the superfluid circulates about a singular normal (non-superfluid) core. This flow is quantised because the phase of the helium’s macroscopic wave function must change by 2π on going once around the core and returning to the same point. This macroscopic wavefunction with a well-defined phase is the essence of the ordered state and its symmetry. You can have a vortex or an “antivortex”, depending on whether the flow is clockwise or anticlockwise. These vortices cost energy but can be excited at finite temperatures. At low enough temperatures the vortex and antivortex bind into a pair. When they unbind the motion of single vortices disrupts the phase coherence and destroys the superfluidity; this unbinding occurs at a well-defined temperature, and the superfluid density abruptly drops to zero.

Torsional oscillator used in this work. Helium film is formed on surface of graphite, contained in the sample cell. The frequency of torsional oscillations, driven and detected capacitatively, is shifted down, relative to the cell empty of helium, by the film locked to the graphite surface. The torsional oscillator acts as a sensitive microbalance. The sample can be cooled to 0.001K by an ultralow temperature platform. With the onset of superfluidity, which appears on decreasing the temperature, the superfluid part of the helium film becomes decoupled from the motion of graphite, resulting in an increase in frequency.

Contacts and sources:

Royal Holloway, University of London


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