Simplicity - complexity. About condensed matter and topology.

In recent years dark matter (DM) interactions have attracted great interest, because they may stabilize magnetic structures with a unique chirality and non-trivial topology. The inherent coupling between the various properties provided by DM interactions is potentially relevant for a variety of applications. The, perhaps, most extensively studied material in which DM interactions are important is the cubic B20 compound MnSi, the magnetic field and pressure dependence of the magnetic properties of MnSi. At ambient pressure this material displays helical order. Under hydrostatic pressure a non-Fermi liquid state emerges, where a partial magnetic order, reminiscent of liquid crystals, is observed in a small pocket. Recent experiments strongly suggest that the non-Fermi liquid state is not due to quantum criticality. Instead it may be the signature of spin textures and spin excitations with a non-trivial topology.

Zaanen has written a short popular paper about why this superconduction is interesting. Well worth reading.

About the Condensed Matter Theory Group
The theory group conducts basic research over a wide swath of theoretical physics, ranging from strongly correlated electrons to first principle electronic structure theory to the statistical mechanics of complex systems. Elastic and inelastic neutron scattering techniques are used to study cooperative phenomena in complex solids.

High-Tc materials that carry current with no resistance is one field of research. The scientists looked for changes in the magnetic response over a range of temperature, from the non-superconducting state to below the transition temperature (Tc) where the material becomes a superconductor. Unlike the dramatic changes observed in electronic behavior as the material is cooled below the transition temperature, there were only minor changes in magnetic behavior.

This finding challenges the validity of the most popular theoretical models currently used to predict magnetic properties from electronic measurements.
“If the dual existence of localized and free-flowing electrons is important, we want to look for other materials that have those characteristics, but transition to superconductivity at even higher temperatures,” Tranquada said. From the article:

“The calculations based on the material’s electronic properties — which change dramatically as the material is cooled and transitions from its electrically resistive state to become a superconductor — predicted there would be a similar large change in magnetic characteristics below the transition temperature (Tc),” said Brookhaven physicist Guangyong Xu. “But our direct measurements of the magnetic properties showed surprisingly little change. This implies that the model the theorists have been using to describe these magnetic properties is incomplete.”

It’s not that the magnetic properties are completely unrelated to the electronic properties; they are both still part of the same system, the scientists emphasize. Magnetism, after all, comes from the relative arrangements of the directions in which electrons spin, like a collection of tiny bar magnets.

“It could be that the magnetism somehow drives the electronic structure, rather than the other way around — or that something underlying both magnetism and electronic structure influences both but in different ways,” Xu said.

“You can think of it as the foreground and the background of a painting,” Tranquada suggested. “We are interested in the superconductivity, which is what stands out — the foreground. And we know electrons are involved in that by pairing up to carry current with no resistance. But are those same electrons defining the magnetic properties? Or do other, ‘background’ electrons define the magnetism?”

The magnetic measurements showed that some of the magnetic characteristics of the original “parent” compound — which is an insulator — remain when the material becomes a superconductor. This suggests that there may be two kinds of electrons: some moving around like waves to carry the current while others remain in relatively fixed positions to produce the magnetism.

The heavy fermion phenomenon is found in a wide variety of materials - mostly metals combined with rare-earth elements - in which there is a periodic array of atoms that have a magnetic moment. Many heavy-fermion materials can become superconductors at very low temperatures, a puzzler because magnetism and superconductivity usually don't coexist. Electrons moving through a particular uranium compound appear "heavy" because their motion is constantly interrupted by interaction with the uranium atoms.

For decades physicists have been fascinated and frustrated by "heavy fermions" - electrons that move through a conductor as if their mass were up to 1,000 times what it should be. URu2Si2, composed of uranium, ruthenium and silicon, was examined. At about 55 kelvins (degrees above absolute zero, -273 degrees Celsius), it begins to show heavy fermion behavior. At 17.5 kelvins it goes through a complex phase transition in which its conductivity, ability to absorb heat and other properties change. Theorists attribute this to a "hidden order" in the material's electrons, but what that might be remained a mystery. mobile electrons in the sample, rather than flitting lightly from atom to atom, were interacting strongly with the uranium atoms, in effect diving down into their lower energy levels for picoseconds. This confirms a theoretical explanation for the heavy fermion phenomenon that electrons, which have a tiny magnetic moment, interact with the magnetic moments of uranium atoms. They are not really "heavy," but move as if they were.

Spectroscopic imaging scanning tunneling microscopy reveals a "hidden order" of electrons, seen as bright areas, within uranium ruthenium silicate as it is cooled to very low temperatures. Seeing this hidden order for the first time has unraveled a 25-year-old physics mystery. A video here.


Molecule-level.
"People know about high-spin molecules, but no one has been able to bring together the chemistry and physics to make controlled contact with these high-spin molecules," Dan Ralph said. The work is published in the June 10 online edition of the journal Science. First author is Joshua Parks, a former graduate student in Ralph's lab.

The researchers made their observations by stretching individual spin-containing molecules between two electrodes and analyzing their electrical properties. They watched electrons flow through the cobalt complex, cooled to extremely low temperatures, while slowly pulling on the ends to stretch it. At a particular point, it became more difficult to pass current through the molecule. The researchers had subtly changed the magnetic properties of the molecule by making it less symmetric.

After releasing the tension, the molecule returned to its original shape and began passing current more easily - thus showing the molecule had not been harmed. Measurements as a function of temperature, magnetic field and the extent of stretching gave the team new insights into exactly what is the influence of molecular spin on the electron interactions and electron flow. See pictures here.

Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds, letter to Nature, 2009. Walker et al. says:

However, the absolute intensities of spin fluctuations measured in neutron scattering experiments vary widely, and are usually much smaller than expected from fundamental sum rules, resulting in ‘missing’ INS intensity. Magnetic excitations in the one-dimensional related compound, Sr2CuO3, for which an exact theory of the dynamical spin response has recently been developed. In this case, the missing INS intensity can be unambiguously identified and associated with the strongly covalent nature of magnetic orbitals. We find that whereas the energies of spin excitations in Sr2CuO3 are well described by the nearest-neighbour spin-1/2 Heisenberg Hamiltonian, the corresponding magnetic INS intensities are modified markedly by the strong 2p–3d hybridization of Cu and O states. Hence, the ionic picture of magnetism, where spins reside on the atomic-like 3d orbitals of Cu2+ ions, fails markedly in the cuprates.

So magnetism isn't what it should either? Normally to keep things simple, to describe the magnetism of the copper atoms, people tend to use a spin distribution based on isolated copper atoms. But in reality, the spin density must be spread out along the strong copper-oxygen covalent bonds that are part of the structure of the material and which are responsible for the remarkable magnetic properties in the first place.

Now the team has shown how to correctly compare theoretical models to experimental data, they are hoping that the hunt for the answer to high-temperature superconductivity in the cuprate materials can be reached more quickly.

It is widely believed that the magnetism of the copper atoms, which as this study shows is that of copper-oxygen covalent complexes, plays a vital role in superconductivity.

Dimensions.
Disappearing Superconductivity Reappears - in 2-D. Scientists studying a material that appeared to lose its ability to carry current with no resistance say new measurements reveal that the material is indeed a superconductor — but only in two dimensions. Equally surprising, this new form of 2-D superconductivity emerges at a higher temperature than ordinary 3-D superconductivity in other compositions of the same material. Publ.in the November 2008 issue of Physical Review B.


A hard-to-detect form of superconductivity occurs?
Tranquada and his colleagues have been studying a layered material made of lanthanum, barium, copper, and oxygen (LBCO) where the ratio of barium to copper atoms is exactly 1 to 8, and at the mysterious 1:8 ratio, the transition temperature at which superconductivity sets in drops way down toward absolute zero. At a particular temperature, a big drop was seen in resistance when the current was flowing parallel to the layers, but not when it was flowing perpendicular to them. At the same time they measured the onset of weak “diamagnetism,” an effect in which magnetic fields are pushed out of the sample. “This is one of the key properties of a superconductor — the Meissner effect.” Like the drop in resistance, the Meissner effect occurred in only two dimensions, within the planes. There is a subtle form of superconductivity confined within the two-dimensional planes, For some reason the material is unable to coherently couple that superconductivity between the planes.

This material exhibits another interesting property: an unusual pattern of charge and magnetism known as “stripes,” which many theorists have long assumed was incompatible with superconductivity. Stripes find their origin in the microscopic quantum fluctuations?

Stripe order in the copper oxide planes involves both a modulation of the charge density (blue), detectable with x-ray diffraction, and a modulation of the arrangement of magnetic dipole moments (spin directions) on copper atoms (magenta arrows)from Tranquada group.

A power point talk here. Resonance is about spin. Dynamic spin promote and static spin destroys superconductivity. More static spins means less dynamic spins.

Asymmetric superconducting domes in the phase diagram, due to an electron-hole asymmetry in the Fermi surface (FS) and nesting condition due to di fferent e ffective masses for di fferent FS sheets. This built-in EHA from the band structure, which matches well with observed asymmetric superconducting domes in the phase diagram, strongly supports FS near-nesting driven superconductivity in the iron pnictides. The band structure undergoes unconventional band folding that leads to the formation of Dirac cones?, says Neupane et.al.

Our results suggest that spin fluctuations associated with the collinear magnetic
structure appear to be universal in all Fe-based superconductors, and there is a strong correlation between superconductivity and the character of the magnetic order/fluctuations in this system. says Xu et al.. Our results suggest that static magnetic order exists in all non-superconducting samples. The proper tuning of these correlations may be the key for enhancing superconductivity.


Relaxors.
Relaxors is the name given to a special class of materials called relaxor ferroelectrics. The hallmark of relaxors is a highly frequency-dependent dielectric response that peaks broadly at a temperature that is unrelated to any structural phase transition.Video here.
Why do relaxors have such an exceptional electromechanical response. The explanation is dependent on "polar nanoregions" - tiny, nanometer-scale regions within the relaxors. The team established a link between polar nanoregions and the relaxors' ability to deform in response to an electric field, or to have a pulse of electric current induced by a deforming physical force.
The chemical short-range order in these materials, which are primarily compositionally disordered oxides, plays probably a key role in determining the bulk response. Dielectric Raman scattering, and piezoelectric force have been used to explore the behavior, and also diffuse scattering, which reflects the presence of short-range ordered, atomic displacements. Then there are revealed another diffuse scattering through its dependence on an oriented electric field. When studying relaxor systems, the existence of complex nano-scale polar structures will have to be carefully taken into consideration; indeed, these may affect the lifetimes of phonons propagating along these two sets of directions.

While the spin resonance occurs at an incommensurate wave vector compatible with nesting, neither spin-wave nor Fermi-surface-nesting models can describe the magnetic dispersion. We propose that a coupling of spin and orbital correlations is key to explaining this behavior. If correct, it follows that these nematic fluctuations are involved in the resonance and could be relevant to the pairing mechanism. Such a coupling has already been proposed for the antiferromagnetic phase.

Can spontaneous symmetry breaking play a role in a dynamical reduction of quantum physics to classical behavior? The surprising outcome that spontaneous symmetry breaking imposes a fundamental limit to the time that a system can stay quantum coherent. What does all of this have to do with the dynamical phenomenon of decoherence? Decoherence refers to the fact that the quantum information encoded in some microscopic state entangles in the course of its time evolution with environmental degrees of freedom. The crucial point is that spontaneous symmetry breaking is intrinsically linked to the presence of a spectrum of 'environmental states.' In a rigorous fashion, the quantum information carried by these states cannot be retrieved when the body is macroscopic. To what extent can this thin
spectrum be a source of decoherence, intrinsically associated with the fact that quantum measurements need classical measurement machines.


Topology forms stability.
Spin-orbit coupling causes novel forms of electronic organization that can be
captured by topology, says Zaanen, 2009 and do not change upon deformation. The so far most complex form of magnetic order observed: In the presence of a magnetic field,
the electron spins in manganese silicide (MnSi) form a lattice of topological “particles” called skyrmions. The spins form a hexagonally closest packed arrangement of topologically stable knots parallel to an applied magnetic field. However, these patterns now occur in the space of wave vectors of the electron wave functions associated with this metallic surface. Their shapes and topology are dictated by a bulk insulating state. Unlike ordinary insulators, this bulk is a macroscopic object that carries a net quantum entanglement. In the quantum world where every state is influenced by every other state in a way that has no counterpart in the realm of everyday experience. This bulk entanglement in turn dictates how the surface quantum states are linked together.
The aspect of relativity that matters for spin-orbit coupling is the unification of electricityand magnetism by the principle of relative motion. When a magnetic dipole, such as the electron spin, moves relative to an electrical field at rest, it experiences the latter as a magnetic field, that also maximizes magnetic ordering. Such helical magnetism forms spontaneously. However, when a magnetic field is applied (between 0.1 and 0.2 T), a mysterious “A phase” is found. It is the “skyrmion lattice”. The reasons for its stability are complicated and include help from thermal fluctuations, but the key feature is that the red regions in panel B of the figure (the skyrmions) crystallize as if they were atoms. Topology forms in vectors that can point in arbitrary directions in space, such as the magnetization of MnSi. The magnetic order forms topological knots, skyrmions.

Skyrmions represent topologically stable field configurations with particle-like properties. The spontaneous formation of a two-dimensional lattice of skyrmion lines, a type of magnetic vortex, in the chiral itinerant-electron magnet MnSi. The skyrmion lattice stabilizes at the border between paramagnetism and long-range helimagnetic order perpendicular to a small applied magnetic field regardless of the direction of the magnetic field relative to the atomic lattice. Mühlbauer et. al 2009 experimentally establishes magnetic materials lacking inversion symmetry as an arena for new forms of crystalline order composed of topologically stable spin states.

Physics wievpoint. A skyrmion in a two-dimensional magnet. The small arrows represent the magnetization direction. The magnetic field B is applied in the upwards direction. For skyrmion lines in a three-dimensional magnet, as suggested by recent Hall effect measurements for MnSi, this pattern describes the magnetization in planes perpendicular to B.

The Hall effect in MnSi contains contributions besides the ordinary Hall effect: the anomalous and topological Hall effects. The anomalous Hall effect is due to the nonvanishing average magnetization in an applied magnetic field. Neubauer et al. [1] observe another contribution to the Hall effect that is sharply restricted to the A phase. They show that a lattice of skyrmion lines would lead to a topological Hall effect, which can be described by an effective magnetic field proportional to the concentration of skyrmions. The observed contribution has the predicted magnitude and sign, strongly supporting the skyrmion picture for the A phase. But also the pressure invokes.

Many years ago Skyrme showed that topologically stable objects of a nonlinear field theory for pions can be interpreted as protons or neutrons. Twenty years ago it has been predicted that skyrmions exist in anisotropic spin systems with chiral
spin-orbit interactions, where they are expected to form crystalline structures.

If correct, this would imply that nematic excitations are a key feature of the normal state from which the superconductivity develops.

Zaanen:

Entanglement refers to the “spooky” quantum phenomenon that correlates the information in quantum states together in ways that make it possible to compute exponentially faster than with classical states; this is the idea behind quantum computing. Typically, only a few microscopic degrees of freedom can be entangled because under normal circumstances, the contact with the classical macroscopic world will destroy the entanglement long before the quantum system itself becomes macroscopically large. However, topological effects help protect its net entanglement
against collapse. These can be viewed as an electronic “nothingness” that is quite akin to the fundamental vacuum of the Dirac theory. This “insulating nothingness” can have topological structure. The quantum entanglements of all occupied electron states can combine in one overall topological quantity, forming the “topological insulator” that carries a global entanglement. The electrodynamics of topological insulators is also quite strange: When an electrical charge is brought to the surface, it will bind automatically to a magnetic monopole formed in the bulk, and this “dyon” should behave like particle with fractional quantum statistics. Alternatively, when a superconductor is brought into contact with a topological insulator, its magnetic vortices are predicted to turn into particles that can be used for topological quantum computing.

Zero point energy field, zero energy ontology.
Zero-point field is sometimes used as a synonym for the vacuum state, the energy of the ground state. In cosmology, the vacuum energy is one possible explanation for the cosmological constant.
Zero energy ontology is used in TGD. "In zero energy ontology positive and negative energy states correspond to infinite integers and their inverses respectively and their ratio to a hyper-octonionic unit. The wave functions in this space induced from those for finite hyper-octonionic primes define the quantum states of the sub-Universe defined by given CD (cone) and sub-CDs (hierarchy). These phases can be assigned to any point of the 8-dimensional imbedding space M8 interpreted as hyper-octonions so that number theoretic Brahman=Atman identity or algebraic holography is realized!"

In topological surface state on 3D topological insulator, the electrons obey the 2D Dirac equations. Since the surface state of topological insulator has a suppressed backward scattering for nonmagnetic impurities, this is a promising material for designing the quantum curcuit. Therefore, electric control of transport on the surface of topological insulator is an important issue. In fact, the chiral edge channels are predicted to appear at the interface of two ferromagnets with magnetization along z and −z directions, i.e., perpendicular to the surface. The energy dispersion of these states is almost linear in the momentum with the velocity sensitively depending on the strength of the gate voltage. The energy is also restricted to be positive or negative depending on the strength of the gate voltage. Consequently, the local density of states near the gated region has an asymmetric structure with respect to zero energy.
Dirac fermions in solids. In 2005 experiments on graphene, a single layer of carbon atoms, were first reported. These exhibited exotic physical properties such as a universal minimum conductivity and an anomalous integer quantum Hall effect. These phenomena are due to the fact that the hexagonal lattice of graphene exhibits two Dirac points with a linear dispersion relation, which lead to a long-wavelength description in terms of massless Dirac Fermions.

This has led to the question as to how the Kondo effect, the local screening of f-moments by the conduction electrons, gets destroyed as the system undergoes a phase change. In one approach to the problem, Kondo lattice systems are studied through a self-consistent quantum impurity problem, the Bose-Fermi Kondo Model (BFKM). This approach has been termed the Extended Dynamical Mean Field Theory (EDMFT)
Mapping of the Kondo lattice model onto an effective quantum impurity model augmented with self-consistency conditions within the extended dynamical mean field theory.

Seamus Davis and John Tranquada together with Aharon Kapitulnik (Stanford) have been honoured with the 2009 Heike Kamerlingh Onnes Prize for outstanding superconductivity experiments. Named after the winner of the 1913 Nobel Prize in physics for the discovery of superconductivity and related research, the Onnes Prize is awarded every three years for outstanding experiments that illuminate the nature of superconductivity – the disappearance of electrical resistance in certain materials at specific temperatures, mostly in the range of nearly absolute zero. The basic idea behind superconductivity is that electrons, which ordinarily repel one another because they have like charges, pair up to carry electrical current with no resistance. Future room-temperature devices would make this cheap.