Tag: parity symmetry

A new path to explaining the absence of antimatter

Our universe was believed to have been created with equal quantities of matter and antimatter, only for antimatter to completely disappear over time. We know that matter and antimatter can annihilate each other but we don’t know how matter came to gain an upper hand and survive to this day, creating, stars, planets, and – of course – us.

In the theories that physicists have to explain the universe, they believe that the matter-antimatter asymmetry is the result of two natural symmetries being violated. These are the charge and parity symmetries. The charge (C) symmetry is that the universe would work the same way if we replaced all the positive charges with negative charges and vice versa. The parity (P) symmetry refers to the handedness of a particle. For example, based on which way an electron is spinning, it’s said to be right- or left-handed. All the fundamental forces that act between particles preserve their handedness except the weak nuclear force.

According to most particle physicists, matter won the war against antimatter through some process that violated both C and P symmetries. Proof of CP symmetry violation is one of modern physics’s most important unsolved problems.

In 1964, physicists discovered that the weak nuclear force is capable of violating C and P symmetries together when it acts on a particle called a K meson. In the 2000s, a different group of physicists found more evidence of CP symmetry violation in particles called B mesons. These discoveries proved that CP symmetry violation is actually possible, but they didn’t bring us much closer to understanding why matter dominated antimatter. This is because of particles called quarks.

Quarks are the smallest known constituent of the universe’s matter particles. They combine to form different types of bigger particles. For example, all mesons have two quarks each. All the matter that we’re familiar with are instead made of atoms, which are in turn made of protons, neutrons, and electrons. Protons and neutrons have three quarks each – they’re baryons. Electrons are not made of quarks; instead, they belong to a group called leptons.

To explain the matter-antimatter asymmetry in the universe, physicists need to find evidence of CP symmetry violation in baryons, and this hasn’t happened so far.

On December 7, a group of researchers from China published a paper in the journal Physical Review D in which they proposed one place where physicists could look to find the answer: the decay of a particle called a lambda-b baryon to a D-meson and a neutron.

Quarks come in six types, or flavours. They are up, down, charm, strange, top, and bottom. A lambda-b baryon is the name for a bundle containing one up quark, one down quark, and one strange quark. A D-meson is any meson that contains a charm quark. In the process the researchers have proposed, the D-meson exists in a superposition of two states: a charm quark + an up anti-quark (D0 meson) and a charm anti-quark and an up quark (D0 anti-meson).

The researchers have proposed that the probability of a lambda-b baryon decaying to a D0 meson versus a D0 anti-meson could be significantly different as a result of CP symmetry violation.

The proposal is notable because the researchers have tailored their prediction to an existing experiment that, once it’s upgraded in future, will collect data that can be used to look for just such a discrepancy. This experiment is called the LHCb – ‘LHC’ for Large Hadron Collider and ‘b’ for beauty.

The LHCb is a detector on the LHC, the famous particle-smasher in Europe that slams energetic beams of protons together to pry them open. The detectors then study the particles in the detritus and their properties. LHCb in particular tracks the signatures of different types of quarks. Physicists at CERN are planning to upgrade LHCb to a second avatar that’s expected to begin operating in the mid-2030s. Among other features, it will have a 7.5-times higher peak luminosity – a measure of the number of particles the detector can detect.

If the lambda-b baryon’s decay discrepancy exists in the new LHCb’s observed data, the decay proposed in the new study will be one way to explain it, and pave the way for proof of CP symmetry violation in baryons.

Amorphous topological insulators

A topological insulator is a material that conducts electricity only on its surface. Everything below, through the bulk of the material, is an insulator. An overly simplified way to understand this is in terms of the energies and momenta of the electrons in the material.

The electrons that an atom can spare to share with other atoms – and so form chemical bonds – are called valence electrons. In a metal, these electrons can have various momenta, but unless they have a sufficient amount of energy, they’re going to stay near their host atoms – i.e. within the valence band. If they do have energies over a certain threshold, then they can graduate from the valence band to the conduction band, flowing throw the metal and conducting electricity.

In a topological insulator, the energy gap between the valence band and the conduction band is occupied by certain ‘states’ that represent the material’s surface. The electrons in these states aren’t part of the valence band but they’re not part of the conduction band either, and can’t flow throw the entire bulk.

The electrons within these states, i.e. on the surface, display a unique property. Their spins (on their own axis) are coupled strongly with their motion around their host atoms. As a result, theirs spins become aligned perpendicularly to their momentum, the direction in which they can carry electric charge. Such coupling staves off an energy-dissipation process called Umklapp scattering, allowing them to conduct electricity. Detailed observations have shown that the spin-momentum coupling necessary to achieve this is present only in a few-nanometre-thick layer on the surface.

If you’re talking about this with a physicist, she will likely tell you at this point about time-reversal symmetry. It is a symmetry of nature that is said to (usually) ‘protect’ a topological insulator’s unique surface states.

There are many fundamental symmetries in nature. In particle physics, if a force acts similarly on left- and right-handed particles, it is said to preserve parity (P) symmetry. If the dynamics of the force are similar when it is acting against positively and negatively charged particles, then charge conjugation (C) symmetry is said to be preserved. Now, if you videotaped the force acting on a particle and then played the recording backwards, the force must be seen to be acting the way it would if the video was played the other way. At least if it did it would be preserving time-reversal (T) symmetry.

Physicists have known some phenomena that break C and P symmetry simultaneously. T symmetry is broken continuously by the second law of thermodynamics: if you videographed the entropy of a universe and then played it backwards, entropy will be seen to be reducing. However, CPT symmetries – all together – cannot be broken (we think).

Anyway, the surface states of a topological insulator are protected by T symmetry. This is because the electrons’ wave-functions, the mathematical equations that describe some of the particles’ properties, do not ‘flip’ going backwards in time. As a result, a topological insulator cannot lose its surface states unless it undergoes some sort of transformation that breaks time-reversal symmetry. (One example of such a transformation is a phase transition.)

This laboured foreword is necessary – at least IMO – to understand what it is that scientists look for when they’re looking for topological insulators among all the materials that we have been, and will be able, to synthesise. It seems they’re looking for materials that have surface states, with spin-momentum coupling, that are protected by T symmetry.

Physicists from the Indian Institute of Science, Bengaluru, have found that topological insulators needn’t always be crystals – as has been thought. Instead, using a computer simulation, Adhip Agarwala and Vijay Shenoy, of the institute’s physics department, have shown that a kind of glass also behaves as a topological insulator.

The band theory described earlier is usually described with crystals in mind, wherein the material’s atoms are arranged in a well-defined pattern. This allows physicists to determine, with some amount of certainty, as to how the atoms’ electrons interact and give rise to the material’s topological states. In an amorphous material like glass, on the other hand, the constituent atoms are arranged randomly. How then can something as well-organised as a surface with spin-momentum coupling be possible on it?

As Michael Schirber wrote in Physics magazine,

In their study, [Agarwala and Shenoy] assume a box with a large number of lattice sites arranged randomly. Each site can host electrons in one of several energy levels, and electrons can hop between neighboring sites. The authors tuned parameters, such as the lattice density and the spacing of energy levels, and found that the modeled materials could exhibit symmetry-protected surface currents in certain cases. The results suggest that topological insulators could be made by creating glasses with strong spin-orbit coupling or by randomly placing atoms of other elements inside a normal insulator.

The duo’s paper was published in the journal Physical Review Letters on June 8. The arXiv preprint is available to read here. The latter concludes,

The possibility of topological phases in a completely random system opens up several avenues both from experimental and theoretical perspectives. Our results suggest some new routes to the laboratory realization of topological phases. First, two dimensional systems can be made by choosing an insulating surface on which suitable [atoms or molecules] with appropriate orbitals are deposited at random (note that this process will require far less control than conventional layered materials). The electronic states of these motifs will then [interact in a certain way] to produce the required topological phase. Second is the possibility of creating three dimensional systems starting from a suitable large band gap trivial insulator. The idea then is to place “impurity atoms”, again with suitable orbitals and “friendly” chemistry with the host… The [interaction] of the impurity orbitals would again produce a topological insulating state in the impurity bands under favourable conditions.

Agarwala/Shenoy also suggest that “In realistic systems the temperature scales over which one will see the topological physics … may be low”, although this is not unusual. However, they don’t suggest which amorphous materials could be suitable topological insulators.

Thanks to penflip.com and its nonexistent autosave function, I had to write the first half of this article twice. Not the sort of thing I can forgive easily, less so since I’m loving everything else about it.