Phonons
A Crystal’s Ripples, in Whole Steps
A Crystal Rings
Strike a tuning fork and it rings at one clear pitch. Inside the steel, atoms sit in neat rows, each held to its neighbors by bonds that pull back like springs. Push one atom and the push runs on through the bonds as a wave, the sound of a solid, which crosses steel at about 6 kilometers a second. A fork’s note is a slower kind, its prongs bending to and fro. Every shiver of a crystal, however messy, is a sum of such waves, each with its own length and its own pitch.
A crystal’s waves have one limit that a string’s do not. No wave can be shorter than two atoms, each atom swinging against the next, because between the atoms there is nothing to carry a finer ripple. So a crystal holds only so many waves: three for each of its atoms, one for each way an atom can move. Long waves are ordinary sound, and their pitch rises as they shorten. Near the shortest the pitch stops rising, at a few trillion to about ten trillion swings a second in most solids and about 35 trillion in diamond, whose light atoms and stiff bonds make some of the highest notes known. There the wave also stops running: two atoms long, each atom swinging against the next, it stands in place, and the waves close to it only crawl.
A crystal whose repeating pattern holds more than one atom, such as table salt or diamond, has a second kind of wave. Salt’s rows alternate sodium and chlorine, so neighbors can swing together, as in sound, or against each other, sodium one way and chlorine the other. Swinging against each other is the higher note, about five trillion swings a second. Sodium carries a positive charge and chlorine a negative one, and light of that frequency, deep in the infrared, pushes them apart in just this way. Salt throws such light back almost like a mirror. Bounce the glow of a lamp off several salt crystals in turn, and what survives is far-infrared light near that note.
Engineers build with such waves. Nearly every phone filters its radio signals through chips that turn them into sound running across or through a crystal, sized so that only the wanted frequencies ring and pass on. A quartz watch counts the swings of a tiny quartz fork, 32,768 a second.
Energy Comes in Steps
The glow of hot, dark bodies can be explained only if each of light’s own waves inside them takes energy in whole steps, with the size of a step set by its pitch: twice the pitch, twice the step. The same rule holds for the vibrations of atoms in a solid. Each wave of a crystal can take or give energy only in whole steps: one, or two, but never two and a half.
One step of a crystal’s wave is called a phonon, from the Greek for sound, as photon comes from the Greek for light. A wave holding three steps holds three phonons, and a warm crystal holds a crowd of them, spread over all its waves. A single step travels through the crystal as a ripple, and it is always given or taken whole, never in part. Even with every step taken away, half a step stays in every wave. Quantum mechanics does not allow an atom a sharp place and a sharp speed at once, so each keeps a spread that no cooling removes. That lowest state does not change in time: measure where an atom sits, again and again, and the answers scatter.
The steps can be watched one at a time. Send neutrons from a nuclear reactor through a crystal and measure how fast each comes out. Most cross unchanged. Some leave behind a single phonon and come out slower by one step’s worth of energy. In a warm crystal, others pick one up and come out faster by the same step. A neutron’s change of speed and the angle it turns through give the length of the wave it left or took. Sweeping the angle maps every note of a crystal.
Light can count phonons too. A wave of visible light is thousands of atoms long, so it reaches only a crystal’s longest waves. Long sound waves barely change it. But a long wave of neighbors swinging against each other is a high note. In crystals such as diamond, light scattered by the crystal comes out with its color shifted by that note. In salt, for a reason of symmetry, the same swing shows only in infrared light. A rover on Mars reads the minerals of Martian rocks this way. An X-ray short enough to reach the shortest carries so much energy that a phonon changes it by about a part in a million, and only a few instruments in the world can notice that. Neutrons from a reactor are about as long as the gap between atoms and carry about as much energy as a phonon, which is why they do the job.
The Energy Diamond Would Not Take
A simple rule says that warming a solid element by one degree takes the same energy for each of its atoms, whatever the element. Classical physics explains it. Each atom can jiggle in three directions, and in a warm solid each direction gets an equal share of energy for the motion and as much again for the stretch of the bonds. Diamond breaks the rule. At room temperature it takes only about a quarter of the energy the rule asks for, and less still when cold.
The steps explain it. The atoms’ warm jostling hands out energy at random, in amounts of a typical size set by the temperature. A wave whose single step costs much more than that is almost never given one, so it stays frozen and takes no share of the energy. Diamond’s notes are high and their steps large, so at room temperature most of its waves are still frozen. Lead’s notes are low, and all of them are awake well below room temperature. This was one of the first puzzles about ordinary matter that the quantum explained. A closer look adds one thing: long, low waves wake first, so near absolute zero the energy it takes to warm a solid’s vibrations by a degree falls with the cube of the temperature, as measured. In a metal, the free electrons’ share falls more slowly and wins in the deepest cold.
Heat on the Move
Phonons also carry heat. Warm one end of a crystal and more of its waves run from the warm end toward the cold one than the other way, and the difference is the flow of heat. Longer waves carry most of it: they run fastest and travel farthest before they are scattered, while the shortest barely move. In metals, free electrons carry most of the heat. In an electrical insulator phonons carry nearly all of it, and diamond, with its fast waves, conducts heat about five times as well as copper. Slivers of diamond draw the heat from some of the most powerful lasers and radio chips.
What stops phonons is anything that breaks the crystal’s perfect order: stray atoms, atoms of a different mass, the crystal’s edges, and other phonons. Picture one wave made shorter and shorter. At two atoms long it is as short as the atoms can show. Made shorter still, the atoms, which are all there is, move as a longer wave running the other way. Two phonons that meet can merge into just such a wave, carrying both their energies and both their pushes along the rows, and then it runs back.
So what a phonon carries is not quite momentum. It is kept when phonons meet, but only up to whole steps set by the spacing of the atoms, and physicists call it crystal momentum. The merger that throws a wave back is called Umklapp, German for flipping over. It turns heat back toward where it came from, and it is why even a flawless crystal resists the flow of heat. It needs short, high waves, which freeze out in the cold, so a pure crystal cooled far below room temperature conducts heat many times better, down to a peak some tens of degrees above absolute zero. Colder still, the phonons already run from face to face of the crystal before anything else stops them, so their runs can grow no longer, and as fewer are left it conducts less again.
The Glue in Many Superconductors
The atoms’ vibrations can also tie electrons together. Cooled far enough, some metals lose all resistance to electric current. Mercury gives a clue: made from heavier isotopes, it loses its resistance at a lower temperature. The mass of the atoms matters, so their vibrations are involved. An electron passing through the metal pulls the positive atoms near it slightly inward. The heavy atoms are slow to spring back, and a second electron feels the pull they leave. Two electrons that repel each other end up bound in a pair, held by the swing of the atoms between them. The pairs are huge, hundreds to thousands of atoms across, and overlap one another.
Other things equal, the quicker the vibrations, the warmer such a pair can survive, and hydrogen, the lightest atom, vibrates quickest of all. Compounds rich in hydrogen, squeezed to well over a million times the pressure of air, superconduct up to about minus 20 °C, their pairs held by the atoms’ vibrations. A recent claim of room temperature in one of them still awaits confirmation. Certain copper oxides superconduct at ordinary pressure up to about minus 140 °C. One of them, squeezed and then released while cold, has been reported to show signs of it up to about minus 120 °C, a result not yet repeated by another group. What binds their pairs is still argued over, most likely magnetism rather than the atoms’ vibrations.
A Particle That Needs Matter
A phonon is missing from every list of nature’s building blocks. It exists only inside matter, a crystal, a glass or a liquid: take the atoms away and there is nothing left to ripple. Physicists call such a thing an emergent particle, or a quasiparticle. Inside a crystal it is a particle in the same sense as a photon: a ripple that comes only in whole lumps. It bounces off flaws and edges, and it can be made, counted and destroyed one at a time: experiments now hold a single phonon in a speck of crystal and pass it to a quantum bit and back.
The difference shows in its momentum. Empty space is the same everywhere, so shifting an experiment by any distance changes nothing, and that is why the momentum of a particle in empty space is kept exactly. A crystal looks the same only when shifted by whole steps of its rows, so its waves keep only crystal momentum, the smaller kind that Umklapp flips over. The pattern repeats across physics. Magnetic order has its own ripples, called magnons. Fundamental particles are ripples too, in fields that fill space. Some physicists have proposed that those fields themselves emerge from a deeper medium, as a crystal’s waves emerge from its atoms. None of these proposals has been confirmed.
