Lauren B Drescher

Continued below! 👇

We believe we observed this in our paper and we shall finally get to it in the next thread!

In the 2010s, it was realized that the force originating from the change in carrier density is different depending on the energy of the carriers. So if the carriers relax and change their energies after their excitation, does that change the phase of the phonon oscillation? /16

So in the rug-pull, we would expect a cosine motion, but if we have an impulsive part, we also get a sine motion. The two added together will imprint a phase on the motion.
Where could this phase come from? /15

Now the pendulum will be at the extreme end, start to swing to the center and to the other side and then back. We can describe this this with a cosine-function. Giving the kick is called an impulsive excitation, moving the pendulum (which can be described as adding a constant force) displacive /14

A little diagram showing the two ways of starting an oscillation

Let's look at our pendulum again and two ways we can start swinging the pendulum. Give it a kick (short force) from the rest position and it will start swinging left and right. We can describe this with a sine-function. Alternatively, we can move where the pendulum is anchored (pull the rug!). /13

In the semimetal antimony (Sb), which was one of the materials in the original study, the authors observed a unexplained phase difference of the oscillation with respect to their model, which was attributed to an impulsive component in a paper following. Why is the phase so important? /12

They noted that either the temperature of the electrons or the number of excited electrons can be taken as the starting point of the derivation, for which they didn't expect any differences. But if the formation of the temperature of the electrons takes some time, will this cause a difference? /11

So, using very fast (ultrafast) time-resolved spectroscopy we can observe the thermalizations of electrons. Does it matter for the rug-pull?
Going back to the paper I mentioned yesterday, there is an interesting detail in the derivation of the model the authors provided /10

In metals, this can be very quick, just a few femtoseconds, as we (and others) recently investigated using a similar technique. /9

Luckily, the electrons would very much like to be Fermi-Dirac distributed, since it is the most favorable distribution for them. So they are going to quickly exchange energy between each other and the lattice to reach this distribution. How fast depends on the material, temperature and wavelength /8

Microscopically a temperature describes the distribution of states. For the electrons (Fermions) this is described by the Fermi-Dirac distribution, for the phonons (Bosons) by the Boltzmann distribution. So it's hard to assign a temperature if the particles aren't distributed like that /7

Instead it is transferred via quanta of energy (photons). These photons have a frequency and promote electrons from lower to higher energy levels. The distribution of energy after interaction of light therefor represents the available transitions as well as the frequencies of the light used /6

That is if we are working on picosecond (ps) timescales, if we increase the temporal resolution and look on the femtosecond (fs) scale, we see differences appearing. Why? We can go back to Einstein's photoelectric effect to recall that light doesn't continuously depose energy into the solid /5

If our laser is around the visible wavelengths, it is likely exciting electrons and those move fast than the heat of the lattice. So lets consider this: The laser is heating the electrons which are in turn heating the lattice. This is called the two-temperature model. And it works pretty good /4

If the light is absorbed and not re-emitted, ultimately we are going to heat up the solid. This is a good description in the long term, but on shorter timescales isn't suffice and wouldn't explain what we see, it doesn't fit with how heat is spreading following laser absorption. We can do better /3

While we could start from first-principles and solve the problem numerically, we probably won't learn much. But we can model something from what we know and start with thermodynamics. What happens if we point a laser beam at a solid? /2

Let's continue! We want to learn how long it takes light to pull the rug out from under a crystal lattice, or to put it closer to jargon, understand how electronic excitation leads to displacive coherent phonon motion. First, how do we model the interaction of light with solids? /1

However, since their temporal resolution (~60fs) was similar to the period of the phonon vibration oscillations (>125fs) one question lingered: How fast is the rug pulled? Tomorrow, I will continue why this question arose and how we use attosecond transient spectroscopy to find out.

This was observed in the early 90s, and nicely described in this paper. Using femtosecond lasers, a periodic change of reflectivity in several materials is observed which they connected to the "displacive excitation of coherent phonons" - the rug pull. /15 journals.aps.org/prb/abstract...

As we discussed, they can only move in vibrational modes, so a phonon is created. Since the excitation of the electrons is very fast, this is like moving the rug out from under the ions (and moving it to a new place). They all start moving at the same time, creating a motion that we call coherent/14

Now what happens if we increase the energy of our system, eg by hitting it with visible light. This leads to the electrons being promoted to higher levels. Since they now sit at a higher level, there is no reason for the ions not be at their favorite position and they start to move. But... /13

This is called a Peierls distortion (in a solid, in a molecule it's the Jahn-Teller effect). Typically the symmetry of the lattice is lifted in one dimension, so that the energy in the electronic part of the solid is lower, at the expense of the ionic part of the solid (the lattice). /12

High symmetry = less states are different. To distribute our electrons, they need to occupy higher bands which the electrons DO NOT LIKE (costs a lot of energy). But they can compromise, convince the ions to move to a less symmetric orientation so that more electrons can populate lower bands. /11

An issue arises due to the symmetry: The electrons have to adapt to the symmetry of the lattice (well they can form extra structures on top of the lattice but let's not get into that now), but as Fermions there can also only ever be two electrons in the same state (with opposite spins). /10

It's a lot of factors and can get very complicated, especially if there are different ions involved and electron orbitals (d-levels!) and electrostatic or relativistic effects. Let's say everything is spherical and the atoms would like to relax to a cubic lattice, simply minimizing Coulomb forces /9

the probability for this happen is very low, so it's not very effective. But there is a second, much more effective way which I like to call the "rug pull", and it brings us back to the favorable positioning of the ions in the lattice. What determines the position to which the ions relax to? /8

Yes! One way is using a Raman process: Here we give the lattice a "little kick" by using what is called a two-photon process: One photon of light excites the system (electronically) and the second photon brings the system back to the electronic ground state, but adds a vibration. But... /7

Besides thermal activation of these phonons, we can use light to activate them. Since oscillating motion of charge (the ions) forms an antenna they couple to electromagnetic radiation. The frequency of these phonons lies in the GHz to THz range (microwaves!). Can we also use visible light? /6

A swinging pendulum is a harmonic oscillator and that means it stores energy! The energy in the oscillations of the atoms is most of what we call the temperature. Also, since everything is quantum, the vibrational modes and energies are quantized and we call them phonons. Don't worry about it. /5