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A few minutes after the Germans...John Abercrombie.

Hot Cracks and Addressing Questions in the Origin of Life.

I spent part of my day yesterday reading about cracks in two ways, first in thinking about fracture toughness in silicon nitride, a cool material, which is not the subject of this post, and then about the effect of heat flowing through a crack to cause the polymerization of nucleotides into nucleic acids, which is the subject of this post.

I described my renewed interest in this topic here: Open source paper on "Defining Life."

Over the weekend, I found myself thinking about the anti-entropy that life is, and went poking around in the library.

Here's a cool paper I found on exactly that subject, the difficult case or the origin of nucleic acids, since many people postulate that life arose from an "RNA world:" Heat flux across an open pore enables the continuous replication and selection of oligonucleotides towards increasing length (Moritz Kreysing†‡, Lorenz Keil‡, Simon Lanzmich‡ and Dieter Braun, Nature Chemistry volume 7, pages 203–208 (2015))

Entropy is discussed in the introduction:

From a wide range of exploratory experiments much is known about the capabilities and limitations of chemical replication systems1–6. It has become increasingly clear that such replicators are delicate systems that require a suitable supportive microenvironment to host non-equilibrium conditions. These conditions permit the sustainment of molecular evolution and the synthesis of molecules against equilibrating forces1,7–9. To the same end, modern cells provide active compartments of reduced entropy that protect genetic information against its thermodynamically favoured decay8,10. This is facilitated by sophisticated membrane-trafficking machinery and a metabolism that feeds on chemical low-entropy sources or light energy (Fig. 1a).

It has been known since Spiegelman’s experiments in the late 1960s11 that, even if humans assist with the assembly of an extracellular evolution system, genetic information from long nucleic acids is quickly lost. This is because shorter nucleic acids are replicated with faster kinetics and outcompete longer sequences. If mutations in the replication process can change the sequence length, the result is an evolutionary race towards ever shorter sequences.

In the experiments described here we present a counterexample. We demonstrate that heat dissipation across an open rock pore, a common setting on the early Earth12 (Fig. 1b), provides a promising non-equilibrium habitat for the autonomous feeding, replication and positive length selection of genetic polymers...

...Here we extend the concept to the geologically realistic case of an open pore with a slow flow passing through it. We find continuous, localized replication of DNA together with an inherent nonlinear selection for long strands. With an added mutation process, the shown system bodes well for an autonomous Darwinian evolution based on chemical replicators with a built-in selection for increasing the sequence length. The complex interplay of thermal and fluid dynamic effects, which leads to a length-selective replication (Fig. 1c, (1)–(4)), is introduced in a stepwise manner.

The caption:

a, Modern cells feed on chemical energy, which enables them to host, maintain and replicate information-coding polymers, processes necessary for Darwinian evolution. b, The flux of thermal energy across geological cracks near a heat source (the white smoker28 is adapted from an image courtesy of Deborah S. Kelley). c, (1) A thermal gradient across a millimetre-sized crack induces the accumulation of molecules by thermophoresis and convection. (2) A global throughflow imports nutrients into the open pore. (3) Exponential replication is facilitated by the local convection, which shuttles the molecules repetitively between warm and cold, and thus induces the cyclic denaturation of nucleotides. (4) The combination of influx, thermophoresis and convection selectively traps long molecules and flushes out short ones. The inflow speed determines the cut-off size of the resulting length selection. Mechanisms (1) to (4) are described in detail in this article.

The authors take dilute short DNA fragments and drive the through a crack which has a temperature gradient on either end, the direction of flow being from hot to cold.

Here's a schematic picture from the paper:

A convective flow cycles the growing nucleic acid chain, and the overall flow determines the size of the DNA that exits from the system, and the heat provides the energy required for sequence replication:

Exponential replication by convective thermal cycling. Besides continuous feeding and length-selective trapping, the asymmetrically heated pore offers another important feature relevant to the origin of life: laminar convective temperature cycling of the accumulated nucleic acids20,21. This opens the door to Watson–Crick-type replication mechanisms, which are otherwise hindered by the considerable energy costs required to separate double-stranded oligonucleotides22. The thermal cycling can be predicted from a fluid dynamics model that includes thermophoresis and diffusion (Fig. 4a). It is sufficient to separate cyclically double-stranded DNA (dsDNA) to drive exponential base-by-base replication with duplication times on the order of minutes, as documented by SYBR Green I fluorescence (Fig. 4b and Supplementary Movie 4).

The famous PCR technique, albeit a process using a thermally stable enzyme as a catalyst, also relies on heat for replication - the authors do some PCR work in their experiments.

However in this case, the enzyme is omitted, and the reaction takes place via cycling through thermal gradients.

Another picture:

The caption:

a, The temperature gradient drives oligonucleotides horizontally from warm to cold by thermophoresis and simultaneously triggers the vertical thermal convection of water. Its combination results in a length-dependent accumulation at the bottom of an elongated pore within minutes (see Supplementary Movie 2). b, The accumulation of dilute double-stranded oligonucleotides (100–1,000mer) at the bottom is monitored within a 100 µm thin and 2 mm high capillary via SYBR Green I fluorescence. c, The accumulation is dynamic: the nucleotides cycle between the warm and cold sides, visualized in white for a single 500mer of DNA.

Another figure shows the effect of flow rate on strand length:

a, A steady upwards feeding flow is triggered by opening the asymmetrically heated pore. A ladder of dsDNA (20–200 bp, 20 bp steps) was injected into the trap. Subsequent flushing of the capillary with pure buffer at a single velocity (vs = 6 µm s–1) revealed the filter's thresholding characteristics—lengths ≤80 bp flow through the pore whereas longer strands are trapped. b, An asymmetric flow pattern is generated by the superposition of the upwards flow and the convection. Thermophoresis pushes the long strands into the downwards flow and traps them. Short strands are subjected to the overall upwards flow and leave the pore. The trapping is a function of the feeding flow speed. c, The velocity of the external flow vs tunes the fractionation of nucleic acids. As in the experiment before, a DNA ladder was initially introduced at a low flow velocity, which was then sequentially increased. The released DNA was measured using gel electrophoresis. d, The fraction of trapped DNA obtained from the electrophoresis gel constitutes a selection landscape of this thermal habitat in favour of long oligonucleotides. The velocity-dependent trapped fraction is described by a fluid dynamics model (see Methods). Error bars reflect the signal-to-noise ratio of the gel images (see Supplementary Fig. 11 for details).

Finally "size selection habitats" are shown:

The caption:

Figure 4 | Selection of a replicating DNA population that occupies the thermal habitat. a, Strands are subjected to temperature oscillations by the combination of thermophoresis, convection, feeding flow and diffusion. Simulations of stochastic molecule traces show that strands of 75 bp cycle inside the system for 18 minutes on average. In comparison, 36mers, owing to their enhanced diffusion, show faster temperature cycles, but are flushed out of the system after five minutes. b, Taq DNA polymerase-assisted replication of 80mer dsDNA by convective temperature cycling. Quantitative SYBR Green I fluorescence measurements show an exponential replication with a doubling time of 102 seconds (see Supplementary Movie 4). c, An open pore (see Fig. 1c) was seeded with a binary population of nucleic acids. Quantitative gel electrophoresis revealed sustainable replication for only the long strand. Short strands became diluted and then extinct despite their faster replication. d, Relative concentrations of the two competing species inside the thermal habitat. The selection pressure of the thermal gradient altered the composition of the binary population with time (yellow diamonds) in good agreement with an analytical replication model. The absolute fitness values were 1.03 and 0.87 for long and short strands, respectively. Without the thermal gradient, the short oligonucleotides won over the long strands (blue circles), analogous to the Spiegelman experiment. Error bars reflect the signal-to-noise ratio of the gel images (see Supplementary Fig. 11 for details).

The authors write:

On the hot early Earth, the pore system we describe was probably widespread because of porous, partially metallic volcanic rock, both near the surface and at submarine sites. As metals have a more than 100-fold larger thermal conductivity than water23, metallic inhomogeneities near the pores can focus the thermal gradient from centimetres down to a micrometre-sized cleft (Supplementary Fig. 1). The kinetics of replication and selection were realized in the most simple geometrical setting of a single pore section with dimensions of 0.07 mm× 3.5 mm. Metallic inclusions do allow thermal gradients to be focused up to 100-fold to reach the thermal gradients of realistic geological settings (Supplementary Fig. 1)...

...and in their conclusion state:

...Our experiments reveal how temperature gradients, the most simple out-of-equilibrium setting, can give rise to local environments that stabilize molecular replication against the entropic tendencies of dilution, degradation and negative length selection. A thermal gradient drives replication of oligonucleotides with an inherent directional selection of long over short sequence lengths. Interestingly, when replication and trapping inside the pore reach their steady state, the newly replicated molecules leave the trap with the feeding flow. This ensures an efficient transfer of the genetic polymers to neighbouring pore systems. Heat dissipation across porous rock was probably in close proximity to other non-equilibrium settings of pH, ultraviolet radiation and electrical potential gradients, all of which are able to drive upstream synthesis reactions that produce molecular building blocks. An exciting prospect of the presented experiments is the possible addition of mutation processes to achieve a sustained Darwinian evolution of the molecular population inside the thermal gradients of the early Earth. Accordingly, the onset of molecular evolution could have been facilitated by the natural thermal selection of rare, long nucleic acids in this geologically ubiquitous non-equilibrium environment.

In another paper, not cited here that I encountered this weekend, John D. Sutherland, who has done very exciting work demonstrating a potential path for sugar containing phosphorylated sugars to arise out of simple molecules, used a Churchillian phrase to discuss where we are with explaining the generation of life from prebiotic very simple molecules, saying that the science of the prebiotic generation of life has reached "the end of the beginning."

Fascinating stuff, I think.

I hope you're having a pleasant week thus far.

Open source paper on "Defining Life."

As I age and more and more come face to face with the inevitably of dying, I wonder more and more, having experienced the real beauty of being alive, of whence life came to be.

I have always wanted to read Schroedinger's famous book, "What is Life?" but probably will never find the time.

Nevertheless, I resolved to spend some time reading this review article, Prebiotic Systems Chemistry: New Perspectives for the Origins of Life (Kepa Ruiz-Mirazo†, Carlos Briones‡, and Andrés de la Escosura*§ Chem. Rev., 2014, 114 (1), pp 285–366), when, not far in, I came across the following text:

The complete picture and implications of this issue come out only when we try to specify the requisites that, in principle, any type of system (i.e., not only an organic chemical one) should actually fulfill to be considered alive. Opening or generalizing the problem of the nature of life, and thus of its origins, makes it richer, wider, and more challenging, as can be reflected in the recent merging of the traditional field of origins of life and the younger ones of synthetic biology and astrobiology. Indeed, the main questions addressed by astrobiology are the origins, evolution, and distribution of life in the universe.6−8

However, we do not aim to discuss here in detail the issue of defining life: the reader is referred to a special issue of the journal Origins of Life and Evolution of Biospheres,9 or to a comprehensive anthology of articles on this subject.10

When I see references I'd like to pick up, I always email them to myself for my library time, and I usually send the reference as a link to the paper when possible so I can use my library time efficiently.

But when I generated the link to reference 9, I found that it opened at home, and thus is open sourced.

It's 244 pages on the question of "What is life," updated from Shroedinger, 85 years ago.

If you're interested, here it is:

Defining Life: Conference Proceedings.

Perhaps I don't know what life it, other than whatever it, it is extraordinarily beautiful, even with the pain, and very much worth living.

Have a great weekend!

My kid is in France learning how to become a Brazilian, calling soccer "football" and complaining...

...about the "dirty tactics" the Swiss used against Brazil in the World Cup.

He shares his office in the lab with four Brazilians, who he says, speak a language that sort of is to Spanish what German is to English.

The Brazilians, he says, are "just like Americans."

After work, his new friends invite him to play "football."

Some day, he says, he'd like to spend time learning Portuguese.

Should I be concerned?

Scaling Graphene.

There's a lot being written about graphene these days. Graphene, for those who don't know, is a carbon allotrope that has the carbons bonded an a series of almost infinite series of fused hexagonal aromatic rings that make it planar. The neat thing about this allotrope is that it is exactly one atom thick. If it's thinker than one atom, it's graphite, most commonly experience by most people as pencil lead.

There are thousands of pictures on the internet. Here's an electron micrograph, out of the Los Alamos National Laboratory, of the stuff with resolution on an atomic scale:

Source Page of the Image.

Graphene is proposed to have many uses and if I actually read all the papers I've seen in which it appears in the title, I'd be able to discuss some of them intelligently, but frankly, I skip over a lot of these papers, quite possibly all of them in fact because I'm too interested in other stuff. Mostly I've just mused to myself about the stuff, particularly its oxide, which I imagined might be functionalized as an interesting carbon capture material, but well, there's lots and lots and lots of those. The problem is not discovering new carbon capture materials; the problem is utilizing them without creating carbon dioxide waste dumps that don't exist and, were they to exist, would be unacceptably dangerous to future generations, not that we care about future generations.

When my son was touring Materials Science Departments at various universities in both "informational" sessions and in "accepted students" forums the word graphene came up a lot. At one such session, we were introduced to a professor who was described as having developed a way to prepare "kg quantities" of graphene, and I meekly raised my hand and asked, "What does a 'kilogram of graphene actually mean?" If I was as rude as I sometimes am around here, I might have asked the question as "Isn't a kilogram of stacked graphene just graphite?"

But I wasn't. I didn't want to screw things up for my kid if he decided to go there. (He didn't.)

At another university, during an informational session for students who might apply, a graduate student, who was writing his thesis at the time, took an interest in my son and decided to give us a full tour of the department. Somehow I used (or muttered) the word "graphene" during the tour and he, a somewhat jaded guy with a decidedly sarcastic edge - my kind of guy - said, "Well, I'm sure it would be useful if they knew how to make it in useful quantities, but they don't."

My son did apply there, by the way, was accepted there, and is, in fact, going there, a wonderful university.

To my surprise I suddenly find myself interested in graphene though because of a recent lecture on a subject about which I know nothing but about which I am interested in finding about more, as I discussed last night in a post in this space: Topological Semimetals.

The paper I linked in that post has the following remark:

Dirac Semimetals
The prototype of a DSM is graphene. The “perfect” DSM has the same electronic structure of graphene; i.e., it should consist of two sets of linearly dispersed bands that cross each other at a single point. Ideally, no other states should interfere at the Fermi level.

Graphene is a "perfect DSM," a "perfect Dirac Semimetal."

And today in my library hour, what should happen but that I was to come across a paper that reports an approach to scaling up graphene.

The paper is here: Exfoliation of Graphite into Graphene by a Rotor–Stator in Supercritical CO2: Experiment and Simulation (Zhao et al, Ind. Eng. Chem. Res., 2018, 57 (24), pp 8220–8229)

I have been and am very interested in supercritical CO2, by the way. "Supercritical" refers to a substance that is neither a liquid nor a gas but exists in a state that has properties of both and can only exist above certain temperatures and pressures called respectively the "critical temperature" and, of course, "the critical pressure." The critical temperature of carbon dioxide is only a little above room temperature, which makes it a readily accessible material.

As my wont lately in this space when discussing scientific papers, I'll do some brief excerpts and invite you to look at the pictures, since whenever I decide whether or not to actually read a paper upon which I stumble (as opposed to a paper that I've sought for some reason), that's what I do, look at the pictures.

From the intro:

Graphene, a two-dimensional carbon material, has garnered attention because of its excellent electronic, mechanical, optical, and thermal properties1−3 and potential application in numerous fields.4−6 Various methods have been proposed for the preparation of graphenes, such as micromechanical exfoliation, 1−3 chemical vapor deposition,7,8 reduction of graphene oxide,9,10 and liquid-phase exfoliation.11−24 Liquid exfoliation was considered to be a scale-up and low-cost method in which ultrasound probe and high-shear mixer were often applied. Liquid exfoliation via the fluid shear stress induced by a high-shear mixer can produce large quantities of defect-free graphene.18−24 A four-blade impeller with high shear rate causing strong turbulence was applied to create graphene.18 A kitchen blender was reported to exfoliate graphite into graphene too.19 Coleman et al. and Liu et al. reported the large-scale production of the graphene in N-methyl-2-pyrrolidone (NMP) and dimethylformamide (DMF) solvent, respectively, using a high-shear rotor− stator mixer,20,21 and the minimum shear rate required was 104 s−1. The exfoliation reason was attributed to the high-shear force induced by the large velocity gradient generated by the high-speed fluid when the high-speed blades expelled the solvents to flow in the narrow gap between the stator and the rotor. The cavitation and collision effects caused by the mixer were also factors to exfoliate graphite into graphene.16 Similarly, Xu et al. used a conical tube as a stator to prepare the graphene in NMP solvent.22 Most recently, supercritical CO2 as a green solvent was used to assist in exfoliating graphene.23. Our group developed a scalable approach to exfoliate graphite into graphene via fluid dynamic force in supercritical CO2 using a rotor−stator mixer.27...

...The purpose of this work is to investigate the exfoliation mechanism of a rotor−stator mixer in supercritical CO2 by a combination of the experiment and CFD simulation and to make the optimal design of the rotor−stator mixer in terms of exfoliation efficiency for the potential industrial application.

CFD is computational fluid dynamics if you didn't know.

Now some pictures...

Here's a schematic of things they evaluate by computer simulation:

The caption:

Figure 1. Computational domains of modeling.

Rotor design and (low, if higher than usual where graphene is concerned) yields:

The caption:

Figure 2. Structure of rotors and the production of graphene. Digital photos of the six-tooth rotor (A) and the cross rotor (B). The yield of graphene made by the cross rotor and six-tooth rotor in different shearing speed (C)

A little discussion of the mathematical physics of the situation:

2.2. Numerical Simulations. Five 3D physical models of the reactor were built. A Eulerian−Eulerian two-fluid model which contains the kinetic theory of a granular flow was used to describe liquid−solid two-phase flow in the reactor.

2.2.1. Eulerian−Eulerian Two-Fluid Equations. Different phases were treated as interpenetration continuum. The conservation equations were solved simultaneously for each phase in the Eulerian framework. Then, the continuity equations for phase n (n = l for the liquid phase, s for the solid phase) can be expressed by


Some more cool math:

2.2. Numerical Simulations. Five 3D physical models of the reactor were built. A Eulerian−Eulerian two-fluid model which contains the kinetic theory of a granular flow was used to describe liquid−solid two-phase flow in the reactor.

2.2.1. Eulerian−Eulerian Two-Fluid Equations. Different phases were treated as interpenetration continuum. The conservation equations were solved simultaneously for each phase in the Eulerian framework. Then, the continuity equations for phase n (n = l for the liquid phase, s for the solid phase) can be expressed by

At the same time, a granular temperature was introduced into the model:


Some simulation results:

The caption:

Figure 5. Contours of velocity at 3000 rpm distribution of horizontal fluid flow pattern induced by an 8-tooth stator (A) and a 10-tooth stator (B).

More simulation showing vessels and rotors:

The caption:

Figure 6. Stator and the contours of velocity and volume fraction in multiwall stator at 3000 rpm (A). The lateral view and the vertical view of the multiwall stator, (B) horizontal, and (C) perpendicular fluid flow pattern induced by multiwall stator; the graphite of volume fraction in (D) eighttooth stator and (E) multiwall stator.

Then they set about making themselves some graphene. It, along with graphene by other processes is pictured here:

The caption:

Figure 10. SEM images of (A) graphite powder, (B) graphene sheets prepared in supercritical CO2, (C) graphene sheets made in water, and (D) graphene sheets prepared in NMP.

NMP is N-methylpyrollidine. I've used it, I'm still alive but know nothing of its toxicology. If it turns out to be toxic, we can use it to make solar cells, whereupon it will be declared "green," no matter what it's effect on living things.

Some more electron micrographs:

The caption:

Figure 11. AFM and TEM images of graphene sheets. (A, B) AFM images of graphene and the height profile along the line shown in the panel; (C−F) TEM images of graphene in low-resolution and in high-resolution; (G) distribution of the number of graphene layers based on TEM.

Nevertheless the yields are not spectacular enough to make industrial application straight forward, although if it turns out that graphene solar cells are "great" we can bet the planetary atmosphere on the expectation that they'll be available "by 2050" when I - happily for many people who don't find me amusing - will be dead.

The caption:

Figure 9. Yield of graphene obtained in supercritical CO2, water, and NMP under different shearing speeds.

Some concluding remarks:

In this work, we explored the exfoliation mechanism of graphite into graphene by the rotor and stator geometry in supercritical CO2 and optimized the rotor−stator structure by combining CFD simulation and experiments. The fluid flow patterns corresponding to the rotor and stator with different structures were analyzed by FLUENT 6.3. The experiment and simulation results show that the graphene yield was influenced by the volume of the active region, which is the gap between the stator and the rotor (including the high-speed fluid), and the effective exfoliation time. These two primary factors are more influenced by the geometry of the stator rather than that of the rotor. The multiwall and the extended-wall stator were demonstrated to enable the yield to be nearly doubled and increased by 40%, respectively...

Love that percent talk!

Interesting, I think, although I think that graduate student had a point.

I hope your Friday will be pleasant and productive.

Chemical Principles of Topological Semimetals

In the midst of the White House generated horror of the last days, I had the guilty pleasure of attending my favorite kind of lecture: A lecture that was not only on a subject about which I know nothing, but on a subject about which I never even heard, topological semimetals.

One of my goals in life is to feel as often as is possible like I'm the dumbest person in the room, and I definitely succeeded in this case.

The lecture was given by Dr. Leslie M. Schoop, the newest faculty member of the Princeton University Department of Chemistry.

I immediately went home after the lecture and began to look into the topic and was pleased to see that I recently downloaded (but clearly didn't read) a review article written by Dr. Schoop and her colleagues.

The article, from which the total of this post is taken is here: Chemical Principles of Topological Semimetals (Leslie M. Schoop,*,† Florian Pielnhofer,‡ and Bettina V. Lotsch, Chem. Mater., 2018, 30 (10), pp 3155–3176)

It's a relatively new, if rapidly expanding field, so I guess I can be excused for knowing nothing at all about it, but it apparently involves some novel particle physics apparently predicted by the mathematical physicist Hermann Weyl during the scientifically transcendent 20th century.

Since it involves the structure of matter, I plan to share this with my son when he returns from Europe, I believe he'll find it cool.

Much of the topic remains over my head, but I thought it might be interesting to post brief excerpts of the paper along with some of the beautiful graphics from it.

The practical application, should it ever develop, would be computers so fast as to revolutionize computation as much as the original digital computer did in the 20th century, the elusive quantum computer: At least this is what Dr. Shoop claimed.

The recent rapid development in the field of topological materials (see Figure 1) raises expectations that these materials might allow solving a large variety of current challenges in condensed matter science, ranging from applications in quantum computing, to infrared sensors or heterogeneous catalysis.(1−8) In addition, exciting predictions of completely new physical phenomena that could arise in topological materials drive the interest in these compounds.(9,10) For example, charge carriers might behave completely different from what we expect from the current laws of physics if they travel through topologically non-trivial systems.(11,12) This happens because charge carriers in topological materials can be different from the normal type of Fermions we know, which in turn affects the transport properties of the material. It has also been proposed that we could even find “new Fermions”, i.e., Fermions that are different from the types we currently know in condensed matter systems as well as in particle physics.(10) Such proposals connect the fields of high-energy or particle physics, whose goal it is to understand the universe and all the particles of which it is composed, with condensed matter physics, where the same type, or even additional types, of particles can be found as so-called quasi-particles, meaning that the charge carriers behave in a similar way as it would be expected from a certain particle existing in free space...

The caption:

Figure 1. Timeline of recent developments in the field of topologically non-trivial materials.

The intro continues:

he field of topology evolved from the idea that there can be insulators whose band structure is fundamentally different (i.e., has a different topology) from that of the common insulators we know. If two insulators with different topologies are brought into contact, electrons that have no mass and cannot be back scattered are supposed to appear at the interface. These edge states also appear if a topological insulator (TI) is in contact with air, a trivial insulator. 2D TIs have conducting edge states, whereas 3D TIs, which were discovered later, have conducting surface states. TIs have already been reviewed multiple times,(13−16) which is why we focus here on the newer kind of topological materials, namely topological semimetals (TSMs)...

The review then discusses the remarkable properties of graphene which Dr. Schoop remarked with some amusement can be made by peeling a single layer of carbon atoms off of graphite with masking tape.

...But let us first take a step back to look with a chemist’s eyes at graphene and try to understand why it is so special. As chemists we would think of graphene as an sp2-hybridized network of carbon atoms. Thus, three out of C’s four electrons are used to form the σ-bonds of the in-plane sp2-hybridized carbon backbone (Figure 2a). The remaining electron will occupy the pz-orbital, and since all C–C bonds in graphene have the same length, we know that these electrons are delocalized over the complete graphene sheet. Since graphene is an extended crystalline solid, the pz-orbitals are better described as a pz-band (Figure 2b). Since there is one electron per C available, this pz-band is exactly half-filled (Figure 2c).

The caption:

Figure 2. Intuitive approach for describing the electronic structure of graphene. (a) Real-space structure of graphene, highlighting the delocalized π-system. (b) Orbital structure and band filling in graphene. (c) Corresponding electronic structure in k-space; only one atom per unit cell is considered. (d) Unit cell of graphene, containing two atoms. (e) Brillouin zone of graphene. (f) Folded band structure of panel (c), in accordance with the doubling of the unit cell. (g) Hypothetical version of distorted bands with localized double bonds. This type of distorted honeycomb can be found in oxide materials such as Na3Cu2SbO6.(58)

Some remarks on graphene as a prototype of the "Dirac Semimetal"

Most TSMs have in common that their unusual band topology arises from a band inversion. Unlike TIs, they do not have a band gap in their electronic structure. There are several classes of TSMs: Dirac semimetals (DSMs), Weyl semimetals (WSMs), and nodal line semimetals (NLSMs). All these kinds exist as “conventional” types; i.e., they are based on a band inversion. In addition, they can also be protected by non-symmorphic symmetry. The latter ones have to be viewed differently, and we will discuss them after introducing the conventional ones.

Dirac Semimetals

The prototype of a DSM is graphene. The “perfect” DSM has the same electronic structure of graphene; i.e., it should consist of two sets of linearly dispersed bands that cross each other at a single point. Ideally, no other states should interfere at the Fermi level. Note that in a DSM, the bands that cross are spin degenerate, meaning that we would call them two-fold degenerate, and thus the Dirac point is four-fold degenerate. When discussing degeneracies within this Review, we will always refer to spin orbitals. In any crystal that is inversion symmetric and non-magnetic (i.e., time reversal symmetry is present), all bands will always be two-fold degenerate. Time reversal symmetry (T-symmetry) means that a system’s properties do not change if a clock runs backward. A requirement for T-symmetry is that electrons at momentum points k and −k have opposite spin, which means that the spin has to rotate with k around the Fermi surface since backscattering between k and −k is forbidden. Introducing a perturbation, e.g., an external magnetic field, lifts the spin degeneracy and violates T-symmetry.

The caption:

Figure 3. Explanation of band inversions. (a) Rough density of states (DOS) of transition metals. Band inversions are possible between the different orbitals within one shell, but the material is likely to be metallic. (b) Band inversion between an s-band and a p-band. (c) Molecular orbital diagram of water. (d) Bands that cross and have the same irreducible representation (irrep) gap. (e) If the irreducible representations are different, the crossing is protected, but SOC might still create a gap.

"SOC" is spin orbit coupling.

Weyl Semimetals:

Weyl Semimetals

The difference between a DSM and a WSM is that, in the latter, the crossing point is only two-fold degenerate.(28,93,94) This is because in WSMs the bands are spin split; thus each band is only singly degenerate. If a spin-up band and a spin-down band cross, this results in a Weyl monopole, meaning that there is a chirality assigned to this crossing. Since there cannot be a net chirality in the crystals, Weyl cones always come in pairs. The resulting Weyl Fermions are chiral in nature and thus will behave physically different from “regular” Fermions. One example of this manifestation is the chiral anomaly, which we will discuss in the Properties and Applications of TSMs section below. Here, we will focus on the requirements necessary to realize a WSM.
In order to have spin split bands, we cannot have inversion (I) and time-reversal (T) symmetry at the same time, since the combination of these two symmetries will always force all bands to be doubly degenerate. In I asymmetric, i.e., non-centrosymmetric crystals, this degeneracy can be lifted with the help of SOC; this is the so-called Dresselhaus effect.(95)

The caption:

Figure 4. Different ways to achieve a Weyl semimetal. (a) Effect of T- and I-symmetry breaking on a single band. (b) The same scenario for a Dirac crossing. In the case of T breaking, two Weyl crossings will appear on the high-symmetry line at different energies. In the case of I breaking, they will appear away from the high-symmetry line. (c) Schematic drawing of a type I (left) and a type II (right) WSM.

Figures for a 3D Dirac Semimetal, trisodium bismuthide, a Zintl salt (at least I knew about Zintl salts for the lecture):

The caption:

Figure 7. (a) Crystal structure of Na3Bi. (b) First Brillouin zone with high-symmetry points and highlighted Dirac points. (c) Bulk band structure. (d) 3D intensity plot of the ARPES spectra at the Dirac point. Panels b and d reprinted with permission from ref (143). Copyright 2014 The American Association for the Advancement of Science. Panel c reprinted with permission from ref (168). Copyright 2017 Springer Nature.

A Weyl Semimetal:

The caption:

Figure 8. (a) Crystal structure of TaAs. (b) Brillouin zone. (c) Band structure without and (d) with SOC. (e) Photoemission spectrum with overlaid calculated band structure. (f) Calculated and measured Fermi surface, displaying the Fermi arcs, which are the signature to identify WSMs. Panels b–d reprinted with permission from ref (149). Copyright 2015 Springer Nature. Panels e and f reprinted with permission from ref (91). Copyright 2015 Springer Nature.

A "Non-symmorphic Topological Semimetal: "

The caption:

Figure 9. (a) Crystal structure of ZrSiS. (b) Brillouin zone in space group 129, with highlighted degeneracy enforced by non-symmorphic symmetry. (c) Bulk band structure of ZrSiS. The two degeneracies enforced by non-symmorphic symmetry at the X point are highlighted in blue (above EF) and orange (below EF). (d) Effect of the c/a ratio of isostructural and isoelectronic analogues of ZrSiS on the non-symmorphically induced degeneracies at X. While most compounds exhibit these crossings below and above the Fermi level, there are two exceptions: HfSiTe and ZrSiTe. (e) ARPES spectrum of ZrSiS near X along Γ-X. Two bands cross at X due to the non-symmorphic symmetry. Above the crossing, a very intensive surface state(205) is visible. Panel b reprinted with permission from ref (207). Copyright 2017 Elsevier. Panel c adapted and panel e reprinted with permission from ref (24). Copyright 2016 Springer Nature. Panel d reprinted with permission from ref (132). Copyright 2016 IOP Publishing.

And now, to generate some interest in saving the world after Elon Musk is done saving the world, a possible application, the ever popular solar hydrogen:

Figure 11. Schematic diagram of a topological Weyl semimetal for catalyzing the dye-sensitized hydrogen evolution. Reprinted with permission from ref (7). Copyright 2017 John Wiley and Sons.

Well, at least the degeneracy here doesn't involve that awful excuse for a human being in the White House.

A little interesting if still obscure, at least to me, science is a great way to escape. It's a pleasure to be the dumbest guy in the room, really a pleasure.

I wish you a pleasant day tomorrow.

The greatest car ever, the car that saved all life on earth, spontaneously ignites.

Tesla spontaneously catches fire with no crash

It's green. It's solar. It's wind turbiney. It's the savior of the common man. We need this car more than life itself. The entire US budget should be devoted to its worship.

People Get Ready.

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2017 Establishes a New Record for Coal and For So Called "Renewables."

The data comes from the BP Statistical Report, which is generally more current than the WEO (published each November) but perhaps not as accurate.

I've downloaded all the data from the BP Report nonetheless, and am going through it. It's an interesting read, showing that things are every bit as bad as I've come to believe, maybe even worse, particularly since energy and environmental issues are filled with so much wishful thinking, outright delusion, and denial on both ends of the political spectrum, this in a world where the center is disappearing.

Other big "winners," besides so called "renewables" and coal were oil and gas, and oh, yes, carbon dioxide emissions.

Carbon Brief: BP Global Data Shows Record Highs for Coal Power

There's a certain amount of "percent talk" here about so called "renewable energy," which is tightly linked to the use of dangerous fossil fuels.

The so called "renewable energy" industry remains what it has always been, trivial, outside of "percent talk" compared to dangerous fossil fuels, and is clearly incompetent to stop their growth.

Oh my God! I was there last evening. This is terrible at a beautiful community event.

My son had a painting on display there.

This is horrible, particularly because "Mothers against gun" had a display there.

Screw the NRA.
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