Inertial Propulsion: The Potential of Eliminating Electron Mass in Graphene

[Mr Vibrating]

Electron Mass Effectively Eliminated in Graphene

http://archive.sciencewatch.com/jan-feb2007/sw_jan-feb2007_page6.htm

Since reading this I've been bothered by the niggling implications of a system in which the value of mass can be varied.. particularly with regards to propulsion.

It seems to me (as a layperson) that what prevents attempted 'inertial' motors from working is mass constancy - whereas the above finding seems to present the possibility of an asymmetric exchange of momentum.

Consider the example of electrons cycling across a graphene/semiconductor interface; if alternate changes in current direction correspond to massive vs massless states then we have a unilateral net force per cycle, no?

I've no doubt others close to this research would have noted the feasibility of such a mechanism if it were indeed implicit, but can find no reference to any arguments specific to this application.. so given how tantalising the possibilities are I'm curious as to what others think.. is this warp drive tech or what?

 

[Mr Vibrating]

..cos i mean like electron inertia might not seem all that useful, until you consider power is a function of frequency and we already have GHz semiconductor tech.. so you could imagine stacks of say thin film silicon/graphene laminates with a fast alternating current thru 'em.. all floating about the place, like.. there'd be all sorts of uses, hovering platform shoes for midgets, levitating ocelots.. two offset opposing ones could generate torque for spin-drying kittens, disorienting the vulnerable, seperating children by weight etc., proper breakthrough stuff..

..or am i just a sucker for a poorly-phrased headline? Seriously, if we have a system wherein the value of mass is variable then that directly impies path-dependent asymmetries are possible. Must be some kind of relativistic clawback but where?

 

[johnpmc]

"if we have a system wherein the value of mass is variable then that directly impies path-dependent asymmetries are possible. Must be some kind of relativistic clawback but where?"

I think the clawback would relate to the 1st law of thermodynamics and E=MC^2

 

[Vanadium 50]

..or am i just a sucker for a poorly-phrased headline?

I'm afraid so. This is a statement about the collective motion of many electrons in a medium, which can be characterized by an effective mass. But there is nothing changing the physical mass of the electron.

 

[Mr Vibrating]

"if we have a system wherein the value of mass is variable then that directly impies path-dependent asymmetries are possible. Must be some kind of relativistic clawback but where?"

I think the clawback would relate to the 1st law of thermodynamics and E=MC^2

As i suspect - although not averse to the idea of a closed system bieng somewhat larger than anticipated (ie. apparent violations vs real ones) you'd expect that anything lost in rest mass would be regained in relativistic momentum for a zero sum game..

 

[Mr Vibrating]

I'm afraid so. This is a statement about the collective motion of many electrons in a medium, which can be characterized by an effective mass. But there is nothing changing the physical mass of the electron.

You're probably correct, still I'm not really getting closure yet..

The quadratic vs linear thing seems suggestive of a possible crossover point:

In a semiconductor there is a quadratic relationship between the energy and momentum of the electrons. But in graphene that relationship is linear. Papers #2 (Geim’s group) and #3 (Philip Kim’s group, Columbia University, New York), published side by side in Nature, report on an important consequence of the linear relationship. They independently discovered that electrons move through the films as if they have no mass. That’s because the energy-momentum relationship means that electron transport is governed by the relativistic Dirac equation.

..it's that "as if" where the ambiguity lies.. what's the difference between reduced mass and effectively reduced mass? Ie. in what respect is it tempered if not 'effectively'? I appreciate that ultimately it's only the net momentum that counts but for now it's not clear that it would balance. Goes-faster-but-gets-lighter gives a kind of logical equality, sure, but how's that pan out?

I mean considering we'd normally expect mass to increase relativistically wrt velocity, the claimed increase in propogation speed through the material seems all the more paradoxical - why does this correspond to effective mass reduction instead?

appreciate this is likely so much fuss over nothing but hey why else are we here.. ;P

 

[f95toli]

Again, effective mass has nothing to do with the physical mass. Effective mass is just a parameter which is introduced in certain models to simplify calculations when dealing with many-particle systems; in the same way fictious forces are introduced in mechanics. It is not "real" mass.
Hence, it has nothing to do with propulsion or the speed of light.

 

[Mr Vibrating]

'Effective mass' here is just my own awkward neologism unfortunately (i think effective momentum is what will count at the end of the day) but the explicit claim appears to be that the increased conductivity in graphene is consistent with the elimination of mass, and thus inertia, of the free electrons.

And i guess that seems to follow a kind of logic.. except it directly implies that flipping the direction of travel in this 'massless' state would be likewise inertia-less.. and an alternating current that was only 'effectively' subject to inertia in one direction would by definition be an equally 'effective' N3 violation...

 

[Vanadium 50]

Regardless, it has nothing to do with propulsion or the speed of light.

 

[Mr Vibrating]

I made no mention of the speed of light yet your claim that it has "nothing to do" with it flatly contradicts the claim of the researchers themselves who describe the speed increase in relation to C (would there be any more meaningful metric?).. and more fundamentally if you were correct and this effect had "nothing to do with the speed of light" then this would invalidate your statement that it's also irrelevant to propulsion.. because conservation of relativistic momentum is currently the only option i see to prevent a net propulsion. And like i said, even then I'm not sure the equation would balance.

Flat out contrarianism isn't science - I'm asking for a little exposition here. If you don't like the question then skip it. If I'm wrong about the implied symmetry break (and no doubt i am) please explain why - that's all I'm asking here..?

 

[f95toli]

But again, they are talking about the effective mass; it is not a "real" mass any more than hole is a "real" particle. They are both tools that are used to simplify calculations when dealing with many-particle systems.
(btw, a hole is essentially an election with negative effective mass; but it is customary to absorb the minus sign into the charge instead).

There are many, many examples of "effective" quantities that are used to simplify calculations; especially in many-particle physics where we almost always deal with collective properties (another example would be the effective charge, which can be less than e when screening effects are taken into account). Hence, whenever the word "effective" is used it implies that hit is not a real property in that it can not be attributed to a single particle.

Note that in order to talk about effective mass you need a system that is so large that you have a periodic lattice (in the sense that one can use a periodic boundary condition), this is needed because otherwise there is no well-defined wave-vector which in turn means that the concept of effective mass loses its meaning.

 

[Mr Vibrating]

Thanks for engaging.. but then we come back to the question of in what sense this property is "effective"?

Presumably adjusting for mass as a mechanism to formulate the increased conductivity isn't an arbitrary decision - it's evidently in some sense a meaningful 'effect' or they wouldn't be invoking it.

So why would it no longer be 'effective' with regards to the implied symmetry break? That's the question. In other words why would it only apply when the current direction's constant - because if it switches direction while in this 'effectively massless' state then ergo it likewise does so without inertia?

 

[Mr Vibrating]

Found another mention of the effect on physorg:

http://www.physorg.com/news161529738.html

 

[K^2]

Effective electron mass is purely a mathematical tool in solid state physics. Collective motion of the electrons is described by quasi-particles with effective mass. The mass they are talking about is simply a number you need to put into Schroedinger's Equation to get a wave of a "single" particle that behaves on its own the same way as electrons behave together.

This mass being very low results in many interesting properties, but has nothing to do with momentum carried by electrons or propulsion.

 

[Mr Vibrating]

FWIW I'm probably not expressing myself entirely cogently but hopefully you're getting my drift - if the purported 'effective mass' change is to accommodate a decreased inertia under accelerations, then by virtue of the exact same arguments changing the current direction between massive and massless states leaves a net unbalanced inertia and the system gains momentum..

 

[K^2]

No, it does not. These are quasi-particles. They are not real. The total mass is still the mass of electrons. Fact that each quasi-particle is lighter just means you'll have more quasi-particles to describe the same flow. Again, total mass doesn't change.

 

[Mr Vibrating]

Effective electron mass is purely a mathematical tool in solid state physics. Collective motion of the electrons is described by quasi-particles with effective mass. The mass they are talking about is simply a number you need to put into Schroedinger's Equation to get a wave of a "single" particle that behaves on its own the same way as electrons behave together.

This mass being very low results in many interesting properties, but has nothing to do with momentum carried by electrons or propulsion.

But I'm asking WHY does this mass not have anything to do with momentum, as it normally would?

I haven't seen the term "effective mass" mentioned in these articles, apart from the headline reading .."electron mass effectively eliminated.." - as in "all but eliminated".

And the repeated assertions this has nothing to do with propulsion are disingenuous - the references I'm giving aren't talking about propulsion but conductivity. I'm asking specifically WHY this change mass wouldn't have a corresponding inertial profile?

It's not the sematic difference I'm interested in but the corporeal effect - either the effects of electron mass are reduced or they are not. If they are (as explicitly claimed) then why wouldn't these results carry over into the inertial implications?

It seems to me we can't have it both ways - if the purpose of invoking mass reduction is to explain increased acceleration due to decreased inertia then why does this standard relationship no longer hold in the application i describe? It's just a slight twist on the exact same scenario..

 

[K^2]

It's a quasi-particle. It's not real. There are no particles with lower mass actually in the material. There are just ordinary electrons with their ordinary electron mass. The effective mass is just a number that goes into an equation to make that equation work. That's it.

 

[Mr Vibrating]

No, it does not. These are quasi-particles. They are not real. The total mass is still the mass of electrons. Fact that each quasi-particle is lighter just means you'll have more quasi-particles to describe the same flow. Again, total mass doesn't change.

The articles make no mention of these being quasi-electrons - could you provide references for this claim?

From the physorg peice:

Even at room temperature, electrons in graphene are more than 100 times more mobile than in silicon.

Graphene apparently owes this enhanced mobility to the curious fact that its electrons and other carriers of electric charges behave as though they do not have mass.

And furthermore:

The Georgia Tech/NIST team tracked these massless electrons in action, using a specialized NIST instrument to zoom in on the graphene layer at a billion times magnification

..hence I'm getting the impression these are real particles rather than notional ones.
Either way though this distinction alone still doesn't answer the question - if they're real enough to render the effect in the first place then the application i describe depends on them being no more or less existential!

 

[K^2]

The articles make no mention of these being quasi-electrons - could you provide references for this claim?

A popular article does not describe the exact physics of the phenomenon? Really? I'm shocked. For reference on effective mass and how it affects conduction properties, see any solid state physics text.

Either way though this distinction alone still doesn't answer the question - if they're real enough to render the effect in the first place then the application i describe depends on them being no more or less existential!

Sure, you can look at it this way, but their numbers are not conserved and their charge is not conserved. When you change their mass, you change the number of particles in the system. Again, the total mass of all these quasi-particles is still just the total mass of the electrons. Doesn't matter what you do with it, when you shift them back and forward, you are still just shifting the combined mass of the electrons which never changes. So again, it has absolutely no impact on total momentum.

 

[Mr Vibrating]

It's a quasi-particle. It's not real. There are no particles with lower mass actually in the material. There are just ordinary electrons with their ordinary electron mass. The effective mass is just a number that goes into an equation to make that equation work. That's it.

..it has to be a number that describes a real quantity or magnitude!

A phonon is a unit of thermal energy, a given phonon itself might not be real but the energy it describes is.. etc., so why are you invoking "quasi electrons" when these articles do not, and in what sense is it meaningful if not effectively? The conductivity of graphene isn't merely a number plugged into an equation, it's more than that - it's a physical property.

You seem to be confusing the map with the territory and concluding there IS no territory. What's the map for then? lol..

 

[K^2]

It's effective mass. Effective mass applies to quasi-electrons, not the real ones. Real electrons have a real mass. Not effective mass. Again, feel free to actually open up a text on Solid State. Need a recommendation? I think I might have something at undergraduate level. Though, undergraduate texts usually don't cover the subject too well.

And you are getting it backwards. Low effective mass doesn't result in high conductivity. High conductivity results in low effective mass. The number is there to fit the model to the data. You can obtain a theoretical estimate for that effective mass by other means, and that's why it's of interest, but it still doesn't describe any real property of any real particle.

 

[Mr Vibrating]

A popular article does not describe the exact physics of the phenomenon? Really? I'm shocked. For reference on effective mass and how it affects conduction properties, see any solid state physics text.

Right. Don't ask at a physics forum. Go and look it up in a book. can't aswer a question? intervene anyway and try deflect it. Nice..

Sure, you can look at it this way, but their numbers are not conserved and their charge is not conserved. When you change their mass, you change the number of particles in the system. Again, the total mass of all these quasi-particles is still just the total mass of the electrons. Doesn't matter what you do with it, when you shift them back and forward, you are still just shifting the combined mass of the electrons which never changes. So again, it has absolutely no impact on total momentum.

Sorry I'm trying to follow but struggling - i understand distinctions between things like group speed vs phase speed, i understand real vs quasi particles, i understand equivalence and covariance and conjugate variables etc. but I'm not understanding why 'effective mass' is the answer here. You skirt around possible explanations without offering a coherent mechanism - are you suggesting that the elementary charge of the electrons decreases inversely to their mass and/or speed, or that the quantity of free electrons decreases with their mass and inversely to their speed? Neither of these seem realistic and neither has any obvious effect on momentum - a million massless electrons have the same inertia as one massless electron, ditto with regards to charge variation (?) - how would that compensate the reduced inertia?

I'm not trying to be difficult i just cannot for the life of me see how my application of the effect differs from theirs - it's just the inescapable corollary of the exact same dynamic..

 

[ZapperZ]

..it has to be a number that describes a real quantity or magnitude!

A phonon is a unit of thermal energy, a given phonon itself might not be real but the energy it describes is.. etc., so why are you invoking "quasi electrons" when these articles do not, and in what sense is it meaningful if not effectively? The conductivity of graphene isn't merely a number plugged into an equation, it's more than that - it's a physical property.

You seem to be confusing the map with the territory and concluding there IS no territory. What's the map for then? lol..

I think it is you who are confusing the issue. By the very use of the term "effective mass", one IS explicitly invoking quasi particle concept via the Landau's Fermi Liquid theory. Effective mass would be meaningless for free particles that have no many-body properties. Only when there are such many-body phenomenon can the concept of "effective mass" be meaningful. So even when the article makes no mention of quasi-electrons, the very fact that the concept of effective mass is employed automatically implies that these are quasiparticles, and all the physics involved in such a concept are valid.

The "conductivity" may be a physical property, but it gives you no information on the transport phenomena, i.e. you do not know HOW those charge careers moved in the solid. For that, one requires a theoretical understanding of the solid, especially in terms of band structure of the material. There are many examples where these are used as the starting point to derive various properties of the solid, including its conductivity/resistivity, often as a function of temperature, which is a more difficult thing to do.

Zz.

 

[Mr Vibrating]

It's effective mass. Effective mass applies to quasi-electrons, not the real ones. Real electrons have a real mass. Not effective mass. Again, feel free to actually open up a text on Solid State. Need a recommendation? I think I might have something at undergraduate level. Though, undergraduate texts usually don't cover the subject too well.

..so what they were observing at a billion times magnification were mathmatical abstractions? Synaesthetic artifacts eh..

And you are getting it backwards. Low effective mass doesn't result in high conductivity. High conductivity results in low effective mass.

both articles explicitly refer to the conductivity boost being caused by the increased electron mobility... "moving as if they have no mass". References are given..

The number is there to fit the model to the data. You can obtain a theoretical estimate for that effective mass by other means, and that's why it's of interest, but it still doesn't describe any real property of any real particle.

What's being claimed is a material property - some detail is given:

In a semiconductor there is a quadratic relationship between the energy and momentum of the electrons. But in graphene that relationship is linear. Papers #2 (Geim’s group) and #3 (Philip Kim’s group, Columbia University, New York), published side by side in Nature, report on an important consequence of the linear relationship. They independently discovered that electrons move through the films as if they have no mass. That’s because the energy-momentum relationship means that electron transport is governed by the relativistic Dirac equation.

In semiconductors, electron transport is ruled by the non-relativistic Schrödinger equation. So electrons in graphene behave like relativistic particles and travel at about 106 m s-1. Although that speed is about 300 times slower than the velocity of light, it is much faster than the speed of electrons in conductors. The electrons travel sub-micron distances without scattering, something unheard of in semiconductors. Suddenly, ballistic transistors, in which electrons barrel through the device like a bullet, begin to look feasible.

..so to avoid muddying the waters with conflicting interpretations it looks to me like the most likely reason my circuit wouldn't work is because relativistic momentum would take up the slack of the effective mass reduction, balancing the net inertial forces - ie. essentially making up the difference with radation pressure. And the problem i have with that is that the speed's 300x lower than C while the mass is "effectively eliminated", which seems like a whopper of a disparity.. I was kind of hoping for an answer that would tie up the articles to this question...

appreciate any attempts tho..

 

[K^2]

Have you tried to read the post right above yours?

What do you expect scientists to see under "billion times magnification" (there is a clear scientific description...)? Actual electrons floating about? Maybe they used tiny scales to weigh them after that?

both articles explicitly refer to the conductivity boost being caused by the increased electron mobility...

By mobility boost. Not by decrease in mass. The electrons do not actually get lighter.Let me try to explain this. Graphine is effectively two dimensional. That means its phase space is also two-dimensional. That means that the radius of the Fermi surface grows as square root of electron density, rather than as cube root like in normal conductors. That means that Fermi Energy of electrons is ridiculously high. That means a big chunk of their total energy comes from momentum, rather than rest mass.

Models that are normally used to describe conduction are non-relativistic. If you use normal electron mass, at these energies, you end up with nonsensical results. The way to fix it is to pretend that electrons are much lighter, and describe behavior with these lighter electrons. These are your quasi-particles with almost no effective mass. It's just a description. Nothing else. The actual physics and the actual conductivity properties are described by physics of real electrons with normal mass. Then these light electrons are invented to describe the same qualities of material with simpler physics. It's the conductivity that forces you to use the low mass.

And if you open up any descent book on Solid State Physics and just start reading, you can learn about it. I cannot explain to you what takes several weeks of lectures over a few posts in a forum. I told you what these articles mean, if you want to actually understand it, you'll have to read a textbook. That's how it works with physics forums.

 

[Mr Vibrating]

I think it is you who are confusing the issue. By the very use of the term "effective mass", one IS explicitly invoking quasi particle concept via the Landau's Fermi Liquid theory. Effective mass would be meaningless for free particles that have no many-body properties. Only when there are such many-body phenomenon can the concept of "effective mass" be meaningful. So even when the article makes no mention of quasi-electrons, the very fact that the concept of effective mass is employed automatically implies that these are quasiparticles, and all the physics involved in such a concept are valid.

ookay.. The thing is effective mass isn't mentioned anywhere in these articles or anything else I've read on the matter - the headline of one read "..mass effectively eliminated" and some folks got the wrong end of the stick.. thinking it was a question of SSP/CMP or whatever. Much has been written about the morphology and geometry of the graphene lattice in relation to electron transport and all the descriptions I've seen so far have been in the context of discrete particles. The term "effective mass" was only introduced to this thread by you guys telling me that its not real mass, which is wonderfully enlightening, if not particularly useful..

I myself only mentioned "effective momentum", and then in reference to relativistic mass..

The "conductivity" may be a physical property, but it gives you no information on the transport phenomena, i.e. you do not know HOW those charge careers moved in the solid. For that, one requires a theoretical understanding of the solid, especially in terms of band structure of the material. There are many examples where these are used as the starting point to derive various properties of the solid, including its conductivity/resistivity, often as a function of temperature, which is a more difficult thing to do.

Zz.

.. a fair bit of detail can be found being the material of the moment, so I've done the minimum legwork you'd expect.. it's just the implications of this mass reduction effect that's bugging me.

honestly I'm not trying to advocate woo, and wouldn't bother yuz lot if i hadn't been chewing it over a good 6 months already, the fun is finding the flaws yourself after all.. but I'm stumped.

 

[Mr Vibrating]

Just to mix it up a bit, this 'un came up the other day:





(and the guy's name is Mr Coulombe - how cool is that?)

Any takers on whether this is an EM-dependent effect, or could it be done with purely mechanical actuators? and please check the control runs before complaining! (vids from a thread on the Steorn forum)

 

[ZapperZ]

ookay.. The thing is effective mass isn't mentioned anywhere in these articles or anything else I've read on the matter - the headline of one read "..mass effectively eliminated" and some folks got the wrong end of the stick.. thinking it was a question of SSP/CMP or whatever. Much has been written about the morphology and geometry of the graphene lattice in relation to electron transport and all the descriptions I've seen so far have been in the context of discrete particles. The term "effective mass" was only introduced to this thread by you guys telling me that its not real mass, which is wonderfully enlightening, if not particularly useful..

I myself only mentioned "effective momentum", and then in reference to relativistic mass..

But this "mass" in graphene IS the effective mass. I hesitate to tell you to actually read the paper (S. V. Morozov et al., Phys. Rev. Lett. 100, 016602 (2008)), because you seem to have a rather adverse reaction when someone asks you to actually go to the horse's mouth and get the info first hand. One can already reason this out because an 'electron', cannot simply lose its mass for no apparent reason. Thus, when we have a condensed matter system such as this, and one talks about electrons being almost massless, this is a condensed matter physics concept, and we're talking about effective mass. You don't have to accept or believe it if you find it difficult, but that's the fact! You can take it, or leave it. It doesn't matter to me.

Zz.

 

[Mr Vibrating]

Have you tried to read the post right above yours?

What do you expect scientists to see under "billion times magnification" (there is a clear scientific description...)? Actual electrons floating about? Maybe they used tiny scales to weigh them after that?

The physorg article says they tracked the energy states of free electrons. Have you read it or just the bits i quoted?

By mobility boost. Not by decrease in mass. The electrons do not actually get lighter.

but according to physorg:

Graphene apparently owes this enhanced mobility to the curious fact that its electrons and other carriers of electric charges behave as though they do not have mass

Let me try to explain this. Graphine is effectively two dimensional. That means its phase space is also two-dimensional. That means that the radius of the Fermi surface grows as square root of electron density, rather than as cube root like in normal conductors. That means that Fermi Energy of electrons is ridiculously high. That means a big chunk of their total energy comes from momentum, rather than rest mass.

Models that are normally used to describe conduction are non-relativistic. If you use normal electron mass, at these energies, you end up with nonsensical results. The way to fix it is to pretend that electrons are much lighter, and describe behavior with these lighter electrons. These are your quasi-particles with almost no effective mass. It's just a description. Nothing else. The actual physics and the actual conductivity properties are described by physics of real electrons with normal mass. Then these light electrons are invented to describe the same qualities of material with simpler physics. It's the conductivity that forces you to use the low mass.

And if you open up any descent book on Solid State Physics and just start reading, you can learn about it. I cannot explain to you what takes several weeks of lectures over a few posts in a forum. I told you what these articles mean, if you want to actually understand it, you'll have to read a textbook. That's how it works with physics forums.

Charming exposition lol but are you saying that is the extent of these "independent discoveries" - the mere application of an already-existing curve fitting model? Because the thrust of the issue as far as i could make out were findings that unbound electrons were behaving more like bosons, and that this was the underlying mechanism behind the mobility boost.

Not that the property of effective mass was being adjusted to compensate the effect. Why the papers and big announcements? Why use microscopy when a pen and paper would do..?

I'll have to think it over and maybe come back when that's sunk in, cheers..

 

[f95toli]

honestly I'm not trying to advocate woo, and wouldn't bother yuz lot if i hadn't been chewing it over a good 6 months already, the fun is finding the flaws yourself after all.. but I'm stumped.

The main problem here is that there is no "easy" answer to your question, the concept of effective mass and how/why is used is very complicated and is not properly covered until you study at the graduate and post-graduate level (and then only if you specialize in an area linked to solid state physics).
It is very possible that most of the material (and in the case of the text you linked to extremely likely) that you've come across has been written by people who don't understand it themselves and many of them might not understand the difference between effective and real mass. Another problem is that graphene is still a "hot" topic and there is a lot of hyperbole, some of it coming from people who should know better.

 

[f95toli]

Charming exposition lol but are you saying that is the extent of these "independent discoveries" - the mere application of an already-existing curve fitting model? Because the thrust of the issue as far as i could make out were findings that unbound electrons were behaving more like bosons, and that this was the underlying mechanism behind the mobility boost.

Not that the property of effective mass was being adjusted to compensate the effect. Why the papers and big announcements? Why use microscopy when a pen and paper would do..?

To some extent yes. The main reason for why so many people are interested is that graphene is a very interesting material from a technological point of view and it is also a very nice 2D "toy system" which allow us to experimentally study effects that were previously only studied theoretically; but there is very little actuall new physics there (which is why there has been such rapid progress). It is mostly a case of plugging the the dispersion curve of graphene (with the "vanishing" effective mass) into existing models.

(I should perhaphs point out that I belong to a research group where there are several people who work on applcations of graphene, so I am in no way trying to diminish its importance; but it is not THAT interesting from a fundamental point of view)

 

[Mr Vibrating]

But this "mass" in graphene IS the effective mass. I hesitate to tell you to actually read the paper (S. V. Morozov et al., Phys. Rev. Lett. 100, 016602 (2008)), because you seem to have a rather adverse reaction when someone asks you to actually go to the horse's mouth and get the info first hand. One can already reason this out because an 'electron', cannot simply lose its mass for no apparent reason. Thus, when we have a condensed matter system such as this, and one talks about electrons being almost massless, this is a condensed matter physics concept, and we're talking about effective mass. You don't have to accept or believe it if you find it difficult, but that's the fact! You can take it, or leave it. It doesn't matter to me.

Zz.

If you can't provide a free PDF or summit i ain't paying to read, saw the abstract tho and while it may well deal in CMP terms it's not addressing the specific issue. If you've got a subscription Miller et al's Observing the quantization of zero mass carriers in graphene is the physorg source.

 

[ZapperZ]

If you can't provide a free PDF or summit i ain't paying to read, saw the abstract tho and while it may well deal in CMP terms it's not addressing the specific issue. If you've got a subscription Miller et al's Observing the quantization of zero mass carriers in graphene is the physorg source.

You missed the whole point of my post and the reference. You were asking why all these "effective mass" coming up. I'm showing WHY. Obviously, you didn't get it. Instead, you complained that you have no access to the paper.

Zz.