# Tag Info

7

I am still not sure what you precisely want to be a Klein Bottle, but let me make some comments that might help you clarify what exactly you want to know. (Warning: I am writing this while being very tired, people are invited to correct me.) First of all one must be careful to distinguish band structure of the bulk from band structure of a semi-infinite ...

5

As an ex-physicist who now works as a quant in power markets I think it's safe to say the physics of the matter will be swamped by the economics in commodities and how power markets work. Two things to note: power prices are set by markets and not by the viability of the technology (prime mover) solar is hard to make money with w/o a long term Power ...

5

Although it's not strictly what happens, you can think of the bonds around a carbon atom as repelling each other because the electrons localised into those bonds want to get as far away from each oither as possible. That's why when a carbon atom forms three bonds you get the bonds separated by 120º. When you have four bonds they arrange themselves into a ...

3

There is such a material where each carbon atom binds to four other atoms. It's not a square lattice (due to the character of the so-called sp3-hybridization: the energetically most stable configuration is in 3D, not 2D). There are several standard bondings for carbon (and many other materials): the sp2-hybridization is in 2D and has three bonds (like ...

3

According to this article: http://physics.aps.org/articles/v5/24: The statement that in graphene the "conduction electrons are massless" is because the energy levels (bands) are proportional to their momenta. So the $E = \sqrt{p^2+m^2}$ relation of a free electron becomes $E\propto p$ in graphene. Massless particles travel all at the same speed because ...

3

A decent terrestrial space elevator could be built with a material with a tensile strength of 50 Gigapascals (including a decent safety factor), so this material may suffice. Note that there is no prospect of having one 100,000 km nanotube - they would actually be much shorter (maybe 10 cm) and held together by the much weaker inter-tube molecular bonds (if ...

2

When the Möbius strip is cut down the middle you don't get two cylinders. See here and here for example. Fig. 3(b) should be interpreted as two cylinders, each with an extra (and different, thus two cases, $y<0$ and $y>0$) on-site potential that accounts for the twist. After the transformation the field operators obey periodic boundary conditions so ...

2

1) The Bloch theorem comes from the fact that the group of translations is Abel, thus its representations are defined by number which is called $\mathbf{k}$. It means that when you translate (by let's say vector $\mathbf{a}$) the wavefunction with given $\mathbf{k}$ it is multiplied by exponent $e^{i\mathbf{ka}}$ (more or less by definition), which gives you ...

2

The answer you'll get from most high-energy physicists is that there are no implications whatsoever. Lorentz invariance is extraordinarily well-tested: see, e.g., http://arxiv.org/abs/0801.0287. In particular, there are many relevant operators in the Standard Model that one would expect to be generated if physics at a high scale is not Lorentz-invariant. ...

2

When silicene is buckled on the substrate it has a substantial band gap or in other words it can be turned on or off thus making it appropriate for digital applications. Graphene doesn't have a band gap so it isn't so good for digital circuits. Although techniques have been developed to produce a band gap and transistors have been made, they say that the ...

2

The group velocity $v_g$ of a wave packet (that's the speed of the maximum of the wave packet) is given by $v_g=\frac{\partial\omega}{\partial k}$. In this case, $\frac{\partial\omega}{\partial k}=\frac 1 \hbar\frac{\partial E}{\partial k}$, which easily evaluates to $v_g=\frac{3ta}{2}=:v_f$ for $k=0$. That's actually the definition of $v_f$: it is the group ...

1

I think you are looking for something like this: We measured the elastic properties and intrinsic breaking strength of free-standing monolayer graphene membranes by nanoindentation in an atomic force microscope. The force-displacement behavior is interpreted within a framework of nonlinear elastic stress-strain response, and yields second- and ...

1

In the atomic ground state a carbon atom has the electronic configuration $1s^22s^22p^2$. In the sp$^2$ hybridization the $2s$, $2p_x$, and $2p_y$ participate in the formation of the three $\sigma$ bonds and the $2p_z$ orbital forms a $\pi$ bond. According to molecular orbital theory this $2p_z$ state would form the bonding ($\pi$) and anti-bonding orbitals ...

1

Resistivity is the relevant parameter for three-dimensional materials. Sheet resistance (less commonly called "sheet resistivity") is the relevant parameter for two-dimensional materials, and its inverse is called "sheet conductance" or "sheet conductivity". In the Novoselov paper you cited, they talk about sheet resistance and sheet conductance. Please ...

1

There are, in fact, a wide variety of techniques for producing graphene other than the scotch-tape method. A very good review of these techniques can be found in this recent review article: http://onlinelibrary.wiley.com/doi/10.1002/adma.201202321/abstract It is extremely difficult to obtain the dimensions you require using the scotch-tape method. In my ...

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The real economics will come into play via electricity. Space based solar transmitting electricity down graphene cables solves our energy crisis basically forever. Once you build the first cable, building more is an order of magnitude cheaper. Once you make that initial investment, the solar farms become trivial, although it will take years if not decades to ...

1

In the paper of J.M. McCLURE(1956), he showed how to directly calculate the momentum matrix. (eq.2.5,2.6) Diamagnetism of Graphite,Phys. Rev. 104, 666–671 (1956) http://prola.aps.org/abstract/PR/v104/i3/p666_1

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Sorry, just a reference. Both Neumann and Dirichlet boundary conditions occur. See http://www.springerlink.com/content/h757664275612765/ "Hexagon quantum billiard."

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