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39

The Nobel website scientific background is good. Basically, when you try to make gallium nitride, you usually end up with a material that is (1) chock-full of defects, and (2) n-doped (even when you were trying to p-dope it). So blue LEDs required The invention of MOCVD technology for growing crystals (early 1970s); Finding the right recipe to grow good ...


19

Because the electrical force on an electron is around 10^39 times that of gravity. Given the equivalence between gravitational and acceleration forces, you would have to shake it quite hard. Before you got to the point where an electron would drop out the entire material would disintegrate and all kinds of other phenomena would take precedence over you ...


14

Because there is an energy barrier between the metal and vacuum. Consider the ions in the metal as a uniformly distributed positive charge. Near the metal surface, the free electron wave function spread out a little into the vacuum, thus near the surface of metal the electric dipole forms with the electric field points to vacuum. Thus a gradual potential ...


7

The book The Blue Laser Diode: The Complete Story deals with the issues of p-type doping of GaN. The difficulty of growing high quality GaN crystalline films lies in the problem of finding a suitable substrate material. (...) The link above points to the chapter you may be interested in.


5

First let me make two comments before answering the question. The difference between metal and insulator rest in the existence of the itinerant electron Fermi surface or not. Ising (or Heisenberg) model is just an effective theory of local moments (localized electrons in the atoms), which contains no information of the itinerant electron, so there is no ...


4

I think that you are really interested in the $q$-state clock model, which is similar to the Potts model, and is defined as follows. Fix an integer $q\geq2$. For each $i\in\mathbb{Z}^d$, let $$ \theta_i \in \bigl\{\frac{2\pi}{q} k\,:\, k\in\{0,1,\ldots,q-1\}\bigr\}, $$ and define the spin at site $i$ by $$ \mathbf{S}_i = (\cos\theta_i,\sin\theta_i) . $$ The ...


4

The "critical" part was in finding and producing a structure with a large enough bandgap to produce blue photons. The first LEDs produced relatively longwave infrared (IR) photons, which have far less energy than the green or blue photons now available from LEDs. In general, the larger the desired bandgap, the harder it is to manufacture a suitable ...


3

The main justification for considering the Ising model is that it's exactly solvable in one & two dimensions (and that it shows critical behavior which is universal in some sense). It is not particularly meaningful as an approximation to a real physical system. The Heisenberg model does a much better job, but it is also a lattice model. If you really ...


2

Additionally, blue was the last of the primary colours so its invention made the production of white LEDs possible. Ordinary lamps could then be replaced with extremely energy efficient LED alternatives.


2

I wanted to post this as a comment, but it grew too long. The final question that was a bit hidden, but that several other users seemed to be also interested in, would be about why the blue LED was maybe so much harder to construct than the red one. Reading through Steve B's link to the nobel scientific background provides me with enough information that I ...


2

Critical exponents are properties of the RG fixed point that drives the phase transition. They are computed by linearising the RG flow equations close to the fixed point. The exponents are the derivatives of the beta functions evaluated at the fixed point. They know nothing of the way you approach the fixed point. In particular if you are flowing slightly ...


2

In spin liquids, the ordered state is broken by zero-point fluctuations even at $T=0$. Even though it is common for spin liquids to be frustrated, it is not necessarily so. The $S=1$ Heisenberg spin chain (AFM), for example, is a spin liquid without being frustrated. The name spin liquid comes (I believe), from the exponentially decaying correlation (like ...


2

To grasp the relevant physics at a sloppy level, perhaps you simply need a few examples. You know a concept is commonly constructed by the manner you refer to it together with other concepts. Symmetry breaking usually results in ground state degeneracy and long range order. Order parameter field aids you in identifying degenerate sectors with the symmetries ...


1

A small comment first: usually people call this theory as a Chern-Simons theory in (2+1)d, while the BF theory usually refers to a similar theory in (3+1)d. But anyways, this naming is not important. The U(1) Chern-Simons theory in (2+1)d is always formulated in the following general form $$S=\int\frac{\mathrm{i}}{4\pi}K^{IJ} a^I\wedge \mathrm{d}a^J.$$ The ...


1

By inhomogeneous I assume you mean disordered, i.e., a system with a noisy/random potential landscape. I'm not sure which Mahan book you are referring to, however I found Akkermans and Montambaux' Mesoscopic Physics of Electrons and Photons to give a good discussion of the problem of wave propagation in disordered media. Essentially the problem is "solved" ...


1

The statement is not true, because there are counter examples. A U(1) spin liquid is gapless, but it is insulating. An $s$-wave superconductor is fully gapped, but it is (super)conducting.


1

The statistical ensembles differ in the constraints imposed to them. In the canonical ensemble, the number of particles $N$, the volume $V$ and the temperature $T$ are fixed. In the grand-canonical ensemble, the number of particles is not fixed, it is determined by the chemical potential $\mu$, which plays the same role on $N$ as temperature on energy or ...


1

There is a very nice property that works, in practice, for most systems that is that of equivalence between the Gibbs' ensembles in the thermodynamic limit. The prototypical example is that of the equivalence between the canonical ensemble and the microcanonical ensemble. One way to state it is to say that the free energy $F(T,N,V) \equiv -k_BT \ln Q(T,N,V) ...


1

For a metal, the permittivity can is typically described by the Drude model with a permittivity given by, \begin{equation} \epsilon = \epsilon' - i\epsilon'' = \epsilon_\infty - \frac{\omega_p^2}{\omega(\omega - i\gamma)} = \epsilon_\infty - \frac{\omega_p^2}{\omega^2 + \gamma^2} + i\gamma\omega\frac{\omega_p^2}{\omega^2 + \gamma^2} \end{equation} where ...


1

My previous comments are almost ok, your actual problem seems to be that you do not average over the magnetization. You are measuring <cos(theta)>, which is the average of m_x. So just change m = magnetization_cossin(); to magnetization_cossin(&mx, &my); where you define void magnetization_cossin(double* mx, double* my) { int x, y, z; ...


1

Your understanding is basically correct. Some materials, intrinsic semiconductors, have small band gaps so that at room temperature (for example) there is enough thermal energy around to promote some electrons to the conduction band, and some holes to the valence band. These materials have the kind of gap that you describe, but are not insulators. Another ...


1

It is not generally true that a gapped system is insulating. Or more precisely, this statement is not detailed enough to be said true or false generically. One case where this is true is for non-interacting particles (say, free electron in a lattice). For interacting particles, it is much more subtle. In particular, just stating "gapped system" is not ...



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