1
vote
0answers
59 views

Energy of an Electron in a One Dimensional Periodic Potential

First, we consider the time independent Schrodinger equation of the form: $$\bigg(-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+u(x) \bigg)\phi_A(x)=E_A\phi_A(x)$$ Where $u(x)$ is a potential created by a ...
4
votes
1answer
87 views

Crystal Momentum in a Periodic Potential

I'm working through some basic theory on periodic potentials, and I would appreciate help in understanding the crystal momentum. Suppose we have a Bravais lattice with lattice vectors $\textbf{R}$. ...
0
votes
1answer
43 views

Jahn-Teller effect is based on the Born-Oppenheimer approximation?

I am now reading the quantum mechanics textbook by Landau and Lifshitz. In section 102, they discuss the Jahn-Teller effect. It seems that they assume the Born-Oppenheimer approximation. There is ...
3
votes
0answers
59 views

Why do people say “Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon).”?

Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st ...
1
vote
2answers
83 views

Bloch theorem, Energy, Free electron

I'm trying to learn on my own a bit of solid physics to tackle semiconductors afterwards. I'm struggling with the Energy versus $k$ diagrams for a free electron which shows that for a single value of ...
2
votes
2answers
77 views

What is the performance of a silicon crystal that makes it an essential component to computing

I'm on a thread of interest in the precise physics that allow the creation of the computing process. It began as a question posted in search of an understandable explanation of what physical form ...
-1
votes
0answers
23 views

why does muon hop rate in metals change with temperature like this

you can find this figure in this pdf we use ╬╝SR to study the superconductor properties,,but I don't quite understand the T^-9 slope, does muon trapped in an interstitial site and hop rate drop with ...
2
votes
4answers
164 views

I don't get band structure of solids

If the energy levels of bound electrons are discrete, why do band structures in solids arise?
1
vote
1answer
63 views

Sold-State Band Structure - connection between Fermi Energy, Fermi Level and Work Fuction

I've been struggling with the concepts of these three terms - Fermi Energy, Fermi Level and work fuction. Now, I was given these definitions (in the context of semi-conductors): Fermi Level is the ...
4
votes
1answer
99 views

Why is effective mass of holes positive?

i am trying to understand this. I know that the effective mass of electrons or holes is calculated as: $$m^* = \frac{h^2}{(4\pi^2)\frac{d^2E}{dk^2}}$$ Now,if i look at this plot for example: I ...
0
votes
0answers
21 views

Why a multilayer OLED is generally more efficient than a single layer OLED?

Could anyone give me a brief explanation why multilayer OLEDS as more efficient than single layer OLEDs? What other advantages exist for multilayer OLEDs over single layer OLEDs?
2
votes
1answer
140 views

Does the Bohr van Leeuwen Theorem also apply to ferromagnetism?

I know that the Bohr-van Leeuwen theorem shows that there could be not consistent pure classical explanation of dia- and paramagnetism. Does the same theorem also rule out a consistent classical ...
3
votes
1answer
57 views

Is the ferromagnetism of iron understood completely?

In Feynman's lecture notes, he said that it is not (at his time). How is the situation today? Can first-principle calculation accounts the ferromagnetism of iron quantitatively now?
1
vote
0answers
22 views

Magnetic moment with external magnetic field on a lattice?

Consider a system in which atoms are located in a regular lattice, each atom having a spin $1/2$ and an associated intrinsic magnetic moment $\mu_0>0$. Assume that each atom interacts only weakly ...
1
vote
1answer
55 views

Coulomb potential in atoms other than hydrogen

The energy of an electron on $H$ atom is given by the formula: $-13.6 \; \text{eV}/n^2$. The constant value is born from $H$ dielectric constant and efective mass of the electron. My question is: ...
1
vote
3answers
59 views

Excitons in metals-do they exist?

Recently I red an article "Surface Enhanced Fluorescence". It is a topical review by Emmanuel Fort and Samuel Gresillon. Here it is: ...
2
votes
1answer
63 views

Hamiltonian for the Periodic Kitaev Model

The Hamiltonian for a system of spinless fermions on a 1D chain (with chemical potential $\mu=0$) is given by $$ H=-\sum_j\left( c^\dagger_{j+1} c_j+h.c.\right)+\Delta \sum_j \left( ...
1
vote
0answers
50 views

Should Brillouin zone be a continuous object rather than a discrete one in the thermodynamic limit?

For example, just consider a 1D atom chain with $N$ sites and lattice constant $a=2\pi$, under periodic boundary conditions, the crystal momentum reads as $k=\frac{n}{N}\frac{2\pi}{a}=\frac{n}{N}$, ...
0
votes
0answers
21 views

Interpreting current in a material as a Stark effect

I apologize if my question is silly but here it is. In the physics of atoms and molecules, we learn about the Stark effect which induces a splitting of degenerate energy levels into sub-energy levels ...
2
votes
1answer
88 views

Kronig-Penney model

I am studying the Kronig-Penney model as treated in the book by Kittel: Introduction to Solid State Physics. In this model one considers a period potential which is zero in the region $[0,a]$ ...
2
votes
2answers
149 views

Bloch's theorem

I am studying Bloch's theorem, which can be stated as follows: The eigenfunctions of the wave equation for a period potential are the product of a plane wave $e^{ik \cdot r}$ times a modulation ...
2
votes
1answer
49 views

How does band gap vary with the cell volume?

How does band gap vary with the cell volume? is there a relation? If the volume is compressed, the interaction between atoms would be more, therefore the perturbation is higher hence the splitting ...
-1
votes
1answer
45 views

Band structure and band index

Please let me know If my understanding is right. For a given $\vec{k}$, $H$ is a function of $\vec{k}$ the energies vary discretely for $n$ ie.,the band index. For a given $n$, we choose all the ...
0
votes
0answers
48 views

Density of States of Free Particle in One Dimensions

I am using Quantum Mechanics by David H. McIntyre, chapter. This is problem 15.7: Find the density of states $g(E)$ for the case of a free particle in one dimension; further, show that the density of ...
1
vote
0answers
54 views

Ion-neutralization processes and its energies

Ionization energies/Electron affinities are well mapped. I wonder about opposite processes... I imagine for anion the necessary energy will be equal to the electron affinity (energy released when ...
0
votes
0answers
46 views

band gaps in tight binding model

What happens at the zone boundaries of the brillouin zones in the tight binding model? How does the band gap originate in the TB model?
2
votes
0answers
29 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
1
vote
0answers
71 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
0
votes
2answers
45 views

Why does chemical potential smaller than zero mean nondegeneracy and vice versa

In Mudelung's book, Introduction to Solid-State Theory, I have a confusion about the statement. Here, $x$ should be $\frac{\mu}{k_B T}$. I am cofused about his statement. Why does $x<0$ mean ...
4
votes
2answers
185 views

Why does $c_{-k,-\sigma}$ create a particle with momentum $k$?

In Mudelung's book, Introduction to Solid-State Theory, I am confused by the following statement. For many applications a further simplification is helpful. The concept of the hole presents us ...
2
votes
0answers
105 views

Derivation of existence of energy band gap in semiconductor (solid State)

I am looking for both a mathematical and a physical reason for energy band gap in metals. For Physical reason, I was told that at each reciprocal lattice, you could have Bragg scattering, that would ...
1
vote
1answer
73 views

What is the significance of the difference in the eigenvalue equations of Bloch functions for electrons vs photons?

any text on photonic crystals will highlight the almost perfect analogy between electrons in a periodic potential and photons in a periodic dielectric. The analogies are: $$V(\vec r + \vec R) = ...
3
votes
0answers
44 views

Separating the hamiltonian for a superlattice — is it this easy?

I've been banging my head against a wall trying to figure out what I'm sure is a very simple problem. I want to solve the Kronig Penney model for a superlattice, which is just a normal periodic 1D ...
1
vote
2answers
434 views

Dispersion Relation (e vs. k) clarification (crystal momentum or electron momentum)

If we get the dispersion relation from the Fourier transform of the lattice vectors then how do we get electrons information? Specifically, for the $k=0$ point of the graph, does this mean the ...
2
votes
2answers
162 views

A conceptual question about Green's function's treatment of interaction

Here we have electron gas and some other stuff. We expand the Hamiltonian to the 1st order of one single harmonic oscillator's displacement $\vec{u}$. Its equilibrium position is at the origin. Then ...
0
votes
2answers
71 views

Is crystal momentum an operator?

My teacher has for Bloch waves the notation $\langle \vec{r}|\vec{k} \rangle = e^{i\vec{k}\cdot \vec{r}}u_{\vec{k}}(r)$ and uses it consistently. However, does this not assume that there is an ...
0
votes
0answers
25 views

Is there a generic term for orbital groups such as $e_g$ and $t_{2g}$?

I am looking for a generic term for sets of atomic orbitals (viz. spherical harmonics) which are grouped by crystal symmetry. The most familiar examples would be $e_g$ and $t_{2g}$ (in cubic ...
1
vote
1answer
120 views

When can i separate spin from the wavefunction?

I am currently working on a Tight-Binding model and for the derivation of nearest neighbor spin interactions I have terms like $$ ...
3
votes
1answer
126 views

Group analysis forbids band-crossing in 1D?

Group analysis forbids band-crossing in 1D in terms of conventional band theory. I read this in a good solid state physics book. But there's no explanation at all. Can anyone help on this?
3
votes
3answers
122 views

Why can we quantize macro(meso)scopic harmonic oscillator?

It is well known that we have got many kinds of quantized macro(meso)scopic harmonic oscillators or so in tiny mechanical systems. People are talking about cavity cooling and so on. However, it is ...
0
votes
1answer
191 views

Overview and doubts about Bloch's theorem and the concept of partial density of states

So I have a large confusion with QM as applied to solid state. The following is a summary of what I know, what I think I know, and what I know I don't know. I hope to stir a discussion that will help ...
1
vote
1answer
109 views

Density of states (treating states in continuum)

If we have a particle in a 3D infinite square well box, with length $L$, e.g. an electron in a conduction metal. By solving the Time independent Schrodinger equation, we can get the formula of ...
2
votes
2answers
450 views

How to interpret band structures

I'm currently taking a Solid State Physics class, and is currently reading about the quantum mechanical description of solids. I then came across the following figure: It's supposed to be the band ...
1
vote
1answer
58 views

Possibility of stable muonic structures?

In an analogy to the neutron, which decays rapidly as a free particle, but when bound in a nucleus it is stable, would it be possible to crease a structure that permits the stability of muons - be it ...
1
vote
2answers
174 views

Bloch wave function orthonormality?

there is this text book that is giving me a hard time for a while now: It shows that Bloch wave functions can be written as $$\Psi_{n\vec{k}}\left(\vec{r}\right) = \frac{1}{\sqrt{V}}e^{i\vec k \vec ...
0
votes
0answers
142 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec ...
2
votes
2answers
686 views

Determining if a semiconductor is n-type, p-type or intrinsic

The probability that an energy state in the conduction band is occupied by an electron is 0.001. Would this semiconductor then be n-type, p-type, or intrinsic? Notation that I use: $E_F$ represents ...
0
votes
1answer
102 views

Photoelectric effect high frequency limit?

The photoelectric effect has a low frequency limit below which nothing is observed. Increasing the frequency energy is enough to free an electron. Continuing to increase the frequency the material ...
2
votes
1answer
339 views

Derivation of Matrix Components of Hamiltonian in Tight Binding Method

Im currently struggling with the description of the tight binding method in the original paper by Slater and Koster from 1954 (where a free version of the paper can be found under this link). In ...
2
votes
1answer
174 views

Connecting Fermi levels and band diagrams to potential diagrams?

I'm trying to make sense of how you can find the potential diagram given the band diagrams of a few adjacent materials. As a simple example, in semiconducting heterostructures, if you have sandwich ...