Solid-state physics studies how macroscopic properties of solids (mechanical, electrical, optical, etc.) result from their microscopic structure. It usually deals with the scale where quantum properties of the particles are substantial.

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Stiffness tensor

Let's have a stiffness tensor: $$ a^{ijkl}: a^{ijkl} = a^{jikl} = a^{klij} = a^{ijlk}. $$ It has a 21 independent components for an anisotropic body. How does body symmetry (cubic, hexagonal ...
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431 views

Simple model of edge states for a two-dimensional topological insulator

Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features? See e.g. the ...
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451 views

The Hendriks-Teller Model

So I am working on understanding the Hendriks-Teller model of 1D disorder. So the way I understand it is the following. You have a random smattering of particles. Each mass is separated by some unit ...
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174 views

Discrete sum over an exponential with imaginary argument, considering only every second lattice site?

Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g., A-A-A-...-A-A (total of N sites) ...
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155 views

What does plasmon look like in 3D band structure graph?

Consider metal, and its reciprocal lattice representation with Fermi surface. What is the correct way to represent a plasmon in this system? M.b. rotating points on the surface? Or 3d membrane-like ...
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2k views

how to find the effective mass of a hole

how can we find out the effective mass of a hole,since a hole in the valence band is just an absence of electron?
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194 views

Why are free electrons free?

This is what I understand so far: in a conductor, the ions have a weak pull on the valence electrons. So when an electric field is applied, the free electrons are able to easily move about. Makes ...
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4answers
104 views

The conduction electrons in metals is a thermal phenomenon?

When applying an external electric field in a metal at absolute zero, there is electrical current? There must be thermal fluctuations in the electron's band to be occurs current?
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5answers
288 views

Is an “infinitely sharp blade” possible?

A staple of science fiction and fantasy is a blade (knife, sword, ...) that cuts through literally any solid object (wood, steel, concrete, skulls, ...) without effort, often even without the need to ...
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1k views

Continuous vs. Discrete Spectra in various materials

I read that the reason solids emit continuous spectra is that they don't have time to let their electrons decay-they are too close together. Given that electrons decay on the order of 100 nanoseconds ...
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108 views

How would a diffraction pattern change if the atoms were triangular instead of spheres?

On a related note, what's a good book/source that would answer questions that go very in depth with these kinds of "what if" questions because I am also asked the same if the atoms were long cylinders ...
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811 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 ...
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152 views

Accelerated charged particles produce electromagnetic radiation, but holes (the charge carriers) do not. Is this correct?

Holes are treated as particles in solid-state physics, so I've had some trouble with reasoning through this properly.
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316 views

What would be the basis vectors for this 2D crystal structure?

In the above image, I have a 2D crystal structure. The lattice vectors are described by: a = {-1/2, -Sqrt[3]/2}; b = {1, 0}; and the location of atoms A and B ...
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1answer
50 views

Why isn't doped silicon a strongly correlated electron system?

Most books on strongly correlated electrons claim that when the number of itinerant electrons is small and the screening length is large, that the system becomes "strongly correlated", (i.e. the ...
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4answers
344 views

Ohm's Law: Drude Model

For a very long time now, I've been thinking about the Drude Model derivation of Ohm's Law. I know that a rigorous derivation requires a Quantum Mechanical approach. However, the mere fact that the ...
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3answers
88 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: ...
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2answers
80 views

On the lattice structures of graphite

My question is the following: What causes graphite to have either a cubic lattice structure or a hexagonal lattice structure? Does it depend on how it is grown? Or is it a random process? I would ...
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2answers
457 views

Why a mono-atomic crystal layer (2D) can't be stable?

According to Peierls and Landau, 2D crystals were thermodynamically unstable. They can't exist! Of course, this theory was disapproved in 2004 (example: graphene). What is the general definition of ...
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81 views

Is this two forms of Hubbard model equivalent?

I have seen two form of Hubbard model, one is: $$H=-t\sum_{<ij>s}c_{is}^\dagger c_{js}+h.c.+U\sum_i(n_{i\uparrow}-1/2)(n_{i\downarrow}-1/2)-\mu\sum_{is}n_{is}$$ The other is a more familiar ...
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295 views

Band gaps: are they at the centre or at the edge of the Brillouin zone?

Reading about electronic band structures, I came across the following: Band gaps open at the edges of the Brillouin zone (BZ), since that is where the Bragg scattering occurs. I am slightly ...
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1answer
156 views

Questions about Statistical Mechanics

For grand partition ensemble, is it true that the introduction of chemical potential allows us to have the sum of number of the particles in each state to be the total number of particles ("On ...
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2answers
164 views

Paramagnetism and large N

In a paramagnetic system, we have: $$N = N_\uparrow + N_\downarrow$$. If we have a large system, with $N >> 1$, is it generally okay to assume $N_\uparrow \approx \frac{N}{2}$ and ...
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144 views

What does the wavevector $\textbf{k}$ mean?

In Ashcroft, Mermin Solid State Physics, Eq. 17.43 is $$ \epsilon(\textbf{k}) = \frac{\hbar^2 k^2}{2m} - e\phi(\textbf{r}) $$ where $\textbf{k}$ is the wavevector and all other symbols have their ...
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2answers
212 views

Eigenfunctions in periodic potential

For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if $$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$ and $$\operatorname ...
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1answer
52 views

Why are (most) solids periodic?

Is there a rigorous proof that periodic arrangements minimize the energy of a group of particles?
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1answer
55 views

Why is the local work function so much lesser than Work Function?

I have been trying to understand the difference between the Work function of a metal and the Local Work Function. I did some experiments to find the Local Work function of Graphite using an STM and ...
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1answer
30 views

Electric Potential of Conductors

I understand that charges in a conductor reside on the surface of a conductor. So why is it that the neutral inside of a conductor and the charged surface are at the same potential?
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1answer
59 views

Why can we allow the speed of light being infinite in case of Surface Plasmons?

I have a problem with understanding of these sentences: We have indicated in the opening paragraph of the Introduction that surface plasmon polaritons are solutions of Maxwell’s equations in ...
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1answer
61 views

What is the quantum Hall resistance R_H as a function of magnetic field?

For the integer quantum Hall effect, the resistance $R_H = h/(ne^2)$, where $n$ is some integer. All of the graphs of $R_H$ as a function of magnetic field, $B$, that I've seen show that at $B = 0$, ...
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1answer
116 views

n-p-n p-n-p and n-n-n heterostructure for LED

I was studying LED Heterostructures and I found out that my book is always giving reference to p-p-n type heterostructure. So I looked up into another book in order to find other type of ...
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1answer
63 views

Getting nonphysical results when solving for the index of refraction of a slab?

I'm trying to computationally find the refractive indices (real and imaginary) for a thin slab suspended in air (so the only indices to deal with are air and my material's). I've experimentally taken ...
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3answers
130 views

How to get conductivity from Green function $\mathcal{G}(x_1,x_2,\tau)$ of inhomogeneous system?

I'd like to study an inhomogeneous system, i.e., momentum is not a good quantum number therein. Therefore, I tried to calculate temperature Green functions like $\mathcal{G}(x_1,x_2;\tau)$, or its ...
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2answers
1k views

Manganese has more unpaired electrons than Iron so why is Iron ferromagnetic Manganese paramagnetic?

Manganese has five unpaired electrons, but Iron has four, then why is Iron ferromagnetic and Manganese paramagnetic? What's that property I'm missing?
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123 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 $$ ...
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1answer
52 views

How do you justify neglecting electron-electron interaction in the Drude model?

I'm sure there's some way to justify it. Maybe a screening effect?
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1answer
139 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 ...
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1answer
63 views

Fermi surface questions

In order to define the fermi surface we must need to know about the momentum space. But I found a little bit about momentum space. Can you elaborate it pleaese? what is the meaning of the line ...
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3answers
166 views

Holes in a P-type semiconductor under external force E

Basically in almost every semiconductor texts, there will be all these concepts concerning electrons, holes, dopants, fermi-levels. However, I have been always confused about the picture of hole ...
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1answer
129 views

Electric field and capacitance across a resistor

Using a simple lattice model of conduction, where electrons are accelerated by an electric field, and are slowed down by bumping into the lattice, you get the following equation for current density: ...
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3answers
801 views

when we rub objects together, what determines which material will pick up electrons?

For example We know glass when rubbed by silk will become positively charged while the silk will be charged negative. What exactly makes glass appropriate for losing electrons in that experiment? (
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337 views

Interpretation of the off-diagonal terms of the conductivity tensor

Say we have the electrical conductivity tensor expressed as a 3x3 matrix. I've seen that if it's cubic material then the conductivity tensor reduces to just the diagonal terms and these are equal, ...
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1answer
396 views

Distinguish electron-like and hole-like orbits in reciprocal space, with reference to the Brillouin Zones

So I have a solid state and thermodynamic exam next week and I've been going through some of the previous exams from years gone by to prepare. I came across this question "Distinguish electron-like ...
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2answers
195 views

Reciprocal lattice and phonon

As we obtain a reciprocal lattice for a given crystal we see that discrete values of wavevectors are allowed but a phonon wavevector spectrum is a continuum. Is there a relation between reciprocal ...
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2answers
114 views

What are some ways of inducing spin polarization?

I saw a talk today and they mentioned how nitrogen-vacancy diamond centers can be used to optically induce spin polarization and now I wonder what other ways there are to induce a spin polarization. ...
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1answer
406 views

Semi-conductor band-gap and deformation potential

Submitting a semi-conductor to stress leads to a deformation in the energy-bands, roughly described by:$$H_{ij} = {\cal{D}}_{ij}^{\alpha\beta}\;\epsilon_{\alpha\beta}$$ $\epsilon$ being the strain ...
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1answer
4k views

Effective Mass and Fermi Velocity of Electrons in Graphene:

In graphene, we have (in the low energy limit) the linear energy-momentum dispersion relation: $E=\hbar v_{\rm{F}}|k|$. This expression arises from a tight-binding model, in fact $E =\frac{3\hbar ...
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1answer
333 views

Formation of the overlap in metal electron bands

I understand that metals have overlapping of valence and conduction bands. But is this because there exists a partial conduction band within the top part of a metal valence band, or because the ...
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1answer
216 views

Nonlinear absorption coefficient and the band gap

How does the nonlinear absorption coefficient depend on the band gap? How can that coefficient be calculated theoretically? (Preferably with an example)
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51 views

Heisenberg Hamiltonian for spin-spin system

I wonder how we should conclude the following Hamiltonian (I mean the 32-18 in the picture below, written in solid state physics by Ashcroft & Mermin.) for spin-spin system? (It is in chapter 32 ...