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.

learn more… | top users | synonyms

1
vote
3answers
308 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
9 views

States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...
1
vote
0answers
244 views
+250

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
3
votes
1answer
61 views

How can one reasonably theoretically model polycrystalline materials?

Many techniques are taught in advanced solid state courses but they are almost all derived for perfectly crystalline materials. For example, band structure really only appears theoretically when you ...
0
votes
0answers
36 views
+100

Coordinate system for crystallographic groups

In the International Tables for Crystallography for each crystallographic group an asymmetric unit is supplied (mathematicians call this a fundamental domain of the group). This region is a bounded ...
0
votes
1answer
254 views

How do the effects of semiconductor doping affect the Hall effect?

For instance, consider number 4 and 5 in the following sample: Using the right hand rule, B points downwards, conventional current points to the right (because of the 5V battery), and therefore, ...
0
votes
0answers
12 views

Tight binding method -kittel [on hold]

Actually my study on tight binding method from Solid state physics- Kittel is in totall mess. There are couple of points I would like myself to clarify on -How $\boldsymbol{<\phi_{m}|\phi_{j}>}$ ...
1
vote
1answer
44 views

Why are (most) solids periodic?

Is there a rigorous proof that periodic arrangements minimize the energy of a group of particles?
3
votes
3answers
98 views

Statistical Mechanics - Distribution of Energies

Consider a state space $\mathbb{X}$. The probability density function under a canonical ensemble is given by the Boltzmann distribution $$\pi_{\mathbb{X}}(x)=\frac{e^{-\beta ...
1
vote
0answers
18 views

Symmetry breaking and band gaps?

Can the discontinuity in the E-K dispersion relation of a periodic lattice (at the boundary of a Brillouin zone) be understood as a consequence of breaking continuous translation symmetry into ...
2
votes
1answer
102 views

How does a band gap arise from the 3D Kronig Penney model?

The Kronig-Penney (KP) model is a classic model that is used to show that a periodic lattice of finite well potential sites will give rise to a band gap. The typical process in solving the KP seems to ...
2
votes
3answers
240 views

Distinguishable, Indistinguishable Paramagnetic Ideal Gas

In the canonical ensemble, the partition function for an ideal gas is given by: $$\frac{Z}{N!}$$ The factor $N!$ accounts for the indistinguishability of the particles of the ideal gas. What ...
14
votes
4answers
707 views

How is potential energy (PE) actually stored in a steel spring at the atomic level?

Elasticity is one the most intriguing phenomena, wiki gives a summary explanation of what happens in a steel spring: the atomic lattice changes size and shape when forces are applied (energy is ...
1
vote
1answer
30 views

How do discretize a finite crystal?

I am trying to find a general method to discretize a finite crystal system. How I have been discretizing systems so far (using Wannier functions): When you have an infinite crystal, you may apply ...
1
vote
0answers
21 views

Why does Pressure Increase the Tc (Critical Temperature) of a Superconductor?

Just a heads up - please make this answer understandable to around 1st year degree level physics - not PhD research. So I can understand it - thanks. I was wondering why they Critical Temperature ...
1
vote
1answer
39 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 ...
6
votes
1answer
133 views

Real part of the AC conductivity has a discrete spectrum => What physics?

If the real part of the AC conductivity $\text{Re}[\sigma(\omega)]$ has a discrete spectrum only, i.e., $\text{Re}[\sigma(\omega)]=a_1\delta(\omega-\omega_1)+a_2\delta(\omega-\omega_2)+\cdots,$ what ...
0
votes
0answers
12 views

Crystal in Magnetic Field

When you have a 2D crystal in a uniform perpendicular magnetic field, you can use the Peierls substitution to convert one tight-binding before-magnetic-field-band into a $q$-bands under the influence ...
0
votes
0answers
9 views

Binding forces in crystalline solids

I am referring to rocks in this instance. Individual crystals grow together in an igneous rock as it solidifies. I know that the SiO4 tetrahedron is the basic building unit of silicate minerals, and ...
1
vote
2answers
88 views

Volume of Brillouin zone is the same as Fourier primitive cell?

In Kittel's solid state text, problem 2.3, he says that the volume of the Brillouin zone is the same as a primitive parallelepiped in Fourier space. Somehow I can't see why this is true. Can someone ...
0
votes
0answers
18 views

Coupling a ferromagnet to an antiferromagnet

Consider a system composed of a thin film of FM material on top of an AFM material. From my research I found that pinning of the FM material occurs when we cool the system from $T_N<T<T_C$ to ...
3
votes
1answer
144 views

Do indirect optical transitions “cool” the material a little?

So I'm reading in Ashcroft and Mermin about indirect optical transitions: So, a photon comes in, and it only excites the electron across the indirect band gap if a phonon with the appropriate wave ...
3
votes
1answer
60 views

Lattice geometry and dispersion relation

Is there a general theorem which gives some information about which influence have the lattice geometry (for example sub-lattice structure, square lattice, honeycomb lattice, lattice symmetries, ...) ...
0
votes
0answers
32 views

The correspondence between real space and reciprocal space

From what I've learned, a point $P=(h\ k\ l)^T$ in the real space can be expressed as a linear combination of the primitive vectors $$A\left(\array{n_1\\n_2\\n_3}\right)=P$$ Where $A=(a_1a_2a_3)$ is ...
1
vote
1answer
63 views

Wannier functions on a ring

Let's say I have a single particle hamiltonian in a periodic potential, for example a 1D lattice such that: $$H = -\frac{\partial_x^2}{2m} + V(x) $$ with $ V(x+a) = V(x)$ where $a$ is the lattice ...
0
votes
1answer
36 views

Why do pores make ceramic opaque?

I want to know how a ceramic transparency is mostly affected by the pores, grain boundary, second phases etc. present inside of it, but the major contribution is due to the pores. Let's consider the ...
1
vote
1answer
182 views

Adiabatic approximation

The adiabatic approximation for solid state systems is rather radical. I was wondering in which cases it breaks down. As it is based on the idea of the nuclii being much heavier than the electrons I ...
1
vote
1answer
53 views

How does current flow in superconductors if Cooper pairs have zero momentum?

I've been reading a lot of condensed matter textbooks, which state both that the net momentum of a Cooper pair in a superconductor is zero, and that Cooper pairs have momentum when they carry current. ...
0
votes
1answer
35 views

How corner atom of a cube is shared by 8 atoms? [closed]

Since each atom is at the corner of a cube and 8 cubes meet at each corner. Therefore each atom is shared by 8 cubes. But I don't visualize it, so please tell how I Visualize it.
0
votes
1answer
79 views

How do I derive the eigenvalues of the 1D Heisenberg model? (Bethe Ansatz)

I've been trying to work through Introduction to the Bethe Ansatz I (by Michael Karbach and Gerhard Muller) in spare time and I am having trouble deriving the eigenvalues given in equation (5) for ...
0
votes
0answers
19 views

intervalley optical phonon scattering

Is there any difference between intravalley and intervalley optical phonon scattering self-energies in NEGF method?(except that electron-phonon coupling constants)
0
votes
1answer
77 views

Photoelectric Effect - How are the electrons regained?

When the photons with enough energy impinge on a photocathode, it emits electrons. Does this mean that the solid will lose all its electron at one point? If not, how are electrons restored?
0
votes
0answers
29 views

Hartree Fock exchange kernel

I would like to understand, how we calculate the exchange kernel of the Hartree Fock equations for a coulomb potential. So in slide 19 here for example you see the result, but I have not the ...
0
votes
2answers
67 views

Bragg diffraction and lattice planes

Crystalline substances show, for certain sharply defined wavelength and incident directions, very sharp peaks of scattered X-ray radiation. From the illustration below we see that we get constructive ...
0
votes
0answers
17 views

How does quantum confinement happen in amorphous or polycrystalline materials?

You can easily find papers where they make a nanostructure (thin film, nanowire, or quantum dot) from methods (ALD, CVD, thermal/egun evaporation) that produce amorphous or polycrystalline structures ...
0
votes
0answers
21 views

Crystallography and symmetry operations

I am trying to figure out the basis for deuterate solid state water. To do so I took the position of the basis atoms from http://rruff.geo.arizona.edu/AMS/amcsd.php and then I applied the symmetry ...
0
votes
1answer
46 views

A problem about solving energy bands by the method of second quantization

In hopping model, we can get the Hamitonian as $H_0=-t\sum a^\dagger_ia_{i'}$. Then we take the fourier transform and put the operator which are in momentum space in the Hamitonian above. However, I ...
0
votes
0answers
36 views

Why don't electrons simply diffuse back when illuminating a photodiode?

Assuming you connect the cathode and the anode with a conductor (no sources), why can't the electron-hole pairs created by the photons diffuse back instead of going through the wire? My reasoning is ...
0
votes
1answer
23 views

Crystal lattices in solid state

I found this problem in Christman's book fundamental of solid state physics What is the Miller index for a plane parallel to both $3\vec{a}+\vec{c}$ and $\vec{b}$, in any lattice?
5
votes
1answer
70 views

To what extent can the superconducting order parameter be thought of as a macroscopic wavefunction?

I know that the order parameter does not obey the Schrodinger equation; it instead obeys the Ginzburg-Landau equation. However, I am unclear as to the situations under which the view of the ...
0
votes
0answers
20 views

Screened potential of charged impurity in a 2-dimentional electron gas

What's the analytical relation of screened potential of charged impurity in a 2-dimentional electron gas?
2
votes
0answers
44 views

Time reversal operator in tight-binding model with second quantization form

In tight binding model, $H=\sum_{r,r'}ta^{\dagger}_{r}a_{r'}+h.c.$.When now conducting a time reversal transformation, what form will this Hamiltonian like? Or how can I express time reversal ...
3
votes
1answer
153 views

In a positively biased PN junction, where do the injection carriers come from?

I am not quite understand i-v character of PN-junction diode. Here is the model in textbook. The PN junction diode can be divided into three regions. They are One depletion region near the PN ...
1
vote
1answer
215 views

Intro to Solid State Physics

I didn't see this listed on the books page so here it is. I'm currently in an introductory Solid State course, and we are using Kittel's book. I have been having a rough time with this book although I ...
1
vote
2answers
73 views

Thomas - Fermi screening

I read in Ashcroft & Mermin's Solid State text that for the Thomas-Fermi approximation to be applicable, the external potential needs to be "slowly varying," What does it mean for a function (in ...
1
vote
1answer
39 views

Influence of applied voltage to an electron of a metal

I would like to ask what would happen to the potential well of an electron being trapped in a metal? If I apply a voltage trying to accelerate the electron out of the potential well. Would It make the ...
0
votes
1answer
26 views

Question about the derivation of tight-binding model in the form of second quantization

There is a step in such derivation that I cannot follow. That is eq(1.74) in http://www.itp.phys.ethz.ch/education/fs13/sst/Lecture-Notes.pdf in page 21. How does these non-crossing terms vanish? ...
1
vote
0answers
27 views

A model for surface adsorption

I have been trying to model the adsorption of an inert gas on the surface of a clean solid. So far my underlying goal is to express the Gibbs energy as a function of the number $N$ of adsorbed ...
0
votes
1answer
173 views

Temperature in a Voltaic Cell

The potential difference across a voltaic cell varies with temperature. But my question is whether the voltage increases or decreases as temperature rises. According to the Nernst equation, the two ...
2
votes
1answer
25 views

The Debye temperature for diamond

To simplify the calculation, let's assume that the average speed of sound in the diamond is simply $v_s=\sqrt{E/\rho}\simeq1.414\times10^4 \ \text{m/s}$, and the Debye frequency $$\omega_D=v_s\left( ...