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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Why are $2\pi$ factors included in the definition of the reciprocal lattice?

I would like to know where the $2\pi$ factors are coming from in the formula for reciprocal vectors in reciprocal lattices. For example, in a simple cubic lattice the primitive vectors are given by ...
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81 views

How to compute matsubara frequency summation over computer?

Matsubara frequency sum usually takes the following form: $S_\eta = \frac{1}{\beta}\sum_{i\omega_n} g(i\omega_n).$ But in my problem, $g(i\omega_n)$ is a lengthy expression, which can not be ...
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Intuitive explanation for the space-dimension dependence of the density of states of a free electron gas

If the Schrödinger Equation is solved in different dimensions for an independent electron in an infinitely high potential, different relations are obtained regarding the DOS. These are: 0D: $D(E) ...
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Work function definition

As in this post How would I calculate the work function of a metal?, the definition is given by "the minimum thermodynamic work (i.e. energy) needed to remove an electron from a solid to a point in ...
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45 views

Why is graphene robust, but graphite not?

Graphite can be thought of as various layers of graphene mounted on top of each other. Graphene is known to be as robust as diamonds, yet graphite can be found in pencils and we all know from ...
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FCC lattice as a stack of triangular lattices

According to Marder, Condensed Matter Physics, Chapter 2: Within the planes normal to the vector [1,1,1], the atoms of an fcc lattice lie in a two dimensional triangular lattice However, he does ...
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Proof that all primitive cells have the same size

A primitive cell of a crystal lattice is a set $A$ such that two copies of $A$ which are translated by a lattice vector do not overlap and such that $A$ tiles the entire crystal. I have read (for ...
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Is there anything akin to molecular chirality for crystalline? [migrated]

For example, in hexagonal closed-packed (HCP) structure, the atoms may be arranged in ABAB stacks or ACAC stacks. Can these two be considered enantiomers? Do they possess different solid state ...
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How differing height of original potential barrier leads to differing energy bands [on hold]

Question: How does differing the height of original potential barrier leads to differing energy bands. From my understanding, (and using the Kronig Penney potential model) lowering the potential ...
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To what extent is the Stoner model relevant for iron?

It is indeed simple and can account for several facts. But the interaction term is a bit artificial. So, to what extent is it relevant?
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39 views

Difference between adsorption and condensation

So I just stumbled across the Wikipedia article on adsorption - and I asked myself, if there is a difference between (physical) adsorption and condensation on a surface? When I look at the water ...
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Is there an intuitive reason for why the reciprocal lattice of FCC is BCC and vice versa?

This can be proved using formulae for generating reciprocal lattice vectors from direct lattice vectors. But does this result have more to it than meets the eye?
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How to prove Bloch function is periodic in reciprocal lattice?

How to prove Bloch function is periodic in reciprocal lattice? I saw in some textbooks this formula: $$ \Psi_{\mathbf{k}} (\mathbf{r}) = \sum_{\mathbf{G}} ...
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38 views

Why is temperature vibration?

Why do the atoms in a crystal vibrate at finite temperature?
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65 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 ...
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27 views

Can the Fermi level go above the conduction band energy if doped heavily enough?

So for n-type Si with donor density $N_d$ and donor energy level $E_d$, $N_d^+ = N_d(1+\frac{1}{1+e^{\beta (E_d - E_f)}/2})$ is the number of ionized donors, so we get an relation between the number ...
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75 views

Goldstone modes of spin density wave

A spin density wave (SDW) is a phase in which a material suddenly shows a periodically modulated spin density $S_{\vec{q}}(\vec{r}) $ below a certain critical tempereature $T_C$. Obviously some kind ...
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Effective mass vs. cyclotron mass of electrons in graphene

Graphene possesses the highest charge carrier mobilities if the Fermi level is close to the Dirac point [see e.g. DOI 10.1103/PhysRevB.81.195434]. The band dispersion is approximately linear to 0.9 eV ...
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Why is Graphene So Strong?

There has been a lot of news about Graphene since its discovery in 2004. And as we are all told it is a revolutionary material which is very strong, conductive and transparent. But what is it about ...
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260 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 ...
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What are the possible reasons of deviation from Curie Weiss behavior well above Tc?

I think existence of other weak interactions which have higher transition temperature than the observed prominent interaction(ferro/antiferro) can perhaps lead to such result but I am confused when ...
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19 views

Chemical potential and origin of pressure in a solid

Pressure of a gas is related to the rate of change of momentum of the particles; the temperature is the mean kinetic energy of the particles. Can the chemical potential be given a similar physical ...
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3k views

Can plasma turn back into gas, solid, or liquid?

I wanted to know if, since basic chemistry teaches you that states of matter can be changed, I was wondering particularly about plasma. I know that virtually all of the Sun is plasma, so I was ...
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Crystal momentum and the vector potential

I noticed that the Aharonov–Bohm effect describes a phase factor given by $e^{\frac{i}{\hbar}\int_{\partial\gamma}q A_\mu dx^\mu}$. I also recognize that electrons in a periodic potential gain a phase ...
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39 views

Are the 14 Bravais lattices really distinct?

I have learned that there are 14 distinct Bravais lattices in 3D and any other thought lattice form could be reduced to or expressed in one of these 14 forms. But the primitive unit cell for f.c.c ...
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280 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 ...
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What material could be used to study magnetic phase transitions in a college laboratory exercise?

I am working to develop a simple laboratory exercise in solid state physics to be conducted by fourth year students of physics. The idea of the exercise is for the student to get some experience in ...
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23 views

Why is conductivity isotropic in a plane perpendicular to the z-axis of a tetragonal crystal?

Considering the symmetry of a tetragonal crystal, how can it be proved that conductivity is isotropic in a plane perpendicular to the z-axis?
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73 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, ...) ...
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48 views

My model of Conductors in “static” condition

My textbook presents an idealization of a conductor as made up of infinitesimal units of charge and derives results. I was not convinced, so I started thinking of how electric fields are in real ...
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45 views

How to find dispersion relation for 1 d topological insulator?

Is it correct to write the dispersion relation for following Hamiltonian where $\sigma_{x}$ act in spin space and $\tau_{x}$ acts in pseudo spin particle hole spin $H_{BdG} (k)=(\xi_{k}+B\sigma_{x}+u ...
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277 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 ...
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1answer
158 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 ...
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201 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 ...
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75 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 ...
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60 views

$T$-invariant Hamiltonians

If $T$ is time-reversal transformation $t\mapsto -t$, Why do $T$-invariant Bloch Hamiltonians obey $$H(-k) = T H(k) T^{-1}$$ and not $$H(k) = T H(k) T^{-1}$$ Somehow I understand the word "invariant" ...
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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. ...
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98 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?
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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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intervalley optical phonon scattering

Is there any difference between modeling of intravalley and intervalley optical phonon scattering in solid?
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77 views

What does $m^*>m_e$ imply? (the effective mass of electron is larger than its rest mass)

From what I understand, the concept of effective mass is just something people come up with to make electrons and holes obey the equation of motion $$ \vec{F}=m^* \vec{a} $$ without dealing with the ...
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Trace part of Hamiltonian

Given an electron in one discrete dimension, the Hamiltonian is given by $H_{n,n'}\in Mat_{N\times N}\left(\mathbb{C}\right)$ acting on $l^2\left(\mathbb{C}^N\right)$ where $N$ is some integer ...
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Optical mode leakage through a layer of gold

The geometry of my semiconductor device is given below. The blue regions are gold, the grey ones - gallium arsenide (n-doped to $2.9 \times 10^{15} \mathrm{cm^{-3}}$). The dimensions are μm, i.e. it ...
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95 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 ...
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799 views

How quickly is motion transferred in a solid object?

Just for example: assume an iron bar one foot in length. If you push on one end, the entire bar will move. This seems instantaneous. but actually, from my understanding, the atoms all push against ...
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Is Differential Geometry used in Solid State?

I'm an undergraduate in physics interested in a career in solid state. While I know that any additional math is helpful--I am on time constraints, and can only take a few supplemental classes. That ...
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1answer
24 views

Resistance of a diode in different regime and the physics of recombination current

I would like to ask question about the resistance of a diode under different regime. Surely, in reverse bias, it has a breakdown voltage, and in forward bias,it rises exponentially according to the ...
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1answer
111 views

Is carrier charge density and carrier mobility constant in a given material?

If we assume the semi-conductor is doped by a variable amount, is there some way I can look up carrier charge density for the material in a reference somewhere? What about carrier mobility?