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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How is contact resistivity defined for a Schottky contact, or the Schottky barrier height for an ohmic contact?

Based on the transfer length method (TLM), one can accurately calculate the contact resistivity for an ohmic contact, by evaluating the absolute resistance measured through the test structure and ...
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47 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 ...
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140 views

Energy dispersion in graphene

Given that graphene has linear energy dispersion near the Fermi level and the dispersion is given by $E=\hbar \nu_F|\vec{K}|$, I would like to determine the density of states. I think it is equal to ...
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59 views

Frequency dependence of permittivity — why not monotonic?

I naively thought that most materials were transparent to radiation of frequencies above their plasma frequency, and opaque to radiation below it. The most intuitive (and analyzed lightly in ...
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203 views

Absorption of a gas into a solid

When a gas interacts with a (crystalline) solid, some scenarios may happen: scattering: gas atoms will not stick or penetrate (do not interact with the solid) Adsorption: gas atoms stick to the ...
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392 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 ...
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589 views

Partition Function for Two Level System

I have a system with $N_s$ sites and $N$ particles, such that $N_s >> N >> 1$. If a site has no particle, then there is zero energy associated with that site. The $N$ particles occupy the ...
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62 views

Why do excitonic absorptions have small bandwidth?

Below is an image of the optical density (proportional to the absorption coefficient) of KBr crystal at low temperature. Indicated at 6.6 ev and 7.7 eV are the absorption by excitons. As you can see, ...
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333 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 ...
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180 views

A few questions about the Fermi Level/Energy

My first question is, how is the Fermi Energy for a material actually determined? I know this derivation, but it seems to say that the Fermi Energy is just based on the electron density (and maybe ...
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204 views

Difference between charge density wave and charge distribution

We can always see modulated charge density, the Friedel Oscillation, around an probe charge due to other electrons' response. Can this be called charge density wave (I believe not)? If not, what is ...
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283 views

valence bands in graphene

In Graphene, each carbon use 3 electrons to form sp2 bonding with neighboring, and in a unit cell, there are 2 carbon atoms, so at least these 6 electrons contribute to 6 valence bands. Then my ...
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103 views

Is this 2D structure triclinic?

The only rotation axis obvious to me is rotation by 360 degrees, the identity. Vertical mirror planes I've been dicing and cutting it through several planes and I still see none. Yet, the structure ...
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176 views

What are the rainbow and ladder approximations in a solid state physics context?

All references I find talk about quarks and gluons, where I have only very limited knowledge about. From it's name (rainbow) I guess it applies to fermions coupled to bosons and we're interested in ...
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218 views

I can't figure out crystal planes with negative intercepts

As seen above, I don't follow how you figure out those planes. It seems they're not using the origin labeled. I'm not really sure I understand spatially what's going on in the left figure so let's ...
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134 views

Electric current streamlines in induction cooking vessel

I am looking for a plot of the typical streamlines of the electric induced currents ("eddy currents") in a induction cooking vessel. How can one theoretically predict the streamlines? How is it ...
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75 views

Estimate the difference between two sets of atoms

I've been working on amorphous structures derived from a crystalline one (using MD) containing $N$ atoms. I want to prove that these structures are different and to quantify their "differentness". One ...
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166 views

Dispersion relation in continuum mechanics

I'm looking at the vibration of a solid having a lattice structure, they obey the following equation: $$\rho\partial_t^2u_i = C_{ijkl}\nabla_j\nabla_ku_{l}$$ with $u(\vec{x},t)$ the displacement to ...
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117 views

How creation of point defects in semiconductors is affected by strain?

When the effect of the strain on solids is discussed, normally the explanation is the following: increasing stress, first point defects created, then dislocations, then plastic deformation starts, ...
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211 views

Inhomogeneous Effective Mass in a 2D Lattice

Consider a tight-binding square lattice in 2D. This lattice has two different nearest neighbor tunneling rates along the x and y directions; call them $J_{x}$ and $J_{y}$. All longer range tunneling ...
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587 views

How robust is Kramers degeneracy in real material?

Kramers theorem rely on odd total number of electrons. In reality, total number of electrons is about 10^23. Can those electrons be so smart to count the total number precisely and decide to form ...
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292 views

A question about definition of Fermi energy

Wikipedia states the definition of Fermi energy as for "a system of non-interacting fermions". If we have to assume free electrons in a solid behave this way before we are able to calculate Fermi ...
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202 views

Fourier analysis in crystallography

What is the best reference for an introduction to the use of Fourier analysis in crystallography?
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735 views

Effective mass in Aluminium lattice?

How do we calculate the effective mass of an electron in an Aluminium lattice? Is there any simple analytical way to work it out?
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In k$\cdot$p theory, how does one calculate the bulk inversion asymmetry coefficients given in table 6.3 in Winkler?

In k$\cdot$p theory, how does one calculate the bulk inversion asymmetry coefficients given in table 6.3 in Winkler? Winkler's book on spin-orbit coupling effects is available free online. In ...
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49 views

What are hot electrons?

What are they? How are they created? And what do they have to do with plasmons? I searched the web, but I would like more reliable and straightforward sources.
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72 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 $[0,a]$ ...
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83 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 ...
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What is $\epsilon_\infty$ in this equation and why can it be neglected in the IR?

I'm reading this paper (warning, PDF) and they mention that the complex permittivity $\epsilon$ and complex conductivity $\sigma$ are related through the equation $$\epsilon - \epsilon_\infty = (4\pi ...
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35 views

Force constant of metals - Kohn anomaly

In Introduction to Solid State Physics (Kittel), it assumed the force constant between plane $s$ and $s+p$ $C_p=A\frac{\sin pk_0a}{pa}$ in metals to represent a Kohn anomaly. It says such a form is ...
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59 views

Out-of-Plane Phonons

I am trying to derive the out-of-plane phonon dispersion relation for a membrane. As far as I can tell, one of the simplest ways to do so is with a Lagrangian of the form: ...
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27 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 ...
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49 views

Does the Fermi sea have plane waves, or wave packets?

Consider a zero-temperature, one-dimensional crystal with allowed electron momenta $k_n = \frac{2\pi n}{L}$. Question: Which is the more correct way to think about the Fermi sea? Sharp plane ...
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96 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 ...
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64 views

Fermi Energy and the Electric Potential

In an extrinsic semiconductor the electric potential is: $$\phi = \frac{1}{q}(E_{\mathrm{F}} - E_{\mathrm{Fi}})$$ where $E_{\mathrm{F}}$ is the Fermi energy, $E_{\mathrm{Fi}}$ is the intrinsic Fermi ...
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73 views

The origin of contact noise?

I was trying to measure the noise of a device with metal probes. I was not sure whether I should trust the results because I was told contact noise might contribute to some degree. I am a little ...
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38 views

Thermal expansion and conductivity

When thinking about how the lattice constant of silicon can be given up to eight decimal places without a remark for the temperature I realized that, it seems most insulators and semiconductors seem ...
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80 views

Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of ...
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129 views

Typical time scales for spin dynamics and lattice vibrations in magnetic solids

In a paper from the 1990s ([1]) on magnetovolume effects in ferromagnets, it is written that in most real situations, the moment (or spin) autocorrelation time is much larger than the period for ...
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Hall effect with similar positive and negative carriers?

The Hall effect includes the transverse (to the flow of current) electric field set up by the charges which accumulate on the edges, to counter the magnetic component of the Lorentz force acting on ...
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86 views

Brillouin Zones in a nanowire

My professor told me something I didn't understand the other day: I was reading a paper on a crystalline nanowire (NW), and in the paper they look at how the band structure changes (from that of the ...
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186 views

How should I think about reciprocal lattice and Miller indices?

When I hear someone talking about a (100) plane or a (111) plane or an (hkl) in general, my first thought is, is the system cubic. The reason I think this is because I tend NOT to think of the planes ...
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The boundary between polycrystalline and crystalline

My current understanding of solid crystalline-like materials (please correct me if I'm wrong!) is that it is a continuum in terms of crystallinity, from amorphous (basically no periodicity) to single ...
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90 views

Phase diagram of SO(5) rotor model

It was originally a problem from Professor Eugene Demler's problem set. Consider an SO(5) rotor model: \begin{align}\mathcal{H}=\frac{1}{\chi} ...
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Is this a correct description of bonding in a metal?

I am reading the paper "Twenty five years of Finnis-Sinclair potentials" by Graeme Ackland, Adrian Sutton, and Vasek Vitek, Philosophical Magazine 2009, 89, 3111-3116. It is a review-type article ...
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397 views

Pauli paramagnetism for electrons with external magnetic field

Apparently it is to be shown that for electrons under an external magnetic field, in the limit as $B\to 0 $ $$ \chi = \frac{dM}{dB} \approx \frac{n\,\mu^{*^2}}{k\,T}\,\frac{f_{1/2}(z)}{f_{3/2}(z)} $$ ...
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103 views

Why does silicon have an indirect gap?

Is there an intuitive explanation as to why silicon has an indirect gap? I have heard that this can explained using pseudopotentials.
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133 views

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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95 views

What is Z3 exciton?

I am searching and studying excitons and I confronted with a term named Z3 exciton. What is it? And what is its difference with, for instance Z1 or Z2 exciton?
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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 ...