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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Sum in the reciprocal lattice

I have to use this property but I don't understand at all the deduction, so I was wondering if someone could help me. We have a crystal lattice with vectors to each atom from one of them $R_j$, and ...
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44 views

Intuition behind modeling quantum impurities as two-level systems

I've been trying to get a basic understanding of quantum impurity problems, starting with the Anderson model. The Wikipedia article (along with some review articles) seems to explain the simplest ...
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96 views

How to find the speed of sound in a monoatomic crystal

My question is about phase and group velocities in a monoatomic crystal. I want to find the speed of sound, so I am using the equation for vibrational modes: ...
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39 views

What happens when you use an electric field to match atom oscillations?

I've been thinking about this question for the last few days: "What happens when you either use an electric field or sound / light to match the frequency of the atomic lattice?" What would happen to ...
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184 views

How to identify a crystal structure by its x-ray reflection bragg angles?

How to identify a crystal structure by its x-ray reflection bragg angles? Suppose we have a crystal sample to examine its crystal structure (e.g. SC, BCC, FCC, etc). What we can get from an X-ray ...
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46 views

Hamiltonians on tensor product states

Solid state & Atomic Physics. The wavefunction for the electrons is $\psi(\mathbf{r}, \mathbf{R})$, where $\mathbf{r}$ is the position of the electron and $\mathbf{R}$ of the nucleus. The ...
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24 views

What is the spin of a magnetic impurity?

I am reading this seemingly important paper Local Magnetic Moment Associated with an Iron Atom Dissolved in Various Transition Metal Alloys. It is strange to me that the magnetic impurity has ...
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22 views

Can one calculate the electric conductivity of iron?

Iron is a commonplace material. It is common knowledge that it conducts. Is it possible to accurately calculate the electric conductivity of iron? With what kind of method? Up to what precision?
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134 views

scaling theory of Anderson localization

Initially, Anderson studied the eigenstates of the tight-binding Hamiltonian $$ H = \sum_n \epsilon_n a_n^\dagger a_n + V \sum_{m,n} a_m^\dagger a_n . $$ His question was whether the eigenstates ...
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71 views

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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121 views

Why is the k=0 phonon neglected when calculating Debye-Waller factor?

When calculating Debye-Waller factor one gets the form: $e^{-2W} = ...
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82 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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31 views

What is the boundary of restorable thermal expansion?

As every book indicates, thermal expansion is a linear process $\frac{\Delta L}{L}=\alpha \Delta T$. Upon heating an object the result is thermal expansion. If we cool it down it is restored its ...
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65 views

Charge density waves: site-centering v.s. bond-centering

Question about charge density wave (CDW): From this Ref. page 13, why bond-centering charge density wave is naturally compatible with the observed coexistence of charge ordering and ...
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29 views

Nuclear spin relaxation, quasi-particle energy and spin spectral density

Below is a measurement of the longitudinal nuclear spin relaxation ($1/T_1$). Ref: Fig 4 of page 24 Competing ground states in low dimensions. My question concerns the statement in this Ref that: ...
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73 views

LOCAL Temperature Gradient and Stress

I'm investigating the thermo-migration failure mechanism in nanoscale ICs interconnects. Typically, a nano wire under thermal stress suffers from material/mass migration or void nucleation if it ...
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236 views

3D Density of states

I have the following dispersion relation: $$\epsilon(\vec{k})=\frac{\hbar}{2}\left(\frac{k_x^2}{m_1}+\frac{k_y^2}{m_2}-\frac{k_z^2}{m_3}\right)$$ (note the minus sign in the third term). And I am ...
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70 views

Bloch's theorem for Semi-Infinite Lattice

If we have a lattice Hamiltonian $$ \sum_{n'\in\mathbb{Z}}H_{n,n'}\psi_{n'} = E\psi_{n} \,\forall n\in\mathbb{Z} $$ such that $ H_{n,n'} = H_{n+q,n'+q}$ for some $q\in\mathbb{N}$ and for all ...
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69 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 ...
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41 views

Discrepancy in introducing Schottky barrier

I have a problem regarding introduction of Schottky barrier in metal-semiconductor junction. Because of this barrier the energies of conduction band vary discontinuously and hence the potential is ...
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923 views

The reciprocal lattice of HCP lattice

There is a very similar question here Reciprocal Lattice of a non-bravais lattice, but I don't fully understand the answer, and the question is now obsolete so I feel that I should ask it again. How ...
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26 views

Proton energy distribution after Si layer

I've been using SRIM to get an approximation of the energy distribution that a beam of monoenergetic incident ions will have after a thin layer of silicon. However, for my purposes it would be better ...
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104 views

Disclinations, dislocations, lattices, Displacement fields and scaling

I am looking up Frank, and Burger vectors and associated material on dislocation/disclination. It seems straightforward describing a lattice and what dislocation means. It is even possible to restrict ...
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203 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 ...
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88 views

Why does inelastic X-ray scattering probe the longitudinal dielectric function as opposed to the transverse dielectric function?

Light is a transverse wave. Therefore, light in the optical range (i.e. visible light) couples to transverse collective excitations of a material when measuring the optical conductivity for instance. ...
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67 views

Physical, intuitive reason for divergence of dielectric constant at electronic percolation transition?

Several papers such as this (warning, PDF) and this (PDF again) talk about how, near the electronic percolation transition for a metallic 2D film, the real part of the dielectric constant diverges ...
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36 views

Most atoms have a nonzero magnetic moment, right?

This is my feeling. But more is different. If atoms form a solid, it is hard to say whether the solid will be ferromagnetic or not.
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34 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 ...
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31 views

How to isolate and verify the source of optical absorption/effects?

This is similar to my other question, but not the same -- that one was about the energy ranges of various absorption mechanisms, and this one is more about experimental techniques to find them. Let's ...
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85 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 $k=\frac{n}{N}\frac{2\pi}{a}=\frac{n}{N}$, ...
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34 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 ...
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61 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 ...
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249 views

Good introduction to many-body Green's function via path integral formulation?

Can anyone kindly provide any information on valuable references or books on this topic? It appears to be prevalent in 90s papers on High-Tc superconductivity or quantum Hall effect, especially in a ...
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111 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 ...
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25 views

Is there a way to quantify how similar a polycrystal should behave to a single crystal?

So in solid state classes we learned about phenomena like band structure and others arising from a periodic potential. Then we get to doing actual experiment and find out that materials being single ...
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64 views

Vacancy Generation / Annihilation Time (Relaxation Time)

Vacancy Generation/Annihilation Time, Recombination Time and Relaxation Time ($\tau$) are all synonymously used in atomic physics literatures. They're defined as the time that it takes for vacancies ...
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147 views

Bloch states at the zone boundary

How do I show that in 1D the Bloch states at the zone boundary $\left(k=\pm\frac{\pi}{a}\right)$ form standing waves? How is it clear, that there is a high- and a low energy state for a finite ...
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36 views

Simple examples for exchange and correlation

Is there an easy, in the best case intuitive, explanation of the difference of exchange and correlation? Is there a simple way to distinguish whether a certain contribution is due to exchange or ...
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198 views

Do I understand measurement of dispersion relation in a solid correctly?

I'm currently doing an introduction to solid state physics course and have a quick question about measurement of the dispersion relation of phonons in a solid: The way I understood it is the ...
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44 views

Is there a difference in binding energy between a regular material and a doped one?

Say Silicon and boron doped silicon. Would the doping affect the binding energy? Could I see this in an XPS spectra?
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305 views

More physical explanation of impurity energy levels in a doped semiconductor?

I'm reading about doped semiconductors in Ashcroft and Mermin. They tell you that when donor impurities are added to a semiconductor, their energy level $E_d$ is just slightly below the conduction ...
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315 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 ...
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189 views

Average number of spin up particles

In a paramagnetic system, where $N = N_\uparrow + N_\downarrow$ is fixed, how does one calculate the average number of spin-up particles $\langle N_\uparrow \rangle$? You can assume we have the ...
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58 views

Long range repulsion in anomalous solids

As far as I know things like rocks, walls, rubber balls, polished tables etc. exert a short range repulsive force on other everyday objects that is responsible for hardness, softness, collisions, ...
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147 views

Is there a derivation of all possible Bravais lattices in 2D and 3D?

Do any of you know a (possibly elegant) derivation of all possible Bravais Lattice and the Crystallographic Group of Lattices in 2 and 3 dimensions? Group theory /abstract nonsense approaches are ...
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423 views

How to demonstrate that there are just 14 types of Bravais lattice?

Is it possible to demonstrate that there are just 14 types of Bravais lattice without the knowledge of group theory?
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89 views

When is the Fermi surface a surface of constant mean curvature?

Fermi surfaces are surfaces of constant energy in reciprocal space. They provide information about the properties of a material in solid state physics. Constant mean curvature surfaces are a superset ...
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131 views

What is the “center of gravity of a band”?

It seems there is a term called "center of gravity of a band" in solid state physics or chemistry which I'm confused about. Could anyone give a formal definition of the term or point to some reference ...
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203 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
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141 views

Sommerfeld results & van Hove singularities

According to Sommerfeld the derivative of the density of states $g'(\varepsilon)$ apears in several thermodynamic quantities. Will this also be the case if one use the correct dispersion relation of ...