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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When I stretch a rubber band, it breaks. When I hold the broken ends together, why doesn't it join again?

The question is simple. When we join the two broken surfaces, what is it that keeps the surfaces from connecting with each other, while earlier they were attached to each other? Also, would the two ...
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How Non-abelian anyons arise in solid-state systems?

Recently it has been studied non-abelian anyons in some solid-state systems. These states are being studied for the creation and manipulation of qubits in quantum computing. But, how these ...
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Reciprocal Lattices

Is there an easy way to understand and/or visualize the reciprocal lattice of a two or three dimensional solid-state lattice? What is the significance of the reciprocal lattice, and why do solid ...
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Turned to steel in the great magnetic field

This is obviously a "fun" question, but I'm sure it still has valid physics in it, so bear with me. How great of a magnetic field would you need to transmute other elements into iron/nickel, if ...
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Graphene and Klein bottle?

I am trying to understand graphene as a topological insulator. The spin orbital interaction in graphene is very small (~10mK?). But if we consider that, then graphene should be a topological ...
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Shine a light into a superconductor

A type-I superconductor can expel almost all magnetic flux (below some critical value $H_c$) from its interior when superconducting. Light as we know is an electromagnetic wave. So what would happen ...
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Can a superconducting wire conduct unlimited current?

A superconducting wire has no electrical resistance and as such it does not heat up when current passes through it. Non-superconducting wires can be damaged by too much current, because they get too ...
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493 views

Is there a method for differentiating fractional quantum Hall states aside from finding Chern numbers?

The ground state for a quantum Hall system on a torus with fractional filling factor can be classified by the Chern number, which is why the Hall conductance is quantized. Is there another method or ...
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How can the Hall effect ever show positive charge carriers?

The Hall effect can be used to determine the sign of the charge carriers, as a positive particle drifting along the wire and a negative particle drifting the other direction get deflected the same (as ...
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180 views

Why does a cathode have to be heated to emit electrons?

Considering that electrons are highly mobile inside of a metal, why do they have such a tough time getting out at the edge of it and continuing their trip ballistically?
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Number density of LO and LA phonons as a function of temperature?

I'd like to know the how the number density of longitudinal optical (LO) and longitudinal acoustic (LA) phonons varies as a function of temperature of the material. Is there a simple expression for ...
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What determines the color of a pure substance and is it possible to predict it?

I have always wondered why salt is white, water is clear and gold is, well, gold. What determines the color of a substance? Does it have something to do with the electrons? And is it possible to ...
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402 views

How metallic surfaces states can emerge in topological insulators?

Topological insulators are materials known to have bulk insulator and metallic surface states. But, what is the origin of these metallic surface states? And how the topology of band could help the ...
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Ferromagnetism with mobile spins

How can electron spins in Iron at room temperature have ferromagnetic order even though they are travelling at very high speeds? One could argue that spin and motion are completely uncorrelated and ...
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Is crystal momentum really momentum?

Almost every solid state physics textbook says crystal momentum is not really physical momentum. For example, phonons always carry crystal momentum but they do not cause a translation of the sample at ...
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444 views

Derivation of the “Bethe sum rule”

I am trying to work out the steps of the proof of the expression: $$\sum_n (\mathcal{E_n}-\mathcal{E_s})|\langle n|e^{i\mathbf{q}\cdot\mathbf{r}}|s \rangle|^2 = \frac{\hbar^2q^2}{2m}$$ from Eq. (5.48) ...
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574 views

Possibility of Bose-Einstein condensation in low dimensions

I remember having a problem (for practice preliminary exams at UC Berkeley) to prove that Bose-Einstein condensation(BEC) is not possible in two dimensions (as opposed to three dimensions): For ...
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What is Fermi surface and why is this concept so useful in metals research?

What is Fermi surface and why is this concept so useful in metals research? Particularly, I can somewhat appreciate the Fermi energy idea - the radius of Fermi surface which is a sphere. But is there ...
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672 views

Mathematical rigorous introduction to solid state physics

I am looking for a good mathematical rigorous introduction to solid state physics. The style and level for this solid state physics book should be comparable to Abraham Marsdens Foundations of ...
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276 views

Is glass a liquid?

I was told by a condensed matter physicist that glass is a liquid with a very high viscosity (it would be more precise to say that it is a supercooled liquid). The example given was that in cathedral ...
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Lagrangian of 2D square lattice of point masses connected by springs

Zee's QFT book mentions the Lagrangian of a square 2D horizontal lattice of point masses, connected by springs, and considering only vertical displacements $q_{i}$, as $ L = \frac{1}{2} ...
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If I take a handful of salt and wait for an infinite time will it become a single crystal?

That pretty much says it. Suppose I have some powder of $NaCl$. It is kept in contact with itself in vacuum. You are free to remove all the disturbances that bother you. Is that true that, well, ...
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675 views

What are the six degrees of freedom of the atoms in a solid?

A monoatomic ideal gas has heat capacity $C_v=1.5$ which comes from the three translational degrees of freedom. For solids at high temperature, $C_v=3$, implying six degrees of freedom. What are ...
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Simulating the evolution of a wavepacket through a crystal lattice

I am interested simulating the evolution of an electronic wave packet through a crystal lattice which does not exhibit perfect translational symmetry. Specifically, in the Hamiltonian below, the ...
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What does “particle number conservation” mean in condensed matter physics?

What exactly does it imply about a condensed matter system to have particle number conserved or not conserved? For example, why does the superconducting phase break particle number conservation while ...
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Why are some materials diamagnetic, others paramagnetic, and others ferromagnetic?

Why are some materials diamagnetic, others paramagnetic, and others ferromagnetic? Or, put another way, which of their atomic properties determines which of the three forms of magnetism (if at all) ...
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489 views

Quantum numbers and the band structure of solids

I got a question concerning the band strucutre of solids. The reference I'm using is the book on solid state physics by Ashcroft/Mermin. My problem is that I don't completely understand the reason ...
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Where does the Berry phase of $\pi$ come from in a topological insulator?

The Berry connection and the Berry phase should be related. Now for a topological insulator (TI) (or to be more precise, for a quantum spin hall state, but I think the Chern parities are calculated in ...
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Topological entanglement entropy only defined for a system in the ground state?

What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
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Positrons versus holes as positive charge carriers

From Wikipedia: [The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain ...
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Nano-particle or Molecule?

What's the difference between something being labeled a "nano-particle" or it being called a "molecule"?
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Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
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Are there solid materials with controllable porosity?

In analogy to piezoelectric materials, where the application of an electrical field creates mechanical deformation in the material, I have the following question. Are there solid materials whose ...
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276 views

Change of basis in non-linear Schrodinger equation

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
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Temperature dependence of resistivity in metals

We know that in high temperature, resistivity in metals goes linearly with temperature. As temperature is lowered, resistivity goes first as $T^5$ due to "electron-phonon" interaction, and then goes ...
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Are electronic wavefunctions in band gap insulators localized? is a single-particle picture sufficient in this case?

I am having trouble understanding the physics of band gap insulators. Usually in undergrad solid state physics one looks at non-interacting electrons in a periodic potential, with no disorder. Then, ...
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Finding difficulties in taking continuum limit in nonlinear sigma model

I am learning nonlinear sigma model from Assa Auerbach's book "Interacting Electrons and Quantum Magnetism" and getting some difficulties in taking continuum limit. I am following chapter 12: The ...
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268 views

Intuition on topologically nontrivial 2D-band structures?

I want to get more intuition on topologically nontrivial band structures. There's this popular 2D two-band model for a topological insulator where $H=\sum_{k}h(\boldsymbol{k})$ (see Qi, Hughes, and ...
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What prevents bosons from occupying the same location?

The Pauli exclusion principle states that no two fermions can share identical quantum states. Bosons, one the other hand, face no such prohibition. This allows multiple bosons to essentially occupy ...
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What is a $p_x + i p_y$ superconductor? Relation to topological superconductors

I often read about s-wave and p-wave superconductors. In particular a $p_x + i p_y$ superconductor - often mentioned in combination with topological superconductors. I understand that the overall ...
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What are “electron holes” in semiconductors?

I'm tutoring senior high school students. So far I've explained them the concepts of atomic structure (Bohr's model & Quantum mechanical model) very clearly. Now the next topic to be taught is ...
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What is the difference between a photon and a phonon?

More specifically, how does a wave-particle duality differ from a quasiparticle/collective excitation? What makes a photon a gauge boson and a phonon a Nambu–Goldstone boson?
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What is the state of matter of a (solid) yogurt?

Maybe this is a silly question, but I'm not quite sure. Consider a solid yogurt. Can we assign a specific state of matter to it? I mean, it behaves like solid. However, if we "mix" it with a spoon, ...
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Why is glass a good conductor of heat?

AFAIK Glass is insulator, it doesn't have free electron. It's said metal is a good conductor of heat because it has free electron, glass doesn't have free electron, why it is a good conductor of heat? ...
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791 views

Basic Question - Green's Functions in Quantum Mechanics

I am trying to learn about Green's functions as part of my graduate studies and have a rather basic question about them: In my maths textbooks and a lot of places online, the basic Greens function G ...
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When is use of the 'effective mass' concept appropriate?

In textbooks the characteristic length scale of an exciton, or an electron bound to dopant atom, in silicon is calculated by analogy to the vacuum case. Bohr radius in vacuum: $$a_0 = \frac{4 \pi ...
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Can Ohm's law break in metals?

I was rereading Purcell's Electricity and Magnetism as research for another question, and I found this passage: In metals Ohm's law is obeyed exceedingly accurately up to current densities far ...
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The Spectral Function in Many-Body Physics and its Relation to Quasiparticles

recently, I stumbled accross a concept which might be very helpful understanding quasiparticles and effective theories (and might shed light on an the question How to calculate the properties of ...
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How to calculate the properties of Photon-Quasiparticles

in recent questions like "How are classical optics phenomena explained in QED (Snell's law)?" and "Do photons gain mass when they travel through glass?" we could learn something about effective ...
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Why does ice melts, waits for 100 degrees and THEN vaporises? Why is not the process of expansion of things continuous?

What I am asking is this: Why can't a body be solid, then solid-ish, then solid-like, then liquid-like, then liquid-ish, then liquid, then vapor-like and then vapor? Why is there a rigid temperature ...