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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398 views

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 ...
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785 views

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 ...
7
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225 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 ...
7
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200 views

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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148 views

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 ...
6
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568 views

Why do Fermi liquids have T^2 resistivity?

I have often read that metals that are Fermi liquids should have a resistivity that varies with temperature like $\rho(T) = \rho(0) + a T^2 $. I guess the $T^2$ part is the resistance due to ...
5
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95 views

Why do people say “Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon).”?

Bosons are either gapped or condensated, except physical principle protected cases (Goldstone boson, photon, etc.). I read this in a paper (version1 of http://arxiv.org/abs/1404.3728v1, 1st page 1st ...
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186 views

What happens to a Luttinger liquid under time reversal?

Suppose you a have an ordinary Luttinger liquid with $$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
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66 views

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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34 views

What is the the real world interpretation of the high dimensionality of quasicrystals?

One of the examples of the problems of 5-fold symmetry is that pentagons tiled on a 2D plane do not completely fill that plane, leaving voids. This may be solved by "folding" it into 3D space, and ...
3
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132 views

Convention in physics for [],{} and operators (QM)

I got a little mixed up with the convention in physics. Usually a hat means an operator. For a given electron-ion Hamiltonian $\hat{H}_{e-n}$, what are the difference between these: 1) ...
3
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116 views

About SU(2) gauge symmetry of the large U limit of the Hubbard model

I have been studying about the SU(2) symmetry in Heisenberg Hamiltonian with a paper 'SU(2) gauge symmetry of the large U limit of the Hubbard model' written by Ian Affleck et al(Phys. Rev. B 38, 745 ...
3
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55 views

Separating the hamiltonian for a superlattice — is it this easy?

I've been banging my head against a wall trying to figure out what I'm sure is a very simple problem. I want to solve the Kronig Penney model for a superlattice, which is just a normal periodic 1D ...
3
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315 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 ...
3
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81 views

Non-Hermiticity when Fourier transforming onto a finite lattice

I'm doing numerical simulations. I have the Haldane model in a honeycomb lattice where $$ H = \sum \limits_{<ij>}a^\dagger_i b_j + h.c $$ Where $i$ belongs to sublattice $A$, and $j$ to ...
3
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113 views

Qualitative argument to determine energy of defects

In a book of "LES HOUCHES - Critical Phenomena, Random systems, Gauge theories" the author Frolich says that: 2D In two dimensions, the mean energy of an isolated point defect in a square area of ...
2
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22 views

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 ...
2
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36 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 ...
2
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76 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 ...
2
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94 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 ...
2
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53 views

Does a conducting wire give off measurable radiation?

In the Drude model (semiclassical, but should still apply here I think), the conducting electrons are in a constant electric field, and, in between collisions with the lattice ions (that happen, on ...
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49 views

Does the real part of the inverse dielectric function have to be negative at some point for Cooper pairs to form?

Electrons naturally repel one another. However, in a superconductor, a phonon-mediated interaction causes the electrons to have a weak attractive interaction. Suppose that the interaction between two ...
2
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78 views

Problem with derivation of phonons in crystal

In this derivation of phonon solutions, everywhere, we are forcefully assuming the wavelike characteristics along the length of the chain. While all we can deduce for finding out the fundamental ...
2
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31 views

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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161 views

What is the Fermi energy of (undoped) graphene?

All of the sources I have found for this online have been wildly unclear. Many use the phrase "Fermi energy" to refer to the "Fermi level" (which is emphatically not what I'm looking for; I want the ...
2
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66 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 ...
2
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51 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 ...
2
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70 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 ...
2
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208 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 ...
2
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0answers
83 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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89 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 ...
2
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54 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 ...
2
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107 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 ...
2
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0answers
139 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 ...
2
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199 views

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 ...
2
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113 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 ...
2
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0answers
91 views

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 ...
2
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0answers
93 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} ...
2
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102 views

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 ...
2
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0answers
127 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.
2
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269 views

Phonon Momentum

I am reading Charles Kittel's solid state physics and wondering what's the mechanism that neutron waves and photons can interact with phonons and the process obey the generalized momentum-energy ...
2
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0answers
99 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?
2
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127 views

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 ...
2
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0answers
463 views

Simple model of edge states for a two-dimensional topological insulator

Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features? See e.g. the ...
2
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0answers
189 views

Discrete sum over an exponential with imaginary argument, considering only every second lattice site?

Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g., A-A-A-...-A-A (total of N sites) ...
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0answers
157 views

What does plasmon look like in 3D band structure graph?

Consider metal, and its reciprocal lattice representation with Fermi surface. What is the correct way to represent a plasmon in this system? M.b. rotating points on the surface? Or 3d membrane-like ...
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18 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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39 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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0answers
26 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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50 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 ...