The study of physical properties condensed phases of matter, including solids and liquids.

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Current operator in continuum model of graphene

For the graphene hamiltonian with NNN hopping, the wavefunctions are of the form: $(\psi_A ,\psi_B)^T$. The current from A(i) to B(j) site in the lattice model is given by: \begin{equation} J_{ij}=\...
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21 views

Obtaining a Positive Hall Coefficient for Electrons Near the Top of a Valence Band

Using a Drude model of charge carriers with a charge $q$ and a mass $m$ (which I allow to take either sign at this stage) in a sample with an applied electric field $\mathbf{E}$ and magnetic field $\...
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24 views

If an anyon picks up a phase upon particle exchange, how can you exchange them twice, isn't that a contradiction if the phase squared is not 1? [duplicate]

I'm trying to understand anyons, as stated on wikipedia, the interchange operator gives a phase https://en.wikipedia.org/wiki/Anyon $|\psi_1\psi_2>=e^{i\theta}|\psi_2\psi_1>$ So when I ...
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1answer
38 views

What is invalidated when turning on many body interactions in a crystal?

I have just started to think about strongly interacting particles and Fermi liquid theory, and I have two questions. For non interacting particles moving in an potential field, we know that the ...
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39 views

Construction of Wannier function for optical lattice potential

Parameters of the Bose-Hubbard model require the knowledge of the Wannier functions from the lowets band of the optical lattice potential $V(x) = V_{0}\sin^{2}(kx)$ according to equations: $$J = \int ...
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27 views

$SU(2)$ symmetry and conservation law in condensed matter systems [closed]

My question has a few parts, I know from Noether that if there is a symmetry in a Hamiltonian, there is a conservation law. What would be the conservation law associated with $SU(2)$ symmetry? $...
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26 views

How many valence bands does Silicon have?

I can't seem to find a concrete answer anywhere online. I am under the impression there are three valence bands before the energy gap in Silicon? (As opposed to Ge, in which there are 4?) Any help ...
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2answers
91 views

Nearly Free Electron Model and the Reduced Zone Scheme

When for example studying the vibrational modes of a one dimensional diatomic chain we find that the dispersion relation $\omega(k)$ is periodic in the one dimensional reciprocal lattice vector $\frac{...
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151 views

Invariant polynomials of the Landau theory of phase transitions (crystal symmetry?)

I'm convinced I'm missing something so obvious but here goes Typically, one can define something like a "general" expansion of an order parameter, ${\boldsymbol \Gamma}$, up to 6th order as follows $...
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11 views

conduction mechanism

How can someone distinguish between hopping and thermal activation conductivity respectevely, if in a Arrhenius plot (Log[σ] to 1000/T) the activation energy is constant and independent of DC electric ...
2
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53 views

Why do we use the anticommutation relation for particle-hole and chiral symmetries?

In physics we say that a quantity is conserved if its operator commutes with Hamiltonian. For example, in condensed matter systems, when the momentum $k$ commutes with the Hamiltonian $H$ as $[H,k]=0$...
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34 views

Turning a k-space integral into an energy integral for a conductivity tensor

Looking over a derivation of the conductivity tensor for magneto-resistance, I got stuck trying to go from (1.133) to (1.134), transforming the k-space integral into one over energy. In this ...
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37 views

Is Thermalization of a subsystem simply the result of Decoherence of its state?

I would appreciate answers that explain both the concepts in short to underline if there are any key differences between the two. Also, how does a localized state survive decoherence?
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25 views

What could be the anharmonicity effect if phonon interact with a tilted interface?

If Phonon propagates through c-axis grown structure and at the end reach a tilted interface of GaN, what phenomena will appear there? How anharmonicity is going to effect the phonon propagation there?...
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9 views

Effective interaction between electron-magnon in ferromagnetic transition metals

I wonder whether there are classical references on an effective theory of electron-magnon interaction in itinerant ferromagnetic metals?
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28 views

Structure Factor for a Simple BCC Lattice

This is an example of a general misunderstanding I am having. The structure factor is given by $$S=\sum_{j}f_je^{i\mathbf{G}.\mathbf{x_j}}$$ where the index $j$ denotes a sum over the atoms within a ...
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1answer
32 views

Derivation of polarizability

I am currently reading some papers on Dirac and Weyl physics on condensed matter. Very often, the following result for the polarizability is used: $$ \Pi(q,\omega) \propto \sum_{k,s,s'} \frac{f_{sk}-...
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1answer
91 views

Equivalence of nonlinear sigma model and the $CP^1$ model

While studying the non-linear sigma model, defined by the action $\mathcal{S} = \int dtd^2x (\partial_\mu n^a \partial^\mu n^a)$ along with the constraint $n^a n^a=1$, people often use the map $n^a = ...
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1answer
79 views

eigenvectors of tight binding Hamiltonian

I am trying to calculate berry connection using tight binding method. The most important part is to calculate $\partial_k u_k(x)$, where $u_k(x)$ is the periodic part of bloch waves, i.e. $\psi_{nk}(x)...
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1answer
72 views

chern number as an obstruction to choose a smooth gauge

In condensed matter physics, I heard that if chern number of a band $n$ is non zero, it is impossible to choose a gauge such that $\psi_{nk}$ is smooth in the whole brillouin zone. However, it is ...
3
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1answer
95 views

Relation between Berry phase and degeneracies, the example of Hall effect in graphene

In principle, the Berry-curvature can be related to the degeneracy of some underlying energy levels, using the adiabatic picture and expanding the Berry's expression in the language of instantaneous ...
2
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1answer
112 views

Simplest Live Demonstration of Adiabatic Transport

I have to give a presentation on Berry phase. I would like to give the simplest live demonstration of adiabatic transport. If I move an object in a loop and return that object back into its original ...
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21 views

Hydraulic conductivity and flow rate

I have several sources that have the following equation relating the change of volume in a cell to the hydraulic conductivity (permeability coefficient) $L$ and pressure differential $\Delta P$: $$ \...
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23 views

Advanced methods of theoretical condensed matter [duplicate]

I am looking for an online course devoted to the advanced methods of theoretical condensed matter physics. It is good if the course offers free materials like lectures, homework assignments etc. ...
1
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1answer
44 views

Understanding FCC and BCC Bravais Lattices

A book I am reading states that one possible definition of a Bravais Lattice is that the surroundings will look the same from whichever lattice point you observe from. Consider for example the simple ...
3
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1answer
67 views

Nesting in Fe-based superconductors

Many studies about iron-based superconductors mention the nesting of Fermi pockets, such as here or here. As far as I understand it it represents some kind of interplay between different Fermi ...
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1answer
48 views

Adiabatic transition from superfluid to Mott insulator?

I have a question about the dynamical passage from superfluid to Mott insulator state in the Bose-Hubbard model. Is it possible to go from superfluid region to the Mott insulator by changing the ...
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40 views

Magnus Expansion in Floquet theory

I wonder how to obtain the second equality as follows in Eq. (44) of http://www.tandfonline.com/doi/abs/10.1080/00018732.2015.1055918?journalCode=tadp20 \begin{eqnarray} K_{eff}^{(1)}[t_0](t)&=&...
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34 views

How do we determine whether the tight binding model is valid for a material?

Right now I know that the tight binding model applies when electrons are tightly localized around the ions in the material. How do we determine whether the electrons are actually tightly localized for ...
4
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1answer
94 views

Why does a Heisenberg magnet break the O(3) symmetry in stead of SU(2)?

As stated in the question, why does a Heisenberg magnet break the $O(3)$ symmetry while degrees of freedom of the underlying spins are $SU(2)$?
4
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1answer
74 views

Density of states in a system of interacting electrons

When we are introduced to the density of states in typical band-theory problems we neglect interaction between electrons, and thus we define the density of states of a sigle particle as: $D(E)=2\int_{...
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15 views

variable range hopping

Having an Arrhenius plot for the logarigthm of conductivity vs 1000/T, I noticed a region in which i assume variable range hopping takes place. Then i draw the plot logarigthm of conductivity vs T^(-...
4
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1answer
135 views

What is the difference between superfluidity and Bose condensation?

My question is about zero-temperature ground state of a Bose system. Suppose that the system stabilizes a BEC order parameter, say $\langle b^+ \rangle$, and fixes its phase. Is this a superfluid? And ...
4
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2answers
92 views

What is the meaning of the zero point of the real part of the dielectric function for a semiconductor?

I basically understand the zero point of the real part of the dielectric function for a metal. It generally corresponds to plasmon. For a metal, if the frequency is lower, the real part is negative ...
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1answer
49 views

Review article recommendation in the field of 2d materials

I am new to 2d materials. I tried to search related review articles in review of modern physics, but did not find anyone covering the whole of the 2d material area. Anybody can recommend some latest ...
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12 views

What is the best book for understanding solid state physics for undergraduates? [duplicate]

I have read Charles Kittel's book. But I thought it is higher than undergraduate level. Can any body suggest a best book which explains from the beginning of the topic?
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1answer
60 views

what does d spacing between planes in a crystal lattice mean?

I have trouble understanding the meaning of d-spacing. d spacing is supposed to give the interplanar distance. for a cubic lattice $$d_{hk \ell}= \frac {a} { \sqrt{h^2 + k^2 + \ell ^2} } $$ What i ...
2
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1answer
64 views

What is the Goldstone mode when rotation symmetry breaks in lattice?

In textbooks for introducing Goldstone mode, people usually consider about phonon as a Goldstone mode emerging from translation symmetry breaking in lattice. However, the rotation symmetry also ...
0
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1answer
51 views

partition function of the U=0 Hubbard model

I'm trying to derive the following partition function for the U=0 Hubbard model: $Z=\prod_\mathbf{k}(1+e^{-\beta(\epsilon_\mathbf{k}-\mu)})$ My try was to use: $Z=\sum_{\sigma,\mathbf{k}} <\...
2
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1answer
49 views

Calculate the laser heating on a crystal

Let's say I'm doing an optical experiment. I focus a laser on a crystal with a certain amount of power. The crystal's temperature is regulated to a certain temperature but it is localy heated by the ...
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1answer
85 views

General properties of Matsubara frequency summations

By properties such as linearity, shifting, commutativity, etc. I was hoping to evaluate something like, $$S_\eta = \dfrac{1}{\beta}\displaystyle\sum_{i\omega} \dfrac{i\omega-\xi_1}{[(i\omega-\xi_2)^2-...
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1answer
50 views

Why does a dynamical gauge field accompany fractionalisation?

I'm trying to understand fractionalisation, of which spin-charge separation is an example. I've read that this is accomplished by introducing a Lagrange multiplier field, which becomes a dynamical ...
2
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2answers
65 views

Fetter & Walecka's derivation of second quantised potential term in many-particle TDSE

For the potential term in the Hamiltonian, I understand that we go through the same process as with the kinetic energy term. On the RHS of the TDSE, we get something like $\frac{1}{2}\sum_{i}\sum_{j\...
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1answer
74 views

What is the correct statement of Kirchhoff's Law of Thermal Emission?

There are various quite different statements in textbooks and other science literature as to Kirchhoff's Law of Thermal Emission. So, what is the correct statement of Kirchhoff's Law of Thermal ...
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1answer
251 views

Density of states for graphene

I have seen a lot of plots for the density of states for graphene: but have been unable to find the calculation explicetely. I know the dispersion relation for graphene is $E_{\pm} (\textbf{k}) =\...
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55 views

In what circumstances, can exchange interaction acquire temperature dependence?

Heisenberg exchange interaction (sometimes called as magnetic stiffness?), originating from the Coulomb interaction and the Fermion statistics, is widely used in theories of magnetism. Conventionally, ...
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2answers
259 views

Is Planck’s proof of Kirchhoff’s Law of Thermal Emission false; and if it is not false why is it not false? [closed]

In his book ‘The Theory of Heat Radiation’, Max Planck adduced his theoretical proof of Kirchhoff’s Law of Thermal Emission. However, there are some problems with that approach, some of which we ...
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1answer
35 views

Can the probability of electron capture in a metal hydride be increased by extreme electric current?

An example of a metal that can hold a lot of hydrogen is palladium. The hydrogen atoms (protons) in the metal lattice are positive and the electrons are negative. When a large electric potential is ...
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1answer
57 views

Elementary question about the quantization of Hall conductivity

In the literature I read that the Hall conductivity is quantized because the Hall conductivity is actually the winding number associated with the mapping from the brillouin zone (a torus) to the space ...
3
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0answers
40 views

Weyl semi metal vs entanglement entropy

In 2+1D, entanglement entropy (EE) is crucial for identifying a topological phase. What happens in 3+1d case? e.g. what are the behaviours of EE in WSM and trivial states?