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

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12
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1answer
448 views

Quasi 1D insulators with strong spin-orbital interaction

We know that the spin-1 chain realizes the Haldane phase which is an example of symmetry protected topological (SPT) phases (ie short-range entangled phases with symmetry). The Haldane phase is ...
4
votes
2answers
84 views

How to write BdG Hamiltonian in graphene?

In Beenakker's paper:Specular Andreev Reflection in Graphene, the BdG Hamiltonian is written as: $$ H_{BdG}=\begin{pmatrix}H-E_F&\Delta\\ \Delta^*& E_F-H\end{pmatrix} $$ from equation (1). ...
3
votes
0answers
62 views

Few questions regarding String-Net theory and the Standard Model

A friend today showed me this post and after reading Prof. Wen's answer, few questions came to my mind. Prof. Wen says: all fermions (elementary or composite) must carry gauge charges (see ...
0
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0answers
18 views

Systems with these temperature dependence of thermal-conductivity

I want to find out examples for systems (of any kind) in which the temperature dependence of thermal-conductivity($\kappa_{T}$) is of type- \begin{equation} T^{-\alpha}~~~~~ where ~~~~~\alpha>0 ...
2
votes
1answer
320 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand ...
2
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0answers
32 views

What is a marginal fermi liquid in a nutshell?

I would like to know what are the main differences between the normal Fermi liquid theory and a marginal fermi liquid theory. What kind of systems can be described by the marginal liquid theory? What ...
1
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0answers
32 views

Tight-binding model parameters fitting from ab-initio calculation results

Or the problem can be rephrased as: How to extract the tight-binding parameters from first principle calculations? I have searched some articles but all of them just give vague descriptions when ...
2
votes
1answer
244 views

What favors island growth of a sputtered material?

What would be the best choice of parameters in general if one would like to get pure island growth (i.e. Volmer-Weber growth) in a sputtering deposition process and what would be a good estimate of ...
1
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0answers
23 views

Effect of Phonon Density change

I am trying to figure out the phonon density change effect on anharmonic decay of phonons. How this two phenomena could be related and what could be the possible effect in such case. Moreover ...
6
votes
1answer
472 views

Jordan Wigner Transformation in 1d Majorana chain

So, I was reading the paper by Fidkowski and Kitaev on 1d fermionic phase http://arxiv.org/abs/1008.4138. It explains the classification of 1d fermionic SPT phases with $\mathbb{Z}_2^T$ symmetry for ...
3
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0answers
62 views

What is physically irreducible representation?

When I use bilbao crystallographic server recently, I noticed a notation called physically irreducible representation. Paper says it is a direct sum of two complex conjugate representations (if ...
2
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0answers
58 views

Second law of thermodynamics in linear response theory

I am wondering about the appearance of irreversibility in the response functions or equivalently the correlation functions in a statistical mechanics system. The main principle that I have seen where ...
3
votes
1answer
117 views

Density of states and elliptic integral

It is known, for example Equation (14) in the graphene review of Castro Neto (arXiv), that the full expression for the density of states (DOS) of graphene is in terms of an elliptic integral. Close ...
0
votes
1answer
30 views

How can wavefunction degeneracy be incoperated into a tight binding model?

Say one wanted to calculate the band structure of the E2u orbital in some molecular crystal, which is the HOMO. How are the two states dealt with in the tight binding hamiltonian?
1
vote
1answer
56 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. ...
1
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0answers
26 views

MFT Approximation for Dilute Bose Gas

The Dilute Bose Gas has quartic Hamiltonian $$H=\sum_{k}\epsilon_k b_k^\dagger b_k+u\sum_{k\,k'q}b_{k+q}^\dagger b_{k'-q}^\dagger b_kb_{k'}.$$ It is said in a reference that Since the lowest ...
1
vote
1answer
31 views

Nonzero stress on crystal at equilibrium volume?

Using a first principles computational method such as DFT, you can calculate the energy of a unit cell at different volumes to obtain a parabolic energy vs. volume curve. The minimum of this curve ...
2
votes
1answer
43 views

What is the magnetic-ordering wave vector?

Like ferromagnetic, antiferromagnetic, the magnetic-ordering are (0,0),(π,0), what is the definition of it? Is there a formula about it?
7
votes
1answer
122 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 ...
5
votes
0answers
92 views

Effective theory of topological insulator in coulomb impurity

I am trying to solve for the Haldane model with a coulomb impurity at one site in the effective theory approach and look for some topology in the solutions of the wave functions. The Hamiltonian near ...
14
votes
2answers
420 views

What is “Dynamical phase transition”?

What is "Dynamical phase transition"? It is a fancy notion now. But what exactly does it mean? What is the difference between it and the conventional phase transition?
1
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0answers
22 views

Why does the plasma frequency of alkali metals decrease with increasing atomic numbers?

Why do the plasma frequencies of the group I alkali metals, Li to Cs, decrease with increasing atomic numbers? I have tried to look at the basic expression for ...
2
votes
0answers
54 views

Intervalley scattering in graphene in presence of impurities

A long range impurity like coulomb impurity does not induce an inter valley scattering between the two Dirac points. Is there any mathematical explanation for the same although this is explained by ...
12
votes
4answers
5k views

What happens when we cut objects?

What is the role of the molecular bonds in the process of cutting something? What is the role of the Pauli exclusion principle, responsible for the "hardness" of matter? Moreover, is all the energy ...
0
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0answers
18 views

Analytical derivation of photonic bandstructure in photonic crystal

It seems the usual way to find the photonic bands of a photonic crystal is to setup the "master equation" $$\nabla\times\left(\frac{1}{\epsilon(\mathbf{r})}\nabla\times\mathbf{H}(\mathbf{r}) ...
3
votes
3answers
199 views

Difference between DMRG (density matrix renomalization group) and MPS (matrix product states)?

I am learning DMRG recently. I noticed there are many papers both in the DMRG approach and MPS (such as variational matrix product state (VMPS) by F.Verstraete and J.I.Cirac) approach. In my eyes, ...
3
votes
1answer
59 views

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} ...
4
votes
1answer
122 views

Where can I get an introduction to the mathematics behind Hofstadter's Butterfly?

Are there any good books that give good mathematical/physical background to the workings of the Hofstadter's Butterfly? I'd appreciate some references. Books or Public access papers will work. ...
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0answers
9 views

Miniband width and Elecron Mobility [closed]

In superlattice, how miniband width and Electron mobility are related? I need detailed qualitative and quantitative description. Thank you.
3
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0answers
20 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 ...
0
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0answers
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 ...
1
vote
1answer
36 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 ...
0
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0answers
35 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 ...
2
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0answers
23 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? ...
0
votes
0answers
25 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 ...
3
votes
2answers
71 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 ...
4
votes
2answers
176 views

Does the Night Mode of the screen display (LCD) save more energy? [closed]

In some cases, we can enable the Night Mode (reversing the bright and dark color of the display; such as White Text, Black Background) for the screen display. LCD(Liquid-crystal display) seems to be ...
2
votes
1answer
101 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 ...
9
votes
3answers
355 views

How to cut a stone on a White Dwarf?

I've heard that white dwarf stars are extremely dense and hard. So, if I had a piece of white dwarf matter, would it be possible to cut it (or otherwise) into a custom shape? How could one do that?
0
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0answers
10 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
votes
1answer
48 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 ...
1
vote
1answer
47 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 ...
1
vote
1answer
85 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 = ...
1
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0answers
32 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 ...
2
votes
0answers
36 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?
0
votes
0answers
23 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 ...
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0answers
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?
1
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1answer
29 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'} ...
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0answers
25 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 ...
1
vote
3answers
1k views

Typical operators in tight binding

Let the tight-binding Hamiltonian be $\sum\limits_{ij} {{t_{ij}}\left| i \right\rangle \left\langle j \right|}$. Where ${\left| i \right\rangle }$ is the atomic orbit at lattice site $i$. My question ...