Questions tagged [condensed-matter]
The study of physical properties of condensed phases of matter, including solids and liquids.
3,263
questions
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Second quantization: periodicity of annihilation and creation operators in momentum space, originally on a lattice
I have a Hamiltonian $H$ on a periodic lattice, which is expressed as, say:
$$H = \sum_{n} (A_n a^\dagger_n a_n + B_n a^\dagger_{n+1} a_n + h.c.)$$
where $A_n$ and $B_n$ are periodic in space (over ...
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15 views
Ballistic conduction of paired electrons (no condensate)
The quantum of conductance is $N\cdot \frac{e^2}{h}$ where $N$ is the number of subbands.
I wonder what happens if particles are paired up (and so the charge of the particle becomes $2e$ or $3e$, ...
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15 views
Pair correlations weakened by the supercurrent
I've been studying the transport properties of a Superconductor (S) - Normal (N) - Superconductor (S) junction. The governing transport equation for SNS configuration in diffusive regime is the Usadel ...
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1answer
33 views
Hamiltonian in real and reciprocal space
I found that sometimes people mentioned that Hamiltonian in real space or Hamiltonian in reciprocal/$k$-space. I wonder what difference of Hamiltonian in real and reciprocal spaces are?
For example, ...
4
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2answers
52 views
Green Function in Open Quantum Systems
Imagine an open quantum system interacting with an environment that admits a density matrix (Markovian) description in terms of Lindbladians ($c$ and $c^\dagger$). Is there a meaningful way to define ...
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On the localized screening of cerium (when compared to iron)
I was reading the paper 'A linear response approach to the calculation of the effective interaction parameters in the LDA+U method' by Cococcioni - (Paper here) .
Quoting from the first paragraph on ...
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26 views
Bloch states under time-reversal symmetry
How can I derive the action of time-reversal symmetry $\hat{T}$ on the eigenstates $\left|\vec{k},n\right\rangle$ of a Bloch Hamiltonian $\hat{H}(\vec{k})$ which is time-reversal symmetric, i.e. $\hat{...
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1answer
17 views
Macroscopic properties of individual spins in a material (magnet) - and their behavior under rotations
I am wondering
(A) about the influence of individual spins on the behavior of a macroscopic object
(B) and about the influence of rotating the macroscopic object on the internal spins
To approach ...
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1answer
30 views
Ground state magnetization of the Heisenberg XXZ chain
The Hamiltonian of the Heisenberg XXZ chain (without external field) has the form
$$
H = -J \sum_{n=1}^{N}\left(S_n^xS_{n+1}^x+ S_n^yS_{n+1}^y + \Delta S_n^zS_{n+1}^z\right).
$$
It is known that this ...
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Is the zero-point energy of helium stronger than other liquids to disfavour freezing?
Under normal atmospheric pressures, liquid helium does not freeze even when cooled very close to absolute zero. This is attributed to the uncertainty principle or due to zero-point energy.
But the ...
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25 views
How did the adiabatic process equations combine to form this new one?
Compressing and cooling air in a Coolgardie Safe, then decompressing
I'm a 10th grader so it would help to explain how, in the answer to the link above, $$T_{cool}\left(\frac{V_{final}}{V}\right)\...
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19 views
Does the Mott metal-insulator transition occur with increasing or decreasing density of valence electrons?
When reading about the Mott metal-insulator transition, it has not become clear to me if the transition from a metal to an insulator occurs with increasing or decreasing density of valence electrons.
...
3
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2answers
41 views
Doping and inter plane coupling for cuprates
I'm not very familiar with high-Tc and I have naive questions on cuprates materials (CuO2). It seems common that everyone treats it as a 2D material for good reasons: in undoped system, there are two ...
0
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1answer
29 views
Amount of free electrons in a metal
How can I calculate the amount of free electrons in a metal?
I search the forum but found nothing
What I want to know is how many electrons can I remove from a metal using photoelectric effect (...
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16 views
Do conductors have temperature coefficient of resistance of order $0.1$ [1/K] at $40 - 160$ Kelvin?
Typical metals have temperature coefficient of resistance with order of magnitude $\sim 0.001$, at $20$ degrees Celsius.
What kind of materials have TCR of order of magnitude $0.1$ at $40 - 160$ ...
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1answer
51 views
Why is the chemical potential of noninteracing bosons negative?
Chemical potential of noninteracting bosons is known to be negative because the Bose-Einstein distribution $[e^{(\epsilon-\mu)/T}-1]^{-1}$ should be free of singularities. However, I don't fully ...
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2answers
35 views
Dispersion relation near Brillouin zones - Periodic potentials
I am trying to wrap my head around periodic potentials and weak periodic potentials from the reduced zone schemes. From the definition of $\psi_k$:
$$
\psi_k(x)=\sum_G C_{k-G}e^{i(k-G)x}
$$
I ...
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87 views
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Book as supplement to Fradkin's “Field Theories of Condensed Matter Physics”
I am trying to read Fradkin's book "Field Theories of Condensed Matter Physics" but I am finding it to be a bit hard to follow at some places. In particular, I find that Fradkin sometimes throws some ...
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24 views
Fermi Energy in Anisotropic Crystal
Suppose I have an anisotropic cristal, so it has, say, energy $$E=a(k_x)^2+b(k_y)^2$$ How would I calculate its Fermi energy?
It doesn't depend only on the length of the vector $k$, so most of the ...
1
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1answer
45 views
How does temperature change after compression in non-adiabatic process?
I understand that in an adiabatic compression, we will do it fast enough to not allow any heat to escape the cylinder. But suppose I can't do it fast enough.
What law - or formula - is used to find ...
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45 views
+50
Meaning of orbital occupations in the Hubbard Model
I was reading the paper 'A linear response approach to the calculation of the effective interaction parametersin the LDA+U method' by Cococcioni et. al (1)
Quoted verbatim from section 3.A),
In ...
0
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1answer
28 views
Binding energy of an exciton
The binding energy of an exciton is usually modeled after the hydrogen atom and varies with charge $q$ as $q^4$. I don't understand why it is $q^4$ and not $q^2$ - If we assume an electron and hole, ...
2
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0answers
30 views
Chiral anomaly in Weyl semimental
In Weyl semimetal, there is an analog of ABJ anomaly, which is a $E \cdot B$ term. The ABJ anomaly can be viewed as winding number because of the homotopy group of sphere $\pi_3(S^3)= \mathbb{Z}$ for ...
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20 views
A derivation about Hall conductance
I am trying to deduce Hall conductance,but somthing is bothering me.
Now I have this experssion:
\begin{equation}
\sigma_{\mu \nu}=\frac{e^{2}}{2} \epsilon_{\mu \nu \rho} \int \frac{d^{3} k}{(2 \pi)^{...
3
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0answers
72 views
Calculating the inelastic quasiparticle lifetime of a screened quantum fluid
I've been studying "Lifetime of a quasiparticle in an electron liquid", by Qian and Vignale. Much of it makes sense, but there is a detail in the calculation of the exchange term that doesn't make ...
2
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1answer
45 views
Does the shifting of the Fermi energy level of an intrinsic semiconductor mean that $n \neq p$?
It has been stressed out in the books that I've consulted that, for an intrinsic semiconductor, $n=p$.
However, with this in mind, they also derivate the following equation:
$$E_{F_i}=\frac{E_c+E_v}{...
0
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1answer
32 views
Compressing and cooling air in a Coolgardie Safe, then decompressing
If I put container of compressed air into a Coolgardie Safe, and brought the temperature down by say 3°C, how am I supposed to calculate the temperature of the air after it is decompressed back to ...
0
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1answer
43 views
Metal-insulator transition (material properties)
When studying about metal-insulator transitions, I was wondering which material properties can give direct information about this phenomena. Also, what information can be derived from these properties....
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0answers
11 views
Trying to understand crystal structures within a solid
I am trying to get a firm understanding of crystal structures in solid state physics but having some issues with the terminology.
If I understand correctly, the lattice are points in a 3-D space so ...
2
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1answer
35 views
How to calculate Spectrum function in condensed matter physics?
Now I known the spectrum function can be measured directly in certain experiments. Suppose Hamiltonian for a system is $H = \epsilon(k)\sigma_x+M(k)\sigma_y$,spectrum function can be calculated as:$A(...
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192 views
Magic angle graphene
In this article here,
it is claimed that the following model for bilayer graphene
$$\mathcal H= \begin{pmatrix} 0 & \mathcal D^*(-r) \\ \mathcal D(r) & 0 \end{pmatrix}, \mathcal D(r)=\begin{...
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33 views
What are the most general symmetries that a Hamiltonian of the form $H=\vec{k}\cdot\vec{\sigma}$ can have?
Hamiltonians of the form $H=\vec{k}\cdot\vec{\sigma}$ with $\vec{k}$ being the crystal momentum and $\sigma_i$ being the $i$-th Pauli matrix (an $su(2)$ generator), are pretty common in the study of ...
3
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1answer
63 views
What does phonon exchange do in the theory of superconductivity?
In the theory of superconductivity, the phonon-mediated electron-electron scattering leads to an effective interaction, the BCS hamiltonian,$$\hat{H}_{\rm BCS}=\sum\limits_{\vec k,\sigma}\epsilon_{\...
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62 views
Numerical renormalization of 2D Ising lattice
I'm trying to make some toy computations on the $2D$ Ising model on a square lattice. I want to apply a renormalization transformation, and try to estimate observables on the renormalized lattice ...
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0answers
18 views
Vortex bound state for chiral $p$-wave half quantum vortex (HQV)
I understand that in a chiral $p$-wave half quantum vortex (HQV) only one spin state winds around the vortex and the other spin has no winding number associate with it. However, would there be an ...
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0answers
41 views
What's the definition of Goldstone Mode?
My question is how to define a Goldstone Mode?
Initially I thought that Goldstone Mode is a consequence of spontaneous symmetry breaking, but later I learned that in Kosterlitz–Thouless transition, ...
2
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2answers
28 views
Tight-binding in a semi-infinite square lattice
I have a problem understanding how changing the boundaries from a periodic lattice to a finite lattice. For example, if we have a 2D square lattice of lattice constant $a$ whose $x$ axis has only $N_x$...
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2answers
55 views
Questions about Kosterlitz–Thouless (KT) transition
Why we extend $\theta$ from $(0,2\pi)$ to $(-\infty, \infty)$? I mean we cannot measure $\theta$ in experiment, can we?
Secondly,the feature of vortex solution (at least in KT transition) can be ...
0
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1answer
25 views
Melting and freezing ice
Suppose I have two ice cubes and I want to stick them without any external material. Can I achieve this by keeping both on one another and extract some more energy from them ( by placing them in ...
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0answers
10 views
What is the correct definition for a Lifschitz transition?
The definition that was given to me by my professor said that a Lifschitz transition is when the topology of the Fermi surface changes. For example, if we have a one-dimensional Fermi surface, we ...
9
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1answer
234 views
Numerical Berry curvature for bosons
I am trying to numerically compute the Berry Curvature for a generic quadratic Bosonic Hamiltonian of the form $$H = \sum_{ij} A_{ij} b_{i}^\dagger b_j + \frac{1}{2} \sum_{ij}\left( B_{ij} b_i b_j + \...
1
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1answer
25 views
How to understand the difference of spin wave excitation for ferromagnetism (quadratic dispersion) and anti-ferromagnetism (linear dispersion)?
As we know, the dispersion of spin excitation (magnon/spin wave) for ferromagnetic(FM) system is quadratic as $k\rightarrow 0$, but is linear for anti-ferromagnetic(AFM) system as $k\rightarrow 0$. I ...
1
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1answer
19 views
Variation of free energy vs. order parameter
In the paper M. Holzmann, G. Baym, Phys. Rev. B 76, 092502 (2007) the following formula (Eq. (18)) is given for a Bose-condensed system:
$$
V\delta F=-\frac12\int d\mathbf{r}d\mathbf{r}'\:\delta\...
1
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1answer
36 views
Does a crystalline ferromagnetic solid break the rotational symmetry twice?
Both Heisenberg ferromagnets and crystalline solids break the rotational symmetry in space. Now consider a crystalline ferromagnetic solid. By virtue of being in a crystalline phase, it already broke ...
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12 views
Lattice harmonics for the point group D$_{3d}$
I have been looking into the concept of lattice harmonics used to construct tight-binding models based on the symmetry of the system instead of going through the standard Fourier transformation ...
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0answers
38 views
Why are energy levels half filled in SSH model?
The SSH model describes states of electrons in a polyacetylene chain, which is modeled as a lattice with two orbitals per site. Now, in many articles it is claimed that in the ground state, half of ...
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60 views
Can the time-reversal operator of a two-level system be represented by a $2\times2$ matrix?
I am studying the time-reversal symmetry in the context of
topological insulators.
As usual, the minimal non-trivial model to be considered is a two-level system with Hilbert space $\newcommand{\ket}[...
2
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1answer
33 views
Defining upper critical dimension
Considering the usual Landau functional of the form:
$$ \beta L[\phi] = \int d^D r [\frac{1}{2} |\nabla \phi(r)|^2 + \frac{r_0}{2} |\phi(r)|^2 + \frac{u_0}{4} |\phi(r)|^4 ] $$
In searching for the ...
3
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3answers
107 views
Dissatisfied with textbook explanations for why $\vec k$ in Bloch's theorem can be restricted to thefirst Brillouin Zone (BZ)
By Bloch's theorem, all the eigenfunctions of a Hamiltonian with a periodic potential $$U({\vec r}+{\vec R})=U({\vec r})$$ can be chosen to have the form $$\psi_{n{\vec k}}({\vec r})=e^{i{\vec k}\...
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How to set chemical potential for particle-hole asymmetric cases in the QUEST library packages for DQMC? [closed]
I am trying to use QUEST library packages for Determinantal Quantum Monte Carlo (DQMC). For particle hole symmetric cases (for example square lattice at half filling) by default it sets the chemical ...
