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

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Confusion between band structure and energy gap of conventional superconductor

Can anyone please clarify my confusion? Why does a superconducting state conducts electricity even if it has an energy gap? The difference between metals and insulators is that there is a gap at the ...
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85 views

Precisely speaking, does photon become massive or the phonon become massive, due to Higgs mechanism in superconductor?

Consider the low-energy field theories of superfluids and superconductors. In superfluids, the spontaneous breaking of the order parameter's phase creates phonons as the massless Goldstone ...
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50 views

Phonon spectrum

I had a question regarding phonon spectrum in condensed matter. Consider a cubic lattice with '$p$' atoms per primitive cell. Consider the lattice plane used for derivation of the phonon spectrum to ...
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1answer
89 views

How is the current equation calculated from Ginzburg-Landau (GL) free energy?

In the Ginzburg-Landau theory, we can get the current expression from GL free energy: $$F = \int dV \left \{\alpha |\psi|^2 + \frac{\beta}{2}|\psi|^4 + \frac{1}{2m^*} \mid (\frac{\hbar}{i}\nabla - ...
2
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1answer
215 views

A naive question about topologically ordered wavefunction?

Topological entanglement entropy (TEE, proposed by Levin, Wen, Kitaev, and Preskill) is a direct characterization of the topological order encoded in a wavefunction. Here I have some confusions, and ...
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36 views

What is the physical significance of the Curie constant?

What is the physical significance of the Curie constant? I understand it depends on the effective moment of the ion and hence must be some measure of it, but what is it exactly? Like some average ...
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42 views

Is there any relation between temperature dependence of resistance and fermi energy in metals?

Given that the resistance varies linearly with temperature in metals, is there any way we can calculate the Fermi energy from this information?
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0answers
21 views

What is the spin of a magnetic impurity?

I am reading this seemingly important paper Local Magnetic Moment Associated with an Iron Atom Dissolved in Various Transition Metal Alloys. It is strange to me that the magnetic impurity has ...
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1answer
42 views

Dielectric constant of Transition Metal Dichalcogenides (TMD)

Why is the in-plane dielectric constant of transition metal dichalcogenides larger than the out-of-plane dielectric constant? Is this because of the spacing between monolayers of the TMD? Why do ...
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44 views

Can a conformal field theory with chiral central charge be gapped out?

Consider a 2-dimensional conformal field theory with nonzero chiral central charge (that is, the central charges of the holomorphic and antiholomorphic sectors are different.) I think that ...
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3answers
198 views

What makes a superconductor topological?

I have read a fair bit about topological insulators and proximity induced Majorana bound states when placing a superconductor in proximity to a topological insulator. I've also read a bit about ...
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27 views

Normal modes and lattice symmetry

In chapter 22 of Ashcroft & Mermin, it says: Theorem: any transformation that leaves $\mathbf{k}$ and the lattice invariant must transform one normal mode with wave-vector $\mathbf{k}$ to ...
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2answers
102 views

Why do objects have size? [closed]

What is the reason objects, like coffee mugs, have size?
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1answer
58 views

why doesn't liquid metal vaporize in a vacuum?

I am wondering why molten metal in a vacuum of electron beam and machines never turns to gas like liquid water does when exposed to a vacuum.
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22 views

ZnO nanorods synthesis

Could someone please let me know the steps to be used for sol-gel method synthesis of ZnO nanorod arrays using PVA as solvent and Zn acetate as precursor? I need vertical and uniformly aligned NR ...
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0answers
26 views

Debye-Huekel Theory and the continuum approximation

This question stems from a problem I was doing on the Debye-Hueckel theory. It says that the continuum approximation which underlies the Debye-Hueckel theory is valid provided that $\lambda_D \gg ...
5
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1answer
63 views

Equivalence classes of mappings from $T^{2}$ to an arbitrary space $X$

I was reading the paper "Homotopy and quantization in condensed matter physics", by J.E Avron et al. ( http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.51.51). There they have classified the ...
3
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1answer
88 views

Phase Transition at Zero Temperature (Not QPT)

As is well known the Ising model exhibits a phase transition, except the one dimensional case in which the phase transition occurs strictly at $T=0$. Now I have always thought that this makes the case ...
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1answer
71 views

Relation between scattering matrix and an effective Hamiltonian

Could somebody provide the proof (or reference to some accessible literature) of relation $$S(E) = 1 + 2πiW^{†} (H_M − E − iπW W^{†} )^{−1} W \tag{2}$$ of arXiv:0806.4889, which relates $S$-matrix to ...
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1answer
85 views

Hartree Fock equations

I don't understand how the Hartree Fock equations define an iterative method! For this discussion, I am referring to the HF equations as described here: click me! Basically if you guess a bunch of ...
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25 views

How to calculate phonon decay rate?

Here, the authors calculate the quality factor for a resonator. They take it as one over phonon decay rate, given by (24). Simplified, (24) looks like this: \begin{equation} \Gamma = \gamma_{N-1,N} - ...
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22 views

Is it possible to write the Lorentz oscillator model using Green's functions concepts?

Is it possible to write: $$\lim_{\gamma_j\rightarrow0}Im\left(\frac{1}{\omega_j^2 - \omega^2 - i\omega \gamma_j}\right)$$ which occurs, for example, in the Drude-Lorentz oscillator model for ...
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1answer
116 views

What does a correlation function measure and how does it do this mathematically?

I would really appreciate if someone could explain. What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ ...
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38 views

How to derive De Haas–van Alphen effect?

I was reading Solid State Physics by Kittel and they manage to derive De Haas–van Alphen effect by invoking the Bohr-Sommerfeld model. This feels unsatisfactory to me. Can someone derive this using ...
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1answer
58 views

Tight binding in the limit of large system size

Suppose that one has a continuous Hamiltonian with spin-orbit interaction, for example $H=-\dfrac{\mathbf{p}^2}{2m} +\kappa({\boldsymbol\sigma}\times\mathbf{p}) + U(x)$ and want to approximate this ...
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2answers
52 views

What kinds of behavioural anomalies can a zero-field-cooled (ZFC) / field-cooled (FC) split indicate?

If a material shows a spiltting in the ZFC and FC curves, is it necessarily superparamagnetic, or could there be any other reason for the irreversibility? I have heard spin glasses also show ZFC-FC ...
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49 views

Time evolution of a discrete 1-d lattice of spin-(1/2) particles under a given Hamiltonian, or special cases thereof

I am trying to get some feel for the dynamics induced on a discrete 1-d lattice of spin-(1/2) quantum particles by the following Hamiltonian $\hat{H} = \sum_{i, j} r_{i j} \left[ ...
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0answers
64 views

How are topological invariants constructed?

I've seen several different definitions for what are called topological invariants, for instance in the context of Majorana unpaired modes, by Kitaev: http://arxiv.org/abs/cond-mat/0010440 ...
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26 views

Defining a gauge field for an anisotropic material under strain

I have a Hamiltonian for a system which is somewhat analogous to graphene but with additional degrees of freedom. The Hamiltonian is $H=\sum_q \Psi^\dagger \mathcal{H}\Psi$ where ...
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54 views

Proof that a traceless strain tensor is pure shear deformation

How can i proove that the traceless part of linear strain tensor $e$ in the Euler description: $$e_{i,j}={ 1 \over 2 } \left({ \partial u_i \over \partial x_j}+{ \partial u_j \over \partial x_i} ...
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1answer
36 views

Coulomb repulsion in the Anderson impurity model

In Phil Anderson's famous paper on impurities, Localized Magnetic States in Metals, he has the following paragraph on page 44, However, I am puzzled by the last sentence: why is the $J$ part ...
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1answer
91 views

How to obtain the asymptotic behavior of Green's function?

This question arose from Eq.(9.135) and Eq.(9.136) in Fradkin's Field theories of condensed matter physics (2nd Ed.). The author mapped quantum-dimer models to an action of monopole gas in $(2+1)$ ...
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99 views

Below what temperature does a semiconductor stop behaving intrinsically?

I understand that for an intrinsic semiconductor $n=p$ where $n$ is the electron carrier concentration and $p$ is the hole concentration.My question is how to calculate the temperature at which the ...
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1answer
100 views

What exactly happens at the second-order phase transition of the 2D Toric code?

For a 2D Toric code specified by $$H = -J_s\sum_{s} \prod_{j\in s} \sigma^x_j - J_p\sum_{p} \prod_{j\in p} \sigma^z_p - h_x\sum_{l} \sigma^x_l - h_z\sum_{l} \sigma^z_l$$ where $s$ denotes stars, $p$ ...
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1answer
89 views

Contructive Proof of 2nd Quantization form of Operators

Is there a constructive proof for these forms of operators in second quantization $$R= \sum \limits_a \sum \limits_b \langle a | R_1 | b \rangle C_a^\dagger C_b $$ using the general form $R = \sum ...
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3answers
67 views

How to find dielectric constants of ferroelectric materials experimentally?

What is the procedure to find out dielectric constant of barium titanate at different temperatures ?
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30 views

How to understand the Bose glass phase has infinite superfluid susceptibility?

The Bose glass phase is characterized by a gapless excitation spectrum, exponential decay of superfluid correlations, finite compressibility and infinite superfluid susceptibility. The disordered ...
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80 views

How is the average particle density defined in condensed matter physics?

I am reading a script where average density is defined as: $n(\vec x) = \langle \hat \rho(\vec x) \rangle = \langle {\hat \Psi^\dagger(\vec x)} \hat \Psi(\vec x) \rangle$ which i absolutely don't ...
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1answer
48 views

Electron-Hole Spin Exchange Interaction

I am stuck with this seemingly "simple" Hamiltonian. I am dealing with an exchange term of a Hamiltonian for two different spin species: $$H_\text{exchange} = - \lambda J \cdot S = ...
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1answer
57 views

Eigenvalues of a nearest-neighbour tight-binding Hamiltonian in (Mahan, 2003)

In this paper by G. D. Mahan, he obtains the following electron Hamiltonian in a nearest-neighbour tight binding scheme: (page 2 of the paper, top of the right column) \begin{align} H_0 &= J_0 ...
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2answers
104 views

Can one define wavefunction for Bogoliubov quasiparticle excitation in a superconductor?

Wavefunction is essentially a single particle concept. It is easily extended to multiparticle system as follows- if one has say five electrons the wavefunction of this five electron state is any ...
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1answer
62 views

Magnetization $\ M$ of a ferromagnet as a function of temperature $T$, nearby $T=0$

Using mean-field theory, the magnetization per spin, $M$, for a ferromagnet always obeys the equation: $M=\frac{g \mu_{\mathrm{B}}}{2}\mathrm{tanh} \left( \frac{2}{g \mu_{\mathrm{B}}} ...
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86 views

Grand canonical Hamiltonian

How to explain introducing "grand canonical" Hamiltonian $$ \hat{H'}= \hat{H}-\mu \hat{N} $$ when we study a quantum system with fixed chemical potential? I understand such a substitution in a ...
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1answer
39 views

Eigenvalue for interacting Hamiltonian [closed]

Consider the Hamiltonian $$H=\omega_{1} a_{1}^\dagger a_{1}+\omega_{2}a_{2}^\dagger a_{2}+\alpha a_{3}^\dagger a_{3}(a_{1}^\dagger a_{2}+a_{2}^\dagger a_{1})$$ with $$ ...
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0answers
104 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 ...
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73 views

In string-net condensation, what does the quantized charge means? [closed]

The electrical charge is quantized strictly for elementary particles. What kind constraints does this fact applied to string-net theory? For the this question, I want to understand why electrical ...
5
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1answer
86 views

Does it make sense to define the mean free path in quantum mechanics?

The mean free path defined in classical molecule dynamics has a strong classical flavor. Is it sensible to generalize the idea to quantum mechanics?
0
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1answer
51 views

Energy gap in Parent hamiltonian of MPS

Given a block injective matrix product state (MPS) with D blocks, how does the energy gap of corresponding parent hamiltonian scale with D? And is there a good reference which gives an analysis of ...
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20 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?
4
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1answer
65 views

Are there any known continuous (non-lattice) quantum error correction codes?

I come from a hep-th background, but I have noticed that quantum information is becoming increasingly common in discussions of AdS/CFT and black hole information, and so I've begun thinking about it ...