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

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Can interacting Hamiltonians always be written in second quantized form?

Is it always possible to write interacting Hamiltonian in a second quantized matrix form like we do it for non-interacting form $$H=\sum _{\alpha\beta}C_\alpha^\dagger h_{\alpha\beta} C_\beta$$ ...
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22 views

Topological S-matrix as an operator in the graphical calculus

My question comes from the following classic paper by Kitaev: Anyons in an exactly solved model and beyond (arXiv link) In Appendix E (pg 86), Kitaev introduces a diagram operator $S_z$ which acts ...
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16 views

Effective mass of almost ideal fermi gas

I am trying to reproduce this famous result of effective mass of almost ideal fermi gas(Galitskii 1958 The energy spectrum of a non-ideal Fermi gas). There are two kinds of ways to find effective ...
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22 views

Connected diagrams in Sine-Gordon action

I consider a bosonic action of the type $$\int dx d\tau\left( \underbrace{a(\nabla\theta)^2+b(\nabla\phi)^2}_{free} +\underbrace{c\cos{4\phi}}_{interaction}\right),$$ and want to treat the cosine term ...
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30 views

About characteristic lengths

I am reading about mesoscopic characteristic lengths.But I am not able to distinguish between phase coherence length $L_{phi}$ and inelastic length $L_{in}$. please tell me the difference and ...
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32 views

What are “two-centre integrals”?

Reading through some condensed matter physics literature I came across the term "two-centre integrals". Could someone explain what is meant by this in general? CONTEXT: "the overlap matrix and the ...
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41 views

Mean size of a Cooper pair [on hold]

I'm having some difficulty with a the calculation of the means quadratic average distance between two electrons of a cooper's pair. I have: $$\Psi(\vec{r}) = \int d^3 \vec{k} e^{i\vec{k} \cdot ...
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3answers
146 views

Spectral properties in Solid state physics

So assume we have a periodic 1d Schrödinger operator $$- f'' + V(x) f(x)= \lambda f(x)$$ and we want $V$ to be periodic. Now if we assume that we are on a finite interval and that we have periodic ...
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35 views

Berry curvature and linear response functions

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...
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19 views

Conductivity from Boltzmznn Equation for a metal in electric field

I'm trying to show that conductivity of a metal in uniform Electric field is: $$ \sigma=\int \frac{d\textbf{k}}{4\pi^3}\left (- \frac{\partial f}{\partial \epsilon} \right )\textbf{v(k)u(k)} $$ where ...
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39 views

Green function for single impurity

I am working on the first problem on self-consistent T-matrix approximation in Chapter 5 of Condensed Matter Field Theory by Altland and Simons. This is on page 234 of the textbook. I have some ...
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15 views

Negative Capacitance in Ferroelectrics

From the Devonshire theory of ferroelectrics we can obtain Polarization vs. Electric Field curve at a given temperature. From the graph it can be seen that a portion of the curve has negative slope ...
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60 views

What is the Difference Between a Type-1 and a Type-2 Superconductor?

As the title says, I was wondering what the difference was between a Type-1 and a Type-2 Superconductor. Especially in terms of the Coherent Length and Penetration Depth of a Magnetic Field - and how ...
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23 views

Why do we use the massive dirac fermion model for MoS2?

I can derive the massive Dirac fermion Hamiltonian using a tight binding model of graphene with a staggered sublattice potential, but many (including Xiao et al, PRL 2012) use this model for MoS2 as ...
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28 views

Green function for interacting system

If we can diagonalize our interacting Hamiltonian then can we write a Green's function like we do for a non-interacting system? Green's function here means Matsubara in frequency-momentum space, ...
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42 views

Proof of Kohn's theorem

In 1961 W. Kohn's paper ( Phys. Rev. 123, 1242 (1961) ) first stated that the electron-electron interaction does not change the cyclotron resonance frequency in a bulk three dimensional gas. I can ...
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20 views

About gauge in QHE

I have a 2D geometry with 4 leads in a square lattice structure. Please tell me how should I apply gauge to such a system that hopping term is translational invariant in the laeds in both directions ...
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17 views

AC conductivity of graphene

The optical conductivity of graphene has two terms, interband term and intraband term. The analytical expression of intraband term is drude like. ...
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85 views

What is the Difference Between BCS Theory and Ginzburg-Landau Theory?

What is the Difference Between BCS Theory and Ginzburg-Landau Theory? I have been studying Superconductivity and I know that Both of the theories (BCS Theory and Ginzburg-Landau Theory) can be used ...
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41 views

Frustrated Heisenberg XXZ Model

At the moment, I am look at the frustrated XXZ Heisenberg model, given by the Hamiltonian \begin{align} H=\sum_{i=1}^N\left(J_1S_i^Z S_{i+1}^Z+J_1'\frac{1}{2}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+)+J_2S_i^Z ...
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1answer
20 views

Exciton in semi-conductor

I don't understand why an exciton describes only the interaction between an electron hole and an electron in the conduction band? How is this interaction different from the interaction between an ...
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66 views

Hartree-Fock correction to $e$-$e$ interaction

The corrections to the energy per electron in a jellium model (uniform distribution of positive ion charge approximation to the regulated long range order ionic array) is given by (in units of Ry) ...
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Validity of the static limit of a dielectric function

In general, the dielectric function $\epsilon(q,\omega)$ reflects the spatial and temporal response of a condensed matter system to an applied potential. If we put an electron into an electron sea, ...
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48 views

Why is the ground state energy of the Heisenberg XXZ Model unbounded for some values of $J$?

At the moment, I'm looking at numerically studying the Heisenberg XXZ model. The Hamiltonian is given below: $$ H=\sum_{j=1}^{N-1}\left(J S_j^z ...
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Fast and slow modes, and the vanishing of certain diagrams during re-normalization

In the middle of pg. 452 of Atland and Simonss Condensed Matter Field Theory, they state the following: Terms of $\mathcal{O}(\phi _{\text{s}}^3\phi _{\text{f}})$ do not arise because the addition ...
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32 views

Why is 2-Dimensional Electron Gas (2DEG) materials interesting?

I noticed lots of research publications about 2DEG materials, e.g. AlGaN/GaN hetero-structures. I want to know what is interesting here. Is there a fundamental physics or technological potential?
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About Rashba spin orbital coupling in graphene zigzag nano ribbon

In zigzag geometry of graphene (GNR),I am not able to understand how the matrices would go .I need your acknowledgement on followiing: I mean,that the rashba spin orbital coupling is given by: Hrso= ...
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99 views

Origin of High-temperature Superconductivity

What is the mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 25 kelvin?
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65 views

Speed of electrons in resistors

What affects the speed of electrons in a resistor? If two resistors are connected in series, they both have the same current; same number of electrons passing at a point per second. Suppose one ...
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30 views

Is there an analytical expression for the conductivity of the surface of topological insulators?

I have a question about the conductivity on the surface of Topological Insulators (TI): Is it accurate to model the conductivity by the Drude model (I read a paper that modeled the conductivity with ...
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24 views

Can we use combined symmetry to simplify the calculation of algebraic PSGs?

In classifying mean-field spin liquids under projective construction, the algebraic projective symmetry group (PSG) approach focus on the mathematical construction of the possible extensions of the ...
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1answer
93 views

Why does graphene exist?

I started to read some articles on graphene and almost all say that graphene was discovered late because physicists thought it would be unstable. Despite this, I didn't found a clear explanation of ...
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36 views

Reason of band inversion in graphene in kane and mele model

I am trying to simulate the graphene zigzag nano ribbon model of kane and mele. But I dont know how the inversion of band is taking place in it.Can anyone please suggest me about this .What makes this ...
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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 ...
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50 views

Why isn't doped silicon a strongly correlated electron system?

Most books on strongly correlated electrons claim that when the number of itinerant electrons is small and the screening length is large, that the system becomes "strongly correlated", (i.e. the ...
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43 views

Does the surface topological order on the boundary of 3D topological insulator also have topological ground state degeneracy?

The boundary of a 3D topological insulator can be fully gapped (under strong interaction) by the surface topological order without breaking the symmetry (see Fidkowski-Chen-Vishwanath, ...
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Metals/Insulators and Electron Counting

I'm a little confused by the description I commonly hear about the electron counting rule in band theory. The general statement I find is that a "solid with an odd number of electrons per unit cell ...
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How legit is this paper claiming to have observed Hawking radiation? [closed]

I recently stumbled upon this paper. In it, the author claims to have found a signature for Hawking radiation in a condensed matter system. I know that experimentalists have been trying to find ...
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1answer
63 views

How does current flow in superconductors if Cooper pairs have zero momentum?

I've been reading a lot of condensed matter textbooks, which state both that the net momentum of a Cooper pair in a superconductor is zero, and that Cooper pairs have momentum when they carry current. ...
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1answer
58 views

How to distinguish between a topological state from from a non-topological one?

How to distinguish between a topological state from from a non-topological one? Is there any standard procedure for identifying the topological features of a given hamiltonian? In general what are the ...
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52 views

Is many-body Hamiltonian valid in strong-correlated system

Condensed-matter textbook often states that there is a many-body Hamiltonian $$ H= \sum_i \frac{ p_i^2}{2m_i} + \sum_{i>j} V_{ij} \tag{1} $$ where $V_{ij} = Z_i Z_j/r_{ij}$. This Hamiltonian ...
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31 views

Hartree Fock exchange kernel

I would like to understand, how we calculate the exchange kernel of the Hartree Fock equations for a coulomb potential. So in slide 19 here for example you see the result, but I have not the ...
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19 views

How does quantum confinement happen in amorphous or polycrystalline materials?

You can easily find papers where they make a nanostructure (thin film, nanowire, or quantum dot) from methods (ALD, CVD, thermal/egun evaporation) that produce amorphous or polycrystalline structures ...
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137 views

Real part of the AC conductivity has a discrete spectrum => What physics?

If the real part of the AC conductivity $\text{Re}[\sigma(\omega)]$ has a discrete spectrum only, i.e., $\text{Re}[\sigma(\omega)]=a_1\delta(\omega-\omega_1)+a_2\delta(\omega-\omega_2)+\cdots,$ what ...
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63 views

Non-abelian bosonization

Reading this review about non-abelian bosonization, Non-abelian bosonization by I.Karmazin, I stumbled about two questions Below equation 6, I don't get the final point in the statement about the ...
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81 views

Symmetry, gauge, and projective symmetry group (PSG)?

My following questions come from the understanding of the relations between the PSGs for two gauge-equivalent mean-field (MF) Hamiltonians (or MF ansatz). Considering the Schwinger-fermion ...
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How to generalize BdG equation in order to match a graphene with a metal superconductor?

I want to generalize BdG equation in order to compute the conductance of a junction of graphene with a metal superconductor. The previous works done until now on this hetrojunction is devotted to use ...
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Tunneling from Dirac material into Schrodinger material?

When a Dirac material, like graphene or TI, has a connection with a normal metal which Schrodinger equation govern on their carriers, how could we manipulate the tunneling of electron from Dirac side ...
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Why isn't there a different phase after fourier transformation in two lattices

I am trying to understand some solutions for graphenes energy dispersion. While most of it is clear, I don't get one step, when changing into k-space. Consindering two sublattices A and B with ...
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51 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 ...