Questions tagged [quantum-transport]
Quantum transport is the study of transport phenomena (the exchange of mass, energy, charge, or momentum in systems out of equilibrium) governed by quantum mechanics. In particular, this includes electron transport (electrical current flow) in micro- and nano-scale systems.
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Spin Hall Effect in 2D Topological Insulator
Suppose the 2D topological insulator has the magnetic element doping in the system and the easy-axis for the magnetization is along the z axis. The the surface gap is opened due to the time-reversal ...
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Tuning fork quality factor measurement using SR 830 lock-in amplifier
I've read about some methods based on SR 830 to conduct measurement on tuning fork Q, such as https://arxiv.org/abs/1809.01584. But I am wondering can I use the sine output signal directly as ...
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How to determine qualitatively the metallic/semimetallic conduction behaviour by comparing chemical potential and thermal energy?
Suppose a material has a semi-metallic dispersion and we want to study electronic transport with small applied electric and magnetic field. Let the chemical potential be positive-valued (i.e. the ...
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Modelling electrical conductivity in low-dimensional nanostructures
I know that the Boltzmann transport equation can be solved under the Relaxation Time Approximation (RTA) to obtain the electrical properties of materials. However, the parameter that I am interested ...
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Transmission function for one decay channel
Usually in a tight-binding system if one wants to compute the tranmission probability one uses the Caroli's formula
$$
T(E) = 4\operatorname{Tr}[\mathrm{Im}(\Sigma_{\rm in})G\mathrm{Im}(\Sigma_{\rm ...
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Efficiency formula in Environment-assisted quantum transport (ENAQT)
I'm currently studying the book quantum effects in biology, in particular, I'm interested in the phenomena of Environment-assisted quantum transport (ENAQT) in photosynthesis.
In ENAQT, they discuss ...
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Why does the Franck-Condon matrix appear to not be unitary when written in the basis of phonon states?
Preliminary: The Franck-Condon (FC) matrix can be defined as
\begin{align}
X & = e^{-x(b^{\dagger} - b)}, \label{eq: FC 1}
\end{align}
where $b^{\dagger}$ and $b$ are standard bosonic creation ...
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Question regarding a special identity for $2\pi\delta(E-\epsilon_\alpha)$
I am reading Datta's book about Quantum Transport at the moment and I stumbled over an identity for the Dirac delta distribution, which is correct since it fullfils all the requirements for the Dirac ...
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Trivial examples for the Chern number from the potential for quantized transport
I'm trying to understand the phenomena of quantized electron transport better. The difficult step is that for any Hamiltonian (where $V(x,t)$ is periodic in both arguments and is a slow function of $t$...
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How does phase coherence length depend on elastic collisions?
In the context of electron transport, it is stated in many references that the elastic scattering does not destroy phase coherence, but inelastic scattering is the source of the phase loss of ...
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Intuitive way of understanding carrier mobility dependence with Fermi Level
I want to understand how does the carrier mobility $\mu$ vary with $E_F/k_bT$ in semiconductors. Is there any intuitive way of understanding this problem, let's say in the degenerate or non-degenerate ...
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Group Velocity Formalism vs. Current Operator Formalism in band theory
There are at least two ways to argue about the velocity (or current) in band theory.
The first one is the group-velocity formalism
$$\mathbf v_g = \frac{1}{\hbar} \nabla_{\mathbf k} \epsilon_{\mathbf ...
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Conductance of an interacting quasi one dimensional wire using the method for a 1D Fermi gas?
Assuming the electrons are non interacting and spin degenerate, the conductance of a quasi one dimensional quantum wire is quantised in units of $2\frac{e^2}{h}$. For small voltages, we simply count ...
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Ballistic Transport and Bloch Oscillations Contradiction
My question is as follows, below this I have included derivations of both effects:
The derivation of Bloch Oscillations implies that in a perfect crystal we will not have net current flow when an ...
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Small time solution to Fokker-Planck equation
In reference to this note, a specific Focker-Planck equation with initial condition $W(\rho, t=0)=\delta(\rho-1)$ have the solution
$$W\left(\rho,t\right)=\dfrac{e^{-\frac{t}{4}}}{\sqrt{\pi}t^{\frac{3}...
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Effective $T$ matrix in Kondo Hamiltonian
Consider the Kondo Hamiltonian
$$H=\sum \epsilon_k c^\dagger_{k\sigma} c_{k\sigma} + J^z S^z \sum c^\dagger_{k'\alpha} \sigma_{\alpha\beta}^z c_{k\beta} + J^{\pm} \sum \left( S^+ c^\dagger_{k',-} c_{k,...
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Why Kubo formula can be applied to calculate conductivity?
It seems that Kubo formula is widely adopted to calculate conductivity, or at least Hall conductivity [for example, in the famous paper by TKNN: PRL 49 405-408 (1982)].
However, the derivation of ...
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Can we add the resistivity due to different scattering mechanisms?
Suppose there's a metal in which electrons interact with themselves and with the phonons. The hamiltonian might look like this
\begin{equation}
H= \sum_{k}\epsilon_k c^\dagger_k c_k + \sum_{k}\...
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How to write down the collision integral for any interaction in the Boltzmann equation?
I'm studying the Boltzmann equation
\begin{equation}
\Big[\frac{\partial}{\partial t}+\vec{v}\cdot\nabla_{r}+\frac{1}{m}\vec{f}\cdot\nabla_{v}\Big]f(v,r,t)=\frac{df}{dt}\Bigg|_{coll}
\end{equation}
...
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Energy of band of $d$-dimensional semiconductor when voltage $V$ is applied across
Let's say we have a one-dimensional semiconductor and I apply a voltage $V$ across it, I want to calculate the energy of a parabolic band, when a source and drain voltage is applied across it. I ...
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Advected Dirac comb with random number of teeth which are born and die
I'm looking for a topic which I struggle to put into words. It's a reasonable consideration which I expect has been carefully studied. I hope someone can tell me the name of it and offer some guidance ...
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Demonstration that electric current at equilibrium is zero in crystals
As it is well known, electrons at equilibrium (no external field) do not conduct electric current, i.e.
$\int_{BZ} dk\,v_{k}\,f(\epsilon_k)=0$
where $f(\epsilon_k)$ is the Fermi-Dirac distribution
$...
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Comparing the Madelung and Groenewold-Moyal pictures of quantum mechanics
We can consider a dynamical theory to be a "transport theory" if it can be described entirely by a series of continuity equations of the form:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot \left({...
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Energy and momentum conservation argument for electron-phonon transitions in Bilayer Graphene
I'm reading a paper which says that the interband transitions ($\pi_1^* \rightarrow \pi_2^*$) involving phonons at $q= 0 $ and $ q = K$ in Bilayer Graphene are prohibited by energy and momentum ...
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Kubo formula derivation
In the derivation of the Kubo formula for conductivty we write the total hamiltonian as $$H_{\text{tot}}=H_0+H_{\text{ext}}$$ where $$H_{\text{tot}}=H(A_0+A_{\text{ext}}),$$ $$H_0=H(A_0)$$ and $$H_{\...
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