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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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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33 views

Missing factor in high-temperature phonon-limited resistivity of graphene (E. H. Hwang et al.)

I am trying to understand this paper by E. H Hwang and S. Das Sarma, where Boltzmann transport theory and relaxation time approximation are used to calculated the phonon-limited resistivity of ...
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40 views

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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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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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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Localization coefficient, elementary question

About a question of notation on how to compute the localization length. I take the definition from Mello and Kumar. For an energy eigenstate written in some basis \begin{equation} |\Psi_\alpha\rangle ...
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18 views

Overdetermined set of equations for two-band model analysis

I'm trying to analyze the resistivity data of a semimetal using the two-band model with both electron- and hole-like carriers: $\rho_{xx} = \frac{1}{e}\frac{(n_h\mu_h + n_e\mu_e)+(n_h\mu_e+n_e\mu_h)\...
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Defining energy current in a Normal metal - Superconductor junction

Background Consider a NS-junction modelled by the BdG equation in the seminal paper by Blonder-Tinkham-Klapwijk (G. E. Blonder, M. Tinkham, and T. M. Klapwijk Phys. Rev. B 25, 4515): \begin{equation} ...
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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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Magnetic field dependence of resistance

Experimentally, under the application of an external perpendicular magnetic field, we observe a change in the longitudinal resistance. However, in the theoretical development starting from the Drude ...
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39 views

Feynman diagrams in quantum transport theory

I'm looking to find references that describe the role that Feynman diagrams play in quantum transport theory. I have heard discussions where it is possible to just insert a self-energy loop into an ...
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593 views

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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87 views

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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39 views

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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58 views

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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104 views

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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112 views

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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73 views

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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160 views

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_{\...