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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Difference of the Transmission Coefficient between Thermal and Charge Conductance by Nonequilibirum Green Function Method

The equation 57 in the reference [Jian-Sheng Wang, Jian Wang and J. T. Lu, Quantum thermal transport in nanostructures, Eur. Phys. J. B 62, 381 (2008)] explains the the transmission coefficient for ...
Kieran's user avatar
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How does graphene Fermi velocity $v_F$ link to the envelope propagation

my questions stemmed from reading the article in Physica E. Vol. 86, 10-16. (https://www.sciencedirect.com/science/article/pii/S1386947716311365) Why does the graphene Fermi velocity $v_F$ appear in ...
Martin.s's user avatar
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Confusion about Luttinger's transport coefficients

I've started reading three papers, one by Luttinger, one by Eich and by Tatara, and I'm confused to how they relate to one another. My understanding is that in Luttinger's paper a "gravitational&...
electronannihilator's user avatar
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How to compose scattering matrices?

Imagine I have a scattering region (denoted as sample). Scattering matrix and transfer matrix gives the same information about scattering. The scattering matrix tells us how incoming modes are ...
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What is procedure for computing effective masses from these three quantities?

Given a reciprocal effective mass tensor in a principle basis $\left[M_E\right]^{-1} = \begin{bmatrix}1/m_l&0&0\\0&1/m_t&0\\0&0&1/m_t\end{bmatrix}$ You can compute the ...
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A problem in solving a PDE of the time-ordered Green function

In the article written by Jauho in 2006 Introduction to the Keldysh nonequilibrium Green function technique, I've tried to operating with whether $g_{k\alpha}^t$ or $g_{k\alpha}^{-1}$ from right to ...
Axia's user avatar
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Charge transmission coefficient

Suppose the left lead, right lead and the scattering region are all the same metallic system; such as iron. Why is the charge transimission coefficient must be a positive integer number at any fermi ...
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Drude model for electron-hole gas

The Drude formula for the conductivity of the electron gas reads: $$\sigma=\frac{\sigma_0}{1-i\omega \tau}.$$ How should it be modified when the hole or electron-hole gas is under the consideration? ...
freude's user avatar
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Double counting and Pauli Exclusion in the semiclassical model of electron dynamics

In the end, I think this question is related to this one (which was never satisfactorily answered), but I extend slightly and therefore am asking a new question. In discussing the semiclassical model ...
EE18's user avatar
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Nonequilibrium green function for interacting systems

In this book by Ryndyk on quantum transport, p. 89, the retarded single-particle nonequilibrium Green function for a non-interacting nanosystem coupled to semi-infinite reservoirs of non-interacting ...
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What does a mode mean in the context of Quantum Transmitting Boundary Method (QTBM)?

The problem statement in the original paper by C.S.Lent and D.J.Kirkner says: Given: The total energy E, the potential energy in each region, $V_{i}(x,y)$, $i=0,1,2,...,n$, and the complex amplitudes ...
prananna's user avatar
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Non-equilibrium green method based on the Hamiltonian with non-orthogonal basis

I am thinking about one question. If the Hamiltonian matrix is based on the non-orthogonal basis, how to compute the charge conductance with the non-equilibrium green function (NEGF) method. Suppose ...
Kieran's user avatar
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Charge conductivity by Non-Equilibrium Green Function Method

I am reading the calculation of charge conductivity by Non-Equilibrium Green Function (NEGF) method in this following paper. Van-Nam Do, Non-equilibirum Green function method: theory and application ...
Kieran's user avatar
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What is the relation between Kubo's formula and the Green-Kubo relations?

In one hand, Kubo's formula is used in linear response quantum mechanics to obtain response functions (conductivity, magnetic susceptibility, dielectric function) and so on in terms of correlation ...
Mauricio's user avatar
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In NEGF electron transport calculations, what is the name of the basis that diagonalises the lead self-energies?

In an NEGF calculation describing electron transport through a field effect transistor, we write down the Green function $$G(\epsilon) = \left[\epsilon I- H - \Sigma_L - \Sigma_R\right]^{-1}$$ where $...
DJames's user avatar
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Voltages at the terminals of a three-terminal system with one voltage probe [closed]

We have a three terminal system with one voltage probe as shown in the picture bellow. If I want to calculate voltages at each terminal, how should I proceed? Should I solve this system of equations $$...
Dio's user avatar
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Does resistance follow anti-Matthiesen's rule for ballistic - hydrodynamic electron transport?

Matthiessen's rule states that resistance due to various scattering mechanisms add up. For example, the resistance due to electron-impurity and electron-phonon interactions in metals is given by $\rho=...
Ramal Afrose's user avatar
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Is current density independent of applied fields for Bloch electrons?

Following Ashcroft-Mermin chapter 12 the semiclassical dynamics is governed by $ \dot{\vec{r}} = \vec{v}_n(\vec{k}) = \frac{1}{\hbar}\frac{\partial \epsilon_n(\vec{k})}{\partial \vec{k}} $ and $ \hbar ...
Uphyscs's user avatar
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Scattering matrix in time domain, causality

In this question, I consider scattering problems in one dimension. In the scattering matrix formulation in quantum mechanics, the scattering outgoing (out) waves can be written as, $$\psi^{(out)}(E)=\...
evening silver fox's user avatar
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Shubnikov-de-Haas effect and Quantum Hall effect

I am wondering if these two phenomena are two names for the same thing or whether these are distinct effects and there are situation where one appears, but the other one doesn't? Both seem to produce ...
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The superconductor's electromagnetic response and Meissner current

We know "In the superconducting state, the DC electrical resistivity is zero." But other situations has confused me a bit. There are several situations that superconductors interact with ...
NCX's user avatar
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For a quantum system with two contacts, how does one construct the contact hamiltonian for NEGF transport?

For context, I have been going through Supriyo Datta's NEGF course, slides, lecture material, and have been learning how to simulate quantum transport in his formalism. For simplicity, consider a 1D-...
jazzloaf's user avatar
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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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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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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 ...
nocopiousmargins's user avatar
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2 answers
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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 ...
MLK's user avatar
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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 $t$...
Abhijeet Melkani's user avatar
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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 ...
highly oscillatory integrand's user avatar
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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 ...
Indeterminate's user avatar
6 votes
1 answer
202 views

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 ...
Laplacian's user avatar
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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 ...
safcphysics's user avatar
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2 answers
303 views

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 ...
safcphysics's user avatar
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1 answer
139 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}...
Boa_Constrictor's user avatar
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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,...
Laplacian's user avatar
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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 ...
atbug's user avatar
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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}\...
P. C. Spaniel's user avatar
9 votes
3 answers
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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} ...
P. C. Spaniel's user avatar
2 votes
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40 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 ...
Indeterminate's user avatar
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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 ...
kevinkayaks's user avatar
8 votes
3 answers
352 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 $...
Gippo's user avatar
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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({...
aghostinthefigures's user avatar
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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 ...
onknc's user avatar
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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_{\...
physshyp's user avatar
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