mirror of https://github.com/abinit/abinit.git
57 lines
2.3 KiB
Markdown
57 lines
2.3 KiB
Markdown
---
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description: How to perform random stopping power calculation
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authors: FB
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---
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<!--- This is the source file for this topics. Can be edited. -->
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This page gives hints on how to perform random stopping power calculation with the ABINIT package.
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## Introduction
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The slowing down of a swift charged particle inside condensed matter has been
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a subject of intense interest since the advent of quantum-mechanics. The
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Lindhard formula [[cite:Lindhard1954]] that gives the polarizability of the
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free electron gas has been developed specifically for this purpose. The
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kinetic energy lost by the impinging particle by unit of path length is named
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the stopping power. For large velocities, the stopping power is dominated by
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its electronic contribution: the arriving particle induces electronic
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excitations in the target. These electronic excitations in the target can be
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related to the inverse dielectric function ε-1( **q** ,ω) provided that linear
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response theory is valid.
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As a consequence, the electronic stopping power randomized over all the
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possible impact parameters reads
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S( **v** ) = (4π Z2/N **q** Ω| **v** |)∑ **q** ∑ **G** Im{- ε-1[ **q** ,
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**v.** ( **q** + **G** )]} ( **v.** ( **q** + **G** )/| **q** + **G** |2),
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where Z and **v** are respectively the charge and the velocity of the
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impinging particle, Ω is the unit cell volume, N **q** is the number of **q**
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-points in the first Brillouin zone, and **G** are reciprocal lattice vectors.
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Apart from an overall factor of 2, this equation is identical to the formula
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published [[cite:Campillo1998]].
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The GW module of ABINIT gives access to the full inverse dielectric function
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for a grid of frequencies ω. Then, the implementation of the above equation is
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a post-processing employing a spline interpolation of the inverse dielectric
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function in order to evaluate it at ω= **v.** ( **q** + **G** ). The energy
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cutoff on **G** is governed by the [[ecuteps]], as in the GW module. The
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integer [[npvel]] and the cartesian vector [[pvelmax]] control the
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discretization of the particle velocity.
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Note that the absolute convergence of the random electronic stopping power is
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a delicate matter that generally requires thousands of empty states together
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with large values of the energy cutoff.
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## Related Input Variables
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{{ related_variables }}
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## Selected Input Files
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{{ selected_input_files }}
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