Rashba Z term

\[ \hat H_{\mathrm{Rashba}\, z} = \sum_{\langle i,j\rangle}\sum_{\sigma\sigma'} \alpha_{ij}^z c_{i\sigma}^\dagger (i\sigma^z)_{\sigma\sigma'} c_{j\sigma'} +\mathrm{h.c.}= \sum_{\langle i,j\rangle}\alpha_{ij}^z\left( i c_{i\uparrow}^\dagger c_{j\uparrow} -i c_{i\downarrow}^\dagger c_{j\downarrow}\right) +\mathrm{h.c.} = i\sum_{\langle i,j\rangle} \frac{\alpha_{ij}^z}{2}\left( \gamma_{i\uparrow}^+ \gamma_{j\uparrow}^+ +\gamma_{i\uparrow}^- \gamma_{j\uparrow}^- -\gamma_{i\downarrow}^+ \gamma_{j\downarrow}^+ -\gamma_{j\downarrow}^- \gamma_{i\downarrow}^- \right) \]

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#include <RashbaZTerm.hpp>

Static Public Member Functions
template<class T >
static void	Fill (Hamiltonian< T > &ham, double rashbaZ, int i, int j)
	Filler. More...

Static Public Attributes
static const std::string	name {"rashbaZ"}

static constexpr size_t	locality {2}

Detailed Description

Rashba Z term

\[ \hat H_{\mathrm{Rashba}\, z} = \sum_{\langle i,j\rangle}\sum_{\sigma\sigma'} \alpha_{ij}^z c_{i\sigma}^\dagger (i\sigma^z)_{\sigma\sigma'} c_{j\sigma'} +\mathrm{h.c.}= \sum_{\langle i,j\rangle}\alpha_{ij}^z\left( i c_{i\uparrow}^\dagger c_{j\uparrow} -i c_{i\downarrow}^\dagger c_{j\downarrow}\right) +\mathrm{h.c.} = i\sum_{\langle i,j\rangle} \frac{\alpha_{ij}^z}{2}\left( \gamma_{i\uparrow}^+ \gamma_{j\uparrow}^+ +\gamma_{i\uparrow}^- \gamma_{j\uparrow}^- -\gamma_{i\downarrow}^+ \gamma_{j\downarrow}^+ -\gamma_{j\downarrow}^- \gamma_{i\downarrow}^- \right) \]

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Member Function Documentation

◆ Fill()

template<class T >

static void Spinfull::RashbaZTerm::Fill	(	Hamiltonian< T > &	ham,
		double	rashbaZ,
		int	i,
		int	j
	)

inlinestatic

Filler.

Template Parameters

T	matrix type, support for: arma::mat, arma::sp_mat

Parameters

ham	hamiltonian container
rashbaY	rashba interaction value \(\alpha_{ij}^z\)
i	site index
j	site index

Member Data Documentation

◆ locality

constexpr size_t Spinfull::RashbaZTerm::locality {2}

static

◆ name

const std::string Spinfull::RashbaZTerm::name {"rashbaZ"}