Rashba X term

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

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#include <RashbaXTerm.hpp>

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

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

static constexpr size_t	locality {2}

Detailed Description

Rashba X term

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

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Member Function Documentation

◆ Fill()

template<class T >

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

inlinestatic

Filler.

Template Parameters

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

Parameters

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

Member Data Documentation

◆ locality

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

static

◆ name

const std::string Spinfull::RashbaXTerm::name {"rashbaX"}