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Commit 03f08268 authored by Jacob Beyer's avatar Jacob Beyer
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Add new table

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\documentclass[aps, prb, twocolumn, showpacs, amsmath, amssymb, amscd,
superscriptaddress, floatfix, longbibliography]{revtex4-2}
superscriptaddress, floatfix, longbibliography, booktabs]{revtex4-2}
\usepackage{braket}
......@@ -15,6 +15,9 @@ superscriptaddress, floatfix, longbibliography]{revtex4-2}
\usepackage[capitalize]{cleveref}
\usepackage{csquotes}
\usepackage{diagbox}
\usepackage{colortbl}
\usepackage{bbold}
\usepackage{pifont}
......@@ -44,7 +47,7 @@ superscriptaddress, floatfix, longbibliography]{revtex4-2}
\node[shape=circle,draw,inner sep=1pt] (char) {#1};}}
\MakeRobustCommand\circled
\newcommand{\su}{SU(2)~}
\newcommand{\su}[1]{SU(2)~}
\newcommand{\bvec}[1]{\boldsymbol #1}
\newcommand{\Ucrit}{U_\mathrm{c}}
......@@ -310,10 +313,12 @@ presented in the following.
\Delta_{s} \Psi \\
\Delta_{p_x} d_x - \Delta_{p_y} d_y
\end{gathered}$ \\
\sym A 2 & --- & $d_z$
\sym A 2 & \textbf{---} & $d_z$
& $\Delta_{p_y} d_x + \Delta_{p_x} d_y$\\
\sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1} & --- & --- \\
\sym B 2 & --- & --- & $\Delta_{f} d_z$ \\[0.5em] \hline \\
\sym B 1 & \numberedHexagon{$\Delta_f$}{-1}{1}{-1}{1}{-1}{1}
& \textbf{---} & \textbf{---} \\
\sym B 2 & \textbf{---} & \textbf{---}
& $\Delta_{f} d_z$ \\[0.5em] \hline \\
\sym E 1 &
\hspace{0.15cm} % Fix spacing in the table
$\begin{bmatrix}
......@@ -333,16 +338,16 @@ presented in the following.
\sym E 2 &
$\left[
\begin{aligned}
\numberedHexagon{$\Delta_{d_{x^2-y^2}}$}{-1}{-1}{2}{-1}{-1}{2} \\
\numberedHexagon{$\Delta_{d_{x^2-y^2}}$}{-1}{-1}{2\phantom{-}}{-1}{-1}{2} \\
\numberedHexagon{$\Delta_{d_{xy}}$}{1}{-1}{0}{1}{-1}{0}
\end{aligned}
\right] $
& ---
& \textbf{---}
& \hspace{0.5cm}
$\begin{gathered}
\begin{bmatrix}
\Delta_{d_{xy}} \\
\Delta_{d_{x^-y^2}}
\Delta_{d_{x^2-y^2}}
\end{bmatrix} \Psi \\
\Delta_f \begin{bmatrix}
d_x \\
......@@ -369,6 +374,51 @@ presented in the following.
\label{tab:irrep_basis_fns}
\end{table}
\begin{table}
\definecolor{cell}{gray}{0.8}
\centering
\begin{tabular}{cccc} \toprule
\diagbox{$\Delta$}{$\sigma$}
& \sym A 1 & \sym A 2 & \sym E 1 \\ \hline
\sym A 1
& \sym A 1 : $\Delta_s \Psi$
& \cellcolor{cell}
& \cellcolor{cell} \\
\sym E 2
& \sym E 2 : $\begin{bmatrix} \Delta_{d_{xy}} \\
\Delta_{d_{x^2-y^2}}\end{bmatrix} \Psi$
& \cellcolor{cell}
& \cellcolor{cell} \\ \hline
\sym B 1
& \cellcolor{cell}
& \sym B 2 : $\Delta_f d_z $
& \sym E 2 : $\Delta_f \begin{bmatrix} d_x \\ d_y \end{bmatrix}$ \\
\sym E 1
& \cellcolor{cell}
& \sym E 1 : $\begin{bmatrix} \Delta_{p_x} \\ \Delta_{p_y} \end{bmatrix}d_z$
& $\begin{gathered} \sym A 1 \oplus \sym B 2 \oplus \sym E 2 : \\
\Delta_{p_x}d_x - \Delta_{p_y}d_y \\
\oplus \\
\Delta_{p_y}d_x + \Delta_{p_x}d_y \\
\oplus \\
\begin{bmatrix}
\Delta_{p_y}d_x - \Delta_{p_x}d_y \\
\Delta_{p_x}d_x + \Delta_{p_y}d_y \end{bmatrix}
\end{gathered}$
\\ \hline
\end{tabular}
\caption{
\captiontitle{Basis functions of irreducible representations}
The first column lists the irreducible representation (irrep) $\gamma$.
The second column is the basis function in real space, for example, as
the bond pairing on nearest neighbour bonds. The third column is the
two-spin basis function, in terms of the typical superconducting psuedo-
vector formulation $(\Psi, \bvec d)$. The fourth column is the total
spatial and two-spin basis function, calculated as decribed in the text.}
\label{tab:irrep_combinations}
\end{table}
The divergent eigenstate will belong to one of the irreps of the point symmetry
group of the lattice (\textit{i.e.} \sym C {6v}).
When the Hamiltonian has an \su 2 spin symmetry, the point symmetry irreps
......
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