Merge pull request #5 from ShuN6211/mod-readme

use math block
ShuN6211 · Aug 7, 2023 · 60428cb · 60428cb
2 parents a0dc5c7 + a902f85
commit 60428cb
Showing 1 changed file with 8 additions and 8 deletions.
diff --git a/README.md b/README.md
@@ -7,22 +7,22 @@ You can get the eigenenergy, eigenfunction and pair potential at each temperatur
 It is known that there are low-energy excitation levels inside the s-wave vortex core in the superconductor.
 These states are got by solving following Bogoliubov-de Gennes equation(BdG eq) self-consistently.
 
-$$
+```math
 \left[-\frac{1}{2k_{F}\xi_{0}}\nabla^{2}-\mu\right]\mathcal{U}_{q}(\boldsymbol{r})+\Delta(\boldsymbol{r})\mathcal{V}_{q}(\boldsymbol{r}) = E_{q}\mathcal{U}_{q}(\boldsymbol{r}) 
-$$
+```
 
-$$
+```math
 \left[\frac{1}{2k_{F}\xi_{0}}\nabla^{2}+\mu\right]\mathcal{V}_{q}(\boldsymbol{r})+\Delta^{*}(\boldsymbol{r})\mathcal{U}_{q}(\boldsymbol{r}) = E_{q}\mathcal{V}_{q}(\boldsymbol{r})  
-$$
+```
 
-$$
+```math
 \Delta(\boldsymbol{r})=g\sum_{E_{q}\leq E_{\mathrm{c}}} \mathcal{U}_{q}(r)\mathcal{V}_{q}^{*}(r)[1-2f(E_{q})] 
-$$
+```
 
 Here, BdG eq is rewritten in dimensionless form using Pippard length $\xi_{0} = \hbar v_{F}/\Delta_{0}$ and zero-temperature bulk gap $\Delta_{0}$.
 $f(E_{q})$ is Fermi distribution function. Solutions in an isolated vortex, especially CdGM mode is given by following form.
 
-$$
+```math
 \begin{bmatrix}
 \mathcal{U}_{n}(r, \theta) \\
 \mathcal{V}_{n}(r, \theta)
@@ -32,7 +32,7 @@ $$
 u_{n}(r)e^{in\theta} \\
 v_{n}(r)e^{i(n + 1)\theta}
 \end{bmatrix}
-$$
+```
 
 
 Here, $n$ corresponds to angular momentum quantum number, i.e. CdGM mode is characterized by this number. In this library, the range of $n$ is integers of in $[-100, 99]$. Note that the part of $u_{n}(r), v_{n}(r)$ in the right side of above formula is one of the target of this library, not the left side of it.