Update index.md

Author: mtian8

docs/index.md

@@ -235,7 +235,11 @@ $$
 $$
 
 $$
-{\mathbf{a}_2} = (\sqrt 3 a/2, - a/2),{\mathbf{a}_3} = ( - \sqrt 3 a/2, - a/2)
+{\mathbf{a}_2} = (\sqrt 3 a/2, - a/2),
+$$
+
+$$
+{\mathbf{a}_3} = ( - \sqrt 3 a/2, - a/2)
 $$
 
 $$
@@ -251,11 +255,23 @@ $$
 $$
 
 Then the Haldane model on a hexagonal lattice can be written as
-$$H(k) = {d_0}I + {d_1}{\sigma _1} + {d_2}{\sigma _2} + {d_3}{\sigma _3}$$
+
+$$
+H(k) = {d_0}I + {d_1}{\sigma _1} + {d_2}{\sigma _2} + {d_3}{\sigma _3}
+$$
+
 $${d_0} = 2{t_2}\cos \phi \sum\nolimits_i {\cos (\mathbf{k} \cdot {\mathbf{b}_i})} = 2{t_2}\cos \phi \left[ {\cos \left( {\sqrt 3 {k_x}a} \right) + \cos \left( { - \sqrt 3 {k_x}a/2 + 3{k_y}a/2} \right) + \cos \left( { - \sqrt 3 {k_x}a/2 - 3{k_y}a/2} \right)} \right]$$
+$$
+
 $$
 {d_1} = {t_1}\sum\nolimits_i {\cos (\mathbf{k} \cdot {\mathbf{a}_i})}  = {t_1}\left[ {\cos \left( {{k_y}a} \right) + \cos \left( {\sqrt 3 {k_x}a/2 - {k_y}a/2} \right) + \cos \left( { - \sqrt 3 {k_x}a/2 - {k_y}a/2} \right)} \right]\\
+$$
+
+$$
 {d_2} = {t_1}\sum\nolimits_i {\sin (\mathbf{k} \cdot {\mathbf{a}_i})}  = {t_1}\left[ {\sin \left( {{k_y}a} \right) + \sin \left( {\sqrt 3 {k_x}a/2 - {k_y}a/2} \right) + \sin \left( { - \sqrt 3 {k_x}a/2 - {k_y}a/2} \right)} \right] \\
+$$
+
+$$
 {d_3} = m - 2{t_2}\sin \phi \sum\nolimits_i {\sin (\mathbf{k} \cdot {\mathbf{b}_i})}  = m - 2{t_2}\sin \phi \left[ {\sin \left( {\sqrt 3 {k_x}a} \right) + \sin \left( { - \sqrt 3 {k_x}a/2 + 3{k_y}a/2} \right) + \sin \left( { - \sqrt 3 {k_x}a/2 - 3{k_y}a/2} \right)} \right] \\
 $$