Supplementary Materials for ”Entropy-Enhanced Fractional Quantum Anomalous Hall Effect”
Gal Shavit
1, 2
1
Department of Physics and Institute for Quantum Information and Matter,
California Institute of Technology, Pasadena, California 91125, USA
2
Walter Burke Institute of Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
OBTAINING THE TRANSITION TEMPERATURE
Beginning with Eq. (1) in the main text, we equate the free energies of the
F
and
I
phases, plugging in the edge entropy,
U
I
−
P
π
2
k
2
B
T
2
3
h
X
j
∈
I
1
v
j
=
U
F
−
P
π
2
k
2
B
T
2
3
h
X
i
∈
F
1
v
i
,
(S1)
where
P
is the perimeter of the device, and
i
and
j
sum over the edge modes in the
F
and
I
phases, respectively. Isolating the
transition temperature
̃
T
,
k
B
̃
T
=
v
u
u
u
t
ℏ
U
F
−
U
I
π
2
3
P
X
i
∈
F
1
v
i
−
X
j
∈
I
1
v
j
−
1
,
(S2)
We may recover Eq. (4) in the main text via the definitions
U
F
−
U
I
= Ω
δu
,
v
∗
=
h
P
i
∈
F
1
v
i
−
P
j
∈
I
1
v
j
i
−
1
, and
3Ω
/