DOI: 10.5061/dryad.0zpc86769
title: Direct magnetic imaging of fractional Chern insulators in twisted MoTe2

description: In the absence of time reversal symmetry, orbital magnetization provides a
 sensitive probe of topology and interactions, with particularly rich
 phenomenology in Chern insulators where topological edge states carry
 large equilibrium currents. Here, we use a nanoscale superconducting
 sensor to map the magnetic fringe fields in twisted bilayers of MoTe2,
 where transport and optical sensing experiments have revealed the
 formation of fractional Chern insulator (FCI) states at zero magnetic
 field. At a temperature of 1.6K, we observe oscillations in the local
 magnetic field associated with fillings ν=−1,−2/3,−3/5,−4/7 and −5/9 of
 the first moiré hole band, consistent with the formation of FCIs at these
 fillings. By quantitatively reconstructing the magnetization, we determine
 the local thermodynamic gaps of the most robust FCI state at ν=−2/3,
 finding −2/3Δ as large as 7 meV. Spatial mapping of the charge density-
 and displacement field-tuned magnetic phase diagram further allows us to
 characterize sample disorder, which we find to be dominated by both
 inhomogeneity in the effective unit cell area as well as inhomogeneity in
 the band edge offset and bound dipole moment. Our results highlight both
 the challenges posed by structural disorder in the study of twisted
 homobilayer moiré systems and the opportunities afforded by the remarkably
 robust nature of the underlying correlated topological states.
description: This README.txt file was generated on 2024-08-30 by Evgeny Redekop 1.
 Title of Dataset: Data for Direct magnetic imaging of fractional Chern
 insulators in twisted MoTe2 2. Author Information A. Principal
 Investigator Contact Information Name: Andrea Young Institution: UCSB
 Address: Broida Hall, 4113 Email:
 [afy2003@ucsb.edu](mailto:afy2003@ucsb.edu) Methods: We used buffer
 acquisition instruments to collect the data and matlab for the analysis.
 Datasets 11926-11928 (magnetic phase diagram data) Column 1: Trace (0)/
 Retrace (1) Column 2: fast axis index Column 3: slow axis index Column 4:
 Bottom gate voltage (V) Column 5: Top gate voltage (V) Column 6: SQUID
 signal 1wx (V) Column 7: SQUID signal DC (V) squidSlope = 500 V/T;
 SR560Gain = 10; SR560GainDC = 20; SR860Sensitivity = 0.001; Dataset 12068
 - 1d (magnetic phase diagram data) Column 1: Trace (0)/ Retrace (1) Column
 2: fast axis index Column 3: slow axis index Column 4: Bottom gate voltage
 (V) Column 5: Top gate voltage (V) Column 6: SQUID signal 1wx (V) Column
 7: SQUID signal DC (V) squidSlope = -500 V/T; SR560Gain = 10; SR560GainDC
 = 20; SR860Sensitivity = 0.05; Dataset 12060 - 1f (magnetic linecut data)
 Column 1: Trace (0)/ Retrace (1) Column 2: slow axis index Column 3: fast
 axis index Column 4: Bottom gate voltage (V) Column 5: Top gate voltage
 (V) Column 6: n0 voltage (V) Column 7: p0 voltage (V) Column 8: SQUID
 signal 1wx (V) Column 9: SQUID signal DC (V) SR_sensitivity = 0.002;
 SR560Gain = 10; SR560GainDC = 20; squidSlope = -200 V/T Dataset 12061 - 1f
 (magnetic linecut data) Column 1: Trace (0)/ Retrace (1) Column 2: slow
 axis index Column 3: fast axis index Column 4: Bottom gate voltage (V)
 Column 5: Top gate voltage (V) Column 6: SQUID signal 1wx (V) Column 7:
 SQUID signal DC (V) SR_sensitivity = 0.002; SR560Gain = 10; SR560GainDC =
 20; squidSlope = -200 V/T Dataset 12140 - 1f_inset:12142 - 1f_inset\_
 (magnetic phase diagram data) Column 1: Trace (0)/ Retrace (1) Column 2:
 slow axis index Column 3: fast axis index Column 4: Bottom gate voltage
 (V) Column 5: Top gate voltage (V) Column 6: n0 voltage (V) Column 7: p0
 voltage (V) Column 8: SQUID signal 1wx (V) Column 9: SQUID signal 1wy (V)
 Column 10: SQUID signal DC (V) SR560GainDC = 20; SR560Gain = 10;
 SR860Sensitivity = 0.0005; squidSlope = 200 V/T; Dataset 11671-11673
 (magnetic 2D video data) Column 1: Trace (0)/ Retrace (1) Column 2: bottom
 gate index Column 3: n0 voltage (V) Column 4: p0 voltage (V) Column 5:
 Bottom gate voltage (V) Column 6: Sample gate voltage (V) Column 7: x
 index Column 8: y index Column 9: x coordinate Column 10: y coordinate
 Column 11: SQUID signal 1wx (V) Column 12: SQUID signal DC (V) squidSlope
 = 280 V/T for 11671 and 100 V/T for 11673; SR560Gain = 10; SR560GainDC =
 50; SR860Sensitivity = 0.005; Dataset 12240 - 3a (magnetic 2D video data)
 Column 1: Trace (0)/ Retrace (1) Column 2: bottom gate index Column 3: n0
 voltage (V) Column 4: p0 voltage (V) Column 5: Bottom gate voltage (V)
 Column 6: Sample gate voltage (V) Column 7: x index Column 8: y index
 Column 9: x coordinate Column 10: y coordinate Column 11: SQUID signal 1wx
 (V) Column 12: SQUID signal DC (V) squidSlope = 500; SR560Gain = 10;
 SR560GainDC = 50; SR860Sensitivity = 0.0005; Dataset 12270 - 3b (magnetic
 2D video data) Column 1: Trace (0)/ Retrace (1) Column 2: bottom gate
 index Column 3: n0 voltage (V) Column 4: p0 voltage (V) Column 5: Bottom
 gate voltage (V) Column 6: Sample gate voltage (V) Column 7: x index
 Column 8: y index Column 9: x coordinate Column 10: y coordinate Column
 11: SQUID signal 1wx (V) Column 12: SQUID signal DC (V) squidSlope = 500;
 SR560Gain = 10; SR560GainDC = 50; SR860Sensitivity = 0.0005; Dataset 11756
 - 4d:11759 - 4d (magnetic phase diagram data) Column 1: Trace (0)/ Retrace
 (1) Column 2: slow axis index Column 3: fast axis index Column 4: Bottom
 gate voltage (V) Column 5: Top gate voltage (V) Column 6: SQUID signal 1wx
 (V) squidSlope = 200 V/T; SR560Gain = 10; SR860Sensitivity = 0.005;
 Dataset 12273 - 4f (magnetic phase diagram data) Column 1: Trace (0)/
 Retrace (1) Column 2: bottom gate index Column 3: n0 voltage (V) Column 4:
 p0 voltage (V) Column 5: Bottom gate voltage (V) Column 6: Sample gate
 voltage (V) Column 7: x index Column 8: y index Column 9: x coordinate
 Column 10: y coordinate Column 11: SQUID signal 1wx (V) Column 12: SQUID
 signal DC (V) squidSlope = 500 V/T; SR560Gain = 10; SR560GainDC = 50;
 Folder "Script" contains all the scripts necessary for
 reproducing the data presented in the manuscript.
 "OpenDataVaultFile2.m" can be used for reading the data from the
 .txt files provided in folder "Data". All the scripts are
 written in Matlab 2022b.