README file for Data from: Thermal transport of helium-3 in a strongly 
confining channel.


Authors: 
Lotnyk, Dmytro; Eyal, Anna; Zhelev, Nikolay; Sebastian, Abhilash; Smith, 
Eric; Terilli, Michael; Wilson, John; Mueller, Erich; Einzel, Dietrich; 
Saunders, John; Parpia, Jeevak


Author Contacts: 
1. Dmytro Lotnyk, dmytro.lotnyk@gmail.com 
2. Jeevak Parpia, jmp9@cornell.edu , 510 Clark Hall, Cornell University, 
Ithaca, NY 14853


Abstract: 
The investigation of transport properties in normal liquid helium-3 and its 
topological superfluid phases provides insights into related phenomena in 
electron fluids, topological materials, and putative topological 
superconductors. It relies on the measurement of mass, heat, and spin 
currents, due to system neutrality. Of particular interest is transport in 
strongly confining channels of height approaching the superfluid coherence 
length, to enhance the relative contribution of surface excitations, and 
suppress hydrodynamic counter-flow. Here we report on the thermal conduction 
of helium-3 in a 1.1 $\mu$m high channel. In the normal state we observe a 
diffusive thermal conductivity that is approximately temperature independent, 
consistent with interference of bulk and boundary scattering. In the 
superfluid, the thermal conductivity is only weakly temperature dependent, 
requiring detailed theoretical analysis. An anomalous thermal response is 
detected in the superfluid which we propose arises from the emission of a 
flux of surface excitations from the channel.


Keywords:
Normal 3He, Superfluid3He, Thermal Conductivity of a Fermi Liquid. Confined 
Fluid, Fountain Pressure, Surface Mediated Thermal Conduction.


Sponsorship Information:
This work was supported at Cornell by the NSF under DMR-1708341, 2002692 
(Parpia), PHY-1806357 (Mueller), in London by the EPSRC under EP/J022004/1. 
John Wilson's participation was supported in part by the Cornell Center for 
Materials research with funding from the Research Experience for 
Undergraduates program (DMR-1719875). In addition, the research leading to 
these results has received funding from the European Union’s Horizon 2020 
Research and Innovation Programme, under Grant Agreement no 824109. 
Fabrication was carried out at the Cornell Nanoscale Science and Technology 
Facility (CNF) with assistance and advice from technical staff. The CNF is a 
member of the National Nanotechnology Coordinated Infrastructure (NNCI), 
which is supported by the National Science Foundation (Grant NNCI-1542081).


License:
CC BY license (Creative Commons Attribution 4.0 International License). The 
CC BY license allows for maximum dissemination and re-use of open access 
materials and is preferred by many research funding bodies. Under this 
license users are free to share (copy, distribute and transmit) and remix 
(adapt) the contribution including for commercial purposes, providing they 
attribute the contribution in the manner specified by the author or licensor 
(http://creativecommons.org/licenses/by/4.0/legalcode).

Please cite this dataset as: Lotnyk, Dmytro; Eyal, Anna; Zhelev, Nikolay; 
Sebastian, Abhilash; Smith, Eric; Terilli, Michael; Wilson, John; Mueller, 
Erich; Einzel, Dietrich; Saunders, John; and Parpia, Jeevak. (2020) Data 
from: Thermal transport of helium-3 in a strongly confining channel 
[dataset]. Cornell University Library eCommons Repository. 
https://doi.org/10.7298/4fhq-e356. 


Related Publications:
1.	Thermal transport of helium-3 in a strongly confining channel, Nature 
Communications, Lotnyk, Dmytro; Eyal, Anna; Zhelev, Nikolay; Sebastian, 
Abhilash; Smith, Eric; Terilli, Michael; Wilson, John; Mueller, Erich; 
Einzel, Dietrich; Saunders, John; and Parpia, Jeevak. (2020) 
2.	3He specific heat and thermometry at millikelvin temperatures, Physical 
Review B, Greywall, D.S. v33 (1986), pp 7520 - 7538, 
http://dx.doi.org/10.1103/PhysRevB.33.7520 
3.	3He melting-curve thermometry at millikelvin temperatures, Physical 
Review B, Greywall, D.S., v31 (1985},pp 2675 – 2683, 
http://dx.doi.org/10.1103/PhysRevB.31.2675  
4.	Thermal conductivity of normal liquid 3He, Physical Review B}, author = 
{Greywall, D.S., v29 (1984), pp 4933 - 4945, 
http://dx.doi.org/10.1103/PhysRevB.29.4933  
5.	The A-B transition in superfluid helium-3 under confinement in a thin 
slab geometry, Nature Communications, Zhelev, N., Abhilash, T.S., ,Smith, 
E.N., Bennett, R.G., Rojas, X., Levitin, L., Saunders, J. and Parpia, 
J.M., v8 (2017), pp15963, http://dx.doi.org/10.1038/ncomms15963 
6.	Fabrication of microfluidic cavities using Si-to-glass anodic bonding, 
Review of Scientific Instruments, Zhelev, N., Abhilash, T.S., Bennett, 
R.G., Smith, E.N., Ilic, B., Parpia, J.M., Levitin, L.V., Rojas, X., 
Casey, A., and Saunders, J., v89 (2018), pp 073902, 
http://dx.doi.org/10.1063/1.5031837
7.	Anomalous Heat and Momentum Transport Arising from Surface Roughness in a 
Normal 3He Slab, Journal of Experimental and Theoretical Physics, Sharma, 
P., v126 (2018), pp 201-209, https://doi.org/10.1134/S1063776118020073 
8.	Quantum Transport in Mesoscopic 3He Films: Experimental Study of the 
Interference of Bulk and Boundary Scattering, Physical Review Letters, 
Sharma, P., Corcoles, A., Bennett, R. G., Parpia, J. M., Cowan, B., 
Casey, A., and Saunders, J., v107 pp 196805, (2011), 
https://link.aps.org/doi/10.1103/PhysRevLett.107.196805
9.	Heat flow in superfluid 3He, Journal of Low Temperature Physics, Johnson, 
R. T., Kleinberg, R. L., Webb, R. A., and Wheatley, J. C.", v18 (1975), 
pp 501—517 https://doi.org/10.1007/BF00116140
10.	Phase Diagram of the Topological Superfluid 3He Confined in a Nanoscale 
Slab Geometry, Science, Levitin, L. V., Bennett, R. G., Casey, A., and 
Cowan, B., Saunders, J., Drung, D., Schurig, Th., and Parpia, J. M, v340 
(2013), pp 841-844, http://science.sciencemag.org/content/340/6134/841
11.	Spin-independent transport parameters for superfluid 3He-B, Journal of 
Low Temperature Physics, v54, (1984) pp 427–474 
https://link.springer.com/article/10.1007/BF00683612  
12.	Finite-Size Effects and Shear Viscosity in Superfluid 3He-B, Physical Review 
Letters, Einzel, Dietrich and Parpia, Jeevak M., v58 (1987) pp1937-1940, 
https://link.aps.org/doi/10.1103/PhysRevLett.58.1937 
13.	Fragility of surface states in topological superfluid 3He. Heikkinen, P. 
J. et al., Preprint at https://arxiv.org/abs/1909.04210v2 (2019).
14.	Fundamental dissipation due to bound fermions in the zero-temperature 
limit. Autti, S. et al. Preprint at https://arxiv.org/abs/2002.10865 
(2020).


Data description.
The data described in this data set were refined from a raw data set where 
the frequency, quality factor (Q) and temperature were recorded while the 
temperature was being swept (for details see paper). A higher than ambient 
drive voltage resulted in heat pulses to one fork. The response in Q of both 
forks were recorded and the resulting fits and their analysis are compiled in 
the figures and data sets included here. The data files plotted in the 
publication are available in separate folders eg Fig2Data_and_fits, and 
Supplemental 

Figure 2 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig2Data_and_fits
Figure 3 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig3Data_and_fits
Figure 4 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig4Data_and_fits
Figure 5 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig5Data_and_fits
Figure 6 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig6Data_and_fits
Figure 7 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig7Data 
Figure 8 sources data from Lotnyk_etal2020figure_data_files_JP2020-09-
15>_Fig8CalcMeanFreePaths.

A collection of all the figures in the main manuscript is contained in the 
Lotnyk_etal2020figure_files folder.

The Supplemental Information contains 6 data files and 7 figures (one is an 
image of parts of the experiment). These can be found in 
Lotnyk_etal2020Supplementv9-15-2020
Supplemental Figure 1 sources data from 
Lotnyk_etal2020supplemental_figure_data_files>_SuppFig1
Supplemental Figure 2 sources data from 
Lotnyk_etal2020supplemental_figure_data_files>_SuppFig2
Supplemental Figure 3 sources data from 
Lotnyk_etal2020supplemental_figure_data_files>_SuppFig3
Supplemental Figure 4 sources data from 
Lotnyk_etal2020supplemental_figure_data_files>_SuppFig4
Supplemental Figure 6 sources data from 
Lotnyk_etal2020supplemental_figure_data_files>_SuppFig6
Supplemental Figure 7 sources data from 
Lotnyk_etal2020supplemental_figure_data_files>_SuppFig7

A collection of all the figures in the supplementary manuscript is contained 
in the Lotnyk_etal2020supplemental_figure_files folder.


Abbreviations Used Information
[s] seconds
[mK] milliKelvin
Q Quality factor of fork.
Tau [s] Thermal time constant
R_th, R_eff [K/W] Thermal resistance 
K_Eff [W/m-K] Thermal Conductivity
Lambda [cm] Viscous Mean free path [cm]


File-specific Information

Figure 2
File: Fig2ac_22bardata.csv
Column 1: universal time [s] is the x axis
Column 2: Q is the y-axis, plotted in fig 2(a).
Column 3: Temperature [mK], derived from the Q, plotted in Fig 2(c). 
These data are in the superfluid phase. 

File: Fig2bd_22bardata.csv
Column 1: universal time [s] is the x axis
Column 2: Q is the y-axis, plotted in fig 2(b)
Column 3: Temperature [mK], derived from the Q, plotted in Fig 2(d)
These data are in the normal state. 

File: Fig2ac_22bar_fit.csv
Column 1: universal time [s] is the x axis
Column 2: Q is the y-axis fit shown in red, plotted in fig 2(b)
Column 3: Fitted Temperature [mK], derived from the Q, plotted in Fig 2(c)
These fits are to data in the superfluid phase.

File: Fig2bd_22bar_fit.csv
Column 1: universal time [s] is the x axis
Column 2: Q is the y-axis fit shown in red, plotted in fig 2(b)
Column 3: Fitted Temperature [mK], derived from the Q, plotted in Fig 2(d)
These fits are to data in the normal state.

Figure 3
General information: Figure 3 plots the measured recovery time constant, Tau, 
fitted in fits shown in Fig 2. The tau was converted to the thermal 
resistance (R_th) using estimates for the heat capacity from Greywall’s data 
(see paper for references and Methods for procedure). The heat capacity for 
the two points in the superfluid phase were taken manually from calculations 
done separately using the heat capacity in the superfluid phase. 
The calculations for thermal resistance reference a Boundary Resistance 
derived from the Lancaster data [LBR] on sheet silver in parallel with the 
thermal resistance for bulk 3He, and 3He with impurity scattering with a mean 
free path of 1.1 micrometers. 

File: fig3_0barexpdata.csv 
Column 1: T[mK] is the x axis
Column 2: Tau [s] y-axis data in Fig 3a. 
Column 3: Error in Tau
Column 4: Rth [K/W] is the is the y-axis data in Fig 3c. 

File: fig3_22barexpdata.csv
Column 1: T[mK] is the x axis 
Column 2: Tau [s] y-axis data in Fig 3b 
Column 3: Error in Tau
Column 4: Rth [K/W] y-axis Fig 3d.

File: fig3_Rcalc_0and22bar_LancasterRk.csv 
Column 1: T [mK] is the x-axis
Column 2: Reff [K/W] Imp. Lim. 3He in parallel with LBR Y axis Fig 3d solid 
line 22bar.
Column 3: Reff [K/W] Bulk 3He in parallel with LBR Y axis Fig 3d dotted line 
22bar.
Column 4: Reff [K/W] Imp. Lim. 3He in parallel with LBR Y axis Fig 3c solid 
line 0bar.
Column 5: Reff [K/W] Bulk 3He in parallel with LBR Y axis Fig 3c dotted line 
0bar.           
File: fig3_Taucalc_0and22bar_LancasterRk.csv
Column 1: T [mK] is the x-axis
Column 2: Tau_bulk 22bar [s] Imp. Lim. 3He in parallel with LBR Y axis Fig 3b 
solid line.                                                                                   
Column 3: Tau imp 22bar [s] Bulk 3He in parallel with LBR Y axis Fig 3b 
dotted line.
Column 4: Tau_bulk 0bar [s] Imp. Lim. 3He in parallel with LBR Y axis Fig 3a 
solid line. solid line 0bar.
Column 5: Tau imp 0bar [s] Bulk 3He in parallel with LBR Y axis Fig 3a dotted 
line.

Figure 4
General information: Figure 4 plots the effective thermal conductivity, 
Kappa_Eff vs temp below 10 mK. Geometric factors covert R_Eff from fig3 to 
kappa of Fig 4. The calculations for thermal conductivity reference a 
Boundary Resistance derived from the Lancaster data [LBR] on sheet silver in 
parallel with the thermal resistance for bulk 3He, and 3He with impurity 
scattering with a mean free path of 1.1 micrometers. 

File: fig4_0barkappadata.csv 
Column 1: T[mK] is the x axis fig 4(a)
Column 2: Keff [W/m-K] y axis is the thermal conductivity measured fig 4(a).  

File: fig4_22barkappadata.csv
Column 1: T[mK] is the x axis fig 4(b)
Column 2: Keff [W/m-K] y axis is the thermal conductivity measured fig 4(b).  

File: fig4_kappa_Calc_0and22bar_Fig4ab.csv 
Column 1: T [mK] is the x-axis in both fig4(a) and fig 4(b)
Column 2: Kappa22bar_imp_Fig 4b [W/K-m] Impurity limited 3He in parallel with 
LBR Y axis solid line.
Column 3: Kappa22bar_bulk_Fig 4b [W/K-m] Bulk 3He in parallel with LBR Y axis 
dotted line 22bar.
Column 4: Kappa0bar_imp_Fig 4a [W/K-m] Imp. Lim. 3He in parallel with LBR Y 
axis Fig 4a solid line 0bar.
Column 5: Kappa0bar_bulk_Fig 4a [W/K-m] Bulk 3He in parallel with LBR Y axis 
Fig 4a dotted line 0bar.           

Figure 5
General information: Figure 5 plots the measured time constant Tau [s] in Fig 
5a, and effective thermal conductivity, Kappa_Eff in Fig 5 (b) vs T/Tc in the 
superfluid phase at 3 pressures, 0 bar, 9 psi (0.62 bar) and 22 bar. The 
calculations show results for K_eff obtained at two different scattering 
parameters at 21 bar.  

File: fig5_0bardata_ab.csv 
Column 1: T[mK] temperature in mK.
Column 2: T/Tc  Temperature normalized to transition temperature (x axis) in 
both Fig 5(a) and Fig 5(b).
Column 3: tau [s] fitted decay time in (s) y axis in fig 5(a) for 0 bar data
Column 4: err in tau [s].
Column 5: Kappa_eff [W/m-K] effective thermal conductivity y axis in Fig 5(b) 
for 0 bar data. 

File: fig5_9psidata_ab.csv 
Column 1: T[mK] temperature in mK.
Column 2: T/Tc  Temperature normalized to transition temperature (x axis) in 
both Fig 5(a) and Fig 5(b).
Column 3: tau [s] fitted decay time in (s) y axis in fig 5(a) for 0.62 bar 
data
Column 4: err in tau [s].
Column 5: Kappa_eff [W/m-K] effective thermal conductivity y axis in Fig 5(b) 
for 0.62 bar data. 

File: fig5_22bardata_ab.csv 
Column 1: T[mK] temperature in mK.
Column 2: T/Tc  Temperature normalized to transition temperature (x axis) in 
both Fig 5(a) and Fig 5(b).
Column 3: tau [s] fitted decay time in (s) y axis in fig 5(a) for 22 bar data
Column 4: err in tau [s].
Column 5: Kappa_eff [W/m-K] effective thermal conductivity y axis in Fig 5(b) 
for 22 bar data. 

File: fig5b_Dietrichresult.csv 
Column 1: T/Tc Temperature normalized to transition temperature (x axis) in 
Fig 5(b). 
Column 2: K_eff calculated for lambda_1^- =0.9 at 21 bar dashed line in Fig. 
5(b)
Column 3: T/Tc Temperature normalized to transition temperature (x axis) in 
Fig 5(b).
Column 4: K_eff calculated for lambda_1^- =2 at 21 bar solid line in Fig. 
5(b)

Figure 6
General information: Figure 6 plots the Q vs Universal time [s] for the HEC 
and IC forks. The HEC fork Q had to be filtered (15 points running average) 
as the fork was noisy in comparison to the IC fork. Data was taken at 0 bar.

File: fig6HEC_data.csv 
Column 1: Universal time [s] x axis
Column 2: Unfiltered Q.
Column 3: Q filtered y-axis

File: fig6IC_data.csv
Column 1: Universal time [s] x axis
Column 2: Unfiltered Q y axis

Figure 7
General information: Figure 7 plots the local temperature normalized to Tc at 
the HEC and IC forks (y axis) against the normalized melting curve 
temperature T/Tc for three representative temperatures (low, medium and near 
Tc). The HEC fork Q had to be filtered (15 points running average) as the 
fork was noisy in comparison to the IC fork. 

File: fig7_3x3_panel.csv
Column 1: Lists which panel data is for eg 7a, 7b,
Column 2: Pressure in bar
Column 3: Which fork data is for HEC* (for local temp in HEC) and IC 
(inferred temp for IC) both normalized to Tc.
Column 4: T/Tc – x axis temperature from melting curve thermoemeter.
Column 5: T_loc/Tc (of HEC* or IC) – y axis

Figure 8
General information: Figure 8 plots the bulk viscous mean free path vs T/Tc 
or Tc/T at the 3 studied pressures in the superfluid.  The points were 
digitized from a plot sent by Einzel to the PI. Some errors in digitization 
led to blank points that are not plotted.

File: fig8_a.csv 
Column 1: T/Tc 0bar x axis fig 8(a)
Column 2: Lambda 0bar [cm] y axis. fig 8(a)
Column 3: T/Tc 0.62bar x axis fig 8(a)
Column 4: Lambda 0.62bar [cm] y axis. fig 8(a)
Column 5: T/Tc 22bar x axis. fig 8(a)
Column 6: Lambda 22bar [cm] y axis. fig 8(a)

File: fig8_bc.csv.csv
Column 1: T/Tc 0bar x axis fig 8(b)
Column 2: Lambda 0bar [cm] y axis. fig 8(b,c)
Column 3: T/Tc 0.62bar x axis fig 8(b)
Column 4: Lambda 0.62bar [cm] y axis. fig 8(b,c)
Column 5: T/Tc 22bar x axis fig 8(b)
Column 6: Lambda 22bar [cm] y axis. fig 8(b,c)
Column 7: Tc/T x axis 0bar fig 8(c)
Column 8: Tc/T x axis 0.62bar fig 8(c)
Column 9: Tc/T x axis 22bar fig 8(c)


Supplementary Information Figures. 

Supplementary Figure 1
General information: Plots the calculated heat thermal conductivity Kappa 
(T/Tc) through the channel on account of hydrodynamic heat flow at two 
pressures. Two estimates of the slip limited viscosity were used, one scaling 
from 135 um data from Einzel & Parpia PRL (solid lines), the other using a 
simple extrapolation formula (dashed lines).

File: SuppFig1_0bar.csv
Column 1: T/Tc x axis
Column 2: Kappa0bar_extrapolated [W/K-m] y axis
Column 3: Kappa0bar_simplified [W/K-m] y axis

File: SuppFig1_22bar.csv
Column 1: T/Tc x axis
Column 2: Kappa22bar_extrapolated [W/K-m] y axis
Column 3: Kappa22bar_simplified [W/K-m] y axis

Supplementary Figure 2
General information: Plots the measured local temperatures (y axis) in the 
IC, HEC normalized to Tc vs T/Tc (with offsets) from the melting curve 
thermometer(x axis) at 3 pressures 0 bar, 0.62 bar (9 psi) and 22 bar. Dark 
colors are HEC, and lighter colors are IC data. 

File: Suppfig2_0bar_HEC.csv
Column 1: T/Tc x axis
Column 2: RawlocalT/Tc
Column 3: Filteredlocal T/Tc
Column 4: Shifted RawlocalT/Tc
Column 5: ShiftedFiltered T/Tc (shift is 0.2T/Tc) y axis

File: Suppfig2_0bar_IC.csv
Column 1: T/Tc x axis
Column 2: RawlocalT/Tc 
Column 3: Shifted T/Tc (shift is 0.25T/Tc) y axis

File: Suppfig2_9psi_HEC.csv
Column 1: T/Tc x axis
Column 2: Filteredlocal T/Tc (shifted by 0.35 T/Tc) y axis (25 pts average)
Column 3: T/Tc x axis inset
Column 4: Filteredlocal T/Tc (shifted by 0.35 T/Tc) y axis inset

File: Suppfig2_9psi_IC.csv
Column 1: T/Tc x axis
Column 2: local T/Tc (shifted by 0.4 T/Tc) y axis
Column 3: T/Tc x axis inset
Column 4: local T/Tc (shifted by 0.4 T/Tc) y axis inset

File: Suppfig2_22bar_HEC.csv
Column 1: T/Tc x axis
Column 2: RawlocalT/Tc
Column 3: Filteredlocal T/Tc

File: Suppfig2_22bar_IC.csv
Column 1: T/Tc x axis
Column 2: LocalT/Tc
Column 3: Shiftedlocal T/Tc (shifted by 0.1 T/Tc) y axis 

Supplementary Figure 3
General information: Plots the Q (y axis) in the IC, HEC against time. Dark 
solid points HEC, and light open points are IC data. Pulses were applied to 
the HEC. Data files are from two days starting 12 Feb, and continuing to 13 
Feb. 

File: Suppfig3_HEC_12Febdata.csv
Column 1: Universal time [s] (shifted to arbitrary zero) x axis
Column 2: Q HEC
Column 3: Q (15 points average) y axis 

File: Suppfig3_HEC_13Febdata.csv
Column 1: Universal time [s] (shift by same as 12 FebHEC) x axis
Column 2: Q HEC
Column 3: Q (15 points average) y axis

File: Suppfig3_IC_12Febdata.csv
Column 1: Universal time [s] (shift by same as 12 FebHEC) x axis
Column 2: Q IC y axis

File: Suppfig3_IC_13Febdata.csv
Column 1: Universal time [s] (shift by same as 12 FebHEC) x axis
Column 2: Q IC y axis

Supplementary Figure 4
General information: Plots the increase in local temperature after a pulse 
applied to the IC. The increase in temperature DeltaTHEC*/Tc (y axis) is 
plotted against DeltaTIC/Tc (x axis). Supp Fig 4(a) is at 0 bar, (b) is at 
0.62 bar, (c) is at 22 bar. 

File: Suppfig_4_0bar.csv
Column 1: DeltaTIC/Tc first pulse (x axis)
Column 2: DeltaTHEC/Tc first pulse (y axis)
Column 3: DeltaTIC/Tc second pulse (x axis)
Column 4: DeltaTHEC/Tc second pulse (y axis)
Column 5: DeltaTIC/Tc third pulse (x axis)
Column 6: DeltaTHEC/Tc third pulse (y axis)
Column 7: DeltaTIC/Tc fourth pulse (x axis)
Column 8: DeltaTHEC/Tc fourth pulse (y axis)
Column 9: DeltaTIC/Tc fifth pulse (x axis)
Column 10: DeltaTHEC/Tc fifth pulse (y axis)
Column 11: DeltaTIC/Tc sixth pulse (x axis)
Column 12: DeltaTHEC/Tc sixth pulse (y axis)
Column 13: DeltaTIC/Tc seventh pulse (x axis)
Column 14: DeltaTHEC/Tc seventh pulse (y axis)

File: Suppfig_4_9psi.csv
Column 1: DeltaTIC/Tc first pulse (x axis)
Column 2: DeltaTHEC/Tc first pulse (y axis)
Column 3: DeltaTIC/Tc second pulse (x axis)
Column 4: DeltaTHEC/Tc second pulse (y axis)
Column 5: DeltaTIC/Tc third pulse (x axis)
Column 6: DeltaTHEC/Tc third pulse (y axis)
Column 7: DeltaTIC/Tc fourth pulse (x axis)
Column 8: DeltaTHEC/Tc fourth pulse (y axis)
Column 9: DeltaTIC/Tc fifth pulse (x axis)
Column 10: DeltaTHEC/Tc fifth pulse (y axis)
Column 11: DeltaTIC/Tc sixth pulse (x axis)
Column 12: DeltaTHEC/Tc sixth pulse (y axis)
Column 13: DeltaTIC/Tc seventh pulse (x axis)
Column 14: DeltaTHEC/Tc seventh pulse (y axis)

File: Suppfig_4_22bar.csv
Column 1: DeltaTIC/Tc first pulse (x axis)
Column 2: DeltaTHEC/Tc first pulse (y axis)
Column 3: DeltaTIC/Tc second pulse (x axis)
Column 4: DeltaTHEC/Tc second pulse (y axis)
Column 5: DeltaTIC/Tc third pulse (x axis)
Column 6: DeltaTHEC/Tc third pulse (y axis)
Column 7: DeltaTIC/Tc fourth pulse (x axis)
Column 8: DeltaTHEC/Tc fourth pulse (y axis)
Column 9: DeltaTIC/Tc fifth pulse (x axis)
Column 10: DeltaTHEC/Tc fifth pulse (y axis)
Column 11: DeltaTIC/Tc sixth pulse (x axis)
Column 12: DeltaTHEC/Tc sixth pulse (y axis)
Column 13: DeltaTIC/Tc seventh pulse (x axis)
Column 14: DeltaTHEC/Tc seventh pulse (y axis)

Supplementary Figure 6
General information: As in Fig 3 Main paper this Figure plots the measured 
Tau [s] and calculated thermal resistance [R_th], and also the calculated 
thermal resistance for bulk 3He, and impurity limited 3He occupying the 
channel between the IC and the HEC. The parallel boundary resistance 
calculated using Lancaster data (for silver sheet) (LBR) and Andres and 
Sprenger (AS) for sintered silver is also shown (the latter in gray). As in 
Fig 3, main, the first two points in the superfluid Rth are carried over from 
calculations using the heat capacity in the superfluid. 

File: Suppfig6_0bar_Rth_and_Tau.csv 
Column 1: T[mK] is the x axis
Column 2: Tau [s] y-axis data in Supp Fig 6a. 
Column 3: Error in Tau
Column 4: Rth [K/W] is the y-axis data in Supp Fig 6c.

File: Suppfig6_22bar_Rth_and_Tau.csv
Column 1: T[mK] is the x axis 
Column 2: Tau [s] y-axis data in Supp Fig 6b 
Column 3: Error in Tau
Column 4: Rth [K/W] is the y-axis data in Supp Fig 6d.

File: Suppfig6_RthLancasterBR_0bar22bar.csv
Column 1: T [mK] is the x-axis
Column 2: Reff [K/W] Imp. Lim. 3He in parallel with LBR Y axis Supp Fig 6d 
solid line 22bar.
Column 3: Reff [K/W] Bulk 3He in parallel with LBR Y axis Supp Fig 6d dotted 
line 22bar.
Column 4: Reff [K/W] Imp. Lim. 3He in parallel with LBR Y axis Supp Fig 6c 
solid line 0bar.
Column 5: Reff [K/W] Bulk 3He in parallel with LBR Y axis Supp Fig 6c dotted 
line 0bar.   
        
File: Suppfig6_RthAndresSprenger_0bar22bar.csv
Column 1: T [mK] is the x-axis
Column 2: Reff [K/W] Imp. Lim. 3He in parallel with AS Resistance Y axis Supp 
Fig 6d solid grey line 22bar.
Column 3: Reff [K/W] Bulk 3He in parallel with AS Resistance Y axis Supp Fig 
6d dotted line 22bar.
Column 4: Reff [K/W] Imp. Lim. 3He in parallel with AS Resistance Y axis Supp 
Fig 6c solid grey line 0bar.
Column 5: Reff [K/W] Bulk 3He in parallel with AS Resistance Y axis Supp Fig 
6c dotted grey line 0bar. 

File: Suppfig6_TauLancaster _0bar22bar.csv
Column 1: T [mK] is the x-axis
Column 2: Tau 22bar [s] Imp. Lim. 3He in parallel with LBR Y axis Supp Fig 6b 
solid line.
Column 3: Tau 22bar [s] Bulk 3He in parallel with LBR Y axis Supp Fig 6b 
dotted line.
Column 4: Tau 0bar [s] Imp. Lim. 3He in parallel with LBR Y axis Supp Fig 6a 
solid line 0bar.
Column 5: Tau 0bar [s] Bulk 3He in parallel with LBR Y axis Supp Fig 6a 
dotted line 0bar.

File: Suppfig6_TauAndresSprenger_0bar22bar.csv
Column 1: T [mK] is the x-axis
Column 2: Tau 22bar [s] Imp. Lim. 3He in parallel with AS Resistance Y axis 
Supp Fig 6b solid grey line.
Column 3: Tau 22bar [s] Bulk 3He in parallel with AS Resistance Y axis Supp 
Fig 6b dotted grey line.
Column 4: Tau 0bar [s] Imp. Lim. 3He in parallel with AS Resistance Y axis 
Supp Fig 6a solid grey line 0bar.
Column 5: Tau 0bar [s] Bulk 3He in parallel with AS Resistance Y axis Supp 
Fig 6a dotted grey line 0bar. 

Supplementary Figure 7
General information: Figure 7 plots the effective thermal conductivity, 
Kappa_Eff vs temp below 10 mK. Geometric factors covert R_Eff from 
Supplementary fig6 to kappa of Supplementary Fig 7. The parallel boundary 
resistance calculated using Lancaster data (for silver sheet) (LBR) and 
Andres and Sprenger (AS) for sintered silver is also shown (the latter in 
gray). 

File: Suppfig7_0bardata_KappaEff.csv 
Column 1: T[mK] is the x axis supp fig 7(a)
Column 2: Keff [W/K-m] y axis is the thermal conductivity plotted in supp fig 
7(a).  

File: Suppfig7_22bardata_KappaEff.csv
Column 1: T[mK] is the x axis supp fig 7(b)
Column 2: Keff [W/K-m] y axis is the thermal conductivity plotted in supp fig 
7(b).  

File: Suppfig7_LancasterRescalcKappa_Eff_0bar22bar.csv 
Column 1: T [mK] is the x-axis in both Supp fig7(a) and fig 7(b)
Column 2: Kappa_eff22bar_imp+LBR [W/K-m] Impurity limited 3He in parallel 
with LBR Y axis solid line Supp Fig 7b
Column 3: Kappa_eff22bar_bulk+LBR [W/K-m] Bulk 3He in parallel with LBR Y 
axis dotted line Supp Fig 7b
Column 4: Kappa_eff0bar_imp+LBR [W/K-m] Impurity limited 3He in parallel with 
LBR Y axis solid line Supp Fig 7a
Column 5: Kappa_eff0bar_bulk_+LBR [W/K-m] Bulk 3He in parallel with LBR Y 
axis Supp Fig 7a dotted line 0bar.           

File: Suppfig7_AndresSprengercalcKappa_Eff_0bar22bar.csv 
Column 1: T [mK] is the x-axis in both Supp fig7(a) and fig 7(b)
Column 2: Kappa_eff22bar_imp+AS [W/K-m] Impurity limited 3He in parallel with 
AS Res Y axis solid grey line Supp Fig 7b
Column 3: Kappa_eff22bar_bulk+AS [W/K-m] Bulk 3He in parallel with AS Res Y 
axis dotted grey line Supp Fig 7b
Column 4: Kappa_eff0bar_imp+AS [W/K-m] Impurity limited 3He in parallel with 
AS Res Y axis solid grey line Supp Fig 7a
Column 5: Kappa_eff0bar_bulk_+AS [W/K-m] Bulk 3He in parallel with AS Res Y 
axis Supp Fig 7a dotted grey line 0bar.