### Re: [Wannier] How to convert the unit of spin Hall conductivity from "(hbar/e)*S/cm" to "e2/h"?

```Hi Abid,

Your summary looks good.
(i) yes the total thickness
(ii) the thickness needs to be converted to centimeter to cancel the "cm"
in (hbar/e)*S/cm

Best,
Junfeng Qiao
Doctoral Assistant
EPFL THEOS
Switzerland

On Mon, May 3, 2021 at 4:36 PM Abid Rehman  wrote:

>   Dear  Qiao,
> First of all thank you very much for your response and
> explanation provided. I understood your points. I summarized what you have
> said  in the attached picture. Please have a look  at whether it is ok or
> not.
> I have further two supplementary confusions: (i) by "t*hickness along z"*
> you mean thickness of the slab (i.e, Sample thickness+Vacume thickness)  ?
> (ii) Normally th
> [image: picture.jpg]
> e thickness of the slab is in the  Angstrom unit in first-principle
> calculations,So should I take the thickness directly in the Angstrom unit
> or need to convert to cm.?
> Thank You
>
> On Mon, 3 May 2021 at 17:19, Junfeng Qiao  wrote:
>
>> Hi Abid,
>>
>> (hbar/e)*S/cm is the unit of SHC for 3D structures, e^2/h is the unit of
>> AHC
>> for 2D structures. If you are calculating SHC of a 2D structure by using
>> a
>> slab with vacuum, then you could first multiply the result by the
>> thickness
>> along z axis (assuming z axis is the direction normal to the slab plane,
>> i.e.
>> the total thickness of the slab and the vacuum), so now the unit is (hbar/
>> e)*S. Secondly, multiply the result by (-2e/hbar) [i.e. "convert" a spin
>> angular momentum (hbar/2) to a charge (-e)], now the unit is S. Since
>> e^2/hbar
>> ~= 2.434e-4 S, it's easy to do the reverse and you get the unit in e^2/h.
>>
>> Best,
>> Junfeng QIAO
>> Doctoral Assistant
>> EPFL THEOS
>> Switzerland
>>
>> On Sunday, May 2, 2021 9:54:33 AM CEST Abid Rehman wrote:
>> > Hi all,
>> > As we know, The wannier90 gives Spin Hall conductivity in units of
>> > *(hbar/e)*S/cm.
>> > *I want to express the spin Hall conductivity in *e2**/h *unit. So how
>> can
>> > I convert the data from  *(hbar/e)*S/cm *to* e2/h unit?*
>> > Thanks
>>
>>
>>
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```

### Re: [Wannier] How to convert the unit of spin Hall conductivity from "(hbar/e)*S/cm" to "e2/h"?

```Hi Abid,

(hbar/e)*S/cm is the unit of SHC for 3D structures, e^2/h is the unit of AHC
for 2D structures. If you are calculating SHC of a 2D structure by using a
slab with vacuum, then you could first multiply the result by the thickness
along z axis (assuming z axis is the direction normal to the slab plane, i.e.
the total thickness of the slab and the vacuum), so now the unit is (hbar/
e)*S. Secondly, multiply the result by (-2e/hbar) [i.e. "convert" a spin
angular momentum (hbar/2) to a charge (-e)], now the unit is S. Since e^2/hbar
~= 2.434e-4 S, it's easy to do the reverse and you get the unit in e^2/h.

Best,
Junfeng QIAO
Doctoral Assistant
EPFL THEOS
Switzerland

On Sunday, May 2, 2021 9:54:33 AM CEST Abid Rehman wrote:
> Hi all,
> As we know, The wannier90 gives Spin Hall conductivity in units of
> *(hbar/e)*S/cm.
> *I want to express the spin Hall conductivity in *e2**/h *unit. So how can
> I convert the data from  *(hbar/e)*S/cm *to* e2/h unit?*
> Thanks

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```