content_image/430006.jpg content_image/430025.jpg content_image/430016.jpg content_image/430024.jpg content_image/430026.jpg content_image/430027.jpg content_image/430019.jpg content_image/430020.jpg content_image/430022.jpg content_image/430021.jpg content_image/430023.jpg
hospitality the Racah Institute of Physics of the Hebrew University of Jerusalem, where a part of this work has been performed. tions in the second line 

## Appendix A: Current in the linear approximation 

We start with Eq. (29). Using Eqs. (13), (15), and (24), (25) we find after averaging over momentum direc- 

<img src='content_image/430006.jpg'>

This expression formally diverges for large v$_{F}$p due to contribution from regions far from the Dirac points. As we discussed already in Section III we remove this spu- rious divergence by transforming the zero-order terms. With Eqs. (16), (17) we have in the zero-order approxi- mation 

<img src='content_image/430025.jpg'>

The contribution from the zero-order term has the form of Eq. (30) of surface integral over a remote sphere in the momentum space. Using Eq. (A2) we find 

When added to Eq. (A1), this compensates the diverg- ing terms there. As a result, we obtain the converging expression, Eq. (31). The same result can be obtained if we subtract the normal current, i.e., Eq. (A1) for Δ = 0. For T ≪ | Δ | the terms cosh − $^{2}$( E$_{↑}$$_{,}$$_{↓}$/ 2 T ) are small while tanh( E$_{↑}$$_{,}$$_{↓}$/ 2 T ) = 1. Therefore, the first line in Eq. (31) vanishes. The current becomes 

<img src='content_image/430016.jpg'>

Calculating the current with help of Eqs. (16), (17) we obtain Eq. (32). 

<img src='content_image/430024.jpg'>

## Appendix B: Current in the degenerate case 

## 1. Wave functions for weak doping µ ≪ Δ 

Consider Eq. (38) for the state α = 1. We have within the linear approximation in H (1) 

<img src='content_image/430026.jpg'>

and 

<img src='content_image/430027.jpg'>

Since 

are small, in Eqs. (B1) and (B2) we can take the coeffi- cients in the zero order approximation. As a result C$_{12}$ an C$_{14}$ are small (i.e., are proportional to the perturba- tion), while C$_{11}$ and C$_{13}$ are of the order unity. We put C$_{11}$ = C (0) 11 , C$_{13}$ = C (0) 13 while C$_{12}$ = C (1) 12 , C$_{14}$ = C (1) 14 , and find up to the first order terms 

<img src='content_image/430019.jpg'>

<img src='content_image/430020.jpg'>

while 

<img src='content_image/430022.jpg'>

<img src='content_image/430021.jpg'>

<img src='content_image/430023.jpg'>

