JMP  Vol.6 No.9 , August 2015
The Andreev Crossed Reflection—A Majorana Path Integral Approach
Author(s) David Schmeltzer
We investigate the effect of the Majorana Fermions which are formed at the boundary of a p-wave superconductor. When the Majorana overlapping energy is finite we construct the scattering matrix S by mapping the Majorana zero mode to Fermions for which coherent states are defined and a path integral is obtained. The path integral is used to compute the scattering matrix in terms of the electrons in the leads. This method is suitable for computing the conductivity. We investigate a chiral Majorana Hamiltonian and show that in the absence of vortices the conductivity vanishes. We compute the conductivity for p wave superconductor coupled to two metallic leads, and we show that when the overlapping energy between the two Majorana fermions is finite, the Andreev Crossed reflection conductance is finite.
Andreev, Majorana

Cite this paper
Schmeltzer, D. (2015) The Andreev Crossed Reflection—A Majorana Path Integral Approach. Journal of Modern Physics, 6, 1371-1379. doi: 10.4236/jmp.2015.69142.
[1]   Read, N. and Green, D. (2000) Physical Review B, 61, 10267.

[2]   Ivanov, D.A. (2001) Physical Review Letters, 86, 268.

[3]   Alicea, I. (2012) Reports on Progress in Physics, 75, Article ID: 076501.

[4]   Oreg, Y., Refael, G. and Oppen, F. (2010) Physical Review Letters, 105, Article ID: 177002.

[5]   Law, K.T., Lee, P.A. and Ng, T.K. (2009) Physical Review Letters, 103, Article ID: 237001.

[6]   Nillson, J., Akhmerov, A.R. and Beenakker, C.W.J. (2008) Physical Review Letters, 101, Article ID: 120403.

[7]   Fidkowski, L., Alicea, J., Lindner, N.H., Lutchyn, R.M. and Fisher, M.P.A. (2012) Physical Review B, 85, Article ID: 245121.

[8]   Li, J., Fleury, G. and Buttiker, M. (2012) Physical Review B, 85, Article ID: 125440.

[9]   Flensberg, K. (2010) Physical Review B, 82, Article ID: 180516(R).

[10]   Wieder, B.J., Zhang, F. and Kane, C.L. (2014) Physical Review B, 89, Article ID: 075106.

[11]   Beri, B. (2012) Physical Review B, 85, Article ID: 140501.

[12]   Weinberg, S. (2013) Lectures on Quantum Mechanics. Cambridge University Press, Cambridge.

[13]   Nadj, S., Drozdov, I.K., Berniwig, B.A. and Yazdani, A. (2013) Physical Review B, 88, Article ID: 020407.

[14]   Nakahara, M. (2003) Geometry, Topology and Physics. Taylor and Francis Group, New York and London.

[15]   Morandi, G., Sodano, P., Tagliacozzo, A. and Tognetti, V. (2000) Field Theories for Low Dimensional Condensed Matter Systems. Springer-Verlag, Berlin, 9-81. Heinz J. Shulz, Gianaurelio Cuniberti and Pierbiagio Pieri, “Fermi Liquid and Luttinger Liquids”.

[16]   Shankar, R. (1994) Reviews of Modern Physics, 66, 129-192.

[17]   Boyanovsky, D. (1989) Physical Review B, 39, 6744-6756.

[18]   Schmeltzer, D., Bishop, A.R., Saxena, A. and Smith, D.L. (2003) Physical Review Letters, 90, Article ID: 116802.