Magnetization, Spin Current, And Spin-transfer Torque From Su (2) Local Gauge Invariance Of The Nonrelativistic Pauli-schrödinger Theory

In this Brief Report, we consider local gauge symmetries of the nonrelativistic Pauli-Schrödinger theory. From the simplest free Lagrangian density for Pauli two-component spinors, we obtain the spin interaction with a magnetic field and define the spin-current vector without invoking relativistic theory. Applying U (1) ×SU (2) local gauge symmetry, and proceeding via the Noether's theorem, we are able to construct a covariant conserved spin-current density in a natural way. Our approach allow us to understand the main features of spin transport properties and suggests that SU (2) is a fundamental symmetry of nonrelativistic quantum mechanics. © 2008 The American Physical Society.781Wolf, S.A., Awschalom, D.D., Buhrman, R.A., Daughton, J.M., Von Molnar, S., Roukes, M.L., Chtchelkanova, A.Y., Treger, D.M., (2001) Science, 294, p. 1488. , SCIEAS 0036-8075 10.1126/science.1065389Zutic, I., Fabian, J., Das Sarma, S., (2004) Rev. Mod. Phys., 76, p. 323. , RMPHAT 0034-6861 10.1103/RevModPhys.76.323Zhang, S., Levy, P.M., Marley, A.C., Parkin, S.S.P., (1997) Phys. Rev. Lett., 79, p. 3744. , See, for instance, PRLTAO 0031-9007 10.1103/PhysRevLett.79.3744Dartora, C.A., Cabrera, G.G., (2004) J. Appl. Phys., 95, p. 6058. , JAPIAU 0021-8979 10.1063/1.1703825Dartora, C.A., Cabrera, G.G., (2005) Phys. Rev. B, 72, p. 064456. , PRBMDO 0163-1829 10.1103/PhysRevB.72.064456Petit, S., Baraduc, C., Thirion, C., Ebels, U., Liu, Y., Li, M., Wang, P., Dieny, B., (2007) Phys. Rev. Lett., 98, p. 077203. , PRLTAO 0031-9007 10.1103/PhysRevLett.98.077203Berger, L., (1996) Phys. Rev. B, 54, p. 9353. , PRBMDO 0163-1829 10.1103/PhysRevB.54.9353Slonczewski, J., (1996) J. Magn. Magn. Mater., 159, p. 1. , JMMMDC 0304-8853 10.1016/0304-8853(96)00062-5Murakami, S., Nagaosa, N., Zhang, S.-C., (2003) Science, 301, p. 1348. , SCIEAS 0036-8075 10.1126/science.1087128Murakami, S., Nagaosa, N., Zhang, S.-C., (2004) Phys. Rev. B, 69, p. 235206. , PRBMDO 0163-1829 10.1103/PhysRevB.69.235206Jiang, Z.F., Li, R.D., Zhang, S.-C., Liu, W.M., (2005) Phys. Rev. B, 72, p. 045201. , PRBMDO 0163-1829 10.1103/PhysRevB.72.045201Sinova, J., Culcer, D., Niu, Q., Sinitsyn, N.A., Jungwirth, T., MacDonald, A.H., (2004) Phys. Rev. Lett., 92, p. 126603. , PRLTAO 0031-9007 10.1103/PhysRevLett.92.126603Shen, S.Q., Ma, M., Xie, X.C., Zhang, F.C., (2004) Phys. Rev. Lett., 92, p. 256603. , PRLTAO 0031-9007 10.1103/PhysRevLett.92.256603Barnes, S.E., Maekawa, S., (2007) Phys. Rev. Lett., 98, p. 246601. , PRLTAO 0031-9007 10.1103/PhysRevLett.98.246601Hirsch, J.E., (1990) Phys. Rev. B, 42, p. 4774. , PRBMDO 0163-1829 10.1103/PhysRevB.42.4774Meier, F., Loss, D., (2003) Phys. Rev. Lett., 90, p. 167204. , PRLTAO 0031-9007 10.1103/PhysRevLett.90.167204Schutz, F., Kollar, M., Kopietz, P., (2003) Phys. Rev. Lett., 91, p. 017205. , PRLTAO 0031-9007 10.1103/PhysRevLett.91.017205Sun, Q.-F., Guo, H., Wang, J., (2004) Phys. Rev. B, 69, p. 054409. , PRBMDO 0163-1829 10.1103/PhysRevB.69.054409Vernes, A., Gyorffy, B.L., Weinberger, P., (2007) Phys. Rev. B, 76, p. 012408. , PRBMDO 0163-1829 10.1103/PhysRevB.76.012408Sakurai, J.J., (1994) Advanced Quantum Mechanics, , Revised ed. (Addison-Wesley, Reading, MABjorken, J.D., Drell, S.D., (1964) Relativistic Quantum Mechanics, , McGraw-Hill, New YorkGreiner, W., Reinhardt, J., (2002) Quantum Electrodynamics, , 3rd ed. (Springer-Verlag, BerlinWang, Y., Xia, K., Su, Z.B., Ma, Z., (2006) Phys. Rev. Lett., 96, p. 066601. , PRLTAO 0031-9007 10.1103/PhysRevLett.96.066601Sun, Q.F., Xie, X.C., (2005) Phys. Rev. B, 72, p. 245305. , PRBMDO 0163-1829 10.1103/PhysRevB.72.245305Fröhlich, J., Studer, U.M., (1992) Commun. Math. Phys., 148, p. 553. , CMPHAY 0010-3616 10.1007/BF02096549Fröhlich, J., Studer, U.M., (1992) Int. J. Mod. Phys. B, 6, p. 2201. , IJPBEV 0217-9792 10.1142/S0217979292001092Fröhlich, J., Studer, U.M., (1993) Rev. Mod. Phys., 65, p. 733. , RMPHAT 0034-6861 10.1103/RevModPhys.65.733Yang, C.N., Mills, R.L., (1954) Phys. Rev., 96, p. 191. , PHRVAO 0031-899X 10.1103/PhysRev.96.191Weinberg, S., (1996) The Quantum Teory of Fields, 1-2. , Cambridge University Press, CambridgeRyder, L.H., (1996) Quantum Field Theory, , 2nd ed. (Cambridge University Press, CambridgeLove, P.J., Boghosian, B.M., (2004) Physica a, 332, p. 47. , PHYADX 0378-4371 10.1016/j.physa.2003.09.055Wiese, U.-J., (2005) Nucl. Phys. B, Proc. Suppl., 141, p. 143. , 0920-5632Watts, S.M., Grollier, J., Van Der Wal, C.H., Van Wees, B.J., (2006) Phys. Rev. Lett., 96, p. 077201. , PRLTAO 0031-9007 10.1103/PhysRevLett.96.07720

Wess–Zumino supersymmetric phase and superconductivity in graphene

AbstractSupersymmetry is expected to exist in nature at high energies, but must be spontaneously broken at ordinary energy scales. The required energy scale in elementary particle physics is currently inaccessible, but condensed matter could furnish low energy realizations of supersymmetry. In graphene, electrons behave as ‘relativistic’ massless fermions in 1+2 dimensions. Here we propose phenomenologically, assuming that some microscopic parameters can be fine-tuned in graphene, the existence of a supersymmetric Wess–Zumino phase. The supersymmetry breaking leads to a superconductor phase, described by a relativistic Ginzburg–Landau phenomenology

Resonant Magnetic Tunnel Junction At 0° K: I-v Characteristics And Magnetoresistance

In this paper we analyze the main transport properties of a simple resonant magnetic tunnel junction (FM-IS-METAL-IS-FM structure) taking into account both elastic and magnon-assisted tunneling processes at low voltages and temperatures near 0° K. We show the possibility of magnetoresistance inversion as a consequence of inelastic processes and spin-dependent transmission coefficients. Resonant tunneling can also explain the effect of scattering by impurities located inside an insulating barrier. © 2005 American Institute of Physics.973Ando, Y., Murai, J., Kubota, H., Miyazaki, T., (2000) J. Appl. Phys., 87, p. 5209Xiang, X.H., Zhu, T., Du, J., Landry, G., Xiao, J.Q., (2002) Phys. Rev. B, 66, p. 174407Akerman, J.J., Roushchin, I.V., Slaughter, J.M., Dave, R.W., Schuller, I.K., (2003) Europhys. Lett, 63, p. 104Montaigne, F., Nassar, J., Vaurs, A., Van Dau Nguyen, F., Petroff, F., Schuhl, A., Pert, A., (1998) Appl. Phys. Lett., 73, p. 2829Miyazaki, T., Tezuka, N., (1995) J. Magn. Magn. Mater., 139, pp. L231Cabrera, G.G., Falicov, L.M., (1974) Phys. Status Solidi B, 61, p. 539(1975) Phys. Rev. B, 11, p. 2651Jullire, M., (1975) Phys. Lett., 54 A, p. 225Zhang, S., Levy, P.M., Marley, A.C., Parkin, S.S.P., (1997) Phys. Rev. Lett., 79, p. 3744Moodera, J.S., Nowak, J., Van De Veerdonk, R.J.M., (1998) Phys. Rev. Lett., 80, p. 2941Moodera, J.S., Mathon, G., (1999) J. Magn. Magn. Mater., 200, p. 248Cabrera, G.G., Garcia, N., (2002) Appl. Phys. Lett., 80, p. 1782Dartora, C.A., Cabrera, G.G., (2004) J. Appl. Phys., 95, p. 6058Zhang, X., Li, B.Z., Sun, G., Pu, F.C., (1997) Phys. Rev. B, 56, p. 5484N. Ryzhanova, G. Reiss, F. Kanjouri, and A. Vedyayev, arxiv.cond-mat/ 0401006 v2, 12 January 2004Zhang, S., Levy, P.M., (1999) Eur. Phys. J. B, 10, p. 599Tsymbal, E.Y., Sokolov, A., Sabirianov, I.F., Doudin, B., (2003) Phys. Rev. Lett., 90, p. 186602Tsymbal, E.Y., Pettifor, D.G., (2001) Phys. Rev. B, 64, p. 212401Jansen, R., Moodera, J.S., (1999) Appl. Phys. Lett., 75, p. 400Leclair, P., Kohlhepp, J.T., Swagten, H.J.M., De Jonge, W.J.M., (2001) Phys. Rev. Lett, 86, p. 1066De Teresa, J.M., (1999) Phys. Rev. Lett., 82, p. 4288Ferry, X., Goodnick, X., (1997) Transport in Nanostructures, , Cambridge University Press, CambridgeImry, Y., (1997) Introduction to Mesoscopic Physics, , Oxford University Press, New YorkKittel, C., (1963) Quantum Theory of Solids, , Wiley, New Yor

U(1)×su(2) Gauge Invariance Leading To Charge And Spin Conductivity Of Dirac Fermions In Graphene

Gauge symmetries have been identified in graphene and associated with specific physical properties. For instance, the U(1) gauge group is related to electrodynamics in (1+2)-dimensional [(1+2)D] space-time and non-Abelian gauge groups can describe curvature and torsion. Here we demonstrate that the Dirac Lagrangian for massless electrons near the Dirac points is also invariant under the group SU(2) related to local spin rotations, leading to the correct spin-orbit interactions and a rigorous definition for the spin-current density. Furthermore, we computed the charge and spin conductivity within the framework of Kubo linear response theory, using the algebra of relativistic Dirac spinors in (1+2)D space-time. The minimal value of electrical conductivity is predicted to be πq2/h, in agreement with typical experimental findings. © 2013 American Physical Society.8716Wallace, P.R., (1947) Phys. Rev., 71, p. 622. , PHRVAO 0031-899X 10.1103/PhysRev.71.622McLure, J.W., (1957) Phys. Rev., 108, p. 612. , PHRVAO 0031-899X 10.1103/PhysRev.108.612Semenoff, G.W., (1984) Phys. Rev. Lett., 53, p. 2449. , PRLTAO 0031-9007 10.1103/PhysRevLett.53.2449Novoselov, K.S., Jiang, D., Schedin, F., Booth, T.J., Khotkevich, V.V., Morozov, S.V., Geim, A.K., Two-dimensional atomic crystals (2005) Proceedings of the National Academy of Sciences of the United States of America, 102 (30), pp. 10451-10453. , DOI 10.1073/pnas.0502848102Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A., Electric field in atomically thin carbon films (2004) Science, 306 (5696), pp. 666-669. , DOI 10.1126/science.1102896Castro Neto, A.H., (2009) Rev. Mod. Phys., 81, p. 109. , RMPHAT 0034-6861 10.1103/RevModPhys.81.109Das Sarma, S., (2011) Rev. Mod. Phys., 83, p. 407. , RMPHAT 0034-6861 10.1103/RevModPhys.83.407Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A., Two-dimensional gas of massless Dirac fermions in graphene (2005) Nature, 438 (7065), pp. 197-200. , DOI 10.1038/nature04233, PII N04233Zhang, Y., Tan, Y.-W., Stormer, H.L., Kim, P., Experimental observation of the quantum Hall effect and Berry's phase in graphene (2005) Nature, 438 (7065), pp. 201-204. , DOI 10.1038/nature04235, PII N04235McCreary, K.M., (2012) Phys. Rev. Lett., 109, p. 186604. , PRLTAO 0031-9007 10.1103/PhysRevLett.109.186604Mecklenburg, M., Regan, B.C., (2011) Phys. Rev. Lett., 106, p. 116803. , PRLTAO 0031-9007 10.1103/PhysRevLett.106.116803Abanin, D.A., (2011) Phys. Rev. Lett., 107, p. 096601. , PRLTAO 0031-9007 10.1103/PhysRevLett.107.096601Cornaglia, P.S., Usaj, G., Balseiro, C.A., (2009) Phys. Rev. Lett., 102, p. 046801. , PRLTAO 0031-9007 10.1103/PhysRevLett.102.046801Wimmer, M., Adagideli, I., Berber, S., Tomanek, D., Richter, K., Spin currents in rough graphene nanoribbons: Universal fluctuations and spin injection (2008) Physical Review Letters, 100 (17), p. 177207. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.100.177207&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.100.177207Katsnelson, M.I., Novoselov, K.S., Graphene: New bridge between condensed matter physics and quantum electrodynamics (2007) Solid State Communications, 143 (1-2), pp. 3-13. , DOI 10.1016/j.ssc.2007.02.043, PII S0038109807003043, Exploring graphene Recent research advancesFradkin, E., (1986) Phys. Rev. B, 33, p. 3263. , PRBMDO 1098-0121 10.1103/PhysRevB.33.3263Ludwig, A.W.W., Fisher, M.P.A., Shankar, R., Grinstein, G., (1994) Phys. Rev. B, 50, p. 7526. , PRBMDO 1098-0121 10.1103/PhysRevB.50.7526Shon, N.H., Ando, T., (1998) J. Phys. Soc. Jpn., 67, p. 2421. , JUPSAU 0031-9015 10.1143/JPSJ.67.2421Peres, N.M.R., Guinea, F., Castro Neto, A.H., Electronic properties of disordered two-dimensional carbon (2006) Physical Review B - Condensed Matter and Materials Physics, 73 (12), pp. 1-23. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevB.73.125411&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevB.73.125411, 125411Nomura, K., MacDonald, A.H., (2007) Phys. Rev. Lett., 98, p. 076602. , PRLTAO 0031-9007 10.1103/PhysRevLett.98.076602Kumazaki, H., Hirashima, D.S., Effects of impurities in two-dimensional graphite (2006) Journal of the Physical Society of Japan, 75 (5), p. 053707. , http://jpsj.ipap.jp/link?JPSJ/75/053707/pdf, DOI 10.1143/JPSJ.75.053707Lee, P.A., (1993) Phys. Rev. Lett., 71, p. 1887. , PRLTAO 0031-9007 10.1103/PhysRevLett.71.1887Cserti, J., (2007) Phys. Rev. B, 75, p. 033405. , PRBMDO 1098-0121 10.1103/PhysRevB.75.033405Tworzydlo, J., Trauzettel, B., Titov, M., Rycerz, A., Beenakker, C.W.J., Sub-poissonian shot noise in graphene (2006) Physical Review Letters, 96 (24), p. 246802. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.96.246802&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.96.246802Katsnelson, M.I., Zitterbewegung, chirality, and minimal conductivity in graphene (2006) European Physical Journal B, 51 (2), pp. 157-160. , DOI 10.1140/epjb/e2006-00203-1Falkovsky, L.A., Varlamov, A.A., Space-time dispersion of graphene conductivity (2007) European Physical Journal B, 56 (4), pp. 281-284. , DOI 10.1140/epjb/e2007-00142-3Weinberg, S., (1996) The Quantum Theory of Fields, , Cambridge University Press, CambridgeRyder, L.H., (1996) Quantum Field Theory, , Cambridge University Press, CambridgeVozmediano, M.A.H., Kastnelson, M.I., Guinea, F., (2010) Phys. Rep., 496, p. 109. , PRPLCM 0370-1573 10.1016/j.physrep.2010.07.003Mesaros, A., Sadri, D., Zaanen, J., (2010) Phys. Rev. B, 82, p. 073405. , PRBMDO 1098-0121 10.1103/PhysRevB.82.073405Dartora, C.A., Cabrera, G.G., (2008) Phys. Rev. B, 78, p. 012403. , PRBMDO 1098-0121 10.1103/PhysRevB.78.012403Fröhlich, J., Studer, U.M., (1992) Commun. Math. Phys., 148, p. 553. , CMPHAY 0010-3616 10.1007/BF02096549Fröhlich, J., Studer, U.M., (1992) Int. J. Mod. Phys. B, 6, p. 2201. , IJPBEV 0217-9792 10.1142/S0217979292001092Fröhlich, J., Studer, U.M., (1993) Rev. Mod. Phys., 65, p. 733. , RMPHAT 0034-6861 10.1103/RevModPhys.65.733Min, H., Hill, J.E., Sinitsyn, N.A., Sahu, B.R., Kleinman, L., MacDonald, A.H., Intrinsic and Rashba spin-orbit interactions in graphene sheets (2006) Physical Review B - Condensed Matter and Materials Physics, 74 (16), p. 165310. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevB.74.165310&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevB.74.165310Zarea, M., Sandler, N., (2009) Phys. Rev. B, 79, p. 165442. , PRBMDO 1098-0121 10.1103/PhysRevB.79.165442Gmitra, M., Konschuh, S., Ertler, C., Ambrosch-Draxl, C., Fabian, J., (2009) Phys. Rev. B, 80, p. 235431. , PRBMDO 1098-0121 10.1103/PhysRevB.80.235431Gorini, C., Schwab, P., Raimondi, R., Shelankov, A.L., (2010) Phys. Rev. B, 82, p. 195316. , PRBMDO 1098-0121 10.1103/PhysRevB.82.195316Adagideli, I., Lutsker, V., Scheid, M., Jacquod, Ph., Richter, K., (2012) Phys. Rev. Lett., 108, p. 236601. , PRLTAO 0031-9007 10.1103/PhysRevLett.108.236601Onari, S., Ishikawa, Y., Kontani, H., Inoue, J., (2008) Phys. Rev. B, 78, p. 121403. , PRBMDO 1098-0121 10.1103/PhysRevB.78.12140

Can We Explain Why Leptonic Electroweak Interactions Are Chiral?

One of the fundamental ingredients in the standard model of electroweak interactions between fundamental particles is chirality. Currently there are no hints about why nature has chosen the chiral way. The answer to such a fundamental question could be the extension of the whole theory to the superluminal sector of the Lorentz-Poincaré group. Restricting ourselves to leptons, we postulate that the neutrinos are a priori described by a tachyonic Dirac Lagrangian. It could provide a simple explanation for the parity violation in weak interactions and why electroweak theory has a chiral aspect, leading to invariance under a SUL(2) × UY (1) gauge group. Right-handed neutrino becomes sterile and decoupled from the other particles quite naturally. © Copyright EPLA, 2013.1015Weinberg, S., (1996) The Quantum Theory of Fields, 12Ryder, L.H., (1996) Quantum Field Theory, , 10.1017/CBO9780511813900Recami, E., (1986) Riv. Nuovo Cimento., 9, p. 1Recami, E., Rached, M.Z., Dartora, C.A., (2004) Phys. Rev. e, 69 (2). , 10.1103/PhysRevE.69.027602 1539-3755 027602Recami, E., (2001) Found. Phys., 31 (7), p. 1119. , 10.1023/A:1017582525039 0015-9018Caban, P., Rembielinski, J., Smolinski, K.A., Walczak, Z., (2006) Found. Phys. Lett., 19 (6), p. 619. , 10.1007/s10702-006-1015-4 0894-9875Eidelman, S., (2004) Phys. Lett. B, 592 (1-4), p. 1. , 10.1016/j.physletb.2004.06.001 0370-2693Assamagan, K., (1996) Phys. Rev. D, 53 (11), p. 6065. , 10.1103/PhysRevD.53.6065 0556-2821Ehrlich, R., (1999) Phys. Rev. D, 60 (1). , 10.1103/PhysRevD.60.017302 0556-2821 017302Ciborowski, J., Rembielinski, J., (1999) Eur. Phys. J. C, 8 (1), p. 157. , 10.1007/s100529901062 1434-6044Stephenson, G.J., Goldman, T., McKellar, B.H.J., (2000) Phys. Rev. D, 62 (9). , 10.1103/PhysRevD.62.093013 0556-2821 093013Mohapatra, R.N., Nussinov, S., (1997) Phys. Lett. B, 395 (1-2), p. 63. , 10.1016/S0370-2693(97)00054-3 0370-2693Chodos, A., Kostelecký, V.A., Potting, R., Gates, E., (1992) Mod. Phys. Lett. A, 7 (6), p. 467. , 10.1142/S0217732392000422 0217-7323Sakurai, J.J., (1994) Advanced Quantum MechanicsBjorken, J.D., Drell, S.D., (1964) Relativistic Quantum MechanicsGreiner, W., Reinhardt, J., (2002) Quantum ElectrodynamicsChodos, A., Hauser, A.I., Kostelecky, V.A., (1985) Phys. Lett. B, 150 (6), p. 431. , 10.1016/0370-2693(85)90460-5 0370-2693Jentschura, U.D., Wundt, B.J., arXiv:1110.4171v2 [hep-ph]Lawrence, K., Frank, W., (1985) Phys. Rev. Lett., 55 (1), p. 122. , 10.1103/PhysRevLett.55.122 0031-9007Kobayashi, M., Lim, C.S., Nojiri, M.M., (1991) Phys. Rev. Lett., 67 (13), p. 1685. , 10.1103/PhysRevLett.67.1685 0031-9007Fukuda, Y., (1998) Phys. Rev. Lett., 81 (8), p. 1562. , 10.1103/PhysRevLett.81.1562 0031-9007Kirsten, T.A., (1999) Rev. Mod. Phys., 71 (4), p. 1213. , 10.1103/RevModPhys.71.1213 0034-6861Wolfenstein, L., (1999) Rev. Mod. Phys., 71 (2), p. 140. , 10.1103/RevModPhys.71.S140 0034-6861Takaaki, K., Yoji, T., (2001) Rev. Mod. Phys., 73 (1), p. 85. , 10.1103/RevModPhys.73.85 0034-6861Gonzalez-Garcia, M.C., Nir, Y., Neutrino masses and mixing: Evidence and implications (2003) Reviews of Modern Physics, 75 (2), pp. 345-402. , DOI 10.1103/RevModPhys.75.345Razinkowski Marek, J., arXiv:1110.4171v2 [hep-ph]Konoplya, R.A., Zhidenko, A., arXiv:1110.2015 [hep-th]Konoplya, R.A., arXiv:1109.6215 [hep-th]Fukuda, Y., (1998) Phys. Rev. Lett., 81 (6), p. 1158. , 10.1103/PhysRevLett.81.1158 0031-9007Kostelecky, V.A., (2004) Phys. Rev. D, 69 (10). , 10.1103/PhysRevD.69.105009 1550-7998 105009Magueijo, J., arXiv:1109.6055v2 [hep-ph

Generation Of Electric Field By Spin-currents In The U (1) × Su (2) Gauge Invariant Pauli-schrödinger Non-relativistic Theory

The non-relativistic Pauli-Schrödinger theory has a richer gauge structure than usually expected, being invariant under the U (1) × SU (2) gauge group, which allows to define spin-current density vectors and obtains the relevant conserved quantities from Noether's theorem. The electromagnetic fields E and B play the role of the gauge potentials for the SU (2) sector of the gauge group and can possibly contribute with a corresponding invariant curvature self-energy term in the Lagrangian density. From the dynamics of the U (1) and SU (2) gauge fields we show that electric fields can be induced by spin-currents originated from the SU (2) gauge symmetry. © 2010 Elsevier B.V. All rights reserved.3742525962599Wolf, S.A., Awschalom, D.D., Buhrman, R.A., Daughton, J.M., Molnar, S.V., Roukes, M.L., Chtchelkanova, A.Y., Treger, D.M., (2001) Science, 294, p. 1488Prinz, G.A., (1998) Science, 282, p. 1660Zutic, I., Fabian, J., Das Sarma, S., (2004) Rev. Modern Phys., 76, p. 323Zhang, S., Levy, P.M., Marley, A.C., Parkin, S.S.P., (1997) Phys. Rev. Lett., 79, p. 3744. , See for instanceDartora, C.A., Cabrera, G.G., (2004) J. Appl. Phys., 95, p. 6058. , and references thereinDartora, C.A., Cabrera, G.G., (2005) Phys. Rev. B, 72, p. 064456Petit, S., Baraduc, C., Thirion, C., Ebels, U., Liu, Y., Li, M., Wang, P., Dieny, B., (2007) Phys. Rev. Lett., 98, p. 077203Berger, L., (1996) Phys. Rev. B, 54, p. 9353Slonczewski, J., (1996) J. Magn. Magn. Mater., 159, pp. L1Vernes, A., Gyorffy, B.L., Weinberger, P., (2007) Phys. Rev. B, 76, p. 012408Wang, Y., Xia, K., Zhao Ein, S., Ma, Z., (2006) Phys. Rev. Lett., 96, p. 066601Sun, Q.-F., Xie, X.C., (2005) Phys. Rev. B, 72, p. 245305Dartora, C.A., Cabrera, G.G., (2008) Phys. Rev. B, 78, p. 012403Jin, P.-Q., Li, Y.-Q., Zhang, F.-C., (2006) J. Phys. A: Math. Gen., 39, p. 7115Anandan, J., (1989) Phys. Lett. A, 138, p. 347Anandan, J., (1991) Phys. Lett. A, 152, p. 504Goldhaber, A.S., (1989) Phys. Rev. Lett., 62, p. 482Murakami, S., Nagaosa, N., Zhang, S.-C., (2003) Science, 301, p. 1348Murakami, S., Nagaosa, N., Zhang, S.-C., (2004) Phys. Rev. B, 69, p. 235206Jiang, Z.F., Li, R.D., Zhang, S.-C., Liu, W.M., (2005) Phys. Rev. B, 72, p. 045201Sinova, J., (2004) Phys. Rev. Lett., 92, p. 126603Shen, S.Q., Ma, M., Xie, X.C., Zhang, F.C., (2004) Phys. Rev. Lett., 92, p. 256603Ryu, C.-M., (1996) Phys. Rev. Lett., 76, p. 968Barnes, S.E., Maekawa, S., (2007) Phys. Rev. Lett., 98, p. 246601Hirsch, J.E., (1990) Phys. Rev. B, 42, p. 4774Meier, F., Loss, D., (2003) Phys. Rev. Lett., 90, p. 167204Schutz, F., Kollar, M., Kopietz, P., (2003) Phys. Rev. Lett., 91, p. 017205Sun, Q.-F., Guo, H., Wang, J., (2004) Phys. Rev. B, 69, p. 054409Berry, M.V., (1984) Proc. R. Soc. A, 392, p. 45Sun, Q.-F., Guo, H., Wang, J., (2004) Phys. Rev. B, 69, p. 054409Fröhlich, J., Studer, U.M., (1992) Comm. Math. Phys., 148, p. 553Fröhlich, J., Studer, U.M., (1992) Internat. J. Modern Phys. B, 6, p. 2201Fröhlich, J., Studer, U.M., (1993) Rev. Modern Phys., 65, p. 733Lee, T.Y., Ryu, C.M., (1994) Phys. Lett. A, 194, p. 310Medina, E., Lopez, A., Berche, B., (2008) Eur. Phys. Lett., 83, p. 47005Sakurai, J.J., (1994) Advanced Quantum Mechanics. revised ed., , Addison-WesleyBjorken, J.D., Drell, S.D., (1964) Relativistic Quantum Mechanics, , McGraw-HillGreiner, W., Reinhardt, J., (2002) Quantum Electrodynamics. 3rd ed., , Springer-VerlagYang, C.N., Mills, R.L., (1954) Phys. Rev., 96, p. 191Weinberg, S., (1996) The Quantum Theory of Fields, vols. I and II, , Cambridge University Press and references thereinRyder, L.H., (1996) Quantum Field Theory. 2nd ed., , Cambridge University PressAharonov, Y., Casher, A., (1984) Phys. Rev. Lett., 53, p. 319Cimmino, A., Opat, G.I., Klein, A.G., Kaiser, H., Werner, S.A., Arif, M., Clothier, R., (1989) Phys. Rev. Lett., 63, p. 380Ryder, L.H., (1996) Quantum Field Theory. 2nd ed., , Cambridge University PressOh, S., Ryu, C.-M., Suck Salk, S.-H., (1994) Phys. Rev. A, 50, p. 532

The Electron-phonon Interaction From Fundamental Local Gauge Symmetries In Solids

The elastic properties of solids are described in close analogy with General Relativity, by locally gauging the translational group of space-time. Electron interactions with the crystal lattice are thus generated by enforcing full gauge invariance, with the introduction of a gauge field. Elementary excitations are associated with the local gauge, contrasting to the usual interpretation as Goldstone bosons emerging from global symmetry breaking. In the linear limit of the theory, the gauge field displays elastic waves, that we identify with acoustic phonons, when the field is quantized. Coupling with the electronic part of the system yields the standard electron-phonon interaction. If spin-orbit effects are included, unusual couplings emerge between the strain field and the electronic spin current, leading to novel physics that may be relevant for spintronic applications. © 2014 IOP Publishing Ltd.473Kittel, C., (1963) Quantum Theory of SolidsWeinberg, S., (1996) The Quantum Theory of Fields, 12. , 10.1017/CBO9781139644174Kleinert, H., (1989) Gauge Fields in Condensed Matter, 12. , 10.1142/0356Fröhlich, J., Studer, U.M., (1992) Commun. Math. Phys., 148, p. 553. , 10.1007/BF02096549 0010-3616Fröhlich, J., Studer, U.M., (1992) Int. J. Mod. Phys., 6, p. 2201. , 10.1142/S0217979292001092 0217-9792 BFröhlich, J., Studer, U.M., (1993) Rev. Mod. Phys., 65, p. 733. , 10.1103/RevModPhys.65.733 0034-6861Dartora, C.A., Cabrera, G.G., (2008) Phys. Rev., 78. , 10.1103/PhysRevB.78.012403 B 012403Vernes, A., Gyorffy, B.L., Weinberger, P., (2007) Phys. Rev., 76. , 10.1103/PhysRevB.76.012408 B 012408Wang, Y., Xia, K., Su, Z.-B., Ma, Z., Consistency in formulation of spin current and torque associated with a variance of angular momentum (2006) Physical Review Letters, 96 (6), p. 066601. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.96.066601&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.96.066601Sun, Q.-F., Xie, X.C., Definition of the spin current: The angular spin current and its physical consequences (2005) Physical Review B - Condensed Matter and Materials Physics, 72 (24), pp. 1-7. , http://oai.aps.org/oai/?verb=ListRecords&metadataPrefix= oai_apsmeta_2&set=journal:PRB:72, DOI 10.1103/PhysRevB.72.245305, 245305Murakami, S., Nagaosa, N., Zhang, S.-C., Dissipationless quantum spin current at room temperature (2003) Science, 301 (5638), pp. 1348-1351. , DOI 10.1126/science.1087128Murakami, S., Nagaosa, N., Zhang, S.-C., (2004) Phys. Rev., 69. , 10.1103/PhysRevB.69.235206 B 235206Jiang, Z.F., Li, R.D., Zhang, S.-C., Liu, W.M., Semiclassical time evolution of the holes from Luttinger Hamiltonian (2005) Physical Review B - Condensed Matter and Materials Physics, 72 (4), pp. 1-5. , http://oai.aps.org/oai/?verb=ListRecords&metadataPrefix= oai_apsmeta_2&set=journal:PRB:72, DOI 10.1103/PhysRevB.72.045201, 045201Sinova, J., (2004) Phys. Rev. Lett., 92. , 10.1103/PhysRevLett.92.126603 126603Shen, S.Q., Ma, M., Xie, X.C., Zhang, F.C., (2004) Phys. Rev. Lett., 92. , 10.1103/PhysRevLett.92.256603 256603Hirsch, J.E., (1990) Phys. Rev., 42, p. 4774. , 10.1103/PhysRevB.42.4774 0163-1829 BMesaros, A., Sadri, D., Zaanen, J., (2010) Phys. Rev., 82. , 10.1103/PhysRevB.82.073405 B 073405Fonseca, J.M., Moura-Melo, W.A., Pereira, A.R., (2010) Phys. Lett., 374, p. 4359. , 10.1016/j.physleta.2010.08.059 0375-9601 ADartora, C.A., Cabrera, G.G., (2010) Physica, 405, p. 1158. , 10.1016/j.physb.2009.11.027 0921-4526 BSmolyaninov, I.I., Narimanov, E.E., (2010) Phys. Rev. Lett., 105. , 10.1103/PhysRevLett.105.067402 067402Unruh, W.G., (1981) Phys. Rev. Lett., 46, p. 1351. , 10.1103/PhysRevLett.46.1351 0031-9007Unruh, W.G., (1995) Phys. Rev., 51, p. 2827. , 10.1103/PhysRevD.51.2827 0556-2821 DVolovik, G.E., (2003) The Universe in A Helium DropletVozmediano, M.A.H., Katsnelson, M.I., Guinea, F., (2010) Phys. Rep., 496, p. 109. , 10.1016/j.physrep.2010.07.003 0370-1573Furtado, C., Moraes, F., De, M., Carvalho, A.M., (2008) Phys. Lett., 372, p. 5368. , 10.1016/j.physleta.2008.06.029 0375-9601 AUtiyama, R., (1956) Phys. Rev., 101, p. 1597. , 10.1103/PhysRev.101.1597Kibble, T.W.B., (1961) J. Math. Phys., 2, p. 212. , 10.1063/1.1703702Sciama, D.W., (1964) Rev. Mod. Phys., 36, p. 463. , 10.1103/RevModPhys.36.463 0034-6861Hayashi, K., Shirafujif, T., (1980) Prog. Theor. Phys., 64, p. 866. , 10.1143/PTP.64.866 0033-068XHehl, W., McCrea, J.D., Mielke, E.W., Neemann, Y., (1995) Phys. Rep., 258, p. 1. , 10.1016/0370-1573(94)00111-F 0370-1573Ni, W., (2010) Rep. Prog. Phys., 73 (5). , 10.1088/0034-4885/73/5/056901 0034-4885 056901Hehl, F.W., Von Der Heyde, P., Kerlick, G.D., Nester, J.M., (1976) Rev. Mod. Phys., 48, p. 393. , 10.1103/RevModPhys.48.393 0034-6861Hammond, R.T., (2002) Rep. Prog. Phys., 65 (5), p. 599. , 10.1088/0034-4885/65/5/201 0034-4885 201Arcos, H.I., Pereira, J.P., (2004) Int. J. Mod. Phys., 13, p. 2193. , 10.1142/S0218271804006462 0218-2718 DOraifeartaigh, L., Straumann, N., (2000) Rev. Mod. Phys., 72, p. 1. , 10.1103/RevModPhys.72.1 0034-6861Johnston, D.C., (2010) Adv. Phys., 59, p. 803. , 10.1080/00018732.2010.513480 0001-8732Lee, S.-H., (2010) Phys. Rev., 81. , 10.1103/PhysRevB.81.220502 B 220502Dartora, C.A., Cabrera, G.G., (2010) Ann. Phys., NY, 325, p. 1270. , 10.1016/j.aop.2010.03.009 0003-4916Ryder, L.H., (1996) Quantum Field Theory, , 10.1017/CBO9780511813900Misner, C.W., Thorne, K.S., Wheeler, J.A., (1973) GravitationOhanian, H., Ruffini, R., (1994) Gravitation and SpacetimeDartora, C.A., Cabrera, G.G., (2010) Phys. Lett., 374, p. 2596. , 10.1016/j.physleta.2010.04.041 0375-9601 AZiman, J.M., (1960) Electrons and Phonons: The Theory of Transport Phenomena in SolidsMichelini, F., Cavassilas, N., Hayn, R., Szczap, M., (2009) Phys. Rev., 80. , 10.1103/PhysRevB.80.245210 B 245210Zieliński, M., Jaskólski, W., Aizpurua, J., Bryant, G.W., (2005) Acta Phys. Pol., 108, p. 929. , 0587-4246 AZhang, Y.-T., Zhai, F., (2012) J. Appl. Phys., 111. , 10.1063/1.3679568 033705Palyi, A., (2012) Phys. Rev. Lett., 108. , 10.1103/PhysRevLett.108.206811 206811Uchida, K., (2008) Nature, 455, p. 779. , 10.1038/nature07321Jaworski, C.M., (2010) Nature Mater., 9, p. 898. , 10.1038/nmat2860 1476-1122Paul, I., (2011) Phys. Rev. Lett., 107. , 10.1103/PhysRevLett.107.047004 04700