关于两带超导材料NbSe_2的上临界磁场研究
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摘要
2001年日本科学家报道了二元材料二硼化镁在39K左右表现出超导特性,这个发现迅速激起了全世界范围内的研究热潮。理论计算表明,二硼化镁是具有两个超导能隙的超导材料。有关二硼化镁超导体两个能隙的图像后来被比热、核磁共振、电子隧道谱和角分辨光电子谱的实验广泛证实。此后,多能带超导电性在NbSe2等其它材料中也被陆续发现。本论文应用两带Ginzburg-Landau(GL)理论对超导材料NbSe2的上临界磁场进行研究,并计算了超导材料NbSe2上临界磁场的各向异性参数随温度的变化情况。在计算过程中我们运用变分法对两带GL方程进行求解,然后用Mathematica进行编程计算。所得上临界磁场的计算结果,以及上临界磁场各向异性参数随温度的变化曲线均与实验数据相吻合,充分说明了NbSe2的超导电性具有两能隙特性。计算结果还显示,NbSe2较大能隙所对应能带的有效质量各向异性约为10,较小能隙所对应能带的这一数值约为1。根据费米速度和等离子频率的实验数据,我们由此推断较小能隙最有可能产生在Nb原子的成键费米面上
In2011, Japanese scientists discovered that MgB2crystal becomes superconducting at the temperature39K, which aroused a huge research interest in this field all over the world. The theoretical calculations indicate that MgB2is a superconductor with two superconducting gaps. Two-gap scenario of the superconducting MgB2has been testified in many experiments, such as specific heat measurement, nuclear magnetic resonance, electronic tunneling spectrum and angle-resolved photoemission spectrum. Thereafter, some other materials with multi-band superconductivity are discovered. Based on the two-band Ginzburg-Landau (GL) theory, we study the temperature dependence of the upper critical field for superconducting crystal NbSe2. We also calculate the temperature dependence of the anisotropy parameter for the upper critical field. We solve the two-band GL equations by variational method, and then perform the numerical calculations with Mathematica. Our calculations on the upper critical field and the temperature dependence of the anisotropy parameter for upper critical field fit the experimental data well in a broad temperature range. Our results thus support two-gap scenario of the superconducting NbSe2. The calculations also show that the effective mass anisotropy for the band with the larger gap is about10, the other band is almost1. Based on the experimental data from Fermi velocities and plasma frequencies, we expect that the smaller gap is most probably located on the bonding Nb Fermi sheets.
In2011, Japanese scientists discovered that MgB2crystal becomes superconducting at the temperature39K, which aroused a huge research interest in this field all over the world. The theoretical calculations indicate that MgB2is a superconductor with two superconducting gaps. Two-gap scenario of the superconducting MgB2has been testified in many experiments, such as specific heat measurement, nuclear magnetic resonance, electronic tunneling spectrum and angle-resolved photoemission spectrum. Thereafter, some other materials with multi-band superconductivity are discovered. Based on the two-band Ginzburg-Landau (GL) theory, we study the temperature dependence of the upper critical field for superconducting crystal NbSe2. We also calculate the temperature dependence of the anisotropy parameter for the upper critical field. We solve the two-band GL equations by variational method, and then perform the numerical calculations with Mathematica. Our calculations on the upper critical field and the temperature dependence of the anisotropy parameter for upper critical field fit the experimental data well in a broad temperature range. Our results thus support two-gap scenario of the superconducting NbSe2. The calculations also show that the effective mass anisotropy for the band with the larger gap is about10, the other band is almost1. Based on the experimental data from Fermi velocities and plasma frequencies, we expect that the smaller gap is most probably located on the bonding Nb Fermi sheets.
引文
[1]张裕恒.超导物理[M].合肥：中国科学技术大学出版社,2009：84-104,146-189
[2]刘心宇,黄勇,曾中明,等等.MgB2超导电性研究进展[J].材料科学与工程学报,2003,21(1)：104-109
[3]Meissner w., Ochsenfeld R. Ein neuer Effekt bei Eintritt der Supraleitfahigkeit[J]. naturwissenschaften 1933,V21:787
[4]Hess H. F., Robinson R. B., Dynes R. C., et al. STM Observation of the Abrikosov Flux Lattice and the Density of States Near and Inside a Fluxoid[J]. Phys. Rev. Lett.,1989,V62:214-216
[5]Hess H. F., Robinson R. B., Dynes R. C., et al. Vortex-core structure observed with a scanning tunneling microscope[J]. Phys. Rev. Lett.,1990,V64(22):2711-2714
[6]Pfalzgraf B. W., Spreckels H. The anisotropy of the upper critical field HE, and electrical resistivity in 2H-NbS2[J]. Phys. C,1987,V20(27):4359-4367
[7]Dalrymple B. J., Prober D. E. Upper Critical Fields of the Superconducting Layered Compounds Nb1-xTaxSe2[J]. Journal of Low Temperature,1984,V56(5-6):545-574
[8]Kortus J., Mazin I.I., Belashchenko K. D., et al. Superconductivity of Metallic Boron in MgB2[J]. Phys. Rev. Lett.2010,V86(20):4656
[9]苏希玉,侯艳丽,侯芹英,等等.掺杂对二硼化镁上临界磁场的影响[J].低温物理学报.2007,V30(1)：70-73
[10]公不锋,苏希玉,王建阳,等等.在两带京兹堡朗道理论下MgB2的超导参量的研究[J].超导技术,2005,34(1)：52-55
[11]叶德枢,王洪涛,王璐,等等NbSe2晶体的制备及电学特性的研究[J],物理测试,2007,25(1)：20-22
[12]Sanchez D., Junod A., Muller J., et al. Specific heat of 2H-NbSe2 in high magnetic fields[J]. Physica B,1995,V204:167-175
[13]Yokoya T., Kiss T., Chainani A., et al. Fermi Surface Sheet-Dependent Superconductivity in 2H-NbSe2[J]. Science,2001,V294(21):2518-2520
[14]Boaknin E., Tanatar M. A., Paglione J. et al. Multiband superconductivity in NbSe2 from heat transport[J]. Phys. Rev. Lett.,2003,V90(11):117003[4 pages]
[15]Rodrigo J. G., Vieira S., STM study of multiband superconductivity in NbSe2 using a superconducting tip[J]. Physica C,2004,V404:306-310
[16]Fletcher J. D., Carrington A., Diener P., et al. Penetration Depth Study of Superconducting Gap Structure of 2H-NbSe2[J]. Phys. Rev. Lett.,2007,V98(05):057003 [4 pages]
[17]Huang C. L., Lin J.-Y., Chang Y. T., et al. Experimental evidence for a two-gap structure of superconducting NbSe2:a specific heat study in external magnetic fields[J]. Phys. Rev. B, 2007, V76(21):212504 [4 pages]
[18]Hossain M.D., Salman Z., Wang D., et al. Low-field cross spin relaxation of 8Li in superconducting NbSe2[J]. Phys. Rev. B,2009,V79(14):144518 (6 pages)
[19]Johannes M. D., Mazin I. I., Howells C. A.. Fermi-surface nesting and the origin of the charge-density wave in NbSe2[J]. Physical Review B,2006,V73(20):1-8
[20]Bardeen J., Cooper L. N., Schrieffer J. R., Theory of Superconductivity [J], Phys. Rev. 1957,V108:1175-1204
[21]赵继军,陈岗.超导BCS理论的建立[J].大学物理,2007,26(1)：46-51
[22]Ginzburg V.L., Landau L. D., k teorii sverkhrovodimosti, Eksperim Zh. i Teor. Fiz., 1950,V20:1064-1082
[23]Arai M., Kita T. Ab Initio Calculations of Hc2 for Nb, NbSe2, and MgB2[J]. Jounal of Physical Society of Japan,2004,V73(11):2924
[24]Valla T., Fedorov A. V., Johnson P. D., et al. Quasi-Particle Spectra, Charge-Density-Wave, Superconductivity and Electron-Phonon Coupling in 2H-NbSe2[M]. Phys. Rev. Lett.. (2004),V92(8):086401[4 pages]
[25]Shakeripour H., Petrovic C, Taillefer L. et al. Heat transport as a probe of superconducting gap structure[J]. New J. Phys,2009,V11(5):055065
[26]Borisenko S. V., Kordyuk A. A., Zabolotnyy V. B., et al. Two energy gaps and Fermi-surface "arcs" in NbSe2[J]. Physical Review Letters,2009,V 102(16):166402
[27]Mu G, Yang H., Wen H. H. Multiband effect in the noncentrosymmetric superconductors Mg12-δIr19B16 revealed by Hall effect and magnetoresistance measurements [J]. Phys. Rev. B, 2009,V82(5):052501 [4 pages]
[28]Zehetmayer M., Weber H. W., et al. Experimental evidence for a two-band superconducting state of NbSe2 single crystals [J], Physical Review B,2010,V82(l):014524
[29]Dao V. H., Zhitomirsky M. E. Anisotropy of the upper critical field in MgB2 the two-gap Ginzburg-Landau theory[J]. The European Physical Journal B-Condensed Matter and Complex Systems,2005,V44(2):183-188
[30]Todor M., Evgeni P.. Thermodynamics of anisotropic-gap and multiband clean BCS superconductors [J]. Physics B,2002,V16(24):3573-3586
[31]Kaushik S. D., Patnaik S.. Intergrain Connectivity and Resistive Broadening in Vortex State A Comparison BetweenMgB2,NbSe2 and Bi2Sr2Ca2Cu3O10Superconductors[J]. Applied Superconductivity,2007,V17(2):3016-3019
[32]Ravikumar G, Sahni V C., Mishra P. K. et al. Manifestation of history dependent critical currents via dc and ac magnetization measurements in single crystals of CeRu2 and 2H-NbSe2[J]. Physical Review B,1998,V57(18):11069-11072
[33]Sologubenko A. V., Landaul I. L., Ottl H. R., et al. Unusual Magnetic-Field-Induced Phase Transition in the Mixed State of Superconducting NbSe2[J]. Phys. Rev. Lett.,2003, V91(19):197005 [4 pages]
[34]Steep E., Rettenberger S., Meyer F., et al. dHvA studies of NbSe2 using the torque method[J]. Physica B,1995,V204(1-4):162-166
[35]Berger H., Cabo L., Carballeira C., et al. In-plane and transverse superconducting fluctuation diamagnetism in the presence of charge-density waves in 2H-NbSe2 single crystals[J]. Phys. Rev. B,2007,V75(9):094509
[36]Zhitomirsky M. E., Dao V. H.. Ginzburg-Landau theory of vortices in a multigap superconductor[J]. Physical Review,2004,V69(5):054508[11pages]
[37]章立源.超导理论[M].北京：科学出版社,2006：29-57
[38]刘兵,章立源.超导物理学发展简史[M].西安：陕西科学技术出版社,1988：27-44
[39]廷哈姆M..超导电性导论[M].邵惠民,丁宏宇,张其瑞.北京：科学出版社,1985：19-91
[40]刘永长,马宗青.MgB2超导体的成相与掺杂机理[M].北京：科学出版社,2009：4-23
[41]吴尝.MgB2材料在超导科学中的研究[J].淮南师范学院学报,2006,8(3)：42-44
[42]张朝阳,刘艳清,魏茂彬,等等.NbSe2纳米颗粒的制备与表征[J],吉林师范大学学报,自然科学版,2009,30(2)：81-82
[43]李飞.掺杂MgB2超导块材的制备及其性能研究[D].成都：西南交通大学硕士论文,2009
[44]唐耀龙.超导材料发展概述[J].中国高新技术企业,2011(21)：1-2
[45]章立源.超导电性及其新进展系统[J].工程与电子技术,1988(3)：1-6
[46]刘桦.超导纳米材料的合成与物性研究[D].合肥：中国科学技术大学硕士论文,2009
[47]王洪滨.超导体及其近期发展和应用前景[J].南京邮电学院学报,1988,8(2)：128-134
[48]闫果,王庆阳,刘国庆.末套管法制备碳掺杂MgB2线材及其超导电性[J].科技导报,2008,26(1)：28-31
[49]苏希玉,张宪科,翟建华.二带模型与MgB2的超导电性超导技术[J].低温与超导,2007,35(1)：56-58
[50]闫果,冯勇,卢亚锋.热处理温度对MgB2超导材料的超导电性及微观结构的影响[J].低温物理学报,2005,27(1)：796-800
[51]夏庆林,易健宏,李丽娅.新型超导体MgB2超导电性及制备技术进展[J].粉末冶金技术,2006,24(1)：69-74
[52]刘敏霞.两带Ginzburg-Landau理论分析两带超导体Lu2Fe3Si5的表面临界磁场[J].物理学报,2011,1(60)：017401-017405
[53]Kacmarc J., Pribulova Z., Marcenat C., et al. Specific-heat measurements of superconducting NbS2 single crystal in an external magnetic field:Study on the energy gap structure[J]. Phys. Rev. B,2010,V82(1):1-6
[2]刘心宇,黄勇,曾中明,等等.MgB2超导电性研究进展[J].材料科学与工程学报,2003,21(1)：104-109
[3]Meissner w., Ochsenfeld R. Ein neuer Effekt bei Eintritt der Supraleitfahigkeit[J]. naturwissenschaften 1933,V21:787
[4]Hess H. F., Robinson R. B., Dynes R. C., et al. STM Observation of the Abrikosov Flux Lattice and the Density of States Near and Inside a Fluxoid[J]. Phys. Rev. Lett.,1989,V62:214-216
[5]Hess H. F., Robinson R. B., Dynes R. C., et al. Vortex-core structure observed with a scanning tunneling microscope[J]. Phys. Rev. Lett.,1990,V64(22):2711-2714
[6]Pfalzgraf B. W., Spreckels H. The anisotropy of the upper critical field HE, and electrical resistivity in 2H-NbS2[J]. Phys. C,1987,V20(27):4359-4367
[7]Dalrymple B. J., Prober D. E. Upper Critical Fields of the Superconducting Layered Compounds Nb1-xTaxSe2[J]. Journal of Low Temperature,1984,V56(5-6):545-574
[8]Kortus J., Mazin I.I., Belashchenko K. D., et al. Superconductivity of Metallic Boron in MgB2[J]. Phys. Rev. Lett.2010,V86(20):4656
[9]苏希玉,侯艳丽,侯芹英,等等.掺杂对二硼化镁上临界磁场的影响[J].低温物理学报.2007,V30(1)：70-73
[10]公不锋,苏希玉,王建阳,等等.在两带京兹堡朗道理论下MgB2的超导参量的研究[J].超导技术,2005,34(1)：52-55
[11]叶德枢,王洪涛,王璐,等等NbSe2晶体的制备及电学特性的研究[J],物理测试,2007,25(1)：20-22
[12]Sanchez D., Junod A., Muller J., et al. Specific heat of 2H-NbSe2 in high magnetic fields[J]. Physica B,1995,V204:167-175
[13]Yokoya T., Kiss T., Chainani A., et al. Fermi Surface Sheet-Dependent Superconductivity in 2H-NbSe2[J]. Science,2001,V294(21):2518-2520
[14]Boaknin E., Tanatar M. A., Paglione J. et al. Multiband superconductivity in NbSe2 from heat transport[J]. Phys. Rev. Lett.,2003,V90(11):117003[4 pages]
[15]Rodrigo J. G., Vieira S., STM study of multiband superconductivity in NbSe2 using a superconducting tip[J]. Physica C,2004,V404:306-310
[16]Fletcher J. D., Carrington A., Diener P., et al. Penetration Depth Study of Superconducting Gap Structure of 2H-NbSe2[J]. Phys. Rev. Lett.,2007,V98(05):057003 [4 pages]
[17]Huang C. L., Lin J.-Y., Chang Y. T., et al. Experimental evidence for a two-gap structure of superconducting NbSe2:a specific heat study in external magnetic fields[J]. Phys. Rev. B, 2007, V76(21):212504 [4 pages]
[18]Hossain M.D., Salman Z., Wang D., et al. Low-field cross spin relaxation of 8Li in superconducting NbSe2[J]. Phys. Rev. B,2009,V79(14):144518 (6 pages)
[19]Johannes M. D., Mazin I. I., Howells C. A.. Fermi-surface nesting and the origin of the charge-density wave in NbSe2[J]. Physical Review B,2006,V73(20):1-8
[20]Bardeen J., Cooper L. N., Schrieffer J. R., Theory of Superconductivity [J], Phys. Rev. 1957,V108:1175-1204
[21]赵继军,陈岗.超导BCS理论的建立[J].大学物理,2007,26(1)：46-51
[22]Ginzburg V.L., Landau L. D., k teorii sverkhrovodimosti, Eksperim Zh. i Teor. Fiz., 1950,V20:1064-1082
[23]Arai M., Kita T. Ab Initio Calculations of Hc2 for Nb, NbSe2, and MgB2[J]. Jounal of Physical Society of Japan,2004,V73(11):2924
[24]Valla T., Fedorov A. V., Johnson P. D., et al. Quasi-Particle Spectra, Charge-Density-Wave, Superconductivity and Electron-Phonon Coupling in 2H-NbSe2[M]. Phys. Rev. Lett.. (2004),V92(8):086401[4 pages]
[25]Shakeripour H., Petrovic C, Taillefer L. et al. Heat transport as a probe of superconducting gap structure[J]. New J. Phys,2009,V11(5):055065
[26]Borisenko S. V., Kordyuk A. A., Zabolotnyy V. B., et al. Two energy gaps and Fermi-surface "arcs" in NbSe2[J]. Physical Review Letters,2009,V 102(16):166402
[27]Mu G, Yang H., Wen H. H. Multiband effect in the noncentrosymmetric superconductors Mg12-δIr19B16 revealed by Hall effect and magnetoresistance measurements [J]. Phys. Rev. B, 2009,V82(5):052501 [4 pages]
[28]Zehetmayer M., Weber H. W., et al. Experimental evidence for a two-band superconducting state of NbSe2 single crystals [J], Physical Review B,2010,V82(l):014524
[29]Dao V. H., Zhitomirsky M. E. Anisotropy of the upper critical field in MgB2 the two-gap Ginzburg-Landau theory[J]. The European Physical Journal B-Condensed Matter and Complex Systems,2005,V44(2):183-188
[30]Todor M., Evgeni P.. Thermodynamics of anisotropic-gap and multiband clean BCS superconductors [J]. Physics B,2002,V16(24):3573-3586
[31]Kaushik S. D., Patnaik S.. Intergrain Connectivity and Resistive Broadening in Vortex State A Comparison BetweenMgB2,NbSe2 and Bi2Sr2Ca2Cu3O10Superconductors[J]. Applied Superconductivity,2007,V17(2):3016-3019
[32]Ravikumar G, Sahni V C., Mishra P. K. et al. Manifestation of history dependent critical currents via dc and ac magnetization measurements in single crystals of CeRu2 and 2H-NbSe2[J]. Physical Review B,1998,V57(18):11069-11072
[33]Sologubenko A. V., Landaul I. L., Ottl H. R., et al. Unusual Magnetic-Field-Induced Phase Transition in the Mixed State of Superconducting NbSe2[J]. Phys. Rev. Lett.,2003, V91(19):197005 [4 pages]
[34]Steep E., Rettenberger S., Meyer F., et al. dHvA studies of NbSe2 using the torque method[J]. Physica B,1995,V204(1-4):162-166
[35]Berger H., Cabo L., Carballeira C., et al. In-plane and transverse superconducting fluctuation diamagnetism in the presence of charge-density waves in 2H-NbSe2 single crystals[J]. Phys. Rev. B,2007,V75(9):094509
[36]Zhitomirsky M. E., Dao V. H.. Ginzburg-Landau theory of vortices in a multigap superconductor[J]. Physical Review,2004,V69(5):054508[11pages]
[37]章立源.超导理论[M].北京：科学出版社,2006：29-57
[38]刘兵,章立源.超导物理学发展简史[M].西安：陕西科学技术出版社,1988：27-44
[39]廷哈姆M..超导电性导论[M].邵惠民,丁宏宇,张其瑞.北京：科学出版社,1985：19-91
[40]刘永长,马宗青.MgB2超导体的成相与掺杂机理[M].北京：科学出版社,2009：4-23
[41]吴尝.MgB2材料在超导科学中的研究[J].淮南师范学院学报,2006,8(3)：42-44
[42]张朝阳,刘艳清,魏茂彬,等等.NbSe2纳米颗粒的制备与表征[J],吉林师范大学学报,自然科学版,2009,30(2)：81-82
[43]李飞.掺杂MgB2超导块材的制备及其性能研究[D].成都：西南交通大学硕士论文,2009
[44]唐耀龙.超导材料发展概述[J].中国高新技术企业,2011(21)：1-2
[45]章立源.超导电性及其新进展系统[J].工程与电子技术,1988(3)：1-6
[46]刘桦.超导纳米材料的合成与物性研究[D].合肥：中国科学技术大学硕士论文,2009
[47]王洪滨.超导体及其近期发展和应用前景[J].南京邮电学院学报,1988,8(2)：128-134
[48]闫果,王庆阳,刘国庆.末套管法制备碳掺杂MgB2线材及其超导电性[J].科技导报,2008,26(1)：28-31
[49]苏希玉,张宪科,翟建华.二带模型与MgB2的超导电性超导技术[J].低温与超导,2007,35(1)：56-58
[50]闫果,冯勇,卢亚锋.热处理温度对MgB2超导材料的超导电性及微观结构的影响[J].低温物理学报,2005,27(1)：796-800
[51]夏庆林,易健宏,李丽娅.新型超导体MgB2超导电性及制备技术进展[J].粉末冶金技术,2006,24(1)：69-74
[52]刘敏霞.两带Ginzburg-Landau理论分析两带超导体Lu2Fe3Si5的表面临界磁场[J].物理学报,2011,1(60)：017401-017405
[53]Kacmarc J., Pribulova Z., Marcenat C., et al. Specific-heat measurements of superconducting NbS2 single crystal in an external magnetic field:Study on the energy gap structure[J]. Phys. Rev. B,2010,V82(1):1-6