d-波超导体中节点准粒子的能隙生成机制及其物理应用
摘要
铜氧化合物高温超导体具有d-波对称性,这将导致其性质与传统的s-波超导体有很大的不同。d-波超导体具有四个节点,在接近零温时的准粒子激发是无能隙的。但是最近若干实验显示出,在某些条件下节点处还可能存在一附加能隙,该能隙会导致一些可观测的实验现象。本文将利用低维场论的方法讨论该能隙的产生机制,并用于实验的解释。
人们普遍认为t-J模型可以很好的描述铜氧化合物高温超导体,但该模型一直到现在都无法严格求解。对t-J模型用隶玻色子技巧做平均场处理,并做涨落分析后,在低能情况下会得到一有效的2+1维U(1)规范场理论。此前的工作主要集中在费米子和规范场的耦合(QED_3)方面,而标量玻色子和规范场的耦合(阿贝尔Higgs模型)往往会被忽略。我们利用1/N展开研究了2+1维量子电动力学(QED_3)与阿贝尔Higgs模型耦合在一起之后的动力学手征对称破缺。在规范对称破缺相,规范玻色子会通过Anderson-Higgs机制获得质量。关于费米子自能的Dyson-Schwinger方程会依赖于两个参数:规范玻色子质量m_A和Higgs玻色子质量m_h。我们发现,对于相对较大的r=m_h/m_A,规范玻色子质量m_A和Higgs玻色子质量m_h的增加都会降低费米子发生手征对称破缺的临界味数N_c。该模型可以用来描述超导体中反铁磁序与超导序的竞争和共存。
但上述模型用于描述混合态会遇到很大的困难,因为使用隶玻色子技巧后,自旋电荷会分离,对涡旋求平均无法实现。为此,我们提出了,在混合态,节点准粒子和准空穴通过库仑相互作用产生激子能隙的机制。在超导体中,库仑相互作用通常是不能产生费米子能隙的,因为它的强度会被超流减弱。只有加外磁场使得超流体密度减小之后,相互作用才变得足够强使得原来无质量的节点费米子获得能隙。通过求解能隙方程,我们发现节点能隙是随着外磁场H的增大而增大的,这可以用于解释热导率随磁场增大而减小的现象。此激子配对产生能隙的机制解释了在输运实验中观察到的由外场引起的热金属到热绝缘体的转变现象,同时也可用于描述在涡旋态中观察到反铁磁序的现象。
The cuprate superconductors have a d-wave symmetry,which will leads its properties different to the traditional s-wave superconductors.The existence of four nodal points in d-wave superconductors provide that the quasiparticle excitations is gapless at zero temperature.Recently,some experiments indicate that there maybe an additional gap in the nodal points,which will lead to many observable phenomenon,we will give a mechanism for this gap generation using the method of low dimensional field theory and explain the experiments.
It is believed that the t-J model can well describe the d-wave cuprate superconductors. But this model have not an exact solution till now.After the slave boson treatment of the t-J model and considering the fluctuatations,the low energy effective theory is a 2+1 dimensional U(1) gauge field theory.Before studies are mainly focus on the coupling between the fermion and gauge field(QED_3),while the coupling between scalar boson and gauge field(Abelian Higgs model) is often neglected. We studied the dynamical chiral symmetry breaking in(2+1)-dimensional QED in the presence of an Abelian Higgs model(Ginzburg-Landau model) at the leading order of 1/N.In the gauge symmetry broken phase,the gauge boson becomes massive via Anderson-Higgs mechanism.The Dyson-Schwinger equation for fermion self-energy depends on two parameters:the gauge boson mass m_A and the Higgs boson mass m_h. It is found that,in the region of large ratio r=m_h/m_A,m_A and m_h reduces the critical fermion number N_c,below which the massless fermion acquires a dynamical mass. This model can describe the competing and coexistance of the antiferromagnetic order and superconducting order in high temperature superconductors.
But the above model will experience huge difficulty in dealing with the mixed state,for the average of the vortex can not be down since the spin and charge is separated after the slave boson treatment.Hence we propose that an excitonic gap can be generated along nodal directions by Coulomb interaction in the mixed state.In a superconductor, the Coulomb interaction usually can not generate any fermion gap since its strength is weakened by superfluidity.It becomes stronger as superfluid density is suppressed by external magnetic field,and is able to generate a gap for initially gapless nodal quasiparticles beyond some critical field H_c.By solving the gap equation,it is found that the nodal gap increases with growing field H,which leads to a suppression of thermal conductivity at zero temperature.This mechanism naturally produces the field-induced thermal metal-insulator transition observed in transport experiments, and this mechanism give an explanation for the antiferromagnetic order observed in the vortex state.
人们普遍认为t-J模型可以很好的描述铜氧化合物高温超导体,但该模型一直到现在都无法严格求解。对t-J模型用隶玻色子技巧做平均场处理,并做涨落分析后,在低能情况下会得到一有效的2+1维U(1)规范场理论。此前的工作主要集中在费米子和规范场的耦合(QED_3)方面,而标量玻色子和规范场的耦合(阿贝尔Higgs模型)往往会被忽略。我们利用1/N展开研究了2+1维量子电动力学(QED_3)与阿贝尔Higgs模型耦合在一起之后的动力学手征对称破缺。在规范对称破缺相,规范玻色子会通过Anderson-Higgs机制获得质量。关于费米子自能的Dyson-Schwinger方程会依赖于两个参数:规范玻色子质量m_A和Higgs玻色子质量m_h。我们发现,对于相对较大的r=m_h/m_A,规范玻色子质量m_A和Higgs玻色子质量m_h的增加都会降低费米子发生手征对称破缺的临界味数N_c。该模型可以用来描述超导体中反铁磁序与超导序的竞争和共存。
但上述模型用于描述混合态会遇到很大的困难,因为使用隶玻色子技巧后,自旋电荷会分离,对涡旋求平均无法实现。为此,我们提出了,在混合态,节点准粒子和准空穴通过库仑相互作用产生激子能隙的机制。在超导体中,库仑相互作用通常是不能产生费米子能隙的,因为它的强度会被超流减弱。只有加外磁场使得超流体密度减小之后,相互作用才变得足够强使得原来无质量的节点费米子获得能隙。通过求解能隙方程,我们发现节点能隙是随着外磁场H的增大而增大的,这可以用于解释热导率随磁场增大而减小的现象。此激子配对产生能隙的机制解释了在输运实验中观察到的由外场引起的热金属到热绝缘体的转变现象,同时也可用于描述在涡旋态中观察到反铁磁序的现象。
The cuprate superconductors have a d-wave symmetry,which will leads its properties different to the traditional s-wave superconductors.The existence of four nodal points in d-wave superconductors provide that the quasiparticle excitations is gapless at zero temperature.Recently,some experiments indicate that there maybe an additional gap in the nodal points,which will lead to many observable phenomenon,we will give a mechanism for this gap generation using the method of low dimensional field theory and explain the experiments.
It is believed that the t-J model can well describe the d-wave cuprate superconductors. But this model have not an exact solution till now.After the slave boson treatment of the t-J model and considering the fluctuatations,the low energy effective theory is a 2+1 dimensional U(1) gauge field theory.Before studies are mainly focus on the coupling between the fermion and gauge field(QED_3),while the coupling between scalar boson and gauge field(Abelian Higgs model) is often neglected. We studied the dynamical chiral symmetry breaking in(2+1)-dimensional QED in the presence of an Abelian Higgs model(Ginzburg-Landau model) at the leading order of 1/N.In the gauge symmetry broken phase,the gauge boson becomes massive via Anderson-Higgs mechanism.The Dyson-Schwinger equation for fermion self-energy depends on two parameters:the gauge boson mass m_A and the Higgs boson mass m_h. It is found that,in the region of large ratio r=m_h/m_A,m_A and m_h reduces the critical fermion number N_c,below which the massless fermion acquires a dynamical mass. This model can describe the competing and coexistance of the antiferromagnetic order and superconducting order in high temperature superconductors.
But the above model will experience huge difficulty in dealing with the mixed state,for the average of the vortex can not be down since the spin and charge is separated after the slave boson treatment.Hence we propose that an excitonic gap can be generated along nodal directions by Coulomb interaction in the mixed state.In a superconductor, the Coulomb interaction usually can not generate any fermion gap since its strength is weakened by superfluidity.It becomes stronger as superfluid density is suppressed by external magnetic field,and is able to generate a gap for initially gapless nodal quasiparticles beyond some critical field H_c.By solving the gap equation,it is found that the nodal gap increases with growing field H,which leads to a suppression of thermal conductivity at zero temperature.This mechanism naturally produces the field-induced thermal metal-insulator transition observed in transport experiments, and this mechanism give an explanation for the antiferromagnetic order observed in the vortex state.
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