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首页> 外文期刊>Zeitschrift fur Physik, B. Condensed Matter >Effective interaction and superconductivity in the t-J model in the large-N limit
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Effective interaction and superconductivity in the t-J model in the large-N limit

机译：大N极限下t-J模型中的有效相互作用和超导性

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摘要

The feasibility of a perturbation expansion for Green's functions of the t - J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel Θ of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations Γ_i i = 1, … 5, of the point group C_(4v) of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike Γ)3 symmetry. The corresponding transition temperature T_c is ～0.01|t| where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ～J/2, strongly repulsive up to ～|t| and attractive towards even higher energies. T_c increases with decreasing doping δ until a d-wavelike bond-order wave instability is encountered near optimal doping at δ_(BO) ～0.14 for J = 0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively.
机译：使用Baym-Kadanoff泛函方法证明了直接针对X算子对t-J模型的格林函数进行扰动展开的可行性。作为一种应用，我们以1 / N扩展的前导顺序为超导阶参数的线性化方程式的内核Θ导出了显式表达式。考虑到瞬时和滞后影响，线性方程式在一个方格上数值求解。根据方晶格的点组C_（4v）的不可约表示Γ_ii = 1，...，5并根据频率的偶数或奇数奇偶性对阶数参数进行分类，我们发现只有偶数频率对才会出现相当强的不稳定性具有d波状Γ）3对称性。对应的转变温度T_c为〜0.01 | t |。其中t是最近邻居跳跃积分。潜在的有效相互作用包括一个有吸引力的瞬时项和一个由于电荷和自旋波动引起的延迟项。后者在〜J / 2以下的低频处具有弱的吸引力，直到〜| t |时具有强烈的排斥力。对更高能量具有吸引力。 T_c随掺杂δ的减小而增加，直到在J = 0.3的δ_（BO）〜0.14的最佳掺杂附近遇到d波状键序波不稳定性为止。 T_c在J中基本上是线性的，并且对另外的第二近邻跳变积分t'不敏感。 T_c的一个相当惊人的特性是，它几乎不受与键序波不稳定性相关的软模或在第二近邻跳频的情况下受到Van Hove奇异性的影响。这个独特的特征反映了这样一个事实，即间隙方程的解涉及离费米表面很远的力矩（由于瞬时项）和许多频率（由于延迟项），因此动量或频率的奇异特性非常平均。有效。

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