平面四费米子模型中激子绝缘体的磁催化与霍尔电导率
Magnetic enhancement and Hall conductivity of excitonic insulators in a Gross--Neveu type model
- Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）
- University of Coimbra（科英布拉大学）
- Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究通过平面四费米子模型，分析磁场对激子绝缘体相的影响，揭示其磁催化效应、霍尔电导率变化规律，为平面费米子系统的激子有序性提供互补特征。
AI中文摘要：
我们采用扩展平面四费米子模型，研究垂直磁场对半导体区域激子绝缘体（EI）相的影响。在大N近似框架下，我们确定了有限温度、化学势和磁场下的标量凝聚体与激子凝聚体的耦合关系。该磁场可增强EI凝聚体并提高其临界温度，为磁催化提供了激子实现方案；而在整个EI相中，标量凝聚体保持恒定。相比之下，由于朗道能级的连续占据，临界化学势随磁场呈非单调变化。磁场还会移动平均场三临界点，并扩大温度-化学势相图的一阶区域。我们进一步分析了霍尔电导率，发现增大磁场会减少平台数量并改变有限霍尔响应的阈值。在所考虑的参数下，EI凝聚体的出现伴随霍尔电导率的特征性变化，包括连续相变附近斜率随磁场的改变。这些结果表明，组合的相结构与霍尔响应可作为平面费米子系统中激子有序性的互补特征。
英文摘要：
We study the effects of a perpendicular magnetic field on the excitonic insulator (EI) phase in the semiconductor regime using an extended planar four-Fermi model. Within the large-$N$ approximation, we determine the coupled scalar and excitonic condensates at finite temperature, chemical potential, and magnetic field. The field enhances the EI condensate and raises its critical temperature, providing an excitonic realization of magnetic catalysis, while the scalar condensate remains constant throughout the EI phase. By contrast, the critical chemical potential depends nonmonotonically on the field because of the successive occupation of Landau levels. The magnetic field also shifts the mean-field tricritical point and enlarges the first-order region of the temperature--chemical-potential phase diagram. We further analyze the Hall conductivity and find that increasing the field reduces the number of plateaus and modifies the threshold for a finite Hall response. For the parameters considered, the emergence of the EI condensate is accompanied by a characteristic change in the Hall conductivity, including a field-dependent change of slope near a continuous transition. These results show that the combined phase structure and Hall response can provide complementary signatures of excitonic ordering in planar fermionic systems.
