insight - Computational Complexity - # Phase Transitions in Two-Dimensional Semimetal with Quadratic Band Crossing Point

Core Concepts

Spinful electron-electron interactions can induce a variety of favorable phase transitions, including quantum anomalous Hall, quantum spin Hall, and nematic states, in a two-dimensional semimetal with a quadratic band crossing point.

Abstract

The authors study the effects of spinful electron-electron interactions on the low-energy instabilities and phase transitions in a two-dimensional (2D) spin-1/2 semimetal with a quadratic band crossing point (QBCP). Using a renormalization group analysis, they find that the 2D QBCP system can flow towards several distinct fixed points in the interaction-parameter space, depending on the initial conditions and the sign of the structure parameter t.

In the Limit case, where all interaction parameters have the same initial value, the system is attracted to the fixed points FP+1 and FP-2, depending on the sign of t. In the Special case, where the initial values of interaction parameters are grouped into six classes, additional fixed points FP+2 and FP+3 emerge for t > 0, and their counterparts FP-1, FP-2, and FP-3 for t < 0.

In the more general case, where all 16 interaction parameters are independent, the authors find that the FP±2 fixed points present in the previous cases disappear due to the strong interplay of interactions. Instead, three new fixed points FP±41, FP±42, and FP±43 are induced.

Approaching these fixed points, the authors demonstrate that the spinful fermion-fermion interactions can induce a number of favorable instabilities accompanied by certain phase transitions. Specifically, the quantum anomalous Hall (QAH), quantum spin Hall (QSH), and nematic (Nem.) site(bond) states are dominant for FP±1, FP±2, and FP±3, respectively. Around FP±41,42,43, QSH becomes anisotropic, with one component leading and the others subleading. Besides, Nem.site(bond), chiral superconductivity, and nematic-spin-nematic (NSN.) site(bond) are subleading candidates nearby these fixed points.

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Stats

The density of states (DOS) at the quadratic band crossing point (QBCP) in the 2D semimetal is finite, in contrast to the vanishing DOS at the Dirac points in 2D Dirac/Weyl semimetals.

Quotes

"In marked contrast to their 2D Dirac/Weyl counterparts, in which the density of state (DOS) vanishes at Dirac points, the 2D QBCP materials possess a finite DOS exactly at their reduced Fermi surfaces (i.e., QBCP)."
"This unique feature together with the gapless quasiparticles (QPs) from discrete QBCPs plays an essential role in activating a plethora of critical behavior in the low-energy regime."

Key Insights Distilled From

by Yi-Sheng Fu,... at **arxiv.org** 10-01-2024

Deeper Inquiries

The instabilities and phase transitions in 2D quadratic band crossing point (QBCP) semimetals exhibit distinct characteristics compared to those in 2D Dirac and Weyl semimetals due to the unique electronic structure and density of states (DOS) at the Fermi level. In Dirac and Weyl semimetals, the DOS vanishes at the Dirac points, leading to a different response to electron-electron interactions. In contrast, 2D QBCP semimetals possess a finite DOS at the quadratic band crossing point, which enhances the susceptibility to electron-electron interactions. This results in a richer variety of instabilities, such as the emergence of quantum anomalous Hall (QAH) and quantum spin Hall (QSH) states, as well as nematic phases, which are more pronounced in the presence of spinful interactions. The study highlights that the spinful fermion-fermion interactions in QBCP systems can induce multiple fixed points (FP±1, FP±2, FP±3, FP±41, FP±42, FP±43) that lead to various phase transitions, including anisotropic QSH states, which are not typically observed in the linear dispersion of Dirac and Weyl semimetals. Thus, the interplay of spin and the finite DOS in QBCP semimetals allows for a more complex landscape of phase transitions and instabilities.

The anisotropic quantum spin Hall (QSH) state that can emerge around the FP±41, FP±42, and FP±43 fixed points presents several promising applications in the field of spintronics and quantum computing. One of the key features of the anisotropic QSH state is its ability to support edge states that are protected by time-reversal symmetry, which can be utilized for robust spin transport. This property is particularly advantageous for developing low-power, high-speed spintronic devices that leverage spin currents for information processing. Additionally, the anisotropic nature of the QSH state may allow for the manipulation of spin states in a controlled manner, enabling the design of novel quantum devices such as topological qubits for quantum computing. Furthermore, the unique electronic properties associated with the anisotropic QSH state could lead to advancements in the development of sensors and transducers that exploit spin-dependent phenomena, enhancing the performance of devices in various applications, including magnetic field sensing and quantum communication.

The insights gained from the study of spinful electron-electron interactions in 2D QBCP semimetals can be extended to investigate the low-energy properties of other semimetal materials by applying similar theoretical frameworks and methodologies. For instance, the renormalization group (RG) analysis employed in this study can be adapted to explore the interaction-driven instabilities in other two-dimensional materials, such as those exhibiting Dirac or Weyl-like dispersions. By considering the specific electronic structures and symmetries of these materials, researchers can identify potential fixed points and phase transitions analogous to those found in QBCP systems. Additionally, the exploration of spinful interactions can be generalized to other materials with strong electron correlations, such as transition metal dichalcogenides or topological insulators, where similar phenomena may arise. The findings regarding the role of finite DOS and the emergence of various phases can guide experimental efforts to synthesize and characterize new materials that exhibit rich low-energy behavior, ultimately contributing to the development of advanced electronic and spintronic devices.

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