First-order quantum phase transition and ferromagnetic phenomenon in corner graphene (2+2).

The flat band system has low electronic kinetic energy and is an ideal platform for constructing strongly correlated systems. Under the interaction and modulation of different degrees of freedom such as charge, spin, orbit, etc., it can breed rich low-temperature phase diagrams with different symmetry quantum states. At the absolute zero limit, phase transitions induced by non-temperature parameters such as pressure, doping, magnetic field, etc. are called quantum phase transitions, and strong quantum fluctuations at the phase transition point often cause strange physical phenomena, such as non-Fermi liquids, unconventional superconductivity, etc. In addition, some long programs in ferromagnetic ground states that are difficult to observe by conventional means will undergo mutations at the first-order quantum phase transition point, which will cause changes in observable physical quantities that can be detected. The study of quantum phase transitions can not only point the way to the discovery of new phases, but also reveal the physical properties of the ground states on both sides of the phase transition point, so it is crucial to find a quantum system with a highly adjustable phase diagram.

The graphene Mohr superlattice is a class of highly adjustable topological flat-band systems, in which the intrinsic spin and valley degrees of freedom are prone to polarization at the integer filling of the band, which induces the emergence of strongly correlated ground states and produces rich strongly correlated phenomena, such as correlated insulating states, superconducting states, magnetism, and quantum anomalous Hall effects. In this field, the N07 research group of the Nanolaboratory of the Institute of Physics of the Chinese Academy of Sciences took the lead in discovering a new class of corner double-layer graphene (2+2) Moiré superlattice system with double-layer graphene as the mother, and observed the associated insulation state with spin polarization at the flat band structure with adjustable spatial electric field and the half-fill in the system (Nat. Phys.16, 520 (2020)). Subsequently, by systematically studying the behavior of resistance as a linear change with temperature, signs of electron-phonon interaction and quantum critical behavior with adjustable electric field were found (PRB 106, 035107 (2022); The spin-valley competition with adjustable electric field was discovered, the valley polarization correlation insulation state and the topological Chern insulation state with Ten number 2 were realized (Nat.Commun.13, 3292 (2022)), and the quantum oscillation behavior in the correlated insulation state was observed (Sci.Bull.68, 1127 (2023)).

Recently, Yang Wei, a distinguished researcher in the N07 research group of the Laboratory of Nanophysics and Devices of the Institute of Physics, Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics, and Zhang Guangyu, a doctoral student, supervised Dr. Liu Le, and others conducted in-depth research on the associated insulation states of spin polarization in corner double-layer graphene. They found a metal-insulator first-order quantum phase transition behavior with adjustable gate voltage near the Mohr conduction band half-fill, which exhibits a step-like longitudinal resistance platform with carrier concentration or space electric field, accompanied by hysteresis effects (Figure 1). By systematically studying the response of the transmission operation to the opposite in-plane and out-of-plane magnetic fields, it is found that there is a ferromagnetic length program of spin polarization inside the associated insulation state (Figure 2). Combining these experiments, they speculated that strong quantum fluctuations at the phase boundary would induce phase separation and seepage behavior in real space, thereby exhibiting a step-like change in resistance with the magnetic field (Figure 3). In addition, under a vertical magnetic field, the orbital Zeeman effect induces spin-valley competition, producing valley polarization and exhibiting an anomalous Hall effect. They further found that there are first-order quantum phase transitions with adjustable gate voltage between these ground states with different symmetries (Figure 4). Finally, under a finite vertical magnetic field, valley-polarized ground states emerge at odd fills (quarters and three-quarters) of the molar conduction band, where there is also a first-order quantum phase transition with adjustable gate voltage and significant hysteresis effects at the boundary between the ground state and the spin-polarized ground state (Figure 5). This work studies the quantum phase transition behavior of 2+2 systems in detail, reveals ferromagnetic long programs and unconventional electromagnetic interactions in correlated insulating states, and these findings deepen people’s understanding of the nature of associative insulating states in corner systems, and provide a new path for studying the quantum phase transition behavior of strongly correlated systems.

Figure 1. First-stage quantum phase transition with adjustable gate voltage at zero magnetic field.

Figure 2. Magnetic field-induced spin-polarized ferromagnetic phase transition.

Figure 3. Phase separation and seepage at the phase boundary.

Figure 4. Rich phases and their phase transitions induced by valley-spin competition under vertical magnetic field.

Figure 5. First-order quantum phase transition behavior at odd fills.

This work was supported by low-temperature support from Prof. Li Lv, Jie Shen Distinguished Researcher, Dr. Guang Yang from the Huairou Comprehensive Extreme Experimental Device of the Institute of Physics, theoretical support from Prof. Jianpeng Liu and Dr. Xin Lv of ShanghaiTech University, and boron nitride samples from Prof. Kenji Watanabe and Prof. Takashi Taniguchi of the National Institute of Materials Science. The work was supported by the Key R&D Program of the Ministry of Science and Technology, the National Natural Science Foundation of China, Pilot B of the Chinese Academy of Sciences, and institutional scientific research. The relevant results were published in Physics Review X, 13, 031015 (2023) under the title “Observation of first-order quantum phase transitions and ferromagnetism in twisted double bilayer graphene”, with doctoral student Liu Le and Dr. Lu Xin of ShanghaiTech University as co-first authors. Yang Wei and Zhang Guangyu are co-corresponding authors. (Source: Institute of Physics, Chinese Academy of Sciences)

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