| The discovery of twisted graphene breathes new life into the field of condensed matter physics.People can build moiré superlattices far beyond the scale of atomic lattice by controlling the new degree of freedom-twisted angle.At this moiré scale,band structures,topological properties,and electronic correlation strengths can be easily tuned.Besides,the unique spin-valley four-fold degeneracy and nearly flat band of twisted graphene systems underlie kinds of strong correlated ground states which give birth to amazing phenomena,such as ferromagnetism,superconductivity,quantum anomalous Hall effect,Chern insulators,quantum critical behaviors,and so on.By virtue of above-mentioned advantages,twisted graphene systems become excellent platforms to study kinds of strong correlated states.Twisted double bilayer graphene,a moiré superlattice made of two twisted stacked bilayer graphene,rapidly becomes an important member of twisted graphene systems due to in-situ electric-field-tunable band structures and spin-polarized correlated insulating states emerging at half filling of energy bands.We will focus on the transport behaviors of this system at cryogenic temperature to investigate novel phases and phase transitions with multi-field control,and try our best to extend and perfect the phase diagram of twisted double bilayer graphene.Our works are divided into three parts:1.Valley-polarized correlated insulating states in twisted double bilayer graphene.Valley-polarized states are intimately related to the orbital magnetization and quantum anomalous Hall effect.However,people only observed spin-polarized states,not yet valley-polarized states in twisted double bilayer graphene.Theories have predicted the perpendicular magnetic field will induce valley-polarized states,which points the way to observe this phenomenon in experiment.We fabricate high-quality twisted double bilayer graphene devices with uniform twisted angle between 1.2~1.5°and observe correlated insulating states induced by perpendicular magnetic field at half filling of valance and conduction bands and at large displacement field.The effective Landé factor g ~ 10 suggests these insulating states are valley-polarized states with large orbital magnetization.Besides,the spin Zeeman effect in tilt magnetic field enhances the energy gap of spin-polarized insulating states while suppresses the energy gap of valley-polarized insulating states,which suggests the competition between spin and valley polarizations at half filling of energy band due to the Pauli exclusion principle.Furthermore,we observe the Chern insulator near the half filling of conduction band at high magnetic field.It has quantized Hall conductance with C = 2,in consistent with theoretical calculations.We also observe band reconstruction induced by magnetic field near the half filling of valance band.The van Hove singularity at low magnetic field turns into the correlated energy gap at high magnetic field.Meanwhile,the four-fold degenerated energy band is also reconstructed into two double degenerated valley subbands,then quantized into a series of completely symmetry breaking Landau levels at high magnetic field.2.Quantum oscillations in correlated insulators.Recently,the phenomena of quantum oscillations in an insulator have attracted wide attention.These anomalous behaviors may indicate a special band structure or the existence of neutral Fermions.We observe quantum oscillations with amplitude as high as 150 kΩ in correlated insulators at half filling of valance band in twisted double bilayer graphene.Such a high amplitude is much larger than that in two-dimensional electron gas.We confirm the quantum oscillations do occur in an insulator according to the temperature dependent resistance and antiphase oscillations between resistance and conductance.Besides,these oscillations can be tuned by the electric field.The frequency decreases linearly with the increase of electric field.To explain the quantum oscillations in an insulator,we use the Hartree-Fock theory and continuum model calculations to construct an inverted band model.It successfully reproduces the electric field tunable quantum oscillations in experiment,which confirms the existence of inverted band structure induced by magnetic field near the half filling of valance band.3.First-order phase transitions and ferromagnetism in twisted double bilayer graphene.Orbital magnetization is ubiquitous in twisted graphene systems,and it will lead to anomalous or quantum anomalous Hall effect in transport measurements.However,Spin magnetization is featureless in transport and only detected by indirect methods of measuring Landé factors.Hence,there has been no direct evidence of ferromagnetic long-range order in spin-polarized correlated states yet.Besides,there are few research works about phase transitions between different correlated ground states.We observe first-order phase transitions driven by gate voltage between normal metal and spinpolarized correlated insulators near the half filling of conduction band in twisted double bilayer graphene.Taking advantage of the hysteresis effect in first-order phase transitions,we demonstrate the two-bit memory and it has potential for applying in cryogenic memory devices in the future.Furthermore,we prove the ferromagnetic longrange order in spin-polarized insulators according to the transport measurements in magnetic field and observe the percolation induced by phase separation between ferromagnetic domains and normal metal near the phase boundary.In perpendicular magnetic field,the large orbital Zeeman effect will induce valley-polarized metal with anomalous Hall effect.More interestingly,we observe universal first-order phase transitions driven by gate voltage at the phase boundary between ground states with different symmetry.In conclusion,we have observed the valley-polarized correlated insulating states in twisted double bilayer graphene,and further studied the quantum oscillations in correlated insulating states.Besides,we have observed the first-order phase transition and ferromagnetic long-range order of spin-polarized correlated insulating states.The above-mentioned results suggest twisted double bilayer graphene contains abundant correlated states,nontrivial topological properties and gate voltage tunable quantum phase transitions,providing an ideal topological flat band system for studying the quantum states in condensed matter physics. |
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