1 Introduction

Graphene is composed of a one-atom-thick sp2 hybridized allotrope of carbon atoms, which takes the form of a two-dimensional (2D) planar honeycomb lattice. It has attracted abundant interest after its first isolation was achieved through the micromechanical cleavage of graphite in 2004 [1,2,3,4]. It has been seen as a promising material for applications in sensor, photonic, and electronic devices because of its excellent properties, such as chemical stability, high carrier mobility, low density, and optical transparency [5,6,7,8,9]. However, contrary to the single-layer graphene (SLG), while combining two or more layers of 2D materials in a specific order to fabricate the multilayer structures [5c. The absorption edge of σLB in Fig. 5c demonstrates a significant expansion, as well as the shifting toward higher energy; it demonstrates the shifting of the α-peak toward lower energy, whereas its intensity is decreased noticeably, which confirms the changing of the band structure of tBLG with the gating. The optical absorption spectra showed notable variations like the shifting of inter-van Hove singularity transition peak and the splitting of interlinear band absorption, as well as the appearance of an extremely strong intra-valence band transition.

Fig. 5
figure 5

a Optical conductivity of some commensurate and incommensurate tBLG structures, and inset shows the leading transition procedures contributing to the formation of the optical conductivity peaks [126]. b Optical conductivity σ1(ω) of the different twisting angle tBLG samples, and inset shows comparison of the observed peak position and theoretical prediction. c Optical conductivity of gated tBLG (θ = 6.4°) for different gate voltages VG [127]. Adapted with permission from Refs. [126, 127]

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The PL excitation spectrum recorded after 2-photon excitation, also the twisting angle-associated tunable linear absorption spectrum, is shown in Fig. 6a [130]. The resonant PL emission was positioned at around ~ 2.0, 2.1 and 2.7 eV, as confirmed by applying 10 nm wide band-pass filters. The domain twisting angles were selected by 1-photon linear absorption spectrum, which spectrally overlaps with the consequent 2-photon PL excitation peaks. The splitting of 2-photon PL excitation and 1-photon absorption peak energies varies with the twisting angle. The PL map of tBLG structure collected at around 1.26 eV excitation shows a significant PL emission enhancement after the 2-photon excitation of 17.5° domains, as compared to the nearby domains (Fig. 6b) [130]. The appreciative band-pass optical filtering confirms the emission energy matches well with the 1-photon absorption resonance at ~ 2.8 eV of the 17.5° domain. This resonant PL variation with the vHs reveals that the electrons will thermalize quickly to low metallic continuum states by electron–electron scattering. The line scanning results of the different graphene films by two different lasers wavelength (633 and 514 nm) are shown in Fig. 6c [7e, f). The photocurrent from both 13° and 7° twisted tBLG domains increases as the incident 532 nm laser power increases from ~ 1 μW to ~ 5 mW, as shown in Fig. 7g. The substantial enhancement in photoresponsivity of 13° twisted tBLG domain below the enlightenment of different incident 532 nm laser power is observed. This twisting angle-dependent photocurrent enhancement holds enormous promise for high-selectivity photodetection applications.

Fig. 7
figure 7

a Schematic representation of a tBLG photodetection device, which comprises of two adjacent tBLG domains with different twisting angles of 7° and 13°. b Optical image of the tBLG photodetection device. c Raman G band intensity map** image of 13° twisting angled tBLG with an enhanced G band intensity at 2.33 eV laser energy. d Current versus source–drain bias curve with laser focus on spot A of 7° and spot B of 13° twisting angle in tBLG with laser off. e, f Scanning photocurrent image and its 3D view of the tBLG device. g Photocurrents generated as a function of incident power at spot A of 7° and spot B of 13° twisting angle of the tBLG device [86]. Adapted with permission from Ref. [86]

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6 Electronic Properties

The perfect and superior characteristics of the bilayer graphene in twisted multilayer graphene (tMLG) than the suspended form of graphene could be attributed to the fact that the tMLG is tens of nanometer in thickness and maintains the graphene layers ultra-clean, as well as free from any substrate influence. These extraordinary properties in tMLG generate from the higher degree of decoupling that occurs from the angular twisting between the layers [133]. Recently, Mogera et al. [134] reported the semiconducting to metallic transition converging behavior of twisted multilayer graphene (tMLG). The temperature-dependent conductivity (σ) of the tMLG device in the 90 K to 273 K temperature range is shown in Fig. 8a. As the temperature increases, the conductivity per layer in the tMLG slowly increases and reaches a maximum at around 180 K and then linearly decreases up to 300 K, which reveals the variation in non-monotonous conductivity with a distinctive semiconducting to metallic conversion on raising the temperature. The sequential difference in device photocurrent under light exposure is shown in Fig. 8b. The photocurrent increases in the semiconducting region and drops with the rising temperature in the metallic region and decreases with no photoresponse at a transition temperature (Fig. 8c). These pristine properties reveal the decoupled nature of the graphene layers in tMLG.

Fig. 8
figure 8

a Variation in temperature-dependent conductivity, σ, of the tMLG device at 90 K to 273 K temperature range, and blue and red lines are power law and linear fit to the curves in the metallic region and semiconducting region, respectively. b Temporal variation in the photocurrent with the intermittent enlightenment of light source measured at 50 mV. c Photoresponse variation indicated by the varying of the current (left) and the resistance (right), measured at different temperatures [134]. d Normalized current distributions of four tBLG domains with different twisting angles. e Interlayer conductance of tBLG with different twisting angles. The orange curve and the red curve indicate a phonon-assisted transport mechanism with and without considering the renormalization of the Fermi velocity, respectively [135]. f Temperature-dependent resistivity (ρ) of tBLG device. g Resistivity (ρ) as a function of carrier density at selected temperatures in tBLG device, h ρ(T) recorded in tBLG devices with different twisting angles near − ns/2 filling [137]. Adapted with permission from Refs. [134, 135, 137]

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The interlayer contact conductance among the BLG with different twisting and stacking structures synthesized by the CVD method is recently discussed by Yu et al. [135]. A statistical method is applied for comparing the twisting angle-dependent current in the tBLG domains. The statistical results for different tBLG domain with various twisting angles are shown in Fig. 8d. The tBLG with a small twisting angle displays a higher current, which indicates excellent contact conductance at no twisting among the graphene layers. Figure 8e shows the interlayer conductance of tBLG with various twisting angles. The interlayer contact conductance decreases with an increase in the twisting angle. The twisting angle propagation to the interlayer potential energy enhances, at the larger twisting angle [136]. The interlayer contact conductance of 0° BLG domain is ~ 4 times higher than the 30° tBLG domain, which reveals the twisting angle-dependent graphene interlayer contact conductance originated from the decoupling and coupling transitions.

Polshyn et al. [137] discussed the electrical transport measurements for different tBLG devices with 0.75° to 2° twisting angles in the room temperature. The resistivity (ρ) of the tBLG domain (θ = 1.06°) measured near the flat band condition for carrier densities spanning the lower-energy band is shown in Fig. 8f, g. The resistance peaks or insulating phases at some integer multiples of ns/4 and superconducting states at different partial band fillings are revealed in Fig. 8f. At nearly all densities, the resistivity (ρ(T)) increases with the increase in temperature and remains steady with the metallic behavior. The resistivity (ρ(T)) measured in tBLG devices with different twisting angles near − ns/2 is shown in Fig. 8h. The resistivity is enhanced sub-linearly with the increase in temperature and reaches the highest point at a temperature TH; the resistivity scales linearly with temperature below the temperature TH. At the lowest temperatures, resistivity diverges from a linear dependence on temperature. The tBLG devices clearly show the resistivity saturation, superconducting, or insulating behavior at moderate temperature regimes. The observed three distinctive temperature regimes are noticeable by the different behavior of resistivity (ρ(T)) depending on the carrier density and twisting angle.

7 Superconductivity

The unusual superconducting behavior of different materials has been studied broadly for the last decades. The weak interlayer interaction creates the interlayer coupling in tBLG, and the strength of interlayer coupling as well as twisting angles equally affects the Fermi velocity and the VHSs of tBLG, which makes the novel electronic state of tBLG, which is different from those in SLG [138,139,140]. The twisting angle among the layers of bilayer graphene decides the degree of interlayer coupling and plays a decisive role in its electronic properties [140]. Recently, Cao et al. [141] reported the unconventional superconductivity in the magic-angle graphene superlattices. The representative device structure of the encapsulated tBLG is shown in Fig. 9a. The mini-Brillouin zone is built from the variation present among the two K or K′ wave vectors for the two graphene monolayers (Fig. 9b). The interlayer hybridization takes place between the Dirac cones in each valley, where the intervalley interactions are intensely suppressed [120, 142]. The longitudinal resistance (Rxx), as a function of temperature (T(K)) for two tBLG devices with 1.16° and 1.05° twisting angles, demonstrated zero resistance at 70 mK revealing the superconducting state (Fig. 9c). The critical temperature (Tc) determined using a resistance of 50% of the non-superconducting state value was about 1.7 and 0.5 K for the two tBLG devices. The two-probe conductance versus carrier density at zero magnetic fields and a 0.4 T perpendicular magnetic field of M1 device is shown in Fig. 9d, which clearly shows the V-shaped conductance created from the renormalized Dirac cones of the tBLG band structure at charge neutrality point (n = 0). It also shows the states of insulating at the superlattice bandgaps n = ± ns. The insulating state at ± 3.2 × 1012 cm−2 is as a result of the presence of single-particle bandgaps in a band structure, as well as the observed conductance minima connected with many body gaps [43]. At 70 mK temperature and − 1.3 × 1012 to − 1.9 × 1012 cm−2 electrons per unit cell, the conductance was significantly high for nil magnetic fields than in the vertical 0.4 T magnetic field (B⊥), which reveals the presence of superconductivity at the magic angle. The density-dependent resistance of the tBLG device with a 1.14° twisting angle plotted almost over the complete flat band density range is shown in Fig. 9e [143]. The tBLG device showed lower charge carrier inhomogeneity (δn < 2 × 1010 cm−2), and at the magic angle (θ = ~ 1.1), the resultant hybridization and moiré superlattice among the graphene layers caused the development of a remote flat band at the charge neutrality point (CNP) [120, 143]. In the flat band, the resistive states are observed at the charge neutrality point (CNP) and ± ns/2 and +3 ns/4. The superconductivity regions emerge in both electron- and hole-doped regions at ~ 10 mK base temperature with the drop** of resistance to zero. However, for ± ns/2 densities, below the base temperature, no sign of superconductivity is observed. The superconductivity appears considerably absent or weak on the lower-density side and extra stronger in the higher-density side of the insulator in both bands.

Fig. 9
figure 9

a Schematic of the tBLG and hexagonal boron nitride-sandwiched device. b The mini-Brillouin zone is made from the difference between the two K (or K′) wave vectors for the two graphene layers [43]. c Four-probe resistance Rxx determined in two devices M1 and M2 with twisting angle of 1.16° and 1.05°, respectively, and the optical image of the device is shown in inset where the darker region is the patterned tBLG. d Two-probe conductance (G2 = I/Vbias) of the device M1 calculated in zero magnetic field (red) and at a vertical field of B⊥ = 0.4 T (blue) [141]. e Temperature dependence of the resistance over the density range required to fill the moiré unit cell [143]. Adapted with permission from Refs. [43, 141, 143]. (Color figure online)

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Recently, Codecido et al. [144] reported both insulating state and superconductivity in a tBLG structure at a ~ 0.93° twisting angle. The ~ 0.93° twisting angle is 15% small than the previously reported magic angle (θ = 1.1 ± 0.1°) [43, 139, 140]. The magnetic field (B) and longitudinal resistance (Rxx) versus an elongated gate voltage (Vg) range at a 1.7 K temperature (Landau fan pattern) are shown in Fig. 10a. The satellite peak is observed at Vg = ± 0.85 V, as the lower-energy moiré bands are filling at densities nm = ± 4 (where nm is the number of charges per moiré unit cell) [43, 141]. The resistance peak appears at Vg = 0.43 V from which an alongside set of Landau levels emanate. The peak on the half-filling and the twofold degeneracy of Landau levels illustrate the breaking of the symmetry of spin valley [145] and the development of a novel quasi-particle Fermi surface. At nm = 0, ± 4, and +2, the resistance peaks are clearly observed in Rxx(Vg) at B = 0 and for different temperatures (0.28 to 5.2 K) (Fig. 10b). The Rxx is zero at T = 280 mK, for 0.51 < Vg < 0.65 revealing the development of superconductivity [43]. The development of superconductivity and conceivably penetrating superconducting regions might be responsible for the increase in Rxx with the increase in temperature at nm = 2. As the temperature (T) decreases, ρ decreases to zero with the two consecutive steep successions at T ~ 0.3 K and T ~ 1.5 K (Fig. 10c); it could be associated with non-Planckian dissipation of the extraordinary metal states [146]. The voltage–current (V–I) curves at two descriptive densities (Vg = 0.58 V and Vg = 0.50 V) are shown in Fig. 10d. The maximum value of the critical current (Ic) is observed at Vg = 0.58 V and observed the supercurrent for an elongated range of density with Ic (~ 1 to 15 nA). The temperature dependence of the resistance peaks is nearly invisible, as the temperature is enhanced above ~ 5 K (Fig. 10d). The Arrhenius plot of resistance with ~ 1 K energy gap is shown in Fig. 10f. The peaks at nm ≈ ± 5 are unlikely to initiate from the angular disorder and single-particle gap as a result of an alignment between graphene and hBN [147, 148]; these features are uncertainly attributed to the development of a novel interrelated insulating state. θ = 0.93° is the lowest twisting angle reported till to the date for tBLG devices showing superconductivity and insulating state.

Fig. 10
figure 10

a Rxx versus magnetic field B and gate voltage Vg, showing a Landau fan pattern. b Rxx(Vg) at different temperatures. c ρ versus temperature when the density is tuned to the superconducting phase. d Voltage–current characteristics at T = 280 mK and Vg = 0.58 V (red) and 0.50 V (blue). e Temperature dependence of the resistance peak. f Arrhenius plot of resistance [144]. Adapted with permission from Ref. [144]. (Color figure online)

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8 Conclusions

The objective of this review paper is to provide detailed information regarding the fabrication of twisted bilayer graphene (tBLG) via different methods, its properties, as well as its technological applicability. The tBLG-related research field has developed at an enormous speed. The prominent tBLG fabrication methods such as micromechanical exfoliation, CVD, graphene flake pickup, CRS, stacking methods, and their unique properties are summarized in the initial sections. The control over the twisting of two graphene layers is the major challenge in the fabrication of tBLG. The twisted bilayer graphene (tBLG) is a novel arrangement, which shows the basic properties are different from those of the stacked bilayer graphene. The variation in line width and position of the (ZO′)L mode illustrates the influence of the twisting angle-dependent electronic band overlaps, onto the Raman spectrum. The continuous variation in optical and electrical properties of tBLG is strongly dependent on the twisting angle (θ) among the two graphene layers. We believe that the development and variation in the optical properties of tBLG would be extensively used in the future in the field of optoelectronics. The tBLG devices displayed non-monotonous conductivity variation, which reveals a semiconductor to metallic transition. The superconducting properties observed in tBLG are due to the electron interactions, which can distinctly influence the properties of moiré superlattices at higher densities and smaller twisting angles. There are quite a few challenges that are related to achieving a control over the twisting of two graphene layers for the development in the fabrication and characterization of twisted bilayer graphene (tBLG). It is expected that theoretical studies will be published in the future to search for novel superconducting and insulating phases of tBLG at a lower temperature.