Introduction
Emergent phenomena
To whatever extent we may imagine our knowledge of the properties of the various ingredients of a living body to be extended and perfected, it is certain that the mere enumeration of the separate actions of those elements will never amount to the action of the living body. yourself. It would be preferable instead to have a vivid picture of the behavior of the wave functions, a simple description of the essence of the factors determining the coherence, and an understanding of the origin of variation in properties from metal to metal.
Novel quantum states of matter in vdW materials
One of the best-known exotic electronic phases is the Quantum Spin Hall (QSH) state, which was designed by Eugene Mele and Charlie Kane in 2005 [18]. Clean interfaces between superconducting and non-superconducting materials are notoriously difficult to realize, and the quality of the interface determines how strong the induced superconductivity in the non-superconducting material will be.
Towards application-oriented devices
Despite the fact that both materials are very sensitive to air, we were able to induce strong superconductivity in WTe2 using this method. It is possible to obtain atomically flat topography and remarkably intact interfaces between two different vdW materials just by layering them on top of each other.
Thesis outline
The dependence of the moiré wavelength on the relative rotation angle (for a heterostructure of a graphene sheet and a material with a lattice constant mismatch of δ) is shown in Eq. WSe2 itself has strong spin-orbit coupling due to the heavy W atoms (spin-orbit is a relativistic effect that links the spin and orbital angular momenta of an electron and is proportional to Z4, where Z is the atomic weight) [85 ].
Physics of Graphene and Twisted Bilayer Graphene (TBG)
Overview of Graphene
The valence and conduction bands of graphene touch at the points K and K' of the Brillouin zone and follow linear dispersion at low energies. One of the most beautiful properties associated with this band structure is Klein tunneling in graphene [25, 26].
Topology and topological phases in graphene
The frequency of the cyclotron orbits is ωc =eB/m, which does not depend on the radius. The phase diagram showing the relationship between this parameter and the topological nature of the gap is shown in Fig.
Inducing spin-orbit coupling in graphene
Three different types of spin-orbit coupling have been proposed to be induced in graphene as a result of the proximity effect with TMDCs. This fitting procedure usually has too much flexibility due to the number of parameters used, which results in large discrepancies for the quoted spin–orbit coupling values.
Search for superconductivity in single-layer graphene
55] studied the behavior of electron-electron interaction in graphene at extremely high carrier densities (1013/cm-2) - carrier densities at which the Fermi level would approach the saddle points (van Hove singularities in density of states) of the π* bands shown in figure. A normal h-BN or SiO2 gate would fail when applying gate voltages proportional to extremely high carrier densities.
Periodic potentials in twisted bilayer graphene
Against this background, we will see why superconductivity in TBG has quickly become one of the most exciting topics in condensed matter physics.
Low angle twisted bilayer graphene
The two monolayers are decoupled for large angles. b), The two Dirac cones start to hybridize around 2◦. c) Around the magic corner, interactions are maximized and a "flat band" is created. Another more conceptual (and less quantitative) way to think about the moiré wavelength (and therefore angle) needed to achieve strong correlations in a 2D conductor is to think in terms of bandwidth and Coulomb energy.
Tear and Stack method
These gaps separate the low-energy flat bands from the higher-energy scattering bands with energy gaps ranging from 10–50 meV. This enabled the study of flat band behavior later on, leading to the observation of superconductivity.
Correlated Insulators and Superconductivity in Magic Angle Twisted
Correlated insulators (CIs) are present for integer fill factors of the moiré unit cell and superconducting pockets. The proximity of the superconducting pockets to the insulating states was analogous to Cuprates leading people to believe that the mechanism of superconductivity in TBG might be similar.
Low control of twist angle
Although the correlated insulation states are clearly visible, superconductivity at these small angles is noticeably absent. The device did not show any sign of superconductivity, but showed clear insulation states that developed to partially fill the flat bands shown for and.
Effect of encapsulating substrate
Different fill factors show different oscillation periods, most likely due to a change in the superconducting region of the device. For higher DC current, the graphene temperature increases, causing the critical current in the junction to decrease.
Superconductivity in TBG/WSe 2 heterostructures
Why WSe 2 with TBG?
Inspired by other strongly correlated electron systems, one could stabilize many phases in TBG depending on the strength of the induced spin-orbit coupling [84]. It was also well established in the literature that monolayer WSe2 was particularly believed to induce stronger spin-orbit coupling than single-layer WSe2.
Outline of devices studied in this chapter
Superconductivity in TBG/WSe 2 close to magic angle
The contact angle for each pair of listed contacts was determined from the Landau fan diagrams, as described in Chapter 4. The fact that this device showed clear superconductivity despite the high angle disorder indicated that WSe2 played an important role.
Fraunhofer-like field dependence: crucial test
3.4, our device showed clear superconducting behavior as well as fully developed correlated insulating states, giving us confidence about the quality of these devices. This is evident from how broad the correlated insulating state is around v=+2, making it difficult to assign a single twist angle to this region.
Superconductivity without insulating states
For this angle, correlated isolation states are also observed for filling factorsν= +2, +3 with activation gaps of ∆+2= 0.68 meV and ∆+3= 0.08 meV, while at other filling factors correlated states are less developed and do not show offensive behavior (see Fig .3.11 and Fig. 3.9). At the smallest angle, θ = 0.79°, together with the lack of insulating conditions at any partial filling, the resistance at full filling is reduced even more as seen in Fig.
What impact does this have on the origin of superconductivity?
The relatively low resistances <2 kΩ measured at full charge, which are less than 15% of the resistance at the charge neutrality point (CNP), suggest a semi-metallic band structure around full charge, consistent with theoretical expectations for TBG atθ and resistivity of a dilute 2D electron gas [100]. Despite the absence of both fully filling bandgaps and correlated insulators, the low resistance superconducting pocket nearν = +2 is surprisingly clearly resolved in Fig. correlated states of metallic nature that may be present at smaller angles and near integer values in analogy to other exotic superconducting systems.
Gap extraction for insulating states
The choice of the exponent (1/3) for VRH is based on a Mott hopping assumption because the exponent must be 1/(d+1) for a Mott insulator and d = 2 for 2 dimensions. If the hopping is assumed to be Efros-Shklovskii VRH, the exponent should be 1/2, and the fit would work quite well for this value as well, since there are so many fitting parameters.
Optimized measurements of resistance near the superconducting pocket 50
Superconducting domes (SC) are indicated by a dashed line indicating half the resistance measured at 2 K. a) For the 0.87◦ area. b) For the 0.79◦ area. Note the absence of correlated insulating states. b) Line sections from a) highlighting the development of the superconducting pocket around +2 fill factor.
Doubly encapsulated TBG/WSe 2 devices
Based on the current generation of devices, it is difficult to determine the exact role of spin-orbit coupling in stabilizing superconductivity at very small angles. If the superconductivity can be suppressed/enhanced by changing the spin-orbit coupling in situ, it will help establish a strong connection between the two.
Constraints imposed on superconductivity
Theoretical modeling of induced spin-orbit coupling in TBG
So by applying Joule heating one can determine the temperature rise in the electron gas by looking at the value of the critical current. Adding a graphene element just adds the length "l" of the transmission line (which reduces the resonant frequency).
Normal state characterization and magnetism in TBG/WSe 2
Behavior in high magnetic field and spin-orbit coupling
However, the mechanism of SOI-induced degeneracy breaking remains the simplest explanation for the observation of the additional even Landau levels (see corresponding discussion in section on Landau level calculations and Fig. 3.22). Landau fan up to 6T showing Landau levels derived from Charge Neutrality Point (CNP) and half-fill (+2). b) Zooming in around CNP, dashed lines are drawn from the charge neutrality point according to the sequenceνL L =±2,±4,.
Quantized Landau Levels
The random step is most likely due to further symmetry breaking by electronic correlations.
Determination of twist angle
Assuming that the area of the unit cell of the moiré superlattice is A and the flux quantum is φ0 = h/e [133], features should appear in fields corresponding to Bfull/n and n*Bfull, where n is an integer is. It is important to point out that we do not observe Pocket-type oscillations for most contact/device pairs we measure.
Evidence for induced spin-orbit coupling in TBG
Weak localization arises from the quantum mechanical treatment of the probability of the electron returning to some point Q. Therefore, the quantum correction in total is exactly half the size of the weak localization correction of opposite sign.
Landau level model calculations
However, we note that the spin-orbit parameters (λI, λR, m) are not forbidden to take different values at the ±κDirac cones (the parameters at±Kare related to time reversal). It is then straightforward to show that the Landau level spectrum corresponding to a Dirac cone with the opposite chirality can be obtained directly by taking the negative of the solutions to Eq.
Search for magnetism
For each feedback voltage, the temperature dependence of the critical current can be extracted from the resonance frequency movement based on the RCSJ model. Measurement of electron channels of thermal conductivity and heat capacity of graphene at low temperature.
Continuous Thermometry in Graphene
Introduction
In these experiments, the authors showed that the magnitude of the Hall thermal conductivity for the 5/2 state was 2.5k0 (where k0 is the universal quantum of thermal conductivity [153]), and their observation confirmed the topological nature of this state. For the case of graphene encapsulated in h-BN, the Josephson effect has been seen for micron-scale junction lengths due to the ballistic nature of graphene [154,155].
Real time thermometry with superconducting circuits
This fact can be used to extract the thermal conductivity by first extracting the dependence of the critical current on the step temperature of the cryostat. For graphene, the blackbody radiation loss is on the order of 10-15pW/K and is usually neglected compared to GWF and Gep.
Characterization of graphene - aluminum Josephson junctions
An advantage of using this method is that by using superconducting electrodes, diffusion in the electrodes can be ideally suppressed due to the existence of the superconducting gap. We also obtain high IcRn products of the order of 0.5∆(∆ is the superconducting gap of aluminum), comparable to the best reported devices in literature.
Device design and measurement setup
A good indicator of contact transparency is multiple Andreev reflection (MAR) where an electron (hole) having energy less than that required to cross the superconducting barrier is reflected sequentially before scattering into the contact. We model combining a CPW, a coupling capacitor and a Josephson junction to arrive at the dependence of a resonant characteristic as a function of critical current.
Backgate modulation of resonance
By changing the back gate voltage, we effectively change the carrier density in the graphene sheet. This means that the resonance frequency also increases when the graphene is doped, the CNP is where the minimum of the resonance frequency occurs.
Heater response
If the heating is applied by a pulse, then after an initial rise, the temperature decays according to the thermal time constant as shown in Fig. showed. However, for continuously applied DC heating, the temperature of the electron gas equilibrates to a certain temperature where incoming power equals the heat loss to the environment.
Inductive readout of temperature
The ideal contact for this heater is a pure ohmic contact because it is easy to extract the current passed through to the flag for an ohmic contact. We use this movement of the resonance in response to applied DC heating power to extract useful thermal parameters for our graphene flake.
Power law extraction and associated physics
One of the most important predictions about graphene that has never been experimentally realized is the Quantum Spin Hall Effect [33]. Maximally localized Wannier orbitals and the extended Hubbard model for twisted bilayer graphene. Physical overview X.
Outlook
TBG encapsulation with other materials
A simple extension to TBG devices after TBG/WSe2 devices would be to encapsulate the TBG with a 2-D ferromagnetic insulator such as CrBr3 (Curie temperature of about 37K). A reliable way to obtain the Quantum Anomalous Hall (QAH) phase in TBG would be highly appreciated in the community.
Shot noise measurements in TBG
This beautiful experiment showed that in the pseudogap state the shot noise was significantly higher than theoretically expected from single particle tunneling. One could then measure the shot noise across this junction to answer the questions about the existence of pairing in the strange metal phase in TBG.
Simultaneous electron transport and Scanning Tunneling Microscopy
A landmark experiment used the measurement of shot noise to observe the 1/3 charge carrier value of Loughlin's fractional quantum Hall state [175]. The entire heterostructure would be made by having only a WSe2 monolayer on top of the TBG (no h-BN).
Bolometry and heat capacity measurements of TBG
One of the major obstacles to bridging this gap between DC transport and STM measurements has been the incompatibility between superconducting transport samples and STM samples. This will allow for a thorough investigation of the percolation paths in TBG together with the determination of the superconducting gap size as well as its nematic behavior.
Quantum Spin Hall effect in graphene through screening
Simultaneous electron transport and Scanning Tunneling Microscopy
132] Codecido, E. et al. Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle. Phonon-induced giant linear-in-t resistivity in magic-angle twisted bilayer graphene: Common strangeness and exotic superconductivity.
