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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Weak localization as a probe of intervalley coherence in graphene multilayers

Spontaneous intervalley coherence is suspected in several different graphene multilayer systems, but is difficult to confirm because of a paucity of convenient experimental signatures. Here we suggest that magneto-conductance features associated with quantum corrections to Drude conductivity can serve as a smoking gun for intervalley coherence that does not break time-reversal symmetry. In this class of ordered multilayer quantum transport corrections can produce weak localization or weak antilocalization, depending on whether the valley order belongs to the orthogonal or symplectic symmetry class. Our analysis motivates low-temperature weak-field magnetoresistance measurements in graphene multilayers in which time-reversal invariant intervalley coherent order is conjectured.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Momentum space AC Josephson effect and intervalley coherence in multilayer graphene

Electron transport driven by the phase coherence and interference of quantum many-body wavefunctions is a fascinating phenomenon with potential technological significance. Superconductivity, for example, enables dissipationless transport through macroscopic phase twisting, while charge-density waves show broadband noise and AC-DC interference once their phase is depinned. We identify an analogous phase-coherent dynamics in the intervalley-coherent (IVC) state frequently observed in rhombohedral multilayer graphene. We show that a static magnetic field drives an oscillating intervalley current, which produces an oscillating orbital magnetization and thereby a detectable AC Hall response. This mechanism is similar to the Josephson effect observed in superconductors but now happening in momentum space. In this analogy, the static magnetic field acts as the DC voltage, while the oscillating intervalley current is the AC Josephson current. We provide microscopic calculations of all the phase-number free-energy parameters in rhombohedral trilayer graphene, establishing this effect as an experimental signature of IVC order.

electronic properties and materials↗
DOE OSTI2022

Gate-defined wires in twisted bilayer graphene: From electrical detection of intervalley coherence to internally engineered Majorana modes

Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as (i) a tool for revealing the nature of correlated insulators and (ii) a platform for Majorana-based topological qubits. We show that the band structure of a gate-defined wire immersed in an intervalley coherent correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the wire by a superconducting TBG region on one side and an intervalley coherent correlated insulator on the other further enables the formation of Majorana zero modes—possibly even at zero magnetic field depending on the precise symmetry-breaking order present. Our proposal not only introduces a highly gate-tunable topological qubit medium relying on internally generated proximity effects but can also shed light on the Cooper-pairing mechanism in TBG.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Twisted symmetric trilayer graphene. II. Projected Hartree-Fock study

The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a twisted-bilayer-graphene- (TBG-) like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Calugaru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings ν = -3, -2, -1, and 0 measured from charge neutrality. We study the phase diagram with w 0 /w 1 , the ratio of AA and AB interlayer hoppings, and the displacement field, which introduces an interlayer potential U and hybridizes the TBG-like bands with the Dirac bands. At small U, we find the ground states at all fillings ν are in the same phases as the tensor products of a Dirac semimetal with the filling ν TBG insulator ground states, which are spin-valley polarized at ν = -3, and fully (partially) intervalley coherent at ν = -2, 0(ν = -1) in the flat bands. An exception is ν = -3 with w 0 /w 1 ≳ 0.7 , which possibly becomes a metal with competing orders at small U due to charge transfers between the Dirac and flat bands. At strong U where the bandwidths exceed interactions, all the fillings ν enter a metal phase with small or zero valley polarization and intervalley coherence. Lastly, at intermediate U, semimetal or insulator phases with zero intervalley coherence may arise for ν = -2, -1, 0. Finally, our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states.

2-dimensional systems↗
DOE OSTI2021

Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram

Here, we derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4) × U(4) symmetry, and we find that the exact ground states at integer filling – 4 ≤ $\textit{ν}$ ≤ 4 relative to charge neutrality are Chern insulators of Chern numbers $ν_C$ = 4 – |$\textit{ν}$ |, 2 – |$\textit{ν}$ |, $\cdots$, |$\textit{ν}$ | – 4, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $\textit{ν}$ = 0 , ± 2 has exact ground states of Chern number 0, while $\textit{ν}$ = ±1, ± 3 has perturbative ground states of Chern number $ν_C$ = ± 1, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second-order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $ν_C$ = 0 (0 < |$ν_C$| < 4 – |$\textit{ν}$ |) at integer fillings $\textit{ν}$ are fully (partially) intervalley coherent, while the insulator states with Chern number |$ν_C$| = 4 – |$\textit{ν}$ | are valley polarized. However, for 0 < |$ν_C$| ≤ 4 – |$\textit{ν}$ |, the fully intervalley coherent states are highly competitive (0.005 meV/electron higher). At nonzero magnetic field |$\textit{B}$ | > 0, a first-order phase transition for $\textit{ν}$ = ± 1, ± 2 from Chern number $ν_C$ = sgn ($\textit{νB}$)(2 – |$\textit{ν}$ |) to $ν_C$ = sgn ($\textit{νB}$)(4 – |$\textit{ν}$ |) is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin-triplet superconductivity from intervalley Goldstone modes in magic-angle graphene

Here, we consider magic-angle graphene in the doping regime around charge neutrality, and we study the connection between a recently proposed intervalley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The intervalley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes that couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and we study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the p-wave channel.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis

Here, motivated by recent experimental observations of correlated metallic phases and superconductivity in rhombohedral trilayer graphene (RTG), we perform an unbiased study of electronic ordering instabilities in hole-doped RTG. Specifically, we focus on electronic states energetically proximate to Van Hove singularities (VHSs), where a large density of states promotes different interaction-induced symmetry-breaking electronic orders. To resolve the Fermi surface near VHSs, we construct a fermionic hot-spot model and demonstrate that a perpendicular electric field can tune different nesting structures of the Fermi surface. Subsequently, we apply a renormalization group analysis to describe the low-energy phase diagrams of our model under both short-range repulsive interactions as well as realistic (long-range) Coulomb interactions. Our analysis shows instabilities towards either intervalley coherent metallic phases or superconducting phases. The dominant pairing channel depends crucially on the nature of Fermi surface nesting—repulsive Coulomb interaction favors spin-singlet d-wave pairing for relatively small displacement field and spin-singlet i-wave pairing for larger displacement field. We argue that the phase diagram of RTG can be well-understood by modeling the realistic Coulomb interaction as the sum of repulsive density-density interaction and ferromagnetic spin-triplet intervalley coherence (IVC) Hund's coupling, while phonon-mediated electronic interactions have a negligible effect on this system, in sharp contrast to twisted graphene multilayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Quantum textures of the many-body wavefunctions in magic-angle graphene

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a √3 x √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of ±2 electrons per moiré unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. Here, we also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands

Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Quantum-critical soft modes drive pairing interactions in which the pair scattering processes are highly collinear and can be classified into two categories: forward scattering and backscattering. Conversely, in conventional phonon mechanisms, Cooper pair scattering is of a generic noncollinear character. In this study, we present a method to discern the kinematic type by observing the evolution of superconductivity while adjusting the Fermi surface geometry. To demonstrate our approach, we utilize the recently reported phase diagrams of untwisted graphene multilayers. Our analysis connects the emergence of superconductivity at “ghost crossings” of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed nonmonotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it lends strong support to a particular quantum-critical superconductivity scenario in which pairing is driven by intervalley coherence fluctuations. These findings offer direct insights into the genesis of pairing in these systems, providing compelling evidence for the electron–electron interactions driving superconductivity. More broadly, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Interaction-induced velocity renormalization in magic-angle twisted multilayer graphene

Abstract Twistronics heterostructures provide a novel route to control the electronic single particle velocity and thereby to engineer strong effective interactions. Here we show that the reverse may also hold, i.e. that these interactions strongly renormalize the band structure. We demonstrate this mechanism for alternating-twist magic-angle three- and four-layer graphene at charge neutrality and in the vicinity of a phase transition which can be described by an Ising Gross-Neveu critical point corresponding, e.g. to the onset of valley Hall or Hall order. While the non-interacting model displays massless Dirac excitations with strongly different velocities, we show that interaction corrections make them equal in the infrared. However, the renormalization group flow of the velocities and of the coupling to the critical bosonic mode is strongly non-monotonic and dominated by the vicinity of a repulsive fixed point. We predict experimental consequences of this theory for tunneling and transport experiments and discuss the expected behavior at other quantum critical points, including those corresponding to intervalley coherent ordering.

Classen, Laura↗
DOE OSTI2020

Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: A Hartree-Fock study

Motivated by the recently observed insulating states in twisted bilayer graphene, we study the nature of the correlated insulating phases of the twisted bilayer graphene at commensurate filling fractions. Iin this work, we use the continuum model and project the Coulomb interaction onto the flat bands to study the ground states by using a Hartree-Fock approximation. In the absence of the hexagonal boron nitride substrate, the ground states are the intervalley coherence states at charge neutrality (filling $\textit{ν}$ = 0 , or four electrons per moiré cell) and at $\textit{ν}$ = –1/4 and –1/2 (three and two electrons per cell, respectively) and the $C_2\mathcal{T}$ symmetry-broken state at $\textit{ν}$ = –3/4 (one electron per cell). The hexagonal boron nitride substrate drives the ground states at all $\textit{ν}$ into $C_2\mathcal{T}$ symmetry broken-states. Our results provide good reference points for further study of the rich correlated physics in the twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Using exact diagonalization, we research the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [U(4) × U(4)] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around ν = ±3,±2,±1 fillings. In the first chiral limit w 0 /w 1 = 0, where w 0 (w 1 ) is the A A (AB) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge ±1 excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes 8 × 8 (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys. Rev. B 103, 205411 (2021)], Song et al. [Phys. Rev. B 103, 205412 (2021)], Bernevig et al. [Phys. Rev. B 103, 205413 (2021)], Lian et al. [Phys. Rev. B 103, 205414 (2021)], and Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] for obtaining a series of exact ground states and excitations holds in a large parameter space. For ν = -3, the ground state is the spin and valley polarized Chern insulator with ν C = ±1 at w 0 /w 1 ≲ 0.9 (0.3) with (without) FMC. At ν = -2, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when w 0 /w 1 ≳ 0.5 t where t ϵ [0,1] is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [Lian. et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [Lian et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. For ν = -3 with/without FMC, when w 0 /w 1 is large, the finite-size gap Δ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at ν = -3 suggests a competition among (nematic) metal, momentum M M (π) stripe and K M -CDW orders at large w 0 /w 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Ground-state order in magic-angle graphene at filling ν = - 3 : A full-scale density matrix renormalization group study

Here we investigate twisted bilayer graphene (TBG) at filling ν = -3 in the presence of realistic heterostrain. Strain amplifies the band dispersion and drives the system beyond the strong-coupling regime of previous theoretical studies. We use DMRG to conduct an unbiased, large-scale numerical calculations that include all spin and valley degrees of freedom, up to bond dimension χ = 24576. We establish a global phase diagram that unifies a number of theoretical and experimental results. Near zero strain we find an intervalley-coherent quantized anomalous Hall (QAH-IVC) state, a competitive strong-coupling order that evaded past numerical studies. A tiny strain around 0.05% drives a transition into an incommensurate Kekulé spiral (IKS) phase, supporting the mean-field prediction in [Kwan, Phys. Rev. X 11, 041063 (2021)2160-330810.1103/PhysRevX.11.041063]. Even higher strains above 0.2% favor a flavor-symmetric metallic order, which may explain metals found at ν = -3 in many experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Mechanism for Anomalous Hall Ferromagnetism in Twisted Bilayer Graphene

Motivated by the recent observation of an anomalous Hall effect in twisted bilayer graphene, here we use a lowest Landau level model to understand the origin of the underlying symmetry-broken correlated state. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an intervalley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Strain-Induced Quantum Phase Transitions in Magic-Angle Graphene

In this work, we investigate the effect of uniaxial heterostrain on the interacting phase diagram of magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values (ε~0.1%-0.2%) drive a zero-temperature phase transition between the symmetry-broken "Kramers intervalley-coherent" insulator and a nematic semimetal. The critical strain lies within the range of experimentally observed strain values, and we therefore predict that strain is at least partly responsible for the sample-dependent experimental observations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spectroscopy of Twisted Bilayer Graphene Correlated Insulators

Here we analytically compute the scanning tunneling microscopy (STM) signatures of integer-filled correlated ground states of the magic angle twisted bilayer graphene (TBG) narrow bands. After experimentally validating the strong-coupling approach at ± 4 electrons/moiré unit cell, we consider the spatial features of the STM signal for 14 different many-body correlated states and assess the possibility of Kekulé distortion (KD) emerging at the graphene lattice scale. Remarkably, we find that coupling the two opposite graphene valleys in the intervalley-coherent (IVC) TBG insulators does not always result in KD. As an example, we show that the Kramers IVC state and its nonchiral U(4) rotations do not exhibit any KD, while the time-reversal-symmetric IVC state does. Our results, obtained over a large range of energies and model parameters, show that the STM signal and Chern number of a state can be used to uniquely determine the nature of the TBG ground state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Detecting Symmetry Breaking in Magic Angle Graphene Using Scanning Tunneling Microscopy

A growing body of experimental work suggests that magic angle twisted bilayer graphene exhibits a "cascade" of spontaneous symmetry-breaking transitions, sparking interest in the potential relationship between symmetry breaking and superconductivity. However, it has proven difficult to find experimental probes which can unambiguously identify the nature of the symmetry breaking. Here, we show how atomically resolved scanning tunneling microscopy can be used as a fingerprint of symmetry-breaking order. Further, by analyzing the pattern of sublattice polarization and "Kekulé" distortions in small magnetic fields, order parameters for each of the most competitive symmetry-breaking states can be identified. In particular, we show that the "Kramers intervalley coherent state," which theoretical work predicts to be the ground state at even integer fillings, shows a Kekulé distortion which emerges only in a magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗