Engineering topics

Yazdani, Ali

Publications and source records attributed to Yazdani, Ali.

At least 19 records

DOE OSTI2024

Fingerprints of composite fermion Lambda levels in scanning tunneling microscopy

A composite fermion (CF) is a topological quasiparticle that emerges from a nonperturbative attachment of vortices to electrons in strongly correlated two-dimensional materials. Similar to noninteracting fermions that form Landau levels in a magnetic field, CFs can fill analogous “Lambda” levels, giving rise to the fractional quantum Hall (FQH) effect of electrons. Here, we show that Lambda levels can be directly visualized through the characteristic peak structure in the signal obtained via spectroscopy with scanning tunneling microscopy (STM) on a FQH state. Complementary to transport, which probes the low-energy properties of CFs, we show that high-energy features in STM spectra can be interpreted in terms of Lambda levels. We numerically demonstrate that STM spectra can be accurately modeled using Jain's CF theory. Our results show that STM provides a powerful tool for revealing the anatomy of FQH states and identifying physics beyond the noninteracting CF paradigm.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Electron– K -phonon interaction in twisted bilayer graphene

We develop an analytic theory to describe the interaction between electrons and K phonons and study its influence on superconductivity in the bare bands of twisted bilayer graphene (TBG). We find that, due to symmetry and the two-center approximation, only one optical K phonon (160meV) of graphene is responsible for the intervalley electron-phonon interaction. Here, this phonon has recently been found in angular-resolved photoemission spectroscopy to be responsible for replicas of the TBG flat bands. By projecting the interaction to the TBG flat bands, we perform the full symmetry analysis of the phonon-mediated attractive interaction and pairing channels in the Chern basis, and show that several channels are guaranteed to have gapless order parameters. From the linearized gap equations, we find that the highest T c pairing induced by this phonon is a singlet gapped s-wave inter-Chern-band order parameter, followed closely by a gapless nematic d-wave intra-Chern-band order parameter. We justify these results analytically, using the topological heavy-fermion mapping of TBG which has allowed us to obtain an analytic form of a phonon-mediated attractive interaction and to analytically solve the linearized and T = 0 gap equations. For the intra-Chern-band channel, the nematic state with nodes is shown to be stabilized in the chiral flat-band limit. While the flat-band Coulomb interaction can be screened sufficiently enough—around the Van Hove singularities—to allow for electron-phonon based superconductivity, it is unlikely that this effect can be maintained in the lower density of states excitation bands around the correlated insulator states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

A microscopic perspective on moiré materials

Quantum materials research has experienced a veritable renaissance in the past 6 years, with a surge of experimental reports of nearly every known electronic phase of matter and of several unique and unexpected phases, all found in an emerging class of highly tunable 2D materials, known as moiré materials1,2,3. Here, moiré materials are designed through either the rotational misalignment of identical 2D atomic crystals or the lattice mismatch of dissimilar 2D atomic crystals (Fig. 1). Both these incommensurability conditions cause long-wavelength (~10 nm) interference patterns between the two constituent atomic lattices, forming an enlarged moiré superlattice that generically hosts flat electronic bands, which are highly conducive to correlated, collective phases of matter.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Direct observation of a magnetic-field-induced Wigner crystal

Wigner predicted that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown evidence for Wigner crystals (WCs). However, a spontaneously formed classical or quantum WC has never been directly visualized. Neither the identification of the WC symmetry nor direct investigation of its melting has been accomplished. Here we use high-resolution scanning tunnelling microscopy measurements to directly image a magnetic-field-induced electron WC in Bernal-stacked bilayer graphene and examine its structural properties as a function of electron density, magnetic field and temperature. At high fields and the lowest temperature, we observe a triangular lattice electron WC in the lowest Landau level. The WC possesses the expected lattice constant and is robust between filling factor ν ≈ 0.13 and ν ≈ 0.38 except near fillings where it competes with fractional quantum Hall states. Increasing the density or temperature results in the melting of the WC into a liquid phase that is isotropic but has a modulated structure characterized by the Bragg wavevector of the WC. At low magnetic fields, the WC unexpectedly transitions into an anisotropic stripe phase, which has been commonly anticipated to form in higher Landau levels. Furthermore, analysis of individual lattice sites shows signatures that may be related to the quantum zero-point motion of electrons in the WC lattice.

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

Broken symmetries and excitation spectra of interacting electrons in partially filled Landau levels

Interacting electrons in flat bands give rise to a variety of quantum phases. One fundamental aspect of such states is the ordering of the various flavours – such as spin or valley – that the electrons can undergo and the excitation spectrum of the broken symmetry states that they form. These properties cannot be probed directly with electrical transport measurements. The zeroth Landau level of monolayer graphene with four-fold spin-valley degeneracy is a model system for such investigations, but the nature of its broken symmetry states – particularly at partial fillings – is still not understood. Here, in this study, we demonstrate a non-invasive spectroscopic technique with a scanning tunneling microscope and use it to perform measurements of the valley polarization of the electronic wavefunctions and their excitation spectrum in the partially filled zeroth Landau level of graphene. We can extract information such as the strength of Haldane pseudopotentials that characterize the repulsive interactions underlying the fractional quantum states. Our experiments also demonstrate that fractional quantum Hall phases are built upon broken symmetry states that persist at partial filling. Our experimental approach quantifies the valley phase diagram of the partially filled Landau level as a model flat band platform which is applicable to other graphene-based electronic systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Hunting for Majoranas

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.

Science & Technology - Other Topics↗

DOE OSTI2023

Insulators at fractional fillings in twisted bilayer graphene partially aligned to hexagonal boron nitride

At partial fillings of its flat electronic bands, magic-angle twisted bilayer graphene (MATBG) hosts a rich variety of competing correlated phases that show sample-to-sample variations. Divergent phase diagrams in MATBG are often attributed to the sublattice polarization energy scale, tuned by the degree of alignment of the hexagonal boron nitride (hBN) substrates typically used in van der Waals devices. Unaligned MATBG exhibits unconventional superconductor and correlated insulator phases, while nearly perfectly aligned MATBG/hBN exhibits zero-field Chern insulating phases and lacks superconductivity. Here we use scanning tunneling microscopy and spectroscopy (STM/STS) to observe gapped phases at partial fillings of the flat bands of MATBG in a new intermediate regime of sublattice polarization, observed when MATBG is only partially aligned (θ Gr-hBN ≈ 1.65°) to the underlying hBN substrate. Under this condition, MATBG hosts not only phenomena that naturally interpolate between the two sublattice potential limits, but also unexpected gapped phases absent in either of these limits. At charge neutrality, we observe an insulating phase with a small energy gap (Δ < 5 meV) likely related to weak sublattice symmetry breaking from the hBN substrate. In addition, we observe new gapped phases near fractional fillings ν = ±1/3 and ν = ±1/6, which have not been previously observed in MATBG. Importantly, energy-resolved STS unambiguously identifies these fractional filling states to be of single-particle origin, possibly a result of the super-superlattice formed by two moiré superlattices. Finally, our observations emphasize the power of STS in distinguishing single-particle gapped phases from many-body gapped phases in situations that could be easily confused in electrical transport measurements, and demonstrate the use of substrate engineering for modifying the electronic structure of a moiré flat-band material.

Physics↗

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 OSTI2021

Evidence for a monolayer excitonic insulator

The interplay between topology and correlations can generate a variety of quantum phases, many of which remain to be explored. Recent advances have identified monolayer WTe 2 as a promising material for doing so in a highly tunable fashion. The ground state of this two-dimensional crystal can be electrostatically tuned from a quantum spin Hall insulator to a superconductor. However, much remains unknown about the gap-opening mechanism of the insulating state. In this work, we report evidence that the quantum spin Hall insulator is also an excitonic insulator, arising from the spontaneous formation of electron–hole bound states, namely excitons. We reveal the presence of an intrinsic insulating state at the charge neutrality point in clean samples and confirm the correlated nature of this charge-neutral insulator by tunnelling spectroscopy. We provide evidence against alternative scenarios of a band insulator or a localized insulator and support the existence of an excitonic insulator phase in the clean limit. These observations lay the foundation for understanding a new class of correlated insulators with nontrivial topology and identify monolayer WTe 2 as a promising candidate for exploring quantum phases of ground-state excitons.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.

valley symmetry↗

DOE OSTI2021

Evidence for unconventional superconductivity in twisted bilayer graphene

The emergence of superconductivity and correlated insulators in magic-angle twisted bilayer graphene (MATBG) has raised the intriguing possibility that its pairing mechanism is distinct from that of conventional superconductors, as described by the Bardeen–Cooper–Schrieffer (BCS) theory. However, recent studies have shown that superconductivity persists even when Coulomb interactions are partially screened5. This suggests that pairing in MATBG might be conventional in nature and a consequence of the large density of states of its flat bands. In this work, we combine tunnelling and Andreev reflection spectroscopy with a scanning tunnelling microscope to observe several key experimental signatures of unconventional superconductivity in MATBG. We show that the tunnelling spectra below the transition temperature T c are inconsistent with those of a conventional s-wave superconductor, but rather resemble those of a nodal superconductor with an anisotropic pairing mechanism. We observe a large discrepancy between the tunnelling gap Δ T , which far exceeds the mean-field BCS ratio (with 2Δ T /k B T c ~ 25), and the gap Δ AR extracted from Andreev reflection spectroscopy (2Δ AR /k B T c ~ 6). The tunnelling gap persists even when superconductivity is suppressed, indicating its emergence from a pseudogap phase. Moreover, the pseudogap and superconductivity are both absent when MATBG is aligned with hexagonal boron nitride. These findings and other observations reported here provide a preponderance of evidence for a non-BCS mechanism for superconductivity in MATBG.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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 OSTI2020

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene

Interactions between electrons and the topology of their energy bands can create unusual quantum phases of matter. Most topological electronic phases appear in systems with weak electron–electron interactions. The instances in which topological phases emerge only as a result of strong interactions are rare and mostly limited to those realized in intense magnetic fields. The discovery of flat electronic bands with topological character in magic-angle twisted bilayer graphene (MATBG) has created a unique opportunity to search for strongly correlated topological phases. Here we introduce a local spectroscopic technique using a scanning tunnelling microscope to detect a sequence of topological insulators in MATBG with Chern numbers C = ±1, ±2 and ±3, which form near filling factors of ±3, ±2 and ±1 electrons per moiré unit cell, respectively, and are stabilized by modest magnetic fields. One of the phases detected here (C = +1) was previously observed when the sublattice symmetry of MATBG was intentionally broken by a hexagonal boron nitride substrate, with interactions having a secondary role. We also demonstrate that strong electron–electron interactions alone can produce not only the previously observed phase, but also other unexpected Chern insulating phases in MATBG. The full sequence of phases that we observe can be understood by postulating that strong correlations favour breaking time-reversal symmetry to form Chern insulators that are stabilized by weak magnetic fields. Our findings illustrate that many-body correlations can create topological phases in moiré systems beyond those anticipated from weakly interacting models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Observation of backscattering induced by magnetism in a topological edge state

Significance One of the predicted characteristics of helical topological boundary modes is the absence of backscattering when time-reversal symmetry (TRS) is preserved. While previous experiments have provided evidence for this topological protection, inducing backscattering by breaking TRS has yet to be demonstrated. We test this fundamental property by investigating quasiparticle scattering in the one-dimensional topological edge state of bismuth bilayers, coupled to ferromagnetic iron clusters, using a scanning tunneling microscope. Our experimental observations demonstrate that backscattering is induced by magnetism of iron clusters in these topological edge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Cascade of electronic transitions in magic-angle twisted bilayer graphene

Magic-angle twisted bilayer graphene exhibits a variety of electronic states, including correlated insulators, superconductors and topological phases. Understanding the microscopic mechanisms responsible for these phases requires determination of the interplay between electron–electron interactions and quantum degeneracy (the latter is due to spin and valley degrees of freedom). Signatures of strong electron–electron correlations have been observed at partial fillings of the flat electronic bands in recent spectroscopic measurements, and transport experiments have shown changes in the Landau level degeneracy at fillings corresponding to an integer number of electrons per moiré unit cell. However, the interplay between interaction effects and the degeneracy of the system is currently unclear. Here in this paper we report a cascade of transitions in the spectroscopic properties of magic-angle twisted bilayer graphene as a function of electron filling, determined using high-resolution scanning tunnelling microscopy. We find distinct changes in the chemical potential and a rearrangement of the low-energy excitations at each integer filling of the moiré flat bands. These spectroscopic features are a direct consequence of Coulomb interactions, which split the degenerate flat bands into Hubbard sub-bands. We find these interactions, the strength of which we can extract experimentally, to be surprisingly sensitive to the presence of a perpendicular magnetic field, which strongly modifies the spectroscopic transitions. The cascade of transitions that we report here characterizes the correlated high-temperature parent phase from which various insulating and superconducting ground-state phases emerge at low temperatures in magic-angle twisted bilayer graphene.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

High mobility in a van der Waals layered antiferromagnetic metal

Van der Waals (vdW) materials with magnetic order have been heavily pursued for fundamental physics as well as for device design. Despite the rapid advances, so far, they are mainly insulating or semiconducting, and none of them has a high electronic mobility—a property that is rare in layered vdW materials in general. The realization of a high-mobility vdW material that also exhibits magnetic order would open the possibility for novel magnetic twistronic or spintronic devices. Here, we report very high carrier mobility in the layered vdW antiferromagnet GdTe 3 . The electron mobility is beyond 60,000 cm 2 V –1 s –1 , which is the highest among all known layered magnetic materials, to the best of our knowledge. Among all known vdW materials, the mobility of bulk GdTe 3 is comparable to that of black phosphorus. By mechanical exfoliation, we further demonstrate that GdTe 3 can be exfoliated to ultrathin flakes of three monolayers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A modular ultra-high vacuum millikelvin scanning tunneling microscope

We describe the design, construction, and performance of an ultra-high vacuum (UHV) scanning tunneling microscope (STM) capable of imaging at dilution-refrigerator temperatures and equipped with a vector magnet. The primary objective of our design is to achieve a high level of modularity by partitioning the STM system into a set of easily separable, interchangeable components. This naturally segregates the UHV needs of STM instrumentation from the typically non-UHV construction of a dilution refrigerator, facilitating the usage of non-UHV materials while maintaining a fully bakeable UHV chamber that houses the STM. Here, the modular design also permits speedy removal of the microscope head from the rest of the system, allowing for repairs, modifications, and even replacement of the entire microscope head to be made at any time without warming the cryostat or compromising the vacuum. Without using cryogenic filters, we measured an electron temperature of 184 mK on a superconducting Al(100) single crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗