Quantum Hall Phases Research Articles

Fractional quantum Hall phases in high-mobility n-type molybdenum disulfide transistors

AbstractTransistors based on semiconducting transition metal dichalcogenides can, in theory, offer high carrier mobilities, strong spin–orbit coupling and inherently strong electronic interactions at the quantum ground states. This makes them well suited for use in nanoelectronics at low temperatures. However, creating robust ohmic contacts to transition metal dichalcogenide layers at cryogenic temperatures is difficult. As a result, it is not possible to reach the quantum limit at which the Fermi level is close to the band edge and thus probe electron correlations in the fractionally filled Landau-level regime. Here we show that ohmic contacts to n-type molybdenum disulfide can be created over a temperature range from millikelvins to 300 K using a window-contacted technique. We observe field-effect mobilities of over 100,000 cm2 V−1 s−1 and quantum mobilities of over 3,000 cm2 V−1 s−1 in the conduction band at low temperatures. We also report evidence for fractional quantum Hall states at filling fractions of 4/5 and 2/5 in the lowest Landau levels of bilayer molybdenum disulfide.

Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit.

In the presence of strong electronic interactions, a partially filled Chern band may stabilize a fractional Chern insulator (FCI) state, the zero-field analog of the fractional quantum Hall phase. While FCIs have long been hypothesized, feasible solid-state realizations only recently emerged, largely due to the rise of moiré materials. In these systems, the quantum geometry of the electronic bands plays a critical role in stabilizing the FCI in the presence of competing correlated phases. In the limit of "ideal" quantum geometry, where the quantum geometry is identical to that of Landau levels, this role is well understood. However, in more realistic scenarios only empiric numerical evidence exists, accentuating the need for a clear understanding of the mechanism by which the FCI deteriorates, moving further away from these ideal conditions. We introduce and analyze an anisotropic model of a |C|=1 Chern insulator, whereupon partial filling of its bands, an FCI phase is stabilized over a certain parameter regime. We incorporate strong electronic interaction analytically by employing a coupled-wires approach, studying the FCI stability and its relation to the quantum metric. We identify an unusual anti-FCI phase benefiting from nonideal geometry, generically subdominant to the FCI. However, its presence hinders the formation of FCI in favor of other competitive phases at fractional fillings, such as the charge density wave. Though quite peculiar, this anti-FCI phase may have already been observed in experiments at high magnetic fields. This establishes a direct link between quantum geometry and FCI stability in a tractable model far from any ideal band conditions, and illuminates a unique mechanism of FCI deterioration.

Universality of quantum phase transitions in the integer and fractional quantum Hall regimes

Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, the integer quantum Hall (IQH) effects can be understood from the band topology of non-interacting electrons. We report a surprising super-universality of the critical behavior across all FQH and IQH transitions. Contrary to the anticipated state-dependent critical exponents, our findings reveal the same critical scaling exponent κ = 0.41 ± 0.02 and localization length exponent γ = 2.4 ± 0.2 for fractional and integer quantum Hall transitions. From these, we extract the value of the dynamical exponent z ≈ 1. We have achieved this in ultra-high mobility trilayer graphene devices with a metallic screening layer close to the conduction channels. The observation of these global critical exponents across various quantum Hall phase transitions was masked in previous studies by significant sample-to-sample variation in the measured values of κ in conventional semiconductor heterostructures, where long-range correlated disorder dominates. We show that the robust scaling exponents are valid in the limit of short-range disorder correlations.

Nodal spectral functions stabilized by non-Hermitian topology of quasiparticles

In quantum materials, basic observables such as spectral functions and susceptibilities are determined by Green's functions and their complex quasiparticle spectrum rather than by bare electrons. Even in closed many-body systems, this makes a description in terms of effective non-Hermitian (NH) Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance and stability of nodal phases is drastically affected by NH topology. While previous work has mostly considered complex degeneracies known as exceptional points as the NH counterpart of nodal points, we propose to relax this assumption by only requiring a crossing of the real part of the complex quasiparticle spectra, which entails a band crossing in the spectral function, i.e., a nodal spectral function. Interestingly, such real crossings are topologically protected by the braiding properties of the complex Bloch bands, and thus generically occur already in one-dimensional systems without symmetry or fine tuning. We propose and study a microscopic lattice model in which a sublattice-dependent interaction stabilizes nodal spectral functions. Besides the gapless spectrum, we identify nonreciprocal charge transport properties after a local potential quench as a key signature of nontrivial band braiding. Finally, in the limit of zero interaction on one of the sublattices, we find a perfectly ballistic unidirectional mode in a nonintegrable environment, reminiscent of a chiral edge state known from quantum Hall phases. Our analysis is corroborated by numerical simulations both in the framework of exact diagonalization and within the conserving second Born approximation. Published by the American Physical Society 2024

Uniqueness of Landau levels and their analogs with higher Chern numbers

Landau levels are the eigenstates of a charged particle in two dimensions under a magnetic field and are at the heart of the integer and fractional quantum Hall effects, which are two prototypical phenomena showing topological features. Following recent discoveries of fractional quantum Hall phases in van der Waals materials, there is a rapid progress in understanding of the precise condition under which the fractional quantum Hall phases can be stabilized. It is now understood that the key to obtaining the fractional quantum Hall phases is the energy band whose eigenstates are holomorphic functions in both real and momentum space coordinates. Landau levels are indeed examples of such energy bands with an additional special property of having flat geometrical features. In this paper, we prove that, in fact, the only energy eigenstates having holomorphic wave functions with a flat geometry are the Landau levels and their higher Chern number analogs. Since it has been known that any holomorphic eigenstates can be constructed from the ones with a flat geometry such as the Landau levels, our uniqueness proof of the Landau levels allows one to construct any possible holomorphic eigenstate with which the fractional quantum Hall phases can be stabilized. Published by the American Physical Society 2024

Efficient Charge Transfer in Graphene/CrOCl Heterostructures by van der Waals Interfacial Coupling.

Due to the large volume of exposed atoms and electrons at the surface of two-dimensional materials, interfacial charge coupling has been proven as an efficient strategy to engineer the electronic structures of two-dimensional materials assembled in van der Waals heterostructures. Recently, heterostructures formed by graphene stacked with CrOCl have demonstrated intriguing quantum states, including a distorted quantum Hall phase in the monolayer graphene and the unconventional correlated insulator in the bilayer graphene. Yet, the understanding of the interlayer charge coupling in the heterostructure remains challenging. Here, we demonstrate clear evidences of efficient hole doping in the interfacial-coupled graphene/CrOCl heterostructure by detailed Raman spectroscopy and electrical transport measurements. The observation of significant blue shifts and stiffness of graphene Raman modes quantitatively determines the concentration of hole injection of about 1.2 × 1013 cm-2 from CrOCl to graphene, which is highly consistent with the enhanced conductivity of graphene. First-principles calculations based on density functional theory reveal that due to the large work function difference and the electronegativity of Cl atoms in CrOCl, the electrons are efficiently transferred from graphene to CrOCl, leading to hole doping in graphene. Our findings provide clues for understanding the exotic physical properties of graphene/CrOCl heterostructures, paving the way for further engineering of quantum electronic states by efficient interfacial charge coupling in van der Waals heterostructures.

Magnetic and lattice ordered fractional quantum Hall phases in graphene

Magnetic and lattice ordered fractional quantum Hall phases in graphene

Achievement splitting for topological states with pseudospin in phase modulation by using gyromagnetic photonic crystals

As we know, valley-Hall kink states or pseudospin helical edge states are excited by polarized-momentum-locking [left-handed circular polarization (LCP) and right-handed circular polarization (RCP)] because the valley-Hall kink modes or pseudospin polarized modes have intrinsic and local chirality, which is difficult for these states to achieve phase modulation. Here we theoretically design and study a compatible topological photonic system with coexistence of photonic quantum Hall phase and pseudospin Hall phase, which is composed of gyromagnetic photonic crystals with a deformed honeycomb lattice containing six cylinders. A typical kind of hybrid topological waveguide states with pseudospin-characteristic, magnetic field-dependent, and strong robustness against backscattering and perfect electric conductor (PEC) is realized in the present system. Furthermore, we re-design a structure with intersection-liked, achieve splitting for one-way pseudospin quantum Hall edge states by using phase modulation. Robustness of the one-way pseudospin-quantum Hall edge states in splitting has been demonstrated as well. Additionally, PEC inserted in transport channel brings optical path difference in waveguide transmission, which would influence splitting for hybrid topological waveguide states in phase difference modulation. This work not only provides a new way for manipulation (i.e., phase modulation) of hybrid topological waveguide states in compatible topological photonic system from distinct topological classes but also has potential in various applications, such as sensing, signal processing, and on-chip communications.

Quantized heat flow in graphene quantum Hall phases: Probing the topological order

Topological quantum numbers are often used to characterize the topological order of phase having protected gapless edge modes when the system is kept in a space with the boundary. The famous examples in this category are the quantized electrical Hall conductance and thermal Hall conductance, which encodes the topological order of integer and fractional quantum Hall states. Here, we review the recent thermal transport study of integer and fractional quantum Hall states realized in graphene-based van der Waals heterostructures.

Edge-channel transport and spin-polarized interface states in folded graphene ribbons

The fabrication of devices that integrate two or more topological states simultaneously and achieve precise control over their edge state and interface states holds paramount importance. We report the quantized edge-channel transport and spin-polarized interface states in folded graphene ribbons under a magnetic field and predict that fully spin-polarized states can be generated at the interface. Our results also suggest that the system has the potential to exhibit the quantum spin Hall phase, the quantum Hall phase, and a coexistence of both phases. These phases can be manipulated by applying a bias potential and Zeeman splitting. Furthermore, the quantized conductance demonstrates a plateau at 3e2/h, which can be attributed to the presence of fully spin-polarized states. These outcomes provide a foundation for future explorations and manipulations of this novel form of edge-channel transport.

Valley-Polarized Quantum Hall Phase in a Strain-Controlled Dirac System.

In multivalley systems, the valley pseudospin offers rich physics going from encoding of information by its polarization (valleytronics), to exploring novel phases of matter when its degeneracy is changed. Here, by strain engineering, we reveal fully valley-polarized quantum Hall phases in the Pb_{1-x}Sn_{x}Se Dirac system. Remarkably, when the valley energy splitting exceeds the fundamental band gap, we observe a "bipolar quantum Hall phase," heralded by the coexistence of hole and electron chiral edge states at distinct valleys in the same quantum well. This suggests that spatially overlaid counterpropagating chiral edge states emerging at different valleys do not interfere with each other.

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}.

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.

Disorder and quantum transport of the helical quantum Hall phase in graphene

Disorder and quantum transport of the helical quantum Hall phase in graphene

Quantum spin liquids of Rydberg excitations in a honeycomb lattice induced by density-dependent Peierls phases

We show that the nonlinear transport of bosonic excitations in a two-dimensional honeycomb lattice of spin-orbit-coupled Rydberg atoms gives rise to disordered quantum phases which are topological and may be candidates for quantum spin liquids. As recently demonstrated by Lienhard et al. [Phys. Rev. X 10, 021031 (2020)] the spin-orbit coupling breaks time-reversal and chiral symmetries and leads to a tunable density-dependent complex hopping of spin excitations which behave as hard-core bosons. Using exact diagonalization (ED), we numerically investigate the phase diagram resulting from the competition between density-dependent and direct transport terms as well as density-density interactions. In mean-field approximation there is a phase transition from a condensate to a ${120}^{\ensuremath{\circ}}$ phase when the amplitude of the complex hopping exceeds that of the direct one. In the full model a new phase emerges close to the mean-field critical point as a result of quantum correlations induced by the density dependence of the complex hopping. We show that without density-density interactions this phase is a genuine disordered one, has large spin chirality, and is characterized by a nontrivial many-body Chern number. The Chern number is found to be robust to disorder. ED simulations of small lattices with up to 30 lattice sites give indications for a nondegenerate ground state with finite spin and collective gaps and thus for a bosonic integer quantum Hall phase, protected by $\mathrm{U}(1)$ symmetry. On the other hand, while staying finite, the many-body gap varies substantially when different twisted boundary conditions are applied, which points to a gapless phase. For very strong negative nonlinear hopping amplitudes we find another disordered regime with vanishing spin gap. This phase also has a large spin chirality and could be a gapless spin liquid but lies outside the parameter regime experimentally accessible in the Rydberg system.

Phonon-mediated room-temperature quantum Hall transport in graphene

The quantum Hall (QH) effect in two-dimensional electron systems (2DESs) is conventionally observed at liquid-helium temperatures, where lattice vibrations are strongly suppressed and bulk carrier scattering is dominated by disorder. However, due to large Landau level (LL) separation (~2000 K at B = 30 T), graphene can support the QH effect up to room temperature (RT), concomitant with a non-negligible population of acoustic phonons with a wave-vector commensurate to the inverse electronic magnetic length. Here, we demonstrate that graphene encapsulated in hexagonal boron nitride (hBN) realizes a novel transport regime, where dissipation in the QH phase is governed predominantly by electron-phonon scattering. Investigating thermally-activated transport at filling factor 2 up to RT in an ensemble of back-gated devices, we show that the high B-field behaviour correlates with their zero B-field transport mobility. By this means, we extend the well-accepted notion of phonon-limited resistivity in ultra-clean graphene to a hitherto unexplored high-field realm.

Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

Quantum Hall phase in graphene engineered by interfacial charge coupling

The quantum Hall effect can be substantially affected by interfacial coupling between the host two-dimensional electron gases and the substrate, and has been predicted to give rise to exotic topological states. Yet the understanding of the underlying physics and the controllable engineering of this interaction remains challenging. Here we demonstrate the observation of an unusual quantum Hall effect, which differs markedly from that of the known picture, in graphene samples in contact with an antiferromagnetic insulator CrOCl equipped with dual gates. Two distinct quantum Hall phases are developed, with the Landau levels in monolayer graphene remaining intact at the conventional phase, but largely distorted for the interfacial-coupling phase. The latter quantum Hall phase is even present close to the absence of a magnetic field, with the consequential Landau quantization following a parabolic relation between the displacement field and the magnetic field. This characteristic prevails up to 100 K in a wide effective doping range from 0 to 1013 cm−2.

Topological superconductor from the quantum Hall phase: Effective field theory description

We derive low-energy effective field theories for the quantum anomalous Hall and topological superconducting phases. The quantum Hall phase is realized in terms of free fermions with nonrelativistic dispersion relation, possessing a global $U(1)$ symmetry. We couple this symmetry with a background gauge field and compute the effective action by integrating out the gapped fermions. In spite of the fact that the corresponding Dirac operator governing the dynamics of the original fermions is nonrelativistic, the leading contribution in the effective action is a usual Abelian $U(1)$ Chern-Simons term. The proximity to a conventional superconductor induces a pairing potential in the quantum Hall state, favoring the formation of Cooper pairs. When the pairing is strong enough, it drives the system to a topological superconducting phase, hosting Majorana fermions. Even though the continuum $U(1)$ symmetry is broken down to a $\mathbb{Z}_2$ one, we can forge fictitious $U(1)$ symmetries that enable us to derive the effective action for the topological superconducting phase, also given by a Chern-Simons theory. To eliminate spurious states coming from the artificial symmetry enlargement, we demand that the fields in the effective action are $O(2)$ instead of $U(1)$ gauge fields. In the $O(2)$ case we have to sum over the $\mathbb{Z}_2$ bundles in the partition function, which projects out the states that are not $\mathbb{Z}_2$ invariants. The corresponding edge theory is the $U(1)/\mathbb{Z}_2$ orbifold, which contains Majorana fermions in its operator content.

Data For : Quantum Hall phase in graphene engineered by interfacial charge coupling

Data For : Quantum Hall phase in graphene engineered by interfacial charge coupling

Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases.

Chiral gapless boundary modes are characteristic of quantum Hall (QH) states. For hole-conjugate fractional QH phases counterpropagating edge modes (upstream and downstream) are expected. In the presence of electrostatic interactions and disorder these modes may renormalize into charge and upstream neutral modes. Orthodox models of Laughlin phases anticipate only a downstream charge mode. Here we show that in the latter case, in the presence of a smooth confining potential, edge reconstruction leads to the emergence of pairs of counterpropagating modes, which, by way of mode renormalization, may give rise to nontopological upstream neutral modes, possessing nontrivial statistics. This may explain the experimental observation of ubiquitous neutral modes, and the overwhelming suppression of anyonic interference in Mach-Zehnder interferometry platforms. We also point out other signatures of such edge reconstruction.