arXiv subjects

Tonghang Han

Publications and source records attributed to Tonghang Han.

17 recordsLinked to original sources

arXiv2026

Quantum Phase Transitions and Fractional Quantized Anomalous Hall Insulators in Rhombohedral Graphene

Fractional quantum anomalous Hall effect (FQAHE) has been discovered in twisted MoTe$_2$ and rhombohedral graphene/hBN moir\'e superlattices. Such van der Waals heterostructures feature a tuning knob of gate displacement field $D$, which is absent from the conventional fractional quantum Hall systems in two-dimensional electron gases. $D$ plays a critical role in engineering FQAHE and other emergent quantum states and provides an exciting new opportunity to explore their quantum phase transitions. However, the microscopic details of such transitions and temperature-dependent transport have remained mostly elusive. Here we report systematic resistance measurements in rhombohedral pentalayer graphene/hBN moir\'e superlattices. We found that the displacement field-driven phase transitions between Composite Fermi liquid, Fermi liquid, Fractional Chern insulators, and insulating states are described by semi-circle relations of the longitudinal and transverse resistivities (or conductivities), largely unexplored in the fractional quantum Hall systems. This agrees with a spatially separated two-phase picture for the phase transitions and further indicates a new insulator phase--fractional quantized anomalous Hall insulator. By comparing the temperature-dependence of longitudinal resistance with the thermal activation model, we estimated the transport gap sizes in three fractional Chern insulator states. Our work shed light on the quantum and temperature evolutions of fractional Chern insulator states--providing necessary background for anyon-braiding and gate-defined junctions in rhombohedral graphene.

cond-mat.mes-hall↗

arXiv2026

Thermodynamic evidence for interaction-driven first-order topological quantum phase transitions

Topological quantum phase transitions in non interacting systems occur through continuous gap closing and reopening. In strongly interacting systems, however, competing ordered states have long been predicted to drive first order transitions, although this possibility has remained experimentally unresolved. Recent transport studies of correlated phases in charge neutral rhombohedral graphene were interpreted as evidence for continuous topological transitions. Here, using nanoSQUID on tip magnetometry, we directly image the local orbital magnetization of a spin orbit proximitized rhombohedral graphene quantum anomalous Hall (QAH) state. We provide the first real space visualization of a QAH phase with a record Chern number, reconstruct its local thermodynamic gap, and track the evolution of its magnetization across competing correlated states. Combined with self consistent Hartree Fock calculations, these measurements show that the sequential transitions between the layer antiferromagnetic, QAH, and layer polarized insulating states are first order, accompanied by discontinuous changes in orbital magnetization. Near the phase boundaries, we observe fluctuating magnetic domains, providing direct microscopic evidence of phase coexistence between nearly degenerate competing ordered states. Together, these observations provide the first direct thermodynamic evidence for first order topological quantum phase transitions and establish a microscopic framework for understanding interaction driven topological quantum phase transitions through phase competition and coexistence.

cond-mat.mes-hall↗

arXiv2026

Multi-Knob Switchable Chiral Superconductivity Quartet in Rhombohedral Graphene

Chiral superconductors break orbital time-reversal symmetry and may host topological quasiparticles with non-Abelian statistics. In rhombohedral graphene, superconductivity develops from a spin-valley-polarized quarter-metal (QM) parent state and features unique magnetic hysteresis of resistance that indicates orbital time-reversal-symmetry-breaking. Exploring and controlling the full spin-valley flavors of such superconductivity could enable novel superconducting and topological devices, but have remained unexplored. Here we report transport measurements on rhombohedral hexalayer graphene (R6G), which reveal a new superconducting state (SCH) that is induced by an out-of-plane magnetic field, in addition to chiral superconductivity (CSC) similar to those observed in thinner layers. This SCH state emerges above 0.8 T, persists up to 1.6 T and can be switched on/off by magnetic field $H_\perp$, carrier density $n$, and gate displacement field $D$. Quantum oscillations and anomalous Hall measurements show that SCH stems from a field-induced quarter-metal (QM$'$) parent phase, which carries orbital magnetization opposite to that of the zero-field QM. Across the full $(n, D, H_\perp)$ parameter space, superconductivity can be realized from all four spin-valley isospin flavors, establishing a switchable chiral-superconductor quartet in R6G. We interpret the parent-state switching as arising from competition between a Kane-Mele-like spin-valley splitting and magnetic-field coupling to spin-valley-dependent magnetic moments. Our work establishes rhombohedral graphene as a multi-knob platform for different isospin-polarized superconductivities, which enables programmable superconducting networks with possible Majorana modes along domain walls.

cond-mat.supr-con↗

arXiv2026

1/3 Fractional and Gapless Integer Quantum Anomalous Hall States in Rhombohedral Graphene

The fractional quantum anomalous Hall (FQAH) effect occurs in moir\'e superlattices in both twisted bilayer MoTe$_2$ and rhombohedral $n$-layer graphene aligned to hexagonal boron nitride (R$n$G/hBN) as a novel quantum phase driven by intertwined electron correlation and topology. Although several fractional states in the Jain sequence have been identified, the $1/3$ state, the most robust and fundamental state in conventional fractional quantum Hall (FQH) systems, was missing in either FQAH system. Determining whether it exists would have a major impact on understanding the mechanism of FQAH, especially in the theoretically still-debated R$n$G/hBN system. Here we report the FQAH effect at moir\'e filling factor $\nu = 1/3$ in R$5$G/hBN moir\'e superlattice devices, through a combination of quantum capacitance and transport measurements. By tuning the displacement field, we observed a topological phase transition from a $1/3$ fractional Chern insulator (FCI) to a trivial charge density wave state. With the inclusion of the $1/3$ state, the FQAH states in R$5$G/hBN now exhibit a surprising level of particle-hole symmetry about half-filling, closely resembling the behavior of FQH states in the lowest Landau level. Additionally, we perform compressibility and transport measurements at a filling of one electron per moir\'e unit cell, $\nu =1$, and also for $\nu \lesssim 1$, where previous transport measurements displayed the extended quantum anomalous Hall (EQAH) effect. While our transport measurements show no change between the integer quantum anomalous Hall state (IQAH) and the EQAH region, compressibility measurements reveal a distinct transition from a gapped IQAH state to a gapless and highly compressible EQAH state. Our direct thermodynamic characterization of the rich phase diagram paves the way to engineering of anyon braiding and non-Abelian quasiparticles at zero magnetic field.

cond-mat.mes-hall↗

arXiv2026

Reconfigurable chiral superconductivity

Rhombohedral multilayer graphene at high displacement fields hosts superconductivity emerging from a spin valley polarized quarter metal, with transport signatures suggestive of time reversal symmetry (TRS) breaking and chiral superconductivity (CSC). These observations have motivated proposals of topological superconductivity and non-Abelian quasiparticles, yet direct magnetic evidence and microscopic insight into the superconducting state remain lacking, limiting understanding of this unique state. Here we use nanoscale SQUID on tip magnetometry to image isospin-polarized domains in rhombohedral pentalayer graphene and establish CSC via spatially resolved thermodynamic detection of TRS breaking. We find that the density at which domain walls proliferate at elevated temperatures coincides with the onset of CSC, indicating an underlying transition in the parent state that both induces superconductivity and reduces domain wall energy. We further show that the chiral domain structure in the superconducting phase is inherited from the isospin-polarized parent state. Strikingly, the CSC phase exhibits multiple transport regimes governed by configurations of chiral domains separated by highly resistive domain walls. We demonstrate deterministic, ultra low current control of these domains, enabling reversible switching between states of opposite chirality a defining CSC property absent in other superconductors. These results establish rhombohedral graphene as a unique platform for reconfigurable CSC and ultra low power electronic functionality based on controllable isospin textures.

cond-mat.mes-hall↗

arXiv2026

Evidence of Metallic Wigner Crystal in Rhombohedral Graphene

When the Coulomb interaction dominates over kinetic energy, electrons can crystallize into a Wigner crystal (WC). This paradigmatic correlated electronic phase has been realized in two-dimensional electron gases with parabolic band dispersion and completely flat Landau levels under high magnetic fields. Beyond these conventional contexts of electron crystallization, more exotic electron crystals have been postulated but remain unexplored. For example, a metallic Wigner crystal (mWC), in which itinerant carriers coexist with a pinned electron lattice, has been proposed theoretically but considered difficult to realize. Non-parabolic electron bands and quantum geometry may facilitate mWC and other novel topological electron crystals. Here we report transport evidence for WC and mWC in rhombohedral tetra-, penta-, and hexalayer graphene in the charge density range 0.3-0.5x10^12 cm^-2. By flattening the conduction band with a gate-controlled displacement field D, we observe an insulating state at nonzero charge density that shows nonlinear, hysteretic current-voltage relations, signatures of a pinned WC, that are absent from the lower-density insulator. Further increasing D reveals transport dominated by hole-like carriers with density up to only 15% of the nominal electron density, consistent with mWC. This mWC state is closely tied to the WC state, as both collapse simultaneously with increasing temperature or bias voltage. The mWC state shows quantum Hall onset near 0.4 T and disobeys the Streda relation, indicating compressible charge exchange between itinerant holes and the transport-inert WC background. Our results establish rhombohedral graphene as a platform for exploring novel electron crystals, as well as possible nontrivial topology, and new collective modes.

cond-mat.mes-hall↗

arXiv2025

Magnetic Field-Enhanced Graphene Superconductivity with Record Pauli-Limit Violation

Spin-polarized superconductors offer a rare platform for studying electronic correlations, but few candidate systems have been experimentally confirmed to date. Here, we report the observation of a spin-polarized superconducting state, denoted SC5, in WSe2-proximitized rhombohedral trilayer graphene. At in-plane magnetic field B|| = 0 T, SC5 has a critical temperature of 68 mK and an out-of-plane critical magnetic field of only 12 mT. Surprisingly, these values are significantly enhanced as B|| increases, and the superconductivity persists to B|| = 8.8 T. This value corresponds to a record-high Pauli-limit violation ratio of at least 80 among all superconductors, while the true critical field is beyond the limit of our instrument. We conclude that SC5 experiences a canting crossover from Ising-type to spin-polarized superconductor with increased B||.

cond-mat.supr-con↗

arXiv2025

Family of Unconventional Superconductivities in Crystalline Graphene

Unconventional superconductors exhibit multiple broken symmetries and exceed the range of the Bardeen-Cooper-Schrieffer (BCS) theory. For instance, time-reversal symmetry can be broken in addition to the gauge symmetry, resulting in superconductors that can be enhanced or induced by a magnetic field. However, such unconventional superconductivities are more vulnerable to impurities than their BCS counterparts, requiring highly ordered and clean material systems to observe them. Crystalline rhombohedral multilayer graphene is a promising platform to explore unconventional superconductivity due to its superior material quality and gate-tunable strong correlation effects. Here we report transport measurements of rhombohedral tetralayer and pentalayer graphene, where a spectrum of superconductivities in a clean limit are observed. Three of them (SC2-4) show highly unusual enhancements by magnetic fields: 1. SC2 is strengthened by an in-plane field; 2. SC3 is boosted by a small out-of-plane field; 3. SC4 is induced by an in-plane field. All these superconductors are robust against an in-plane field up to 8.5 Tesla, exceeding the Pauli limit of conventional superconductors by tens of times and suggesting their unconventional nature. Moreover, we observed that proximitized spin-orbit coupling generates a plethora of new superconductors in the phase diagram, while maintaining the high quality of bare rhombohedral graphene. Our work establishes a family of new superconductors in rhombohedral multilayer graphene, which also provides an ideal platform to engineer non-Abelian quasiparticles by proximitizing with quantum anomalous Hall states existing in the same material system.

cond-mat.mes-hall↗

arXiv2024

On-Chip Terahertz Spectroscopy for Dual-Gated van der Waals Heterostructures at Cryogenic Temperatures

Van der Waals heterostructures have emerged as a versatile platform to study correlated and topological electron physics. Spectroscopy experiments in the THz regime are crucial, since the energy of THz photons matches that of relevant excitations and charge dynamics. However, their micron-size and complex (dual-)gated structures have challenged such measurements. Here, we demonstrate on-chip THz spectroscopy on a dual-gated bilayer graphene device at liquid helium temperature. To avoid unwanted THz absorption by metallic gates, we developed a scheme of operation by combining semiconducting gates and optically controlled gating. This allows us to measure the clean THz response of graphene without being affected by the gates. We observed the THz signatures of electric-field-induced bandgap opening at the charge neutrality. We measured Drude conductivities at varied charge densities and extracted key parameters, including effective masses and scattering rates. This work paves the way for studying novel emergent phenomena in dual-gated two-dimensional materials.

cond-mat.mes-hall↗

arXiv2024

Signatures of Chiral Superconductivity in Rhombohedral Graphene

Chiral superconductors are unconventional superconducting states that break time reversal symmetry spontaneously and typically feature Cooper pairing at non-zero angular momentum. Such states may host Majorana fermions and provide an important platform for topological physics research and fault-tolerant quantum computing. Despite intensive search and prolonged studies of several candidate systems, chiral superconductivity has remained elusive so far. Here we report the discovery of robust unconventional superconductivity in rhombohedral tetra- and penta-layer graphene in the absence of moir\'e superlattice effects. We observed two superconducting states in the gate-induced flat conduction bands with Tc up to 300 mK and charge density ne as low as 2.4*1011 cm-2 in three tetralayer and two pentalayer devices. Spontaneous time-reversal-symmetry-breaking (TRSB) due to electron's orbital motion is found, and several observations indicate the chiral nature of these superconducting states, including: 1. In the superconducting state, Rxx shows magnetic hysteresis in varying out-of-plane magnetic field B, which is absent from all other superconductors; 2. the superconducting states are immune to in-plane magnetic field and are developed within a spin- and valley-polarized quarter-metal phase; 3. the normal states show anomalous Hall signals at zero magnetic field and magnetic hysteresis. We also observed a critical B of up to 1.4 Tesla, higher than any graphene superconductivity reported so far and indicates a strong-coupling superconductivity close to the BCS-BEC crossover. Our observations establish a pure carbon material for the study of topological superconductivity, and pave the way to explore Majorana modes and topological quantum computing.

cond-mat.mes-hall↗

arXiv2024

Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moir\'e superlattice

Rhombohedral multilayer graphene, with its flat electronic bands and concentrated Berry curvature, is a promising material for the realization of correlated topological phases of matter. When aligned to an adjacent hexagonal boron nitride (hBN) layer, the graphene develops narrow minibands with non-trivial topology. By tuning an externally-applied electric displacement field, the conduction electrons can either be pushed towards or away from the moir\'e superlattice. Motivated by the recent observation of the fractional quantum anomalous Hall effect (FQAHE) in the moir\'e-distant case, we study the opposite moir\'e-proximal case, where the superlattice potential is considerably stronger. We explore the physics within the moir\'e conduction bands through capacitance measurements that allow us to determine the inverse electronic compressibility and extract energy gaps of incompressible states. We observe integer and fractional Chern insulator states at superlattice filling factors v = 1, 2/3, and 1/3 with Streda slopes of -1, -2/3, and -1/3, respectively. Remarkably, the v = 1/3 state persists down to a magnetic field of 0.2 T. In addition, we also observe numerous trivial and topological charge density waves. We map out a phase diagram that is highly sensitive to both displacement and magnetic fields, which tune the system between various ground states by modifying the band dispersion and the structure of the electronic wavefunctions. This work demonstrates displacement field control of topological phase transitions in the moir\'e-proximal limit of rhombohedral pentalayer graphene, creating a highly-tunable platform for studying the interplay between intrinsic band topology and strong lattice effects.

cond-mat.mes-hall↗

arXiv2024

Impact of Spin-Orbit Coupling on Superconductivity in Rhombohedral Graphene

Spin-orbit coupling (SOC) has played an important role in many topological and correlated electron materials. In graphene-based systems, SOC induced by transition metal dichalcogenide (TMD) at proximity was shown to drive topological states and strengthen superconductivity. However, in rhombohedral multilayer graphene, a robust platform for electron correlation and topology, superconductivity and the role of SOC remain largely unexplored. Here we report transport measurements of TMD-proximitized rhombohedral trilayer graphene (RTG). We observed a new hole-doped superconducting state SC4 with Tc = 230 mK. On the electron-doped side, we identified a new isospin-symmetry breaking three-quarter-metal (TQM) phase and observed the nearby weak superconducting state SC3 is significantly enhanced. Surprisingly, the original superconducting state SC1 in bare RTG is strongly suppressed in the presence of TMD - opposite to the effect of SOC on all other graphene superconductivities. Our observations form the basis of exploring superconductivity and non-Abelian quasiparticles in rhombohedral graphene devices.

cond-mat.supr-con↗

arXiv2024

Extended Quantum Anomalous Hall States in Graphene/hBN Moir\'e Superlattices

Electrons in topological flat bands can form novel topological states driven by the correlation effects. The penta-layer rhombohedral graphene/hBN moire superlattice has been shown to host fractional quantum anomalous Hall effect (FQAHE) at ~400 mK, triggering discussions around the underlying mechanism and the role of moire effects. In particular, novel electron crystal states with non-trivial topology have been proposed. Here we report DC electrical transport measurement in rhombohedral penta- and tetra-layer graphene/hBN moire superlattices at electronic temperatures down to ~40 mK. We observed two more FQAH states in the penta-layer devices than previously reported. In a new tetra-layer device, we observed FQAHE at filling factors v = 3/5 and 2/3 at 300 mK. With a small bias current and the lowest temperature, we observed a new extended quantum anomalous Hall (EQAH) state and magnetic hysteresis, where Rxy = h/e2 and vanishing Rxx span a wide range of moire filling factor v from 0.5 to up to 1.3. By increasing the temperature or current, FQAHE can be recovered -- suggesting the break-down of the EQAH states and a phase transition into the fractional quantum Hall liquid. Furthermore, we observed displacement field-induced quantum phase transitions from the EQAH states to Fermi liquid, FQAH liquid and the likely composite Fermi liquid. Our observation establishes a new topological phase of electrons with quantized Hall resistance at zero magnetic field, and enriches the emergent quantum phenomena in materials with topological flat bands.

cond-mat.mes-hall↗

arXiv2023

Large Quantum Anomalous Hall Effect in Spin-Orbit Proximitized Rhombohedral Graphene

The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon featuring quantized Hall resistance at zero magnetic field. We report the QAHE in a rhombohedral pentalayer graphene/monolayer WS2 heterostructure. Distinct from other experimentally confirmed QAHE systems, this system has neither magnetic element nor moir\'e superlattice effect. The QAH states emerge at charge neutrality and feature Chern numbers C = +-5 at temperatures up to about 1.5 K. This large QAHE arises from the synergy of the electron correlation in intrinsic flat bands of pentalayer graphene, the gate-tuning effect, and the proximity-induced Ising spin-orbit-coupling. Our experiment demonstrates the potential of crystalline two-dimensional materials for intertwined electron correlation and band topology physics, and may enable a route for engineering chiral Majorana edge states.

cond-mat.mes-hall↗

arXiv2023

Fractional Quantum Anomalous Hall Effect in a Graphene Moire Superlattice

The fractional quantum anomalous Hall effect (FQAHE), the analog of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The demonstration of FQAHE could lead to non-Abelian anyons which form the basis of topological quantum computation. So far, FQAHE has been observed only in twisted MoTe2 (t-MoTe2) at moire filling factor v > 1/2. Graphene-based moire superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene/hBN moire superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance Rxy = h/(ve^2) at filling factors v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moire superlattice respectively. These features are accompanied by clear dips in the longitudinal resistance Rxx. In addition, at zero magnetic field, Rxy equals 2h/e^2 at v = 1/2 and varies linearly with the filling factor-similar to the composite Fermi liquid (CFL) in the half-filled lowest Landau level at high magnetic fields. By tuning the gate displacement field D and v, we observed phase transitions from CFL and FQAH states to other correlated electron states. Our graphene system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field, especially considering a lateral junction between FQAHE and superconducting regions in the same device.

cond-mat.mes-hall↗

arXiv2023

Orbital Multiferroicity in Pentalayer Rhombohedral Graphene

Ferroic orders describe spontaneous polarization of spin, charge, and lattice degrees of freedom in materials. Materials featuring multiple ferroic orders, known as multiferroics, play important roles in multi-functional electrical and magnetic device applications. 2D materials with honeycomb lattices offer exciting opportunities to engineer unconventional multiferroicity, where the ferroic orders are driven purely by the orbital degrees of freedom but not electron spin. These include ferro-valleytricity corresponding to the electron valley and ferro-orbital-magnetism supported by quantum geometric effects. Such orbital multiferroics could offer strong valley-magnetic couplings and large responses to external fields-enabling device applications such as multiple-state memory elements, and electric control of valley and magnetic states. Here we report orbital multiferroicity in pentalayer rhombohedral graphene using low temperature magneto-transport measurements. We observed anomalous Hall signals Rxy with an exceptionally large Hall angle (tan{\Theta}H > 0.6) and orbital magnetic hysteresis at hole doping. There are four such states with different valley polarizations and orbital magnetizations, forming a valley-magnetic quartet. By sweeping the gate electric field E we observed a butterfly-shaped hysteresis of Rxy connecting the quartet. This hysteresis indicates a ferro-valleytronic order that couples to the composite field E\cdot B, but not the individual fields. Tuning E would switch each ferroic order independently, and achieve non-volatile switching of them together. Our observations demonstrate a new type of multiferroics and point to electrically tunable ultra-low power valleytronic and magnetic devices.

cond-mat.mes-hall↗

arXiv2023

Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene

Rhombohedral stacked multilayer graphene is an ideal platform to search for correlated electron phenomena, due to its pair of flat bands touching at zero energy and further tunability by an electric field. Furthermore, its valley-dependent Berry phase at zero energy points to possible topological states when the pseudospin symmetry is broken by electron correlation. However, experimental explorations of these opportunities are very limited so far, due to a lack of devices with optimized layer numbers and configurations. Here we present electron transport measurements of hBN-encapsulated pentalayer graphene at down to 100 milli-Kelvin. We observed a correlated insulating state with >MOhm resistance at zero charge density and zero displacement field, where the tight-binding calculation predicts a metallic ground state. By increasing the displacement field, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a low magnetic field of ~1 Tesla. At high displacement fields and charge densities, we observed isospin-polarized quarter- and half-metals. Therefore, rhombohedral-stacked pentalayer graphene is the first graphene system to exhibit two different types of Fermi-surface instabilities: driven by a pair of flat bands touching at zero energy, and by the Stoner mechanism in a single flat band. Our results demonstrate a new direction to explore intertwined electron correlation and topology phenomena in natural graphitic materials without the need of moir\'e superlattice engineering.

cond-mat.mes-hall↗