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Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams \textit{et al.}, Science…
Detecting topological order in cold-atom experiments is an ongoing challenge, the resolution of which offers novel perspectives on topological matter. In material systems, unambiguous signatures of topological order exist for topological…
We report the studies of high-quality HgTe/(Cd,Hg)Te quantum wells (QWs) with a width close to the critical one $d_c$, corresponding to the topological phase transition and graphene like band structure in view of their applications for…
We calculate a topological invariant, whose value would coincide with the Chern number in case of integer quantum Hall effect, for fractional quantum Hall states. In case of Abelian fractional quantum Hall states, this invariant is shown to…
Energy dissipation is of fundamental interest and crucial importance in quantum systems. However, whether energy dissipation can emerge inside topological systems remains a question, especially when charge transport is topologically…
Fractional quantum Hall states at a half-filled Landau level are believed to carry an integer number $\mathcal{C}$ of chiral Majorana edge modes, reflected in their thermal Hall conductivity. We show that this number determines the primary…
A van der Waals heterostructure combined with intrinsic magnetism and topological orders have recently paved attractive avenues to realize quantum anomalous Hall effects. In this work, using first-principles calculations and effective model…
We model the quantum Hall effect in heterostructures made of two gapped graphene stripes with different gaps, $\Delta_1$ and $\Delta_2$. We consider two main situations, $\Delta_1=0,\Delta_2\neq0$ and $\Delta_1=-\Delta_2$. They are…
According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
We study a continuum model of the interface of graphene and vacuum in the quantum hall regime via sign-problem-free quantum Monte Carlo, allowing us to investigate the interplay of topology and strong interactions in a graphene quantum Hall…
Recent numerical simulations of flat band models with interactions which show clear evidence of fractionalized topological phases in the absence of a net magnetic field have generated a great deal of interest. We provide an explanation for…
Considering a range of candidate quantum phases of matter, half-integer thermal conductance ($\kappa_{\text{th}}$) is believed to be an unambiguous evidence of non-Abelian states. It has been long known that such half-integer values arise…
Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee…
The quantum Hall effect is the seminal example of topological protection, as charge carriers are transmitted through one-dimensional edge channels where backscattering is prohibited. Graphene has made its marks as an exceptional platform to…
Nontrivial bulk topological invariants of quantum materials can leave their signatures on charge, thermal and spin transports. In two dimensions, their imprints can be experimentally measured from well-developed multiterminal Hall bar…
Starting from Laughlin type wave functions with generalized periodic boundary conditions describing the degenerate groundstate of a quantum Hall system we explictly construct $r$ dimensional vector bundles. It turns out that the filling…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…
The so called quantum spin Hall phase is a topologically non trivial insulating phase that is predicted to appear in graphene and graphene-like systems. In this work we address the question of whether this topological property persists in…