Twisted Material Hosts Topological Superconductivity and Vortices

Researchers are increasingly focused on understanding the interplay between superconductivity and the fractional quantum anomalous Hall (FQAH) effect in twisted materials. Daniele Guerci, Ahmed Abouelkomsan, and Liang Fu, all from the Department of Physics at the Massachusetts Institute of Technology, demonstrate that the superconducting state observed in twisted MoTe₂ is a chiral p-wave superconductor hosting an array of vortices. These vortices are induced by an emergent magnetic field within the moiré superlattice, resulting in a topological superconducting vortex lattice state with a Chern number of one. This work offers a unified understanding of both FQAH and topological superconductivity, potentially paving the way for novel electronic devices and a deeper comprehension of correlated electron systems.

Recent observations in twisted molybdenum ditelluride (MoTe₂) revealed the simultaneous presence of superconductivity and the fractional quantum anomalous Hall effect (FQAH), prompting a detailed theoretical investigation into their underlying connection. The arrangement of electrons within the material creates a unique, ordered structure with implications for future electronic devices. Scientists have uncovered a surprising link between these two distinct quantum phenomena.

This work demonstrates that the superconducting state emerging in these materials is not conventional, but a chiral f-wave superconductor hosting a unique array of vortices, each carrying twice the usual quantum of magnetic flux.

These vortices, induced by an emergent magnetic field arising from the material’s layered structure, form a topological vortex lattice with a Chern number of -1/2, directly resulting in a half-integer thermal Hall conductance. The research establishes a unified framework explaining both phenomena, controlled by the spatial variation of this emergent magnetic field.

Unlike traditional superconductivity induced by external magnetic fields, this system’s superconductivity is enabled by the broken Galilean invariance inherent to the twisted material’s structure. This crucial difference allows for the formation of a vortex lattice locked to the moiré pattern, a periodic disruption in the material’s atomic arrangement, and opens the door to zero-resistance current flow.

At the heart of this discovery lies the intricate interplay between electron interactions and the unique band structure of twisted MoTe₂. By employing both numerical calculations and analytical theory, researchers have shown that repulsive interactions between electrons within a flat Chern band, a special energy level, can drive the formation of this topological superconducting state.

Analysis of the system’s properties reveals the presence of chiral Majorana fermion edge modes, indicating a topological character and potential applications in quantum computing. The implications extend beyond fundamental physics, suggesting new avenues for designing materials with tailored quantum properties. By manipulating the emergent magnetic field through precise control of the material’s structure, it may be possible to engineer novel superconducting devices with enhanced performance and functionality, potentially revolutionizing fields ranging from energy transmission to advanced sensing technologies.

Chiral superconductivity and Majorana modes in moiré twisted molybdenum ditelluride

A 72-qubit superconducting processor serves as the foundation for exploring topological superconductivity and the fractional quantum anomalous Hall (FQAH) effect in twisted molybdenum ditelluride. This work investigates the coexistence of these two phenomena, building upon theoretical predictions of repulsively interacting electrons within a moiré superlattice and its emergent magnetic field.

Central to the methodology is the development of a theoretical framework describing a chiral -wave superconducting state hosting an array of vortices induced by the emergent magnetic field, with flux quanta per moiré unit cell. This approach allows for a detailed examination of the spatial modulation of superconducting density and the potential detection of Majorana zero modes, quasiparticles predicted to exist in topological superconductors.

The team calculated the Chern number, a topological invariant, revealing a value of for the superconducting vortex lattice, which directly implies a half-integer thermal Hall conductance. This calculation relied on projecting two-body interactions onto a basis of ideal Chern wavefunctions, effectively simplifying the complex many-body problem into a more manageable form.

The researchers constructed single-particle wavefunctions crucial for defining the projected Hamiltonian, defining the wavefunction overlaps, Λk,k′+G, which describe the interactions between electrons in the flat Chern band. These overlaps were calculated by integrating over the unit cell, incorporating the spatial modulation of the magnetic field and the wavefunctions themselves.

Once the spectrum of the 2RDM (two-particle density matrix) was obtained, the team extracted the condensate wavefunction, representing the ground state of the superconducting system. The choice of these methods stems from their ability to accurately capture the interplay between fractionalization and superconductivity in twisted transition metal dichalcogenides, accounting for the spatial modulation of the emergent magnetic field and enhancing the clarity of the results.

Majorana edge modes and unconventional vortex lattices in superconducting twisted MoTe2

Calculations reveal a Chern number of 1/2 for the superconducting state, indicating a single chiral Majorana edge mode with a sign opposing the Chern insulator at full band filling. This topological property arises from the interplay between superconductivity and the fractional quantum anomalous Hall effect observed in twisted MoTe₂. Numerical investigations across varying system sizes consistently demonstrated an “odd-even” effect, further establishing the presence of an odd number of these chiral Majorana fermion edge modes.

The research elucidates the microscopic superconducting order parameter through exact diagonalization, confirming off-diagonal long-range order within the material. Analysis of the superconducting state shows it forms a vortex lattice with one vortex per moiré unit cell, a configuration distinct from conventional Abrikosov lattices. Each vortex carries vorticity 2, corresponding to h/e flux quanta, rather than the expected h/2e.

This exotic arrangement stems from strong emergent magnetic fields within the twisted material. The superconducting state exhibits a smooth connection to a chiral topological f-wave superconductor in the weak pairing regime, allowing for computation of the Chern number using a mean-field description of topological superconductivity. For moderate modulations of the emergent magnetic field, a fractional Chern insulator at filling ν = 2/3 coexists with a superconductor for 2/3.

At this transition point, the research identified a clear first-order phase change between the two states. Unlike systems with real magnetic fields, superconductivity is observed in twisted TMDs, a difference attributed to the broken Galilean invariance inherent in the emergent magnetic field. The study highlights a fundamental distinction between twisted TMDs and Landau levels, where superconductivity is absent under a uniform magnetic field.

Galilean invariance, or its lack thereof, plays a key role in allowing superconductivity to emerge in the form of a vortex lattice locked to the moiré lattice. This vortex lattice state, a topological superconductor hosting a chiral Majorana edge mode, differs from lattice models of anyon superconductivity that do not support unpaired Majoranas. The work details the mechanism underlying the emergent magnetic field in twisted TMDs, considering valence band holes experiencing interlayer tunneling and intralayer moiré potentials.

Topological superconductivity emerges from vortex lattices in twisted molybdenum ditelluride

Scientists have long sought materials exhibiting both superconductivity and the fractional quantum anomalous Hall effect, a pairing previously considered a theoretical ideal. Recent observations in twisted molybdenum ditelluride have now confirmed this coexistence, and detailed theoretical work clarifies the unusual nature of the resulting superconducting state.

Rather than a conventional flow of electrons, this material hosts a unique arrangement of vortices, swirling currents, arranged in a topological lattice. This isn’t merely a curiosity; it represents a new pathway towards designing materials with predictable, controllable quantum properties. Achieving this combination proved difficult because both phenomena demand extremely specific conditions.

Superconductivity requires electrons to pair and move without resistance, while the fractional quantum anomalous Hall effect relies on electrons behaving as if they are fractionally charged, emerging from complex interactions within a strong magnetic field. Previous attempts to create such a material often resulted in one effect suppressing the other, or a lack of stability at accessible temperatures.

Calculations suggest the arrangement of these vortices isn’t random, but ordered by the material’s internal structure, creating a state with a measurable thermal Hall effect. This discovery extends beyond fundamental physics, offering potential for new types of electronic devices. The topological nature of the superconducting state implies a degree of protection against imperfections, a critical advantage for building reliable quantum computers.

Questions remain about scaling up these materials and maintaining their delicate properties outside the laboratory. Further research must address the influence of material defects and explore alternative compounds that might exhibit similar behaviour at higher temperatures. Beyond this specific material, the theoretical framework developed here could guide the search for other exotic quantum states, potentially unlocking a new generation of quantum technologies.