arXiv subjects

Max Geier

Publications and source records attributed to Max Geier.

At least 19 recordsLinked to original sources

arXiv2026

Flux-tunable global and local superconductivity in a topological insulator nano-SQUID

Topological systems are defined by global properties that enforce the existence of local boundary modes. Three-dimensional topological insulators (TIs) were among the earliest proposed systems for hosting topological superconductivity, but experimental focus subsequently shifted to other platforms. Here, we revisit bulk-insulating TIs using a columnar nano-superconducting quantum interference device (nano-SQUID) architecture. This geometry optimises the proximity effect on the TI surface and enables simultaneous probing of global superconducting properties - via the critical current through the nano-SQUID - alongside the local states at the ends of the nano-SQUID via tunnel junctions. We observe several global superconducting features that appear to show a flux-driven global phase transition consistent with entering the topological regime, including periodic critical current oscillations and a sign reversal in the superconducting diode effect. Simultaneously, tunnelling spectroscopy reveals spectral jumps in local and nonlocal conductance that align with these global features. However, zero-bias peaks (ZBPs) in local conductance are present both within the predicted topological range of magnetic fields and in theoretically trivial regimes, including at zero magnetic field. Ultimately, the lack of correlation between local ZBP signatures and global signatures emphasises that conclusively identifying Majorana bound states will necessitate a combined approach, integrating the establishment of global topological properties with the use of local and other, more advanced, probes.

cond-mat.mes-hall↗

arXiv2026

Relaxation-driven flat bands and topology in moir\'e transition metal dichalcogenide heterobilayers

Moir\'e transition metal dichalcogenide (TMD) heterobilayers are commonly modeled by a continuum theory that yields topologically trivial bands, in contrast to their homobilayer counterparts which host topological bands and fractional Chern insulators (FCI). We show this conclusion is an artifact of neglecting the pseudomagnetic field generated by lattice relaxation, an effect intrinsic to every moir\'e material. We develop a continuum model that resolves relaxation into three channels: a modified moir\'e potential with higher Fourier harmonics, a pseudoelectric (scalar deformation) potential, and a pseudomagnetic (vector) potential. Using WSe$_2$/WS$_2$ as a prototype, we find that the pseudomagnetic field alone gaps the third and fourth valence bands with Chern numbers $\pm 1$ over a broad range of twist angle and lattice mismatch, while the moir\'e potential correction and pseudoelectric potential narrow the bandwidth and enhance the bandgaps, which survive many-body interactions using neural-network variational Monte Carlo calculations. Relaxation also smoothens the Berry curvature and quantum metric relative to the rigid model, moving the band closer to the ideal Chern limit, beneficial for the quantum anomalous Hall effect, FCI states, and flat-band superconductivity when filled to higher bands. Our work establishes a new framework that connects first-principles calculations, through the continuum model, to many-body observables. Using this framework, we show moir\'e heterobilayers as a new class of topological materials whose topology is driven entirely by intrinsic lattice relaxation.

cond-mat.mes-hall↗

arXiv2026

Large Electron Model: A Universal Ground State Predictor

We introduce Large Electron Model, a single neural network model that produces variational wavefunctions of interacting electrons over the entire Hamiltonian parameter manifold. Our model employs the Fermi Sets architecture, a universal representation of many-body fermionic wavefunctions, which is further conditioned on Hamiltonian parameter and particle number. For interacting electrons in a two-dimensional harmonic potential, a single trained model accurately predicts the ground state wavefunction while generalizing across unseen coupling strengths and particle-number sectors, producing both accurate real-space charge densities and ground state energies, even up to $50$ particles. Our results establish a foundation model method for material discovery that is grounded in the variational principle, while accurately treating strong electron correlation beyond the capacity of density functional theory.

cond-mat.str-el↗

arXiv2026

Predicting magnetism with first-principles AI

Computational discovery of magnetic materials remains challenging because magnetism arises from the competition between kinetic energy and Coulomb interaction that is often beyond the reach of standard electronic-structure methods. Here we tackle this challenge by directly solving the many-electron Schr\"odinger equation with neural-network variational Monte Carlo, which provides a highly expressive variational wavefunction for strongly correlated systems. Applying this technique to transition metal dichalcogenide moir\'e semicondutors, we predict itinerant ferromagnetism in WSe$_2$/WS$_2$ and an antiferromagnetic insulator in twisted $\Gamma$-valley homobilayer, using the same neural network without any physics input beyond the microscopic Hamiltonian. Crucially, both types of magnetic states are obtained from a single calculation within the $S_z=0$ sector, removing the need to compute and compare multiple $S_z$ sectors. This significantly reduces computational cost and paves the way for faster and more reliable magnetic material design.

cond-mat.str-el↗

arXiv2025

Topological Order in Neural Wavefunctions

Topologically ordered states are among the most interesting quantum phases of matter that host emergent quasi-particles having fractional charge and obeying fractional quantum statistics. Theoretical study of such states is however challenging owing to their strong-coupling nature that prevents conventional mean-field treatment. Here, we demonstrate that an attention-based deep neural network provides an expressive variational wavefunction that discovers fractional Chern insulator ground states purely through energy minimization without prior knowledge and achieves remarkable accuracy. We introduce an efficient method to extract ground state topological degeneracy -- a hallmark of topological order -- from a single optimized real-space wavefunction in translation-invariant systems by decomposing it into different many-body momentum sectors. Our results establish neural network variational Monte Carlo as a versatile tool for discovering strongly correlated topological phases.

cond-mat.mes-hall↗

arXiv2025

An integrated neural wavefunction solver for spinful Fermi systems

We present an approach to solving the ground state of Fermi systems that contain spin or other discrete degrees of freedom in addition to continuous coordinates. The approach combines a Markov chain Monte Carlo sampling for energy estimation that we adapted to cover the extended configuration space with a transformer-based wavefunction to represent fermionic states. This sampling is necessary when the Hamiltonian contains explicit spin dependence and, for spin-independent Hamiltonians, we find that the inclusion of spin updates leads to faster convergence to an antiferromagnetic ground state. A transformer with both continuous position and discrete spin as inputs achieves universal approximation to spinful generalized orbitals. We validate the method on a range of two-dimensional material problems: a two-dimensional electron gas with Rashba spin-orbit coupling, a noncollinear spin texture, and a quantum antiferromagnet in a honeycomb moir\'e potential.

quant-ph↗

arXiv2025

Attention is all you need to solve chiral superconductivity

Recent advances on neural quantum states have shown that correlations between quantum particles can be efficiently captured by attention -- a foundation of modern neural architectures that enables neural networks to learn the relation between objects. In this work, we show that a general-purpose self-attention Fermi neural network is able to find chiral $p_x \pm ip_y$ superconductivity in an attractive Fermi gas by energy minimization, without prior knowledge or bias towards pairing. The superconducting state is identified from the optimized wavefunction by measuring various physical observables. We develop a symmetry projection method that reveals the ground state angular momentum and time-reversal symmetry breaking, and a computation of the full two-body reduced density matrix spectrum that reveals the off-diagonal long-range order due to the dominant chiral $p$-wave pairing channel. Our work paves the way for AI-driven discovery of unconventional and topological superconductivity in strongly correlated quantum materials.

cond-mat.supr-con↗

arXiv2025

Directional conductance of Andreev crystals in hybrid Josephson junction arrays

Andreev bound states are coherent electron-hole superpositions that form in a normal metal through repeated Andreev reflection at a superconducting interface. When the length of a superconducting segment is comparable to the coherence length, the bound states on opposite sides of the segment hybridize through quasiparticle tunneling. In a periodic array, these hybridized Andreev bound states form energy bands below the superconducting gap. We develop a theoretical framework for transport in such Andreev crystals. We demonstrate that, at high interface transparency, a constant phase bias between neighboring superconductors renders the bands directional: one band contains only right-moving and the other only left-moving electronic states. This property leads to a directional conductance that enables the device to operate as a flux- and bias-voltage-tunable filter that allows signal transmission in only one direction.

cond-mat.mes-hall↗

arXiv2025

Nodal superconducting gap structure and topological surface states of UTe$_2$

The heavy-fermion compound UTe$_2$ is a candidate for hosting intrinsic spin-triplet superconductivity. At present, however, the type of triplet Cooper pairing realized in UTe$_2$ remains unknown, which calls for further experimental and theoretical investigations. In this paper, we develop a microscopic minimal model for the superconducting phases of UTe$_2$ based on recent findings in the description of its low-energy normal state electronic properties. We apply the resulting theoretical model to extract the nodal gap properties of the allowed superconducting ground states, and determine their associated topological surface states on the experimentally relevant (0-11) cleave plane. We find that the Fermi surface of UTe$_2$ enforces additional point nodes in excess to the point nodes imposed by symmetry, which may reconcile several experiments seemingly in conflict with B$_{2u}$ or B$_{3u}$ pairing symmetries. Furthermore, we map out the in-gap Majorana surface-bound modes existing on the (0-11) surface, and discuss their potential for additional insight into the pairing structure of UTe$_2$.

cond-mat.supr-con↗

arXiv2025

Is attention all you need to solve the correlated electron problem?

The attention mechanism has transformed artificial intelligence research by its ability to learn relations between objects. In this work, we explore how a many-body wavefunction ansatz constructed from a large-parameter self-attention neural network can be used to solve the interacting electron problem in solids. By a systematic neural-network variational Monte Carlo study on a moir\'e quantum material, we demonstrate that the self-attention ansatz provides an accurate and efficient solution without human bias. Moreover, our numerical study finds that the required number of variational parameters scales roughly as $N^2$ with the number of electrons, which opens a path towards efficient large-scale simulations.

cond-mat.str-el↗

arXiv2024

Tunable superconducting diode effect in a topological nano-SQUID

A Josephson diode passes current with zero resistance in one direction but is resistive in the other direction. While such an effect has been observed in several platforms, a large and tunable Josephson diode effect has been rare. Here we report that a simple device consisting of a topological-insulator (TI) nanowire side-contacted by superconductors to form a lateral Josephson junction presents a large diode effect with the efficiency $\eta$ reaching 0.3 when a parallel magnetic field $B_{||}$ is applied. Interestingly, the sign and the magnitude of $\eta$ is tunable not only by $B_{||}$ but also by the back-gate voltage. This diode effect can be understood by modeling the system as a nano-SQUID, in which the top and bottom surfaces of the TI nanowire each form a line junction and $B_{||}$ creates a magnetic flux to thread the SQUID loop. This model further shows that the observed diode effect marks the emergence of topological superconductivity in TI-nanowire-based Josephson junction.

cond-mat.supr-con↗

arXiv2024

Topological Insulator nano-SQUID: Flux-tunable platform for topological superconductivity

Many efforts have been made in the past decade to realize topological superconductivity using superconducting proximity effect, but an ideal platform is still lacking. A 3D topological insulator (TI) is promising for this purpose due to the spin-momentum-locked surface state. Here we propose a novel yet simple TI platform which gives rise to a topological phase that is robust against disorder. It consists of a bulk-insulating rectangular TI nanowire laterally sandwiched by two superconductors. In this structure, the top and bottom surfaces individually work as SNS line junctions, forming a nanometer-scale columnar SQUID in which the nanowire cross-section defines the threading magnetic flux $\Phi$ in axial magnetic fields. We theoretically show that, when the two junctions are asymmetric, a robust topological phase occurs periodically for a wide range of $\Phi$, independently of the chemical potential. Our experiment found that a TI device of this structure indeed behaves as a columnar nano-SQUID where the supercurrent flows only through the top and bottom surfaces with vanishing bulk contribution. Furthermore, the top/bottom asymmetry can be tuned by a back gate, a key ingredient for the topological phase.

cond-mat.mes-hall↗

arXiv2024

Self-correcting GKP qubit in a superconducting circuit with an oscillating voltage bias

We propose a simple circuit architecture for a dissipatively error corrected Gottesman-Kitaev-Preskill (GKP) qubit. The device consists of a electromagnetic resonator with impedance $h/2e^2\approx 12.91\,{\rm k}\Omega$ connected to a Josephson junction with a voltage bias oscillating at twice the resonator frequency. For large drive amplitudes, the circuit is effectively described by the GKP stabilizer Hamiltonian, whose low-energy subspace forms the code space for a qubit protected against phase-space local noise. The GKP states in the codespace can be dissipatively stabilized and error corrected by coupling the resonator to a bath through a bandpass filter; a resulting side-band cooling effect stabilizes the system in the GKP code space, dissipatively correcting it against both bit and phase flip errors. Simulations show that this dissipative error correction can enhance coherence time by factor $\sim 1000$ with NbN-based junctions, for operating temperatures in the $\sim 100\,{\rm mK}$ range. The scheme can be used to stabilize both square- and hexagonal-lattice GKP codes. Finally, a Josephson current based readout scheme, and dissipatively corrected single-qubit Clifford gates are proposed.

quant-ph↗

arXiv2024

Chiral and topological superconductivity in isospin polarized multilayer graphene

A microscopic mechanism for chiral p-wave superconductivity from Coulomb repulsion is proposed for spin- and valley-polarized state of rhombohedral multilayer graphene. The superconducting instability arises when strong Thomas-Fermi screening of the Coulomb potential allows Friedel oscillations to take over - leading to an effective attraction on length scales below the Fermi wavelength. The superconducting critical temperature is largest at low density below a Lifshitz transition to an annular Fermi sea, where the additional pocket strongly enhances Thomas-Fermi screening. The Lifshitz transition also marks a topological phase transition from a trivial to a topological superconducting phase hosting Majorana fermions. The chirality of the superconducting order parameter is selected by the chirality of the valley-polarized Bloch electrons. Our results are in reasonable agreement with observations in a recent experiment on tetralayer graphene [Han, T., Lu, Z., Hadjri, Z. et al., Nature (2025)].

cond-mat.supr-con↗

arXiv2024

Nonreciprocal superconductivity

We introduce the notion of nonreciprocal superconductors where inversion and time-reversal symmetries are broken, giving rise to an asymmetric energy dispersion. We demonstrate that nonreciprocal superconductivity can be detected by Andreev reflection. In particular, a transparent junction between a normal metal and a nonreciprocal superconductor generally exhibits an asymmetric current-voltage characteristic, which serves as a defining feature of nonreciprocal superconductivity. Unlike the superconducting diode effects, our detection scheme has the advantage of avoiding large critical currents that turn the superconducting state to normal. Finally, we discuss candidates for nonreciprocal superconductivity, including graphene, UTe2, as well as engineered platforms.

cond-mat.supr-con↗

arXiv2023

Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe$_2$

The discovery of unconventional superconductivity in the heavy-fermion material UTe$_2$ has reinvigorated research of spin-triplet superconductivity. We perform a theoretical study of coupled two-component spin-triplet superconducting order parameters and their thermodynamic transitions into the superconducting state. With focus on the behavior of the temperature dependence of the specific heat capacity, we find that two-component time-reversal symmetry breaking superconducting order may feature vanishing or even negative secondary specific heat anomalies. The origin of this unusual specific heat behavior is tied to the non-unitarity of the composite order parameter. Additionally, we supply an analysis of the topological surface states associated with the different possible spin-triplet orders: single-component orders host Dirac Majorana surface states in addition to possible bulk nodes. A second component breaking time-reversal symmetry gaps these surface states producing chiral Majorana hinge modes. DFT+$U$ band-structure calculations support that these topological phases are realized in UTe$_2$ when introducing weak superconducting pairing. Our topological analysis suggests measurable signatures for surface-probe experiments to acquire further evidence of the superconducting pairing symmetry.

cond-mat.supr-con↗

arXiv2023

Fermion-parity qubit in a proximitized double quantum dot

Bound states in quantum dots coupled to superconductors can be in a coherent superposition of states with different electron number but with the same fermion parity. Electrostatic gating can tune this superposition to a sweet spot, where the quantum dot has the same mean electric charge independent of its electron-number parity. Here, we propose to encode quantum information in the local fermion parity of two tunnel-coupled quantum dots embedded in a Josephson junction. At the sweet spot, the qubit states have zero charge dipole moment. This protects the qubit from dephasing due to charge noise acting on the potential of each dot, as well as fluctuations of the (weak) inter-dot tunneling. At weak inter-dot tunneling, relaxation is suppressed because of disjoint qubit states. On the other hand, for strong inter-dot tunneling the system is protected against noise affecting each quantum dot separately (energy level noise, dot-superconductor tunneling fluctuations, and hyperfine interactions). Finally, we describe initialization and readout as well as single-qubit and two-qubit gates by pulsing gate voltages.

cond-mat.mes-hall↗

arXiv2023

Non-Abelian holonomy of Majorana zero modes coupled to a chaotic quantum dot

If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved. We characterize the corresponding non-Abelian holonomy for a quantum dot with chaotic classical dynamics using random matrix theory and discuss measurable signatures of the non-Abelian time-evolution.

cond-mat.mes-hall↗