arXiv subjects

Peter J. Hirschfeld

Publications and source records attributed to Peter J. Hirschfeld.

At least 19 recordsLinked to original sources

arXiv2026

Electronic Reconstruction Towards Topological Superconductivity in FeTe

The recent discovery of intrinsic superconductivity in stoichiometric FeTe films has renewed interest in the Te-rich end member of the iron chalcogenides for studies of unconventional and topological superconductivity, yet its intrinsic electronic structure remains unresolved. In this work, we combine molecular beam epitaxy, angle-resolved photoemission spectroscopy (ARPES), electrical transport measurements, density functional theory, and embedded dynamical mean-field theory to track the electronic reconstruction of 20-unit-cell FeTe films as Te annealing progressively removes excess interstitial Fe and drives the system from an antiferromagnetic metal to a superconductor. We find that this evolution is accompanied by recovered quasiparticle coherence, reduced electronic correlations, a Lifshitz transition, and a topological phase transition, yielding dxy-dominated hole and electron pockets that favor inter-pocket scattering. In addition, a shallow dxz/dyz-derived hole band located about 2 meV below the Fermi level may provide an incipient-band pairing channel, while scattering between the two electron pockets at M may offer additional pairing channels. High-resolution polarization-dependent laser ARPES measurements further reveal a topological surface state whose circular dichroism is consistent with the expected orbital-angular-momentum texture of stoichiometric FeTe. These results establish the intrinsic low-energy electronic structure of superconducting FeTe and identify the electronic states most relevant to superconductivity. The coexistence of intrinsic superconductivity and a topological surface state establishes stoichiometric FeTe as a promising platform for exploring topological superconductivity and possible Majorana bound states.

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arXiv2026

Signatures of nodal superconductivity in stoichiometric FeTe

Superconductivity in stoichiometric FeTe opens access to the FeTe endpoint of the Fe(Se,Te) phase diagram, yet the nature of its superconducting pairing state remains unresolved. In this work, we combine scanning superconducting quantum interference device (SQUID) microscopy, electrical transport, scanning tunneling microscopy and spectroscopy (STM/S), and mean-field calculations to investigate the local superfluid response and pairing state of FeTe thin films with tunable stoichiometry. Even in stoichiometric FeTe, we observe micrometer-scale spatial variations in both superfluid stiffness and superconducting transition temperature $T_c$, while the London penetration depth remains non-saturating down to 0.02$T_c$ and follows a power-law temperature dependence with an exponent of approximately 1-1.5. Together with a V-shaped low-energy density of states and two-gap modeling, these results indicate a superconducting state with gap nodes or deep minima, consistent with either a $d$-wave or nodal $s$-wave superconducting state. Our findings establish stoichiometric FeTe as a distinct superconducting regime that departs from the trend toward more isotropic gaps at intermediate Se/Te compositions, providing a new benchmark for modern microscopic theories of iron-chalcogenide superconductivity. Our work also reveals a crossover from weak to rapid suppression of $T_c$ as superfluid stiffness decreases, connecting FeTe to the broader phenomenology observed in unconventional superconductors.

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arXiv2026

Stoichiometric FeTe is a Superconductor

Iron-based superconductors are a fascinating family of materials in which multiple electronic bands and strong antiferromagnetic (AFM) correlations are key ingredients for competing ground states, including antiferromagnetism, electronic nematicity, and unconventional superconductivity. FeTe, unlike its superconducting isostructural counterpart FeSe, has long been regarded as an AFM metal sans superconductivity. In this work, we employ molecular beam epitaxy to grow FeTe films and perform post-growth annealing under a Te flux. By performing spin-polarized scanning tunneling microscopy and spectroscopy, we demonstrate that the AFM order in as-grown FeTe films is induced by interstitial Fe atoms that disrupt the ideal 1:1 stoichiometry. Remarkably, the removal of these interstitial Fe atoms through Te annealing yields stoichiometric FeTe films that show no AFM order and instead exhibit robust superconductivity with a critical temperature of ~13.5K. This superconducting state is further confirmed by the observation of Cooper pair tunneling, zero electrical resistance, and the Meissner effect. Therefore, our results demonstrate that stoichiometric FeTe is inherently a superconductor, overturning a long-held view that it is an AFM metal. This work clarifies the origin of superconductivity in FeTe-based heterostructures and demonstrates the importance of stoichiometry control in understanding the competition between AFM and superconductivity in iron-based superconductors.

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arXiv2025

Determination of gap structure of triplet superconductors from field-dependent Knight shift measurements

We analyze the spin susceptibility of spin-triplet superconductors from the zero-field to finite-field regimes, with emphasis on its implications for Knight-shift measurements. In the zero-field limit, we review the general expression for the static spin susceptibility and highlight the universal zero-temperature sum rule, $\sum_i χ_{ii}(T=0)=2χ^N$, which constrains the residual susceptibility components for any triplet state. Using representative isotropic, helical, and chiral $\vec{d}$-vectors, we illustrate how the Knight shift encodes the spin configuration of the order parameter and show that the sum rule remains robust even for anisotropic Fermi surfaces. We then incorporate magnetic field effects through a semiclassical Doppler shift of quasiparticle energies in the vortex state. The resulting field dependence of the susceptibility - including both longitudinal (Knight-shift) and transverse magnetic susceptibility components - provides a sensitive probe of nodal directions and the momentum dependence of the $\vec{d}$-vector. Applying this framework to UTe$_2$, we demonstrate how the distinct irreducible representations allowed by orthorhombic symmetry can be differentiated by their field-dependent susceptibility.

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arXiv2025

Guided Diffusion for the Discovery of New Superconductors

The inverse design of materials with specific desired properties, such as high-temperature superconductivity, represents a formidable challenge in materials science due to the vastness of chemical and structural space. We present a guided diffusion framework to accelerate the discovery of novel superconductors. A DiffCSP foundation model is pretrained on the Alexandria Database and fine-tuned on 7,183 superconductors with first principles derived labels. Employing classifier-free guidance, we sample 200,000 structures, which lead to 34,027 unique candidates. A multistage screening process that combines machine learning and density functional theory (DFT) calculations to assess stability and electronic properties, identifies 773 candidates with DFT-calculated $T_\mathrm{c}>5$ K. Notably, our generative model demonstrates effective property-driven design. Our computational findings were validated against experimental synthesis and characterization performed as part of this work, which highlighted challenges in sparsely charted chemistries. This end-to-end workflow accelerates superconductor discovery while underscoring the challenge of predicting and synthesizing experimentally realizable materials.

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arXiv2025

Superconductivity with repulsion: a variational approach

We revisit the stability of the superconducting state within mean-field theory in the presence of repulsive pairing interactions, focusing on multiband systems where such channels naturally arise. We show that, when repulsion is present, the self-consistent BCS solution appears as a saddle point of the conventional mean-field free energy, casting doubt on its physical stability. We show that this pathology is an artifact of using a non-variational functional. Recasting the problem with Bogoliubov's variational principle restores a free energy that is bounded from below and places the BCS solution at a genuine minimum. Using a two-band toy model relevant to iron-based superconductors, we demonstrate the stability of the s$_\pm$ state and clarify how projection schemes that rely only on the interaction matrix can misidentify the attractive eigenmode that drives pairing. Our results clarify the instability issue highlighted by Aase et al. and provide a consistent foundation for analyzing fluctuations in the presence of repulsive interactions.

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arXiv2024

Hydride superconductivity: here to stay

The field of hydride superconductivity has recently been mired in a controversy that might divert attention from the question of central importance: do hydrides support genuine superconductivity or not? We examine some key papers from the field, and conclude that hydride superconductivity is real.

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arXiv2024

Robust nodal behavior in the thermal conductivity of superconducting UTe$_2$

The superconducting state of the heavy-fermion metal UTe$_2$ has attracted considerable interest because of evidence for spin-triplet Cooper pairing and non-trivial topology. Progress on these questions requires identifying the presence or absence of nodes in the superconducting gap function and their dimension. In this article we report a comprehensive study of the influence of disorder on the thermal transport in the superconducting state of UTe$_2$. Through detailed measurements of the magnetic field dependence of the thermal conductivity in the zero-temperature limit, we obtain clear evidence for the presence of point nodes in the superconducting gap for all samples with transition temperatures ranging from 1.6~K to 2.1~K obtained by different synthesis methods, including a refined self-flux method. This robustness implies the presence of symmetry-imposed nodes throughout the range studied, further confirmed via disorder-dependent calculations of the thermal transport in a model with a single pair of nodes. In addition to capturing the temperature dependence of the thermal conductivity up to $T_c$, this model allows us to limit the possible locations of the nodes, suggesting a B$_{1u}$ or B$_{2u}$ symmetry for the superconducting order parameter. Additionally, comparing the new, ultra-high conductivity samples to older samples reveals a crossover between a low-field and a high field regime at a single value of the magnetic field in all samples. In the high field regime, the thermal conductivity at different disorder levels differ from each other by a simple offset, suggesting that some simple principle determines the physics of the mixed state, a fact which may illuminate trends observed in other clean nodal superconductors.

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arXiv2024

Accelerating superconductor discovery through tempered deep learning of the electron-phonon spectral function

Integrating deep learning with the search for new electron-phonon superconductors represents a burgeoning field of research, where the primary challenge lies in the computational intensity of calculating the electron-phonon spectral function, $α^2F(ω)$, the essential ingredient of Midgal-Eliashberg theory of superconductivity. To overcome this challenge, we adopt a two-step approach. First, we compute $α^2F(ω)$ for 818 dynamically stable materials. We then train a deep-learning model to predict $α^2F(ω)$, using an unconventional training strategy to temper the model's overfitting, enhancing predictions. Specifically, we train a Bootstrapped Ensemble of Tempered Equivariant graph neural NETworks (BETE-NET), obtaining an MAE of 0.21, 45 K, and 43 K for the Eliashberg moments derived from $α^2F(ω)$: $λ$, $ω_{\log}$, and $ω_{2}$, respectively, yielding an MAE of 2.5 K for the critical temperature, $T_c$. Further, we incorporate domain knowledge of the site-projected phonon density of states to impose inductive bias into the model's node attributes and enhance predictions. This methodological innovation decreases the MAE to 0.18, 29 K, and 28 K, respectively, yielding an MAE of 2.1 K for $T_c$. We illustrate the practical application of our model in high-throughput screening for high-$T_c$ materials. The model demonstrates an average precision nearly five times higher than random screening, highlighting the potential of ML in accelerating superconductor discovery. BETE-NET accelerates the search for high-$T_c$ superconductors while setting a precedent for applying ML in materials discovery, particularly when data is limited.

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arXiv2022

Exact solution for finite center-of-mass momentum Cooper pairing

Pair density waves (PDWs) are superconducting states formed by ``Cooper pairs" of electrons containing a non-zero center-of-mass momentum. They are characterized by a spatially modulated order parameter and may occur in a variety of emerging quantum materials such as cuprates, transition metal dichalcogenides (TMDs) and Kagome metals. Despite extensive theoretical and numerical studies seeking PDWs in a variety of lattices and interacting settings, there is currently no generic and robust mechanism that favors a modulated solution of the superconducting order parameter in the presence of time reversal symmetry. Here, we study the problem of two electrons subject to an anisotropic ($d$-wave) attractive potential. We solve the two-body Schrodinger wave equation exactly to determine the pair binding energy as a function of the center-of-mass momentum. We find that a modulated (finite momentum) pair is favored over a homogeneous (zero momentum) solution above a critical interaction. Using this insight from the exact two-body solution, we construct a BCS-like variational many-body wave function and calculate the free energy and superconducting gap as a function of the center-of-mass momentum. A zero temperature analysis of the energy shows that the conclusions of the two-body problem are robust in the many-body limit. Our results lay the theoretical and microscopic foundation for the existence of PDWs.

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arXiv2021

Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase

An unidentified quantum fluid designated as the pseudogap (PG) phase is produced by electron-density depletion in the CuO$_2$ antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap $Δ_P(\pmb r)$ in real-space, and a characteristic quasiparticle scattering interference (QPI) signature $Λ_P(\pmb q)$ in wavevector space. By studying strongly underdoped Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ at hole-density ~0.08 in the superconductive phase, we detect the $8a_0$-periodic $Δ_P(\pmb r)$ modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find evolution of the scattering interference signature $Λ(\pmb q)$ that is predicted specifically for the temperature dependence of an $8a_0$-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi$_2$Sr$_2$CaDyCu$_2$O$_8$ pseudogap phase.

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arXiv2021

Superconductivity of $β$-Gallium

Elemental gallium can exist in several phases under ambient conditions. The stable $α$ phase has a superconducting transition temperature, $T_c$, of 0.9~K. By contrast, the $T_c$ of the metastable $β$ phase is around 6~K. To understand the significant improvement in $T_c$ in the $β$ phase, we first calculate the electronic structure, phonon dispersion, and the electron-phonon coupling of gallium in the $α$ and $β$ phase. Next, we solve the Eliashberg equations to obtain the superconducting gaps and the transition temperatures. Using these results, we relate the increased $T_c$ in the $β$ phase to structural differences between the phases that affect the electronic and phonon properties. The structure motif of the $α$ phase is Ga$_2$ dimers, which form strong covalent bonds leading to bonding and antibonding states that suppress the density of states at the Fermi level. The $β$-Ga structure consists of arrays of Ga chains that favor strong coupling between the lattice vibrations and the electronic states near the Fermi level. The increased density of states and strong coupling to the phonons for the $β$-Ga chains compared to the $α$ Ga$_2$ dimers enhance superconductivity in the $β$-Ga phase.

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arXiv2019

Quasiparticle Interference and Symmetry of Superconducting Order Parameter in Strongly Electron-Doped Iron-based Superconductors

Motivated by recent experimental reports of significant spin-orbit coupling (SOC) and a sign-changing order-parameter in the Li$_{1-x}$Fe$_x$(OHFe)$_{1-y}$Zn$_y$Se superconductor with only electron pockets present, we study the possible Cooper-pairing symmetries and their quasiparticle interference (QPI) signatures. We find that each of the resulting states - $s$-wave, $d$-wave and helical $p$-wave - can have a fully gapped density of states (DOS) consistent with angle-resolved photoemission spectroscopy (ARPES) experiments and, due to spin-orbit coupling, are a mixture of spin singlet and triplet components leading to intra- and inter-band features in the QPI signal. Analyzing predicted QPI patterns we find that only the spin-triplet dominated even parity $A_{1g}$ (s-wave) and $B_{2g}$ (d-wave) pairing states are consistent with the experimental data. Additionally, we show that these states can indeed be realized in a microscopic model with atomic-like interactions and study their possible signatures in spin-resolved STM experiments.

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arXiv2018

Imaging Orbital-selective Quasiparticles in the Hund's Metal State of FeSe

Strong electronic correlations, emerging from the parent Mott insulator phase, are key to copper-based high temperature superconductivity (HTS). By contrast, the parent phase of iron-based HTS is never a correlated insulator. But this distinction may be deceptive because Fe has five active d-orbitals while Cu has only one. In theory, such orbital multiplicity can generate a Hund's Metal state, in which alignment of the Fe spins suppresses inter-orbital fluctuations producing orbitally selective strong correlations. The spectral weights $Z_m$ of quasiparticles associated with different Fe orbitals m should then be radically different. Here we use quasiparticle scattering interference resolved by orbital content to explore these predictions in FeSe. Signatures of strong, orbitally selective differences of quasiparticle $Z_m$ appear on all detectable bands over a wide energy range. Further, the quasiparticle interference amplitudes reveal that $Z_{xy}<Z_{xz}<<Z_{yz}$, consistent with earlier orbital-selective Cooper pairing studies. Thus, orbital-selective strong correlations dominate the parent state of iron-based HTS in FeSe.

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arXiv2017

Microscopic pairing fingerprint of the iron-based superconductor ${\rm Ba_{1-x}K_xFe_2As_2}$

Resolving the microscopic pairing mechanism and its experimental identification in unconventional superconductors is among the most vexing problems of contemporary condensed matter physics. We show that Raman spectroscopy provides an avenue for this quest by probing the structure of the pairing interaction at play in an unconventional superconductor. As we study the spectra of the prototypical Fe-based superconductor ${\rm Ba_{1-x}K_xFe_2As_2}$ for $0.22\le x \le 0.70$ in all symmetry channels, Raman spectroscopy allows us to distill the leading $s$-wave state. In addition, the spectra collected in the $B_{1g}$ symmetry channel reveal the existence of two collective modes which are indicative of the presence of two competing, yet sub-dominant, pairing tendencies of $d_{x^2-y^2}$ symmetry type. A comprehensive functional Renormalization Group (fRG) and random-phase approximation (RPA) study on this compound confirms the presence of the two sub-leading channels, and consistently matches the experimental doping dependence of the related modes. The synopsis of experimental evidence and theoretical modelling supports a spin-fluctuation mediated superconducting pairing mechanism.

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arXiv2017

Discovery of Orbital-Selective Cooper Pairing in FeSe

The superconductor FeSe is of intense interest thanks to its unusual non-magnetic nematic state and potential for high temperature superconductivity. But its Cooper pairing mechanism has not been determined. Here we use Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the bands surrounding the $Γ= (0,0)$ and $X=(π/ a_{Fe}, 0)$ points of FeSe, and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless, and exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing which, in FeSe, is based preferentially on electrons from the $d_{yz}$ orbitals of the iron atoms.

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arXiv2017

Experimental Demonstration of the Sign Reversal of the Order Parameter in (Li1-xFex)OHFe1-yZnySe

Iron pnictides are the only known family of unconventional high-temperature superconductors besides cuprates. Until recently, it was widely accepted that superconductivity is spin-fluctuation driven and intimately related to their fermiology, specifically, hole and electron pockets separated by the same wave vector that characterizes the dominant spin fluctuations, and supporting order parameters (OP) of opposite signs. This picture was questioned after the discovery of a new family, based on the FeSe layers, either intercalated or in the monolayer form. The critical temperatures there reach ~40 K, the same as in optimally doped bulk FeSe - despite the fact that intercalation removes the hole pockets from the Fermi level and, seemingly, undermines the basis for the spin-fluctuation theory and the idea of a sign-changing OP. In this paper, using the recently proposed phase-sensitive quasiparticle interference technique, we show that in LiOH intercalated FeSe compound the OP does change sign, albeit within the electronic pockets, and not between the hole and electron ones. This result unifies the pairing mechanism of iron based superconductors with or without the hole Fermi pockets and supports the conclusion that spin fluctuations play the key role in electron pairing.

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arXiv2016

Superconducting phase diagram of the paramagnetic one-band Hubbard model

We study spin-fluctuation-mediated superconductivity in the one-band Hubbard model. Higher order effective interactions in $U$ give rise to a superconducting instability which is very sensitive to changes in the Fermi surface topology arising as a function of doping and changes in the band structure. We show the superconducting phase diagram as a function of doping and next-nearest neighbor hopping in the limit of very small Coulomb interaction strength and discuss peculiarities arising at the phase boundaries separating different superconducting domains.

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