Haoyu Guo, Rhine Samajdar, Mathias S. Scheurer, and Subir Sachdev. Submitted. “Gauge Theories for the Thermal Hall Effect”. Publisher's VersionAbstract
We consider the thermal Hall effect of fermionic matter coupled to emergent gauge fields in 2+1 dimensions. While the low temperature thermal Hall conductivity of bulk topological phases can be connected to chiral edge states and a gravitational anomaly, there is no such interpretation at non-zero temperatures above 2+1 dimensional quantum critical points. In the limit of a large number of matter flavors, the leading contribution to the thermal Hall conductivity is that from the fermionic matter. The next-to-leading contribution is from the gauge fluctuations, and this has a sign which is opposite to that of the matter contribution. We illustrate this by computations on a Dirac Chern-Simons theory of the quantum phase transition in a square lattice antiferromagnet involving the onset of semion topological order. We find similar results for a model of the pseudogap metal with Fermi pockets coupled to an emergent U(1) gauge field.
Mathias S. Scheurer and Robert-Jan Slager. Submitted. “Unsupervised machine learning and band topology.” arXiv:2001.01711. Publisher's VersionAbstract
The study of topological bandstructures is an active area of research in condensed matter physics and beyond. Here, we combine recent progress in this field with developments in machine-learning, another rising topic of interest. Specifically, we introduce an unsupervised machine-learning approach that searches for and retrieves paths of adiabatic deformations between Hamiltonians, thereby clustering them according to their topological properties. The algorithm is general as it does not rely on a specific parameterization of the Hamiltonian and is readily applicable to any symmetry class. We demonstrate the approach using several different models in both one and two spatial dimensions and for different symmetry classes with and without crystalline symmetries. Accordingly, it is also shown how trivial and topological phases can be diagnosed upon comparing with a generally designated set of trivial atomic insulators.
E. I. Timmons, S. Teknowijoyo, M. Kończykowski, O. Cavani, M. A. Tanatar, Sunil Ghimire, Kyuil Cho, Yongbin Lee, Liqin Ke, Na Hyun Jo, S. L. Bud'ko, P. C. Canfield, Peter P. Orth, Mathias S. Scheurer, and R. Prozorov. Submitted. “Electron irradiation effects on superconductivity in PdTe2: an application of a generalized Anderson theorem.” arXiv:2001.04673. Publisher's VersionAbstract
Low temperature ~20 K electron irradiation with 2.5 MeV relativistic electrons was used to study the effect of controlled non-magnetic disorder on the normal and superconducting properties of the type-II Dirac semimetal PdTe2. We report measurements of longitudinal and Hall resistivity, thermal conductivity and London penetration depth using tunnel-diode resonator technique for various irradiation doses. The normal state electrical resistivity follows Matthiessen rule with an increase of the residual resistivity at a rate of ~0.77 \(\mu \Omega cm/(C/cm^2)\) London penetration depth and thermal conductivity results show that the superconducting state remains fully gapped. The superconducting transition temperature is suppressed at a non-zero rate that is about sixteen times slower than described by the Abrikosov-Gor'kov dependence, applicable to magnetic impurity scattering in isotropic, single-band s-wave superconductors. To gain information about the gap structure and symmetry of the pairing state, we perform a detailed analysis of these experimental results based on insight from a generalized Anderson theorem for multi-band superconductors. This imposes quantitative constraints on the gap anisotropies for each of the possible pairing candidate states. We conclude that the most likely pairing candidate is an unconventional \(A_{1g}^{+-}\)state. While we cannot exclude the conventional \(A_{1g}^{++}\) and the triplet \(A_{1u}\), we demonstrate that these states require additional assumptions about the orbital structure of the disorder potential to be consistent with our experimental results, e.g., a ratio of inter- to intra-band scattering for the singlet state significantly larger than one. Due to the generality of our theoretical framework, we think that it will also be useful for irradiation studies in other spin-orbit-coupled multi-orbital systems.
Rhine Samajdar and Mathias S. Scheurer. Submitted. “Microscopic theory of superconductivity in twisted double-bilayer graphene.” arXiv:2001.07716. Publisher's VersionAbstract
Small-angle twisted double-bilayer graphene is a correlated moiré superlattice system that has recently been found to exhibit both interaction-induced insulating and superconducting phases with properties different from the related magic-angle twisted bilayer graphene. Here, we develop a microscopic weak-coupling theory for superconductivity in the system starting from a continuum-model description. We study an electron-phonon as well as an entirely electronic pairing mechanism, and discuss the interplay of the two. In each case, the leading superconducting instability transforms under the trivial representation, A, of the point group C3 of the system, while the subleading pairing phases belong to the E channel. The resulting order parameter has no nodal points for electron-phonon pairing but exhibits 6 sign changes on the Fermi surface if the Coulomb interaction dominates. We also discuss the disorder sensitivity of the candidate pairing states.
Wei Wu, Mathias S. Scheurer, Michel Ferrero, and Antoine Georges. Submitted. “Not all doped Mott insulators have a pseudogap: key role of van Hove singularities.” arXiv:2001.00019. Publisher's VersionAbstract
The Mott insulating phase of the parent compounds is frequently taken as starting point for the underdoped high-Tc cuprate superconductors. In particular, the pseudogap state is often considered as deriving from the Mott insulator. In this work, we systematically investigate different weakly-doped Mott insulators on the square and triangular lattice to clarify the relationship between the pseudogap and Mottness. We show that doping a two-dimensional Mott insulator does not necessarily lead to a pseudogap phase. Despite its inherent strong-coupling nature, we find that the existence or absence of a pseudogap depends sensitively on non-interacting band parameters and identify the crucial role played by the van Hove singularities of the system. Motivated by a SU(2) gauge theory for the pseudogap state, we propose and verify numerically a simple equation that governs the evolution of characteristic features in the electronic scattering rate.
Mathias S. Scheurer and Rhine Samajdar. Submitted. “Pairing in twisted double-bilayer graphene and related moiré superlattice systems.” arXiv:1906.03258. Publisher's VersionAbstract
We present a systematic classification and analysis of possible pairing instabilities in graphene-based moiré superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an SU(2)+ x SU(2)- symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. We find that an approximate SU(2)+ x SU(2)- symmetry can generically account for the linear increase of the critical temperature with small magnetic fields, and we map out the possible forms of the phase diagram as a function of temperature and magnetic field. We examine which of the pairing states can arise in mean-field theory and the type of pairing favored in the presence of strong ferromagnetic fluctuations, which are expected to be present in twisted double-bilayer graphene. Finally, we also detail the differences in the classification when the additional microscopic or emergent symmetries relevant for twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are taken into account. Our study illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and could allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.
Harley D. Scammell, Kartik Patekar, Mathias S. Scheurer, and Subir Sachdev. Submitted. “Phases of SU(2) gauge theory with multiple adjoint Higgs fields in 2+1 dimensions.” arXiv:1912.06108. Publisher's VersionAbstract
A recent work proposed a SU(2) gauge theory for optimal doping criticality in the cuprate superconductors. The theory contains Nh Higgs fields transforming under the adjoint representation of SU(2), with Nh=1 for the electron-doped cuprates, and Nh=4 for the hole-doped cuprates. We investigate the strong-coupling dynamics of this gauge theory, while ignoring the coupling to fermionic excitations. We integrate out the SU(2) gauge field in a strong-coupling expansion, and obtain a lattice action for the Higgs fields alone. We study such a lattice action, with O(Nh) global symmetry, in an analytic large Nh expansion and by Monte Carlo simulations for Nh=4 and find consistent results. We find a confining phase with O(Nh) symmetry preserved (this describes the Fermi liquid phase in the cuprates), and Higgs phases (describing the pseudogap phase of the cuprates) with different patterns of the broken global O(Nh) symmetry. One of the Higgs phases is topologically trivial, implying the absence of any excitations with residual gauge charges. The other Higgs phase has Z2 topological order, with `vison' excitations carrying a Z2 gauge charge. We find consistent regimes of stability for the topological Higgs phase in both our numerical and analytical analyses.
D. Singh, Mathias S. Scheurer, A. D. Hillier, and R. P. Singh. Submitted. “Time-reversal-symmetry breaking and unconventional pairing in the noncentrosymmetric superconductor La7Rh3 probed by μSR.” arXiv:1802.01533. Publisher's VersionAbstract
Noncentrosymmetric superconductors have sparked significant research interests due to their exciting properties, such as the admixture of spin-singlet and spin-triplet Cooper pairs. Here we report muSR and thermodynamic measurements on the noncentrosymmetric superconductor La7Rh3 which indicate a fully established superconducting gap and spontaneous time-reversal-symmetry breaking at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in the system. A symmetry analysis identifies ground states compatible with time-reversal-symmetry breaking and the resulting gap functions are discussed. Furthermore, general energetic considerations indicate the relevance of electron-electron interactions for the pairing mechanism, in accordance with hints of spin-fluctuations revealed in susceptibility measurements.
Rhine Samajdar, Mathias S. Scheurer, Shubhayu Chatterjee, Haoyu Guo, Cenke Xu, and Subir Sachdev. 10/7/2019. “Enhanced thermal Hall effect in the square-lattice Néel state.” Nature Physics, 15, Pp. 1290-1294. Publisher's VersionAbstract
Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining Néel state to a state with coexisting Néel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global SO(3) symmetry. The field theory has four different formulations in terms of SU(2) or U(1) gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining Néel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.
Mathias S. Scheurer. 7/31/2019. “Spectroscopy of graphene with a magic twist.” Nature, 572, Pp. 40-41. Publisher's Version
Joaquin F. Rodriguez-Nieva and Mathias S. Scheurer. 5/6/2019. “Identifying topological order through unsupervised machine learning.” Nature Physics, 15, Pp. 790-795. Publisher's VersionAbstract
The Landau description of phase transitions relies on the identification of a local order parameter that indicates the onset of a symmetry-breaking phase. In contrast, topological phase transitions evade this paradigm and, as a result, are harder to identify. Recently, machine learning techniques have been shown to be capable of characterizing topological order in the presence of human supervision. Here, we propose an unsupervised approach based on diffusion maps that learns topological phase transitions from raw data without the need for manual feature engineering. Using bare spin configurations as input, the approach is shown to be capable of classifying samples of the two-dimensional XY model by winding number and capture the Berezinskii–Kosterlitz–Thouless transition. We also demonstrate the success of the approach on the Ising gauge theory, another paradigmatic model with topological order. In addition, a connection between the output of diffusion maps and the eigenstates of a quantum-well Hamiltonian is derived. Topological classification via diffusion maps can therefore enable fully unsupervised studies of exotic phases of matter.
Rhine Samajdar, Shubhayu Chatterjee, Subir Sachdev, and Mathias S. Scheurer. 4/18/2019. “Thermal Hall effect in square-lattice spin liquids: a Schwinger boson mean-field study.” Phys. Rev. B, 99, Pp. 165126. Publisher's VersionAbstract

Motivated by recent transport measurements in high-Tc cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field Ansätze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any T>0, also show a similarly enhanced thermal Hall conductivity.



Subir Sachdev, Harley Scammell, Mathias S. Scheurer, and Grigory Tarnopolsky. 2/25/2019. “Gauge theory for the cuprates near optimal doping.” Phys. Rev. B (Editors' Suggestion), 99, 054516. Publisher's VersionAbstract
We describe the phase diagram of a 2+1 dimensional SU(2) gauge theory of fluctuating incommensurate spin density waves for the hole-doped cuprates. Our primary assumption is that all low energy fermionic excitations are gauge neutral and electron-like, while the spin density wave order is fractionalized into Higgs fields transforming as adjoints of the gauge SU(2). The confining phase of the gauge theory is a conventional Fermi liquid with a large Fermi surface. There is a quantum phase transition to a Higgs phase describing the `pseudogap' at lower doping. Depending upon the quartic terms in the Higgs potential, the Higgs phase exhibits one or more of charge density wave, Ising-nematic, time-reversal odd scalar spin chirality, and Z2 topological orders. It is notable that the emergent broken symmetries in our theory of fluctuating spin density waves co-incide with those observed in diverse experiments. For the electron-doped cuprates, the spin density wave fluctuations are at wavevector (pi,pi), and then the corresponding SU(2) gauge theory only has a crossover between the confining and Higgs regimes, with an exponentially large confinement scale deep in the Higgs regime. On the Higgs side, for both the electron- and hole-doped cases, and at scales shorter than the confinement scale (which can be infinite when Z2 topological order is present), the electron spectral function has a `fractionalized Fermi liquid (FL*)' form with small Fermi surfaces. We also describe the deconfined quantum criticality of the Higgs transition in the limit of a large number of Higgs flavors, and perturbatively discuss its coupling to the Fermi surface excitations.
J.-F. He, C. R. Rotundu, Mathias S. Scheurer, Y. He, M. Hashimoto, K. Xu, Y. Wang, E. W. Huang, T. Jia, S.-D. Chen, B. Moritz, D.-H. Lu, Y. S. Lee, T.P. Devereaux, and Z.-X. Shen. 2/11/2019. “Fermi surface reconstruction in electron-doped cuprates without antiferromagnetic long-range order.” PNAS. Publisher's VersionAbstract
Fermi surface (FS) topology is a fundamental property of metals and superconductors. In electron-doped cuprate Nd2-xCexCuO4 (NCCO), an unexpected FS reconstruction has been observed in optimal- and over-doped regime (x=0.15-0.17) by quantum oscillation measurements (QOM). This is all the more puzzling because neutron scattering suggests that the antiferromagnetic (AFM) long-range order, which is believed to reconstruct the FS, vanishes before x=0.14. To reconcile the conflict, a widely discussed external magnetic field-induced AFM long-range order in QOM explains the FS reconstruction as an extrinsic property. Here, we report angle-resolved photoemission (ARPES) evidence of FS reconstruction in optimal- and over-doped NCCO. The observed FSs are in quantitative agreement with QOM, suggesting an intrinsic FS reconstruction without field. This reconstructed FS, despite its importance as a basis to understand electron-doped cuprates, cannot be explained under the traditional scheme. Furthermore, the energy gap of the reconstruction decreases rapidly near x=0.17 like an order parameter, echoing the quantum critical doping in transport. The totality of the data points to a mysterious order between x=0.14 and 0.17, whose appearance favors the FS reconstruction and disappearance defines the quantum critical doping. A recent topological proposal provides an ansatz for its origin.
Andreas Herklotz, Stefania F. Rus, Nina Balke, Christopher Rouleau, Er-Jia Guo, Amanda Huon, Santosh KC, Robert Roth, Xu Yang, Chirag Vaswani, Jigang Wang, Peter P. Orth, Mathias S. Scheurer, and Thomas Z. Ward. 1/2019. “Designing Morphotropic Phase Composition in BiFeO3.” Nano Letters. Publisher's VersionAbstract
In classical morphotropic piezoelectric materials, rhombohedral and tetragonal phase variants can energetically compete to form a mixed phase regime with improved functional properties. While the discovery of morphotropic-like phases in multiferroic BiFeO3 films has broadened this definition, accessing these phase spaces is still typically accomplished through isovalent substitution or heteroepitaxial strain which do not allow for continuous modification of phase composition postsynthesis. Here, we show that it is possible to use low-energy helium implantation to tailor morphotropic phases of epitaxial BiFeO3 films postsynthesis in a continuous and iterative manner. Applying this strain doping approach to morphotropic films creates a new phase space based on internal and external lattice stress that can be seen as an analogue to temperature–composition phase diagrams of classical morphotropic ferroelectric systems.
Mathias S. Scheurer and Subir Sachdev. 12/11/2018. “Orbital currents in insulating and doped antiferromagnets.” Phys. Rev. B, 98, 235126. Publisher's VersionAbstract
We describe square lattice spin liquids which break time-reversal symmetry, while preserving translational symmetry. The states are distinguished by the manner in which they transform under mirror symmetries. All the states have spontaneous orbital charge currents in the bulk (even in the insulator), but in some cases, orbital currents are non-zero only in a formulation with three orbitals per unit cell. The states are formulated using both the bosonic and fermionic spinon approaches. We describe states with Z2 and U(1) bulk topological order, and the chiral spin liquid with semionic excitations. The chiral spin liquid has no orbital currents in the one-band formulation, but does have orbital currents in the three-band formulation. We discuss application to the cuprate superconductors, after postulating that the broken time-reversal and mirror symmetries persist into confining phases which may also break other symmetries. In particular, the broken symmetries of the chiral spin liquid could persist into the Neel state.
Lars Lauke, Mathias S. Scheurer, Andreas Poenicke, and Jörg Schmalian. 10/8/2018. “Friedel oscillations and Majorana zero modes in inhomogeneous superconductors.” Phys. Rev. B, 98, 134502. Publisher's VersionAbstract
We study the modulations of the superconducting order parameter in the vicinity of edges, magnetic and non-magnetic impurities by self-consistently solving the gap equations of a system with competing interactions in the Cooper channel. It is shown that the presence or absence of Friedel-like oscillations of the superconducting order parameter crucially depends on its symmetry and can, hence, be used to obtain information about the symmetry properties of the condensate. Furthermore, the appearance of competing order parameters at inhomogeneities is discussed. We show that this can lead to the presence of a topologically trivial region close to the boundary of a system that is topologically nontrivial in its bulk. The resulting shift in position of the Majorana bound states is demonstrated to significantly affect its signatures in Josephson-junction experiments. We discuss Josephson scanning tunneling microscopy as a probe to resolve the Friedel-like oscillations as well as the spatial texture of competing s-wave superconductivity and Majorana bound states in the vicinity of the edge of the system.
Alex Thomson, Shubhayu Chatterjee, Subir Sachdev, and Mathias S. Scheurer. 8/6/2018. “Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene.” Phys. Rev. B, 98, 075109. Publisher's VersionAbstract
Serafim Teknowijoyo, Na Hyun Jo, Mathias S. Scheurer, M. A. Tanatar, Kyuil Cho, S. L. Bud'ko, Peter P. Orth, P. C. Canfield, and R. Prozorov. 7/16/2018. “Nodeless superconductivity in type-II Dirac semimetal PdTe2: low-temperature London penetration depth and symmetry analysis.” Phys. Rev. B, 98, 024508. Publisher's VersionAbstract
Superconducting gap structure was probed in type-II Dirac semimetal PdTe2 by measuring the London penetration depth using tunnel diode resonator technique. At low temperatures, the data for two samples are well described by weak coupling exponential fit yielding \(\lambda(T=0)=230\) nm as the only fit parameter at a fixed \(\Delta(0)/T_c\approx 1.76\), and the calculated superfluid density is consistent with a fully gapped superconducting state characterized by a single gap scale. Electrical resistivity measurements for in-plane and inter-plane current directions find very low and nearly temperature-independent normal-state anisotropy. The temperature dependence of resistivity is typical for conventional phonon scattering in metals. We compare these experimental results with expectations from a detailed theoretical symmetry analysis and reduce the number of possible superconducting pairing states in PdTe2 to only three nodeless candidates: a regular, topologically trivial, s-wave pairing, and two distinct odd-parity triplet states that both can be topologically non-trivial depending on the microscopic interactions driving the superconducting instability.
Markus J. Klug, Mathias S. Scheurer, and Jörg Schmalian. 7/2/2018. “Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene.” Phys. Rev. B, 98, 045102. Publisher's VersionAbstract
We determine the information scrambling rate $\lambda_{L}$ due to electron-electron Coulomb interaction in graphene. \(\lambda_{L}\) characterizes the growth of chaos and has been argued to give information about the thermalization and hydrodynamic transport coefficients of
a many-body system. We demonstrate that \(\lambda_{L}\) behaves for strong coupling similar to transport and energy relaxation rates. A weak coupling analysis, however, reveals that scrambling is related to dephasing or single particle relaxation. Furthermore, \(\lambda_{L}\) is found to be parametrically larger than the collision rate relevant for hydrodynamic processes, such as electrical conduction or viscous flow, and the rate of energy relaxation, relevant for thermalization.
Thus, while scrambling is obviously necessary for thermalization and quantum transport, it does generically not set the time scale for these processes. In addition we derive a quantum kinetic theory for information scrambling that resembles the celebrated Boltzmann equation and offers a physically transparent insight into quantum chaos in many-body systems.