arXiv subjects

Mathias S. Scheurer

Publications and source records attributed to Mathias S. Scheurer.

90 records · Page 5Linked to original sources

arXiv2019

Enhanced thermal Hall effect in the square-lattice Néel state

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.

cond-mat.str-el↗

arXiv2019

Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study

Motivated by recent transport measurements in high-$T_c$ 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.

cond-mat.str-el↗

arXiv2019

Gauge theory for the cuprates near optimal doping

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 (and its associated $d$-wave superconductor). 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 $\mathbb{Z}_2$ 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 $(π,π)$, 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 $\mathbb{Z}_2$ 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 fermionic excitations.

cond-mat.str-el↗

arXiv2018

Orbital currents in insulating and doped antiferromagnets

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 non-zero scalar spin chirality, which implies the appearance of 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 $\mathbb{Z}_2$ 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 Néel state.

cond-mat.str-el↗

arXiv2018

Friedel oscillations and Majorana zero modes in inhomogeneous superconductors

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.

cond-mat.supr-con↗

arXiv2018

Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene

We present the electronic band structures of states with the same symmetry as the three-sublattice planar antiferromagnetic order of the triangular lattice. Such states can also be defined on the honeycomb lattice provided the spin density waves lie on the bonds. We identify cases which are consistent with observations on twisted bilayer graphene: a correlated insulator with an energy gap, yielding a single doubly-degenerate Fermi surface upon hole doping. We also discuss extensions to metallic states which preserve spin rotation invariance, with fluctuating spin density waves and bulk $\mathbb{Z}_2$ topological order.

cond-mat.str-el↗

arXiv2018

Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene

We determine the information scrambling rate $λ_{L}$ due to electron-electron Coulomb interaction in graphene. $λ_{L}$ 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 $λ_{L}$ 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, $λ_{L}$ 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.

cond-mat.str-el↗

arXiv2018

Topological order in the pseudogap metal

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory, and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, non-perturbative version of the Luttinger theorem that holds in the Higgs phase.

cond-mat.str-el↗

arXiv2018

Nodeless superconductivity in type-II Dirac semimetal PdTe2: low-temperature London penetration depth and symmetry analysis

Superconducting gap structure was probed in type-II Dirac semimetal PdTe$_2$ 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 $λ(T=0)=230$~nm as the only fit parameter at a fixed $Δ(0)/T_c\approx 1.76$, 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 PdTe$_2$ 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.

cond-mat.supr-con↗

arXiv2018

Pseudogap and Fermi surface topology in the two-dimensional Hubbard model

One of the distinctive features of hole-doped cuprate superconductors is the onset of a `pseudogap' below a temperature $T^*$. Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is hole-like and that, for a broad range of parameters, its opening is concomitant with a Fermi surface topology change from electron- to hole-like. We identify a common link between these observations: the pole-like feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this pole-like feature, and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

cond-mat.str-el↗

arXiv2017

Limits on dynamically generated spin-orbit coupling: Absence of $l=1$ Pomeranchuk instabilities in metals

An ordered state in the spin sector that breaks parity without breaking time-reversal symmetry, i.e., that can be considered as dynamically generated spin-orbit coupling, was proposed to explain puzzling observations in a range of different systems. Here we derive severe restrictions for such a state that follow from a Ward identity related to spin conservation. It is shown that $l=1$ spin-Pomeranchuk instabilities are not possible in non-relativistic systems since the response of spin-current fluctuations is entirely incoherent and non-singular. This rules out relativistic spin-orbit coupling as an emergent low-energy phenomenon. We illustrate the exotic physical properties of the remaining higher angular momentum analogues of spin-orbit coupling and derive a geometric constraint for spin-orbit vectors in lattice systems.

cond-mat.str-el↗

arXiv2016

Selection rules for Cooper pairing in two-dimensional interfaces and sheets

Thin sheets deposited on a substrate and interfaces of correlated materials offer a plethora of routes towards the realization of exotic phases of matter. In these systems, inversion symmetry is broken which strongly affects the properties of possible instabilities -- in particular in the superconducting channel. By combining symmetry and energetic arguments, we derive general and experimentally accessible selection rules for Cooper instabilities in noncentrosymmetric systems which yield necessary and sufficient conditions for spontaneous time-reversal-symmetry breaking at the superconducting transition and constrain the orientation of the triplet vector. We discuss in detail the implications for various different materials. For instance, we conclude that the pairing state in thin layers of Sr$_2$RuO$_4$ must, as opposed to its bulk superconducting state, preserve time-reversal symmetry with its triplet vector being parallel to the plane of the system. All pairing states of this system allowed by the selection rules are predicted to display topological Majorana modes at dislocations or at the edge of the system. Applying our results to the LaAlO$_3$/SrTiO$_3$ heterostructures, we find that while the condensates of the (001) and (110) oriented interfaces must be time-reversal symmetric, spontaneous time-reversal-symmetry breaking can only occur for the less studied (111) interface. We also discuss the consequences for thin layers of URu$_2$Si$_2$ and UPt$_3$ as well as for single-layer FeSe. On a more general level, our considerations might serve as a design principle in the search for time-reversal-symmetry-breaking superconductivity in the absence of external magnetic fields.

cond-mat.supr-con↗

arXiv2016

Mechanism, time-reversal symmetry and topology of superconductivity in noncentrosymmetric systems

We analyze the possible interaction-induced superconducting instabilities in noncentrosymmetric systems based on symmetries of the normal state. It is proven that pure electron-phonon coupling will always lead to a fully gapped superconductor that does not break time-reversal symmetry and is topologically trivial. We show that topologically nontrivial behavior can be induced by magnetic doping without gapping out the resulting Kramers pair of Majorana edge modes. In case of superconductivity arising from the particle-hole fluctuations associated with a competing instability, the properties of the condensate crucially depend on the time-reversal behavior of the order parameter of the competing instability. When the order parameter preserves time-reversal symmetry, we obtain exactly the same properties as in case of phonons. If it is odd under time-reversal, the Cooper channel of the interaction will be fully repulsive leading to sign changes of the gap and making spontaneous time-reversal symmetry breaking possible. To discuss topological properties, we focus on fully gapped time-reversal symmetric superconductors and derive constraints on possible pairing states that yield necessary conditions for the emergence of topologically nontrivial superconductivity. These conditions might serve as a tool in the search for topological superconductors. We also discuss implications for oxides heterostructures and single-layer FeSe.

cond-mat.supr-con↗

arXiv2015

Pair breaking in multi-orbital superconductors: an application to oxide interfaces

We investigate the impact of impurity scattering on superconductivity in an anisotropic multi-orbital model with spin-orbit coupling which describes the electron fluid at two-dimensional oxide interfaces. As the pairing mechanism is under debate, both conventional and unconventional superconducting states are analyzed. We consider magnetic and nonmagnetic spin-dependent intra- and interorbital scattering and discuss possible microscopic realizations leading to these processes. It is found that, for magnetic disorder, the unconventional superconductor is protected against interband scattering and, thus, more robust than the conventional condensate. In case of nonmagnetic impurities, the conventional superconductor is protected as expected from the Anderson theorem and the critical scattering rate of the unconventional state is enhanced by a factor of four due to the spin-orbit coupling and anisotropic masses in oxide interfaces.

cond-mat.supr-con↗

arXiv2015

Pair breaking due to orbital magnetism in iron-based superconductors

We consider superconductivity in the presence of impurities in a two-band model suited for the description of iron-based superconductors. We analyze the effect of interband scattering processes on superconductivity, allowing for orbital, i.e., nonspin-magnetic but time-reversal symmetry-breaking impurities. Pair breaking in such systems is described by a nontrivial phase in an interband-scattering matrix element. We find that the transition temperature of conventional superconductors can be suppressed due to interband scattering, whereas unconventional superconductors may be unaffected. We also discuss the stability of density wave phases in the presence of impurities. As an example, we consider impurities associated with imaginary charge density waves that are of interest for iron-based superconductors.

cond-mat.supr-con↗

arXiv2014

Dimensional crossover and cold-atom realization of topological Mott insulators

We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this phase has remained elusive, our proposal shall help to shed some light on this exotic state of matter by paving the way for a controlled experimental investigation in optical lattices.

cond-mat.quant-gas↗

arXiv2014

Topological superconductivity and unconventional pairing in oxide interfaces

To pinpoint the microscopic mechanism for superconductivity has proven to be one of the most outstanding challenges in the physics of correlated quantum matter. Thus far, the most direct evidence for an electronic pairing mechanism is the observation of a new symmetry of the order-parameter, as done in the cuprate high-temperature superconductors. Like distinctions based on the symmetry of a locally defined order-parameter, global, topological invariants allow for a sharp discrimination between states of matter that cannot be transformed into each other adiabatically. Here we propose an unconventional pairing state for the electron fluid in two-dimensional oxide interfaces and establish a direct link to the emergence of nontrivial topological invariants. Topological superconductivity and Majorana edge states can then be used to detect the microscopic origin for superconductivity. In addition, we show that also the density wave states that compete with superconductivity sensitively depend on the nature of the pairing interaction. Our conclusion is based on the special role played by the spin-orbit coupling and the shape of the Fermi surface in SrTiO$_{3}$/LaAlO$_{3}$-interfaces and closely related systems.

cond-mat.supr-con↗

arXiv2013

Non-adiabatic processes in Majorana qubit systems

We investigate the non-adiabatic processes occurring during the manipulations of Majorana qubits in 1-D semiconducting wires with proximity induced superconductivity. Majorana qubits are usually protected by the excitation gap. Yet, manipulations performed at a finite pace can introduce both decoherence and renormalization effects. Though exponentially small for slow manipulations, these effects are important as they may constitute the ultimate decoherence mechanism. Moreover, as adiabatic topological manipulations fail to produce a universal set of quantum gates, non-adiabatic manipulations might be necessary to perform quantum computation.

cond-mat.mes-hall↗