Mathias S. Scheurer

Topological superconductivity and unconventional pairing in oxide interfaces

Pinpointing 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. Alternatively, 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 non-trivial topological invariants. Topological signatures, in particular Majorana edge states, can then be used to detect the microscopic origin of superconductivity. In addition, we show that also the density wave states that compete with superconductivity sensitively depend on the nature of the pairing interaction.

Nonadiabatic 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.

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 Sr2RuO4 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 triplet 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 LaAlO3/SrTiO3 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 URu2Si2 and UPt3 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.Quantum physics: new rules for superconductivity behaviorsThin sheets represent an important materials source for the realization of exotic electronic states. A noteworthy example is the noncentrosymmetric two-dimensional (2D) superconductor whose broken inversion symmetry is known to have an impact on the superconducting behaviors, such as Cooper instabilities. Now Mathias S. Scheurer at Karlsruhe Institute of Technology in Germany and his colleagues from Germany and USA derive general selection rules for Cooper instabilities in such 2D systems by considering both symmetry and energetic factors. These rules are proved to have wider implications for various materials, such as thin layers of Sr2RuO4, URu2Si2 and UPt3, LaAlO3/SrTiO3 heterostructures, and single FeSe layer. Importantly, the principles could serve as a fundamental guideline in the search for superconductivity with missing time reversal symmetry (TRS) in the absence of external magnetic fields.

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 the 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 the 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 oxide heterostructures and single-layer FeSe.

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.

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

Pair breaking in multiorbital superconductors: An application to oxide interfaces

l=1

Anomalous quantum criticality in an itinerant ferromagnet

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.

Dimensional crossover and cold-atom realization of topological Mott insulators

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.

Hierarchy of information scrambling, thermalization, and hydrodynamic flow in graphene

The dynamics of continuous phase transitions is governed by the dynamic scaling exponent relating the correlation length and correlation time. For transitions at finite temperature, thermodynamic critical properties are independent of the dynamic scaling exponent. In contrast, at quantum phase transitions where the transition temperature becomes zero, static and dynamic properties are inherently entangled by virtue of the uncertainty principle. Consequently, thermodynamic scaling equations explicitly contain the dynamic exponent. Here we report on thermodynamic measurements (as a function of temperature and magnetic field) for the itinerant ferromagnet Sr1-xCaxRuO3 where the transition temperature becomes zero for x=0.7. We find dynamic scaling of the magnetization and specific heat with highly unusual quantum critical dynamics. We observe a small dynamic scaling exponent of 1.76 strongly deviating from current models of ferromagnetic quantum criticality and likely being governed by strong disorder in conjunction with strong electron-electron coupling.