Topological materials

Topological materials

One of the major achievements in condensed matter over the past decades is the observation and protection of topological orders. These phases are not described in terms of symmetry breaking and associated local order parameters but rather by global topological invariants. Although the quantized transverse conductance of quantum Hall states has been known for decades, it was realized that new kinds of topological order can occur in the presence of certain symmetries leading to new types of edge states and excitations in the bulk as well as of defects.

The above developments are, however, just the beginning and are supplemented by many new questions. These entail, for example, the search for new topological materials by the abundance or new combinations of symmetries. Also links to other disciplines such as magnetically ordered systems and systems out of equilibrium provide for a new playing field to discover new symmetry protected orders. Over the past few years it has became evident that the notion of topological phases of matter is not limited to non-interacting systems as they can also be found inside exotic broken symmetry phases in various strongly correlated materials.

Our research is aimed at unveiling the confluence of competing orders, emergent topology and strain engineering in various strong spin-orbit coupled correlated metals. For more details on current and recent research highlights see the collection below.

Topological superconductivity in a phase-controlled Josephson junction
H. Ren, F. Pientka, S. Hart, A. T. Pierce, M. Kosowsky, L. Lunczer, R. Schlereth, B. Scharf, E. M. Hankiewicz, L. W. Molenkamp, B. I. Halperin, and A. Yacoby

Topological superconductors can support localized Majorana states at their boundaries1,2,3,4,5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8,9,10,11,12,13,14,15,16,17,18,19,20,21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

Nature 569, 93 (2019)

Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality
Bitan Roy, Robert-Jan Slager, Vladimir Juricic

Weyl semimetals are exotic materials in which electrons behave more like photons-massless particles moving at a relativistic speed. These semimetals could also lead to devices with unusual electronic and optical properties, such as a "superlens" that can improve the spatial resolution of a scanning tunneling microscope. However, it is unclear how well Weyl semimetals hold on to their bizarre properties in real disordered materials that are littered with impurities. Here, we calculate the impact of randomness on Weyl semimetals. We find that for small amounts of disorder such gapless topological semiconductors are stable, but at intermediate disorder these systems can undergo a quantum phase transition into a metallic phase, where electrons cease to behave as relativistic particles.

Intriguingly, we discover that the nature of this continuous transition is insensitive to the many (if not all) details of impurities, a phenomenon commonly referred to as superuniversality, which leaves its signature on the behavior of various observables, such as specific heat and electrical conductivity. While this concept has been discussed previously in the context of two-dimensional quantum Hall states and one-dimensional disordered quantum wires, here, we present its incarnation in three-dimensional disordered topological materials. These features combined with several other known transitions constitute the global phase diagram of disordered Weyl systems.

Our proposed stability of moderately disordered Weyl systems should encourage practical applicability of such systems in devices, while the global phase diagram should open new research frontiers exploring the arena of disordered topological phases of matter.

Phys. Rev. X 8, 031076 (2018)

Quantum oscillations in insulators with neutral Fermi surfaces
I. Sodemann, D. Chowdhury, T. Senthil

We develop a theory of quantum oscillations in insulators with an emergent Fermi sea of neutral fermions minimally coupled to an emergent U(1) gauge field. As pointed out by Motrunich [Phys. Rev. B 73, 155115 (2006)], in the presence of a physical magnetic field the emergent magnetic field develops a nonzero value leading to Landau quantization for the neutral fermions. We focus on the magnetic field and temperature dependence of the analog of the de Haas-van Alphen effect in two and three dimensions. At temperatures above the effective cyclotron energy, the magnetization oscillations behave similarly to those of an ordinary metal, albeit in a field of a strength that differs from the physical magnetic field. At low temperatures, the oscillations evolve into a series of phase transitions. We provide analytical expressions for the amplitude and period of the oscillations in both of these regimes and simple extrapolations that capture well their crossover. We also describe oscillations in the electrical resistivity of these systems that are expected to be superimposed with the activated temperature behavior characteristic of their insulating nature and discuss suitable experimental conditions for the observation of these effects in mixed-valence insulators and triangular lattice organic materials.

Phys. Rev. B 97, 045152 (2018)

Non-perturbative terahertz high-harmonic generation in the three- dimensional Dirac semimetal Cd3As2
S. Kovalev, R. M. A. Dantas, S. Germanskiy, J.-C. Deinert, B. Green, I. Ilyakov, N. Awari, M. Chen, M. Bawatna, J. Ling, F. Xiu, P. H. M. van Loosdrecht, P. Surówka, T. Oka, Z. Wang

Harmonic generation is a general characteristic of driven nonlinear systems, and serves as an efficient tool for investigating the fundamental principles that govern the ultrafast nonlinear dynamics. Here, we report on terahertz-field driven high-harmonic generation in the three- dimensional Dirac semimetal Cd3As2 at room temperature. Excited by linearly-polarized multi-cycle terahertz pulses, the third-, fifth-, and seventh-order harmonic generation is very efficient and detected via time-resolved spectroscopic techniques. The observed harmonic radiation is further studied as a function of pump-pulse fluence. Their fluence dependence is found to deviate evidently from the expected power-law dependence in the perturbative regime. The observed highly non-perturbative behavior is reproduced based on our analysis of the intraband kinetics of the terahertz-field driven nonequilibrium state using the Boltzmann transport theory. Our results indicate that the driven nonlinear kinetics of the Dirac electrons plays the central role for the observed highly nonlinear response.

Nat. Commun. 11, 2451 (2020)

Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials
Bitan Roy and Vladimir Juricic

Dirac fermions are realized as low-energy excitations in a wide class of condensed matter systems, nowadays known as the Dirac materials, with two-dimensional graphene and surface states of topological insulators being their paradigmatic representatives. Due to linearly dispersing quasiparticles, the Dirac materials are rather stable against weak local interactions, such as the onsite Hubbard repulsion. However, at strong interactions, they may undergo quantum phase transitions through a critical point, succinctly described by an effective Gross-Neveu- Yukawa (GNY) type field theory. Depending on the relative strength among finite range Coulomb interactions the ordered phase may represent either spin- or charge-density-wave. The question then arises what may be the possible experimental imprints of such a quantum phase transition in terms of observables. Researcher from MPIPKS (BR) in collaboration with Nordita (Vladimir Juricic) recently showed that the frequency-dependent electrical conductivity at both zero and finite temperature gets suppressed in the close vicinity to such critical point in comparison to its counterpart in a noninteracting system. Such peculiar, but universal behavior stems from strong interactions among wildly fluctuating gapless fermionic and bosonic order-parameter excitations inside the quantum critical regime, occupied by a relativistic non-Fermi liquid. These results should motivate future investigations of quantum critical transport in Dirac materials in numerical simulations and (possibly) using gauge-gravity duality.

Phys. Rev. Lett. 121, 137601 (2018)