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We investigate the propagation of electromagnetic waves through materials displaying a non-linear Hall effect. The coupled Maxwell-Boltzmann equations for traveling waves can be mapped onto ordinary differential equations that resemble those for the motion of a pendulum. In the weakly non-linear regime relevant for most experiments, we find that the polarization of light displays a Faraday-like precession of its polarization direction that swings back and forth around the direction of Berry dipole vector as the light beam traverses the material. This occurs concomitantly with an oscillation of its degree of polarization, with a characteristic frequency that increases linearly with the intensity of the traveling wave. These effects could be observed by measuring thickness dependent Faraday rotations as well as the emission of lower frequency radiation associated with the polarization oscillations in materials displaying the non-linear Hall effect., Comment: 8 pages (5 main and 3 supplementary) and 2 figures

Electron-phonon coupling (EPC) is foundational in condensed matter physics, determining intriguing phenomena and properties in both conventional and quantum materials. In this manuscript, we propose and demonstrate a novel two dimensional (2D) EPC spectroscopy which allows for direct extraction of EPC matrix elements. We find that two pronounced phonon modes of methylammonium lead iodide (MAPI) at room temperature exhibit highly distinctive EPC behaviors, both in strength, geometry, and temperature dependence across the phase transition. This demonstration indicates the potential of our novel 2D spectroscopy for studying the evolution of mode-resolved EPC at various external conditions and phonon-mediated light induced ultrafast control of condensed materials.

We re-examine the effect of long-range Coulomb interactions on the collective amplitude and phase modes in the incommensurate charge-density-wave ground state of quasi-one-dimensional conductors. Using an effective action approach we show that the longitudinal acoustic phonon protects the gapless linear dispersion of the lowest phase mode in the presence of long-range Coulomb interactions. Moreover, in Gaussian approximation, amplitude fluctuations are not affected by long-range Coulomb interactions. We also calculate the collective mode dispersions at finite temperatures and compare our results with the measured energies of amplitude and phase modes in K$_{0.3}$MoO$_3$. With the exception of the lowest phase mode, the temperature dependence of the measured mode energies can be quantitatively described within a multi-phonon Fr\"{o}hlich model for generic electron-phonon interactions neglecting long-range Coulomb interactions.

We study the transverse electrical conductivity and the corresponding magnetic noise of a two-dimensional U(1) spin liquid state with a spinon Fermi surface. We show that in the quasi-static regime these responses have the same wave-vector dependence as that of a metal but are reduced by a dimensionless pre-factor controlled by the ratio of orbital diamagnetic susceptibilities of the spinons and chargons, correcting previous work. We estimate that this quasi-static regime is comfortably accessed by the typical NV center splittings of a few GHz and estimate that the expected T1 times for an NV center placed above candidate materials, such as the organic dmit and ET salts, monolayer 1T-TaS2/Se2, would range from several tens to a few hundred milliseconds., Comment: 8 pages, 2 figures

We study the relaxation dynamics of driven, two-dimensional semiconductors, where itinerant electrons dress optically pumped excitons to form two Fermi-polaron branches. Repulsive polarons excited around zero momentum quickly decay to the attractive branch at high momentum. Collisions with electrons subsequently lead to a slower relaxation of attractive polarons, which accumulate at the edge of the light-cone around zero momentum where the radiative loss dominates. The bosonic nature of exciton polarons enables stimulated scattering, which results in a lasing transition at higher pump power. The latter is characterized by a superlinear increase of light emission as well as extended spatiotemporal coherence. As the coherent peak is at the edge of the light-cone and not at the center, the many-body dressing of excitons can reduce the linewidth below the limit set by the exciton nonradiative lifetime., Comment: 15 pages, 6 figures

We demonstrate a remarkable property of metallic Fermi liquids: the transverse conductivity assumes a universal value in the quasi-static ($\omega \rightarrow 0$) limit for wavevectors $q$ in the regime $l_{\rm mfp}^{-1} \ll q \ll p_{\rm F}$, where $l_{\rm mfp}$ is the mean free path and $p_{\rm F}$ is the Fermi momentum. This value is $(e^2/h) \mathcal{R}_{\rm FS}/q$ in two dimensions (2D), where $\mathcal{R}_{\rm FS}$ measures the local radius of curvature of the Fermi surface in momentum space. Even more surprisingly, we find that U(1) spin liquids with a spinon Fermi surface have the same universal transverse conductivity. This means such spin liquids behave effectively as metals in this regime, even though they appear insulating in standard transport experiments. Moreover, we show that transverse current fluctuations result in a universal low-frequency magnetic noise that can be directly probed by a spin qubit, such as a nitrogen-vacancy center in diamond, placed at a distance $z$ above of the 2D metal or spin liquid. Specifically the magnetic noise is given by $C\omega \mathcal{P}_{\rm FS}/z$, where $\mathcal{P}_{\rm FS}$ is the perimeter of the Fermi surface in momentum space and $C$ is a combination of fundamental constants of nature. Therefore these observables are controlled purely by the geometry of the Fermi surface and are independent of kinematic details of the quasi-particles, such as their effective mass and interactions. This behavior can be used as a new technique to measure the size of the Fermi surface of metals and as a smoking gun probe to pinpoint the presence of the elusive spinon Fermi surface in two-dimensional systems. We estimate that this universal regime is within reach of current nitrogen-vacancy center spectroscopic techniques for several spinon Fermi surface candidate materials., Comment: 34 pages, 9 figures

One-dimensional systems proximity-coupled to a superconductor can be driven into a topological superconducting phase by an external magnetic field. Here, we investigate the effect of vortices created by the magnetic field in a type-II superconductor providing the proximity effect. We identify different ways in which the topological protection of Majorana modes can be compromised and discuss strategies to circumvent these detrimental effects. Our findings are also relevant to topological phases of proximitized quantum Hall edge states., Comment: 8 pages,6 figures

Unlike classical fluids, a quantum Fermi liquid can support a long-lived and propagating shear sound wave at arbitrarily small wave vectors and frequencies, reminiscent of the transverse sound in crystals, despite lacking any form of long-range crystalline order. This mode is expected to be present in moderately interacting metals where the quasiparticle mass is renormalized to be more than twice the bare mass in two dimensions (2D), but it has remained undetected because it is hard to excite since it does not involve charge density fluctuations, in contrast to the conventional plasma mode. In this work we propose a strategy to excite and detect this unconventional mode in clean metallic channels. We show that the shear sound is responsible for the appearance of sharp dips in the ac conductance of narrow channels at resonant frequencies matching its dispersion. The liquid resonates while minimizing its dissipation in an analogous fashion to a sliding crystal. Ultra-clean 2D materials that can be tuned towards the Wigner crystallization transition such as silicon metal-oxide-semiconductor field-effect transistors, MgZnO/ZnO, p-GaAs, and AlAs quantum wells are promising platforms to experimentally discover the shear sound., Comment: 14 pages, 6 figures

Recently, topological superconductors based on Josephson junctions in two-dimensional electron gases with strong Rashba spin-orbit coupling have been proposed as attractive alternatives to wire-based setups. Here, we elucidate how phase-controlled Josephson junctions based on quantum wells with [001] growth direction and an arbitrary combination of Rashba and Dresselhaus spin-orbit coupling can also host Majorana bound states for a wide range of parameters as long as the magnetic field is oriented appropriately. Hence, Majorana bound states based on Josephson junctions can appear in a wide class of two-dimensional electron gases. We study the effect of spin-orbit coupling, the Zeeman energies, and the superconducting phase difference to create a full topological phase diagram and find the optimal stability region to observe Majorana bound states in narrow junctions. Surprisingly, for equal Rashba and Dresselhaus spin-orbit coupling, well localized Majorana bound states can appear only for phase differences $\phi\neq\pi$ as the topological gap protecting the Majorana bound states vanishes at $\phi=\pi$. Our results show that the ratio between Rashba and Dresselhaus spin-orbit coupling or the choice of the in-plane crystallographic axis along which the superconducting phase bias is applied offer additional tunable knobs to test Majorana bound states in these systems. Finally, we discuss signatures of Majorana bound states that could be probed experimentally by tunneling conductance measurements at the edge of the junction., Comment: 21 pages, 12 figures

Topological superconductors can support localized Majorana states at their boundaries. These quasi-particle excitations have non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner. While 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 scalable to large numbers of states. Here we present a novel experimental approach towards a two-dimensional architecture. Using a Josephson junction made of HgTe quantum well coupled to thin-film aluminum, we are able to tune between a trivial and a topological superconducting state by controlling the phase difference $\phi$ across the junction and applying an in-plane magnetic field. We determine the topological state of the induced superconductor by measuring the tunneling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunneling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunneling conductance develops a zero-bias peak which persists over a range of $\phi$ that expands systematically with increasing magnetic fields. 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 will therefore open new avenues for probing topological superconducting phases in two-dimensional systems., Comment: Supplementary contains resized figures. Original files are available upon request

With the discovery of Majorana quasiparticles in semiconductor-superconductor hybrid structures, topologically protected qubits have emerged as a promising contender for quantum information processing. While the construction of a universal quantum computer with topological protection likely requires significant advances in materials science, intermediate-scale devices are nearly within the reach of current technology. As a near-term milestone for topological qubits, we propose a network of topological superconductors as a simulator of a large variety of quantum spin systems, including those with frustration. Our proposal is founded on existing technology, combining advantages of semiconducting and superconducting qubits. We identify local measurement protocols that give access to information about ground and excited states as well as dynamic correlations. The topological protection of the qubits results in longer coherence times, and relaxation to the groundstate can be controlled by coupling the network an external bath. We conclude by pointing out specific applications of the quantum simulator, e.g., spin liquids, quantum criticality, and thermalization., Comment: 27 pages, 10 figures

Mobile quantum impurities interacting with a fermionic bath form quasiparticles known as Fermi polarons. We demonstrate that a force applied to the bath particles can generate a drag force of similar magnitude acting on the impurities, realizing a novel, nonperturbative Coulomb drag effect. To prove this, we calculate the fully self-consistent, frequency-dependent transconductivity at zero temperature in the Baym-Kadanoff conserving approximation. We apply our theory to excitons and exciton polaritons interacting with a bath of charge carriers in a doped semiconductor embedded in a microcavity. In external electric and magnetic fields, the drag effect enables electrical control of excitons and may pave the way for the implementation of gauge fields for excitons and polaritons. Moreover, a reciprocal effect may facilitate optical manipulation of electron transport. Our findings establish transport measurements as a novel, powerful tool for probing the many-body physics of mobile quantum impurities., Comment: 18 + 11 pages, 4 figures

In the half-filled zero-energy Landau level of bilayer graphene, competing phases with spontaneously broken symmetries and an intriguing quantum critical behavior have been predicted. Here we investigate signatures of these broken-symmetry phases in thermal transport measurements. To this end we calculate the spectrum of spin and valley waves in the $\nu=0$ quantum Hall state of bilayer graphene. The presence of Goldstone modes enables heat transport even at low temperatures, which can serve as compelling evidence for spontaneous symmetry breaking. By varying external electric and magnetic fields it is possible to determine the nature of the symmetry breaking and temperature-dependent measurements may yield additional information about gapped modes., Comment: 5 pages, 3 figures, plus supplementary material

We consider a two-dimensional electron gas with strong spin-orbit coupling contacted by two superconducting leads, forming a Josephson junction. We show that in the presence of an in-plane Zeeman field the quasi-one-dimensional region between the two superconductors can support a topological superconducting phase hosting Majorana bound states at its ends. We study the phase diagram of the system as a function of the Zeeman field and the phase difference between the two superconductors (treated as an externally controlled parameter). Remarkably, at a phase difference of $\pi$, the topological phase is obtained for almost any value of the Zeeman field and chemical potential. In a setup where the phase is not controlled externally, we find that the system undergoes a first-order topological phase transition when the Zeeman field is varied. At the transition, the phase difference in the ground state changes abruptly from a value close to zero, at which the system is trivial, to a value close to $\pi$, at which the system is topological. The critical current through the junction exhibits a sharp minimum at the critical Zeeman field, and is therefore a natural diagnostic of the transition. We point out that in presence of a symmetry under a modified mirror reflection followed by time reversal, the system belongs to a higher symmetry class and the phase diagram as a function of the phase difference and the Zeeman field becomes richer.

Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the $4\pi$-periodic $dc$ Josephson effect predicted for topological Josephson junctions. Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching current measurements., Comment: 25 pages, 13 figures. Accepted by Phys. Rev. B

A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] provides evidence for Majorana zero modes in iron (Fe) chains on the superconducting Pb(110) surface. Here, we study this system by scanning tunneling microscopy using superconducting tips. This high-resolution technique resolves a rich subgap structure, including zero-energy excitations in some chains. We compare the symmetry properties of the data under voltage reversal against theoretical expectations and provide evidence that the putative Majorana signature overlaps with a previously unresolved low-energy resonance. Interpreting the data within a Majorana framework suggests that the topological gap is significantly smaller than previously believed. Aided by model calculations, we also analyze higher-energy features of the subgap spectrum and their relation to high-bias peaks which we associate with the Fe d-bands., Comment: 5+5 pages, 5+6 figures

Experimental evidence for Majorana bound states largely relies on measurements of the tunneling conductance. While the conductance into a Majorana state is in principle quantized to $2e^2/h$, observation of this quantization has been elusive, presumably due to temperature broadening in the normal-metal lead. Here, we propose to use a superconducting lead instead, whose gap strongly suppresses thermal excitations. For a wide range of tunneling strengths and temperatures, a Majorana state is then signaled by symmetric conductance peaks at $eV=\pm\Delta$ with quantized height $G=(4-\pi)2e^2/h$. For a superconducting scanning tunneling microscope tip, Majorana states appear as spatial conductance plateaus while the conductance varies with the local wavefunction for trivial Andreev bound states. We discuss effects of nonresonant (bulk) Andreev reflections and quasiparticle poisoning., Comment: 5 pages, 2 figures plus supplementary material, v2: minor refinements, published version

We combine scanning-tunneling-spectroscopy experiments probing magnetic impurities on a superconducting surface with a theoretical analysis of the tunneling processes between (superconducting) tip and substrate. We show that the current is carried by single-electron tunneling at large tip-substrate distances and Andreev reflections at smaller distances. The single-electron current requires relaxation processes between the impurity-induced Shiba bound state and the quasiparticle continuum, allowing us to extract information on such relaxation processes from our analysis., Comment: 4+ pages, 3 figures; supplementary material: 18 pages, 9 figures

Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the nonabelian Berry phase. We show that these errors can be eliminated by suitably designed counterdiabatic correction terms in the Hamiltonian. We implement the resulting shortcuts to adiabaticity for simple protocols of nonabelian braiding and show that the error suppression can be substantial even for approximate realizations of the counterdiabatic terms., Comment: 5 pages, 3 figures plus supplementary material

A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] gives possible evidence for Majorana bound states in chains of magnetic adatoms placed on a superconductor. While many features of the observed end states are naturally interpreted in terms of Majoranas, their strong localization remained puzzling. We consider a linear chain of Anderson impurities on a superconductor as a minimal model and treat it largely analytically within mean-field theory. We explore the phase diagram, the subgap excitation spectrum, and the Majorana wavefunctions. Owing to a strong velocity renormalization, the latter are localized on a scale which is parametrically small compared to the coherence length of the host superconductor., Comment: to appear in PRL; includes new heuristic section; 5 pages + supplementary material

Chains of magnetic impurities placed on a superconducting substrate and forming helical spin order provide a promising venue for realizing a topological superconducting phase. An effective tight-binding description of such helical Shiba chains involves long-range (power-law) hopping and pairing amplitudes which induce an unconventional topological critical point. At the critical point, we find exponentially localized Majorana bound states with a short localization length unrelated to a topological gap. Away from the critical point, this exponential decay develops a power-law tail. Our analytical results have encouraging implications for experiment., Comment: 4+ pages, 2 figures, plus supplementary material, v3: added references and minor refinements; published version

Recently, it has been suggested that topological superconductivity and Majorana end states can be realized in a chain of magnetic impurities on the surface of an s-wave superconductor when the magnetic moments form a spin helix as a result of the RKKY interaction mediated by the superconducting substrate. Here, we investigate this scenario theoretically by developing a tight-binding Bogoliubov-de Gennes description starting from the Shiba bound states induced by the individual magnetic impurities. While the resulting model Hamiltonian has similarities with the Kitaev model for one-dimensional spinless p-wave superconductors, there are also important differences, most notably the long-range nature of hopping and pairing as well as the complex hopping amplitudes. We use both analytical and numerical approaches to explore the consequences of these differences for the phase diagram and the localization properties of the Majorana end states when the Shiba chain is in a topological superconducting phase., Comment: 14 pages, 9 figures, minor changes, references added; published version

A prominent signature of Majorana bound states is the exotic Josephson effects they produce, the classic example being a fractional Josephson current with 4\pi periodicity in the phase difference across the junction. Recent work established that topological insulator edges support a novel `magneto-Josephson effect', whereby a dissipationless current exhibits 4\pi-periodic dependence also on the relative orientation of the Zeeman fields in the two banks of the junction. Here, we explore the magneto-Josephson effect in junctions based on spin-orbit coupled quantum wires. In contrast to the topological insulator case, the periodicities of the magneto-Josephson effect no longer follow from an exact superconductor-magnetism duality of the Hamiltonian. We employ numerical calculations as well as analytical arguments to identify the domain configurations that display exotic Josephson physics for quantum-wire junctions, and elucidate the characteristic differences with the corresponding setups for topological insulators edges. To provide guidance to experiments, we also estimate the magnitude of the magneto-Josephson effects in realistic parameter regimes, and compare the Majorana-related contribution to the coexisting 2\pi-periodic effects emerging from non-Majorana states., Comment: 8+ pages, 8 figures, minor changes, figures added; published version

We investigate Josephson currents in mesoscopic rings with a weak link which are in or near a topological superconducting phase. As a paradigmatic example, we consider the Kitaev model of a spinless p-wave superconductor in one dimension, emphasizing how this model emerges from more realistic settings based on semiconductor nanowires. We show that the flux periodicity of the Josephson current provides signatures of the topological phase transition and the emergence of Majorana fermions situated on both sides of the weak link even when fermion parity is not a good quantum number. In large rings, the Majorana fermions hybridize only across the weak link. In this case, the Josephson current is h/e periodic in the flux threading the loop when fermion parity is a good quantum number but reverts to the more conventional h/2e periodicity in the presence of fermion-parity changing relaxation processes. In mesoscopic rings, the Majorana fermions also hybridize through their overlap in the interior of the superconducting ring. We find that in the topological superconducting phase, this gives rise to an h/e-periodic contribution even when fermion parity is not conserved and that this contribution exhibits a peak near the topological phase transition. This signature of the topological phase transition is robust to the effects of disorder. As a byproduct, we find that close to the topological phase transition, disorder drives the system deeper into the topological phase. This is in stark contrast to the known behavior far from the phase transition, where disorder tends to suppress the topological phase., Comment: 14 pages, 9 figures, minor changes in the text, published version

A recent experiment [Mourik et al., Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and the formation of Majorana bound states. Motivated by this experiment, we consider the signature of Majorana bound states in the differential tunneling conductance of multi-subband wires. We show that the weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of subbands, when disorder is added to the end of the quantum wire. We also consider how the topological phase transition is reflected in the gap structure of the current-voltage characteristic., Comment: 4+ pages, 5 figures, minor changes in the text and Fig. 5, references added; published version