Broken Inversion Research Articles

Superconducting diode effect under time-reversal symmetry.

In noncentrosymmetric superconductors, superconducting and normal conductions can interchange on the basis of the current flow direction. This effect is termed a superconducting diode effect (SDE), which is a focal point of recent research. The broken inversion and time-reversal symmetry is believed to be the requirements of SDE, but their intrinsic role has remained elusive. Here, we report strain-controlled SDEs in a layered trigonal superconductor, PbTaSe2. The SDE was found exclusively in a strained device with its absence in an unstrained device despite that it is allowed in unstrained trigonal structure. Moreover, the zero-field or magnetic field-even (magnetic field-odd) SDE is observed when the strain and current are along armchair (zigzag) direction The results unambiguously demonstrate the intrinsic SDE under time-reversal symmetry and the critical role of strain-induced electric polarization.

Interaction-driven first-order and higher-order topological superconductivity

We investigate topological superconductivity in the Rashba-Hubbard model, describing heavy-atom superlattice and van der Waals materials with broken inversion. We focus in particular on fillings close to the van Hove singularities, where a large density of states enhances the superconducting transition temperature. To determine the topology of the superconducting gaps and to analyze the stability of their surface states in the presence of disorder and residual interactions, we employ an fRG+MFT approach, which combines the unbiased functional renormalization group (fRG) with a real-space mean-field theory (MFT). Our approach uncovers a cascade of topological superconducting states, including A1 and B1 pairings, whose wave functions are of dominant p- and d-wave character, respectively, as well as a time-reversal breaking A1+iB1 pairing. While the A1 and B1 states have first-order topology with helical and flat-band Majorana edge states, respectively, the A1+iB1 pairing exhibits second-order topology with Majorana corner modes. We investigate the disorder stability of the bulk superconducting states, analyze interaction-induced instabilities of the edge states, and discuss implications for experimental systems. Published by the American Physical Society 2024

Hidden Valley Polarization, Piezoelectricity, and Dzyaloshinskii-Moriya Interactions of Janus Vanadium Dichalcogenides.

Due to the lack of inversion symmetry and the discovery of room-temperature ferromagnetism, two-dimensional semiconducting vanadium-based van der Waals transition-metal dichalcogenides (V-TMDs) are drawing attention for their possible application in spintronics and valleytronics. Here, we show the functional properties enriched by the broken inversion, out-of-plane mirror, and time-reversal symmetries of Janus H-VXY TMDs (X, Y = S, Se, Te). By first-principles calculations, we reveal the intrinsic xy easy-plane magnetism of the Janus vanadium-based TMD monolayers and systematically study their hidden valley polarization and giant magneto band structure. Their strong nearest-neighbor exchange strengths lead to near-room-temperature magnetic phase transitions. The Janus H-VXY system also exhibits piezoelectricity with nonzero e31 and e21. Interestingly, it is found that the right-handed Dzyaloshinskii-Moriya interaction has nonzero in-plane components in our Janus system, with fluctuating magnitudes determined by competence between relaxed bond-angle and atomic index of ligands.

Chiral filtration and Faraday rotation in multi-Weyl semimetals

The Maxwell equations in Weyl semimetals (WSMs) with broken inversion and time-reversal symmetries are modified by the presence of the axion terms b and b0 where, for a simple two-node model, 2ℏb is the vector that connects the two nodes in momentum space and 2ℏb0 is energy separation between the two Dirac points. As is well known, this modification leads to some unique optical properties such as non-reciprocal propagation, dichroism, birefringence and Faraday rotation. In this paper, we study numerically how these properties depend on the various parameters that characterize the WSM such as doping, axion terms, width, scattering time τ for intraband processes and background dielectric constant. More specifically, we study how the wave propagation, transmission coefficient and Faraday rotation depend on these parameters. For example, the threshold frequency ωthr=2eF/ℏ for interband transitions (with eF the Fermi level) can be split in two when b0 is finite. When intraband transitions are considered and b=0, the left (LCP) and right (RCP) circularly polarized lights are evanescent below the intraband plasmon frequency ωp<ωthr but can propagate with almost no attenuation in the frequency range ω∈ωp,ωth. Attenuation becomes really important when τ<1 ps. A finite b leads to different refractive indices for the RCP and LCP wave and controls the frequency ranges ω∈ω+,ωth (for RCP) and ω∈ω−,ωth (for LCP) where they can propagate without dissipation. Below ω+, both waves are evanescent since ω+<ω−. For light propagating along b, we find that ω+ω− decreases (increases) with b. In the thin-film limit, the Faraday rotation angle due to b is directly proportional to the width d of the WSM and to the Chern number n of the Weyl nodes. This linear behavior breaks down for d≳500μm. When d becomes larger than the wavelength λ+λ− of the RCP(LCP) wave inside the WSM, oscillations in the transmission coefficient appear whose shape and amplitude depends on the frequency range considered. Perfect transmission is possible when the quantization condition d=mλ±/2 is satisfied. One can control these oscillations by inserting the WSM between two dielectrics.

Electronic, spintronic, and piezoelectric properties of new Janus ZnAXY ( A=Si,Ge,Sn , and X,Y=S,Se,Te ) monolayers

Two-dimensional (2D) Janus materials due to their asymmetric structures show fascinating spintronic and piezoelectric properties making them a research hot spot in recent years. In this work, inspired by Janus group-III monochalcogenides, we propose $\mathrm{Zn}AXY$ ($A=\mathrm{Si}$, Ge, Sn, and $X/Y=\mathrm{S}$, Se, Te, $X&lt;Y$) monolayers as a novel structure with broken inversion and mirror symmetry. By calculating cohesive energy and phonon dispersion, eight of nine possible $\mathrm{Zn}AXY$ monolayers are proved to be dynamically stable. In addition, thermal stability of these eight structures is confirmed by ab initio molecular dynamics simulations. The electronic band structures of $\mathrm{Zn}AXY$ monolayers indicate that all of them are indirect semiconductors with strong spin-orbit coupling effects. Lack of inversion symmetry gives rise to Zeeman-type spin splitting at the $K$ point of the conduction band with the highest value of 136 meV for ZnSiSeTe. Furthermore, out-of-plane asymmetry results in Rashba spin splitting (RSS) at the \ensuremath{\Gamma} point of the valence and conduction bands in the most compositions of Janus $\mathrm{Zn}AXY$ monolayers. Among them, ZnGeSTe with ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{V}}$ of $1.79\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ and ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{c}}$ of $0.862\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ and ZnSiSTe with ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{V}}$ of $1.537\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ and ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{c}}$ of $0.756\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ are found to be great materials for future spintronic applications. Interestingly, in addition to large RSS, Mexican hat dispersion is observed at the \ensuremath{\Gamma} point of the topmost valence band in these materials. Moreover, the calculated elastic coefficients for the hexagonal $\mathrm{Zn}AXY$ monolayers confirm the mechanical stability of the predicted structures. Finally, Janus $\mathrm{Zn}AXY$ monolayers possess high in-plane (up to 7.46 pm/V) and out-of-plane (up to 0.67 pm/V) piezoelectric coefficients making them appealing alternatives for prevalent piezoelectric materials.

Magneto-optical Kerr effect in Weyl semimetals with broken inversion and time-reversal symmetries

The topological nature of the band structure of a Weyl semimetal leads to a number of unique transport and optical properties. For example, the description of the propagation of an electromagnetic wave in a Weyl semimetal with broken time-reversal and inversion symmetry, for example, requires a modification of the Maxwell equations by the axion field $\theta \left( \mathbf{r},t\right) =2\mathbf{b}\cdot \mathbf{r}-2b_{0}t,$ where $2% \mathbf{b}$ is the separation in wave vector space between two Weyl nodes of opposite chiralities and $2\hslash b_{0}$ is their separation in energy. In this paper, we study theoretically how the axion terms $b_{0}$ and $\bf{b}$ modify the frequency behavior of the Kerr rotation and ellipticity angles $\theta_{K}\left( \omega \right) $ and $\psi_{K}\left( \omega \right) $ in a Weyl semimetal. Both the Faraday and Voigt configurations are considered since they provide different information on the electronic transitions and plasmon excitation. We derive the Kerr angles firstly without an external magnetic field where the rotation of the polarization is only due to the axion terms and secondly in a strong magnetic field where these terms compete with the gyration effect of the magnetic field. In this latter case, we concentrate on the ultra-quantum limit where the Fermi level lies in the chiral Landau level and the Kerr and ellipticity angles have more complex frequency and magnetic field behaviors.

Quantum Linear Magnetoresistance and Nontrivial Berry Phase in High‐Mobility Elemental Tellurium

AbstractElemental Tellurium (Te) is an important p‐type semiconductor with wide practical applications. It is currently of great interest as a chiral crystal with broken inversion and mirror symmetries, and its topological nature is under active discussion. Here the Shubnikov–de Haas (SdH) oscillations with a nontrivial π Berry phase and the quantum linear magnetoresistance (MR) in as‐synthesized high‐mobility Te single crystals are reported. The vapor transport grown Te shows a hollow hexagonal prism structure with tunable carrier density and high mobility of about 1000 cm2 V−1 s−1 at low temperature. For concentration p &gt; 1017 cm−3, the conspicuous SdH oscillations map out the dumbbell‐shaped Fermi surface and the long‐standing peculiar amplitude change with varying magnetic field orientation is explained by careful quantitative analyses. Pulsed magnetic field measurements up to 57 T disclose a quantum linear MR beyond the quantum limit and the Landau fan diagram clearly reveals a topologically nontrivial π Berry phase. This work paves way for the synthesis of high‐mobility Te structures and sheds light onto the intrinsic nontrivial topology of the attractive elemental substance.

Strain engineering of electronic properties and anomalous valley hall conductivity of transition metal dichalcogenide nanoribbons

Strain engineering is a powerful technique for tuning electronic properties and valley degree of freedom in honeycomb structure of two-dimensional crystals. Carriers in + k and − k (opposite Berry curvature) in transition metal dichalcogenide (TMD) with broken inversion symmetry act as effective magnetic fields, where this polarized valleys are suitable for encoding information. In this work, we study the strained TMD nanoribbons by Slater-Koster tight-binding model, which acquires electronic bands in whole Brillouin zone. From this, we derive a generic profile of strain effect on the electronic band structure of TMD nanoribbons, which shows indirect band gap, and also exhibits a phase transition from semiconductor to metallic by applying uniaxial X-tensile and Y-arc type of strain. Midgap states in strained TMD nanoribbons are determined by calculation of localized density of electron states. Moreover, our findings of anomalous valley Hall conductivity reveal that the creation of pseudogauge fields using strained TMD nanoribbons affect the Dirac electrons, which generate the new quantized Landau level. Furthermore, we demonstrate in strained TMD nanoribbons that strain field can effectively tune both the magnitude and sign of valley Hall conductivity. Our work elucidates the valley Hall transport in strained TMDs due to pseudo-electric and pseudo-magnetic filed will be applicable as information carries for future electronics and valleytronics.

Giant second harmonic transport under time-reversal symmetry in a trigonal superconductor

Nonreciprocal or even-order nonlinear responses in symmetry-broken systems are powerful probes of emergent properties in quantum materials, including superconductors, magnets, and topological materials. Recently, vortex matter has been recognized as a key ingredient of giant nonlinear responses in superconductors with broken inversion symmetry. However, nonlinear effects have been probed as excess voltage only under broken time-reversal symmetry. In this study, we report second harmonic transport under time-reversal symmetry in the noncentrosymmetric trigonal superconductor PbTaSe2. The magnitude of anomalous nonlinear transport is two orders of magnitude larger than those in the normal state, and the directional dependence of nonlinear signals are fully consistent with crystal symmetry. The enhanced nonlinearity is semiquantitatively explained by the asymmetric Hall effect of vortex-antivortex string pairs in noncentrosymmetric systems. This study enriches the literature on nonlinear phenomena by elucidating quantum transport in noncentrosymmetric superconductors.

Antiferroelectric negative capacitance from a structural phase transition in zirconia

Crystalline materials with broken inversion symmetry can exhibit a spontaneous electric polarization, which originates from a microscopic electric dipole moment. Long-range polar or anti-polar order of such permanent dipoles gives rise to ferroelectricity or antiferroelectricity, respectively. However, the recently discovered antiferroelectrics of fluorite structure (HfO2 and ZrO2) are different: A non-polar phase transforms into a polar phase by spontaneous inversion symmetry breaking upon the application of an electric field. Here, we show that this structural transition in antiferroelectric ZrO2 gives rise to a negative capacitance, which is promising for overcoming the fundamental limits of energy efficiency in electronics. Our findings provide insight into the thermodynamically forbidden region of the antiferroelectric transition in ZrO2 and extend the concept of negative capacitance beyond ferroelectricity. This shows that negative capacitance is a more general phenomenon than previously thought and can be expected in a much broader range of materials exhibiting structural phase transitions.

Giant valley-polarized spin splittings in magnetized Janus Pt dichalcogenides

We reveal giant proximity-induced magnetism and valley-polarization effects in Janus Pt dichalcogenides (such as SPtSe), when bound to the Europium oxide (EuO) substrate. Using first-principles simulations, it is surprisingly found that the charge redistribution, resulting from proximity with EuO, leads to the formation of two K and K$^{'}$valleys in the conduction bands. Each of these valleys displays its own spin polarization and a specific spin-texture dictated by broken inversion and time-reversal symmetries, and valley-exchange and Rashba splittings as large as hundreds of meV. This provides a platform for exploring novel spin-valley physics in low-dimensional semiconductors, with potential spin transport mechanisms such as spin-orbit torques much more resilient to disorder and temperature effects.

Effects of Bi&lt;sub&gt;2&lt;/sub&gt;Te&lt;sub&gt;3&lt;/sub&gt;(111) and Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;(0001) substrates on electronic and topological properties of Bi(111) bilayer

The bilayer and thin films of Bi(111) have demonstrated novel topological properties. Here, we investigate the electronic structures of Bi/Bi&lt;sub&gt;2&lt;/sub&gt;Te&lt;sub&gt;3&lt;/sub&gt;(111) and Bi/Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;(0001) by combining first-principles and tight-binding approximation calculations. Our results show that the Bi(111) bilayer is a semiconductor with a gap of about 0.2 eV. Its electronic states are strongly disturbed by the interaction with Bi&lt;sub&gt;2&lt;/sub&gt;Te&lt;sub&gt;3&lt;/sub&gt;(111) thin films, no matter whether the substrate has a band gap or Dirac surface state. Moreover, it is hard to see Rashba-type band splittings in such systems. In contrast, it demonstrates clean and giant Rashba-type splittings as strongly hybridized with insulating Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;(0001), which is due to the broken inversion symmetry induced by interfacing and the strong atomic spin-orbit coupling in Bi. Our tight-binding approximation analyses further reveal that the effect of substrate Al&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;3&lt;/sub&gt;(0001) on the band structure of the Bi(111) bilayer is equivalent to the action of external electric field in a range between 0.5 and 0.6 V/Å. Moreover, we find that the strong hybridization between Bi(111) bilayer and the electronic state of the substrate Bi&lt;sub&gt;2&lt;/sub&gt;Te&lt;sub&gt;3&lt;/sub&gt;(111) can lead to a topological phase transition, i.e. the change from a two-dimensional topological insulator into a mediocre insulator. Our study thus provides an insight into the interface-engineering of electronic states of Bi(111) bilayer.

Giant nonlinear Hall effect in twisted bilayer WTe2

In a system with broken inversion symmetry, a second-order nonlinear Hall effect can survive even in the presence of time-reversal symmetry. In this work, we show that a giant nonlinear Hall effect can exist in twisted bilayer WTe2 system. The Berry curvature dipole of twisted bilayer WTe2 (θ = 29.4°) can reach up to ~1400 Å, which is much larger than that in previously reported nonlinear Hall systems. In twisted bilayer WTe2 system, there exist abundant band anticrossings and band inversions around the Fermi level, which brings a complicated distribution of Berry curvature, and leads to the nonlinear Hall signals that exhibit dramatically oscillating behavior in this system. Its large amplitude and high tunability indicate that the twisted bilayer WTe2 can be an excellent platform for studying the nonlinear Hall effect.

Interlayer exciton mediated second harmonic generation in bilayer MoS2

Second-harmonic generation (SHG) is a non-linear optical process, where two photons coherently combine into one photon of twice their energy. Efficient SHG occurs for crystals with broken inversion symmetry, such as transition metal dichalcogenide monolayers. Here we show tuning of non-linear optical processes in an inversion symmetric crystal. This tunability is based on the unique properties of bilayer MoS2, that shows strong optical oscillator strength for the intra- but also interlayer exciton resonances. As we tune the SHG signal onto these resonances by varying the laser energy, the SHG amplitude is enhanced by several orders of magnitude. In the resonant case the bilayer SHG signal reaches amplitudes comparable to the off-resonant signal from a monolayer. In applied electric fields the interlayer exciton energies can be tuned due to their in-built electric dipole via the Stark effect. As a result the interlayer exciton degeneracy is lifted and the bilayer SHG response is further enhanced by an additional two orders of magnitude, well reproduced by our model calculations. Since interlayer exciton transitions are highly tunable also by choosing twist angle and material combination our results open up new approaches for designing the SHG response of layered materials.

Radiative heat and momentum transfer from materials with broken symmetries: opinion

Broken inversion and time reversal symmetries affect the electromagnetic wave modes supported by continuous media, which in turn governs thermal radiation and enables control of radiative heat, linear momentum, and angular momentum transfer. We identify opportunities for exploring thermal radiation in inversion symmetry- and time reversal symmetry-breaking materials and compare and contrast radiative transport phenomena in these systems, especially nonreciprocity. Application of these phenomena can lead to novel methods of thermal management, tunability, and object manipulation at short length scales.

Symmetry mediated tunable molecular magnetism on a 2D material

Symmetries in nanoscale structures can be decisive for their structural, electronic, and magnetic properties, particularly in systems with reduced dimensions. Here we show that the symmetries of a flat metal-organic molecule adsorbed on a transition metal dichalcogenide, a 2-dimensional layered material, have a dramatic effect on the total spin and the intramolecular spin-spin interactions. Using a scanning probe microscope, we find two different molecular spin states by modifying the symmetry of the molecules via the twist angle to the substrate. Additionally, we observe significant non-collinear Dzyaloshinskii–Moriya interaction between two electron spins on the molecule induced by the spin-orbit coupling of the van der Waals coupled layered material with broken inversion symmetry. Our work opens a path for modifying the spin by exploiting symmetries and for studying the nature of surface-induced non-collinear spin-spin interaction within a single molecule which might allow the realization of more complex topological spin structures.

Universal superlattice potential for 2D materials from twisted interface inside h-BN substrate

Lateral superlattices in 2D materials provide a powerful platform for exploring intriguing quantum phenomena, which can be realized through the proximity coupling in forming moiré pattern with another layer. This approach, however, is invasive, material-specific, and requires small lattice mismatch and suitable band alignment, largely limited to graphene and transition metal dichalcogenides (TMDs). Hexagonal boron nitride (h-BN) of antiparallel (AA′) stacking has been an indispensable building block, as dielectric substrates and capping layers for realizing high-quality van der Waals devices. There is also emerging interest on parallelly aligned h-BN of Bernal (AB) stacking, where the broken inversion and mirror symmetries lead to out-of-plane electrical polarization. Here we show the that laterally patterned electrical polarization at a nearly parallel interface within the h-BN substrate can be exploited to create noninvasively a universal superlattice potential in general 2D materials. The feasibility is demonstrated by first principle calculations for monolayer MoSe2, black phosphorus, and antiferromagnetic MnPSe3 on such h-BN. The potential strength can reach 200 meV, customizable in this range through choice of distance of target material from the interface in h-BN. We also find sizable out-of-plane electric field at the h-BN surface, which can realize superlattice potential for interlayer excitons in TMD bilayers as well as dipolar molecules. The idea is further generalized to AB-stacked h-BN subject to torsion with adjacent layers all twisted with an angle, which allows the potential and field strength to be scaled up with film thickness, saturating to a quasi-periodic one with chiral structure.

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

Skyrmion ratchet propagation: utilizing the skyrmion Hall effect in AC racetrack storage devices

Magnetic skyrmions are whirl-like nano-objects with topological protection. When driven by direct currents, skyrmions move but experience a transverse deflection. This so-called skyrmion Hall effect is often regarded a drawback for memory applications. Herein, we show that this unique effect can also be favorable for spintronic applications: We show that in a racetrack with a broken inversion symmetry, the skyrmion Hall effect allows to translate an alternating current into a directed motion along the track, like in a ratchet. We analyze several modes of the ratchet mechanism and show that it is unique for topological magnetic whirls. We elaborate on the fundamental differences compared to the motion of topologically trivial magnetic objects, as well as classical particles driven by periodic forces. Depending on the exact racetrack geometry, the ratchet mechanism can be soft or strict. In the latter case, the skyrmion propagates close to the efficiency maximum.

Linear and nonlinear optical responses in the chiral multifold semimetal RhSi

Chiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and nonlinear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of different kinds of multifold fermions. The characteristic features of the CPGE, which displays a sign change at 0.4 eV and a large non-quantized response peak of around 160 μA/V2 at 0.7 eV, are explained by assuming that the chemical potential crosses a flat hole band at the Brillouin zone center. Our theory predicts that, in order to observe a quantized CPGE in RhSi, it is necessary to increase the chemical potential as well as the quasiparticle lifetime. More broadly, our methodology, especially the development of the broadband terahertz emission spectroscopy, could be widely applied to study photogalvanic effects in noncentrosymmetric materials and in topological insulators in a contact-less way and accelerate the technological development of efficient infrared detectors based on topological semimetals.