Presence Of Time-reversal Symmetry Research Articles

Movable but unavoidable nodal lines through high-symmetry points in 2D materials

Abstract In 2D materials, electronic band contacts often make a non-trivial contribution to a material’s topological properties. Besides band contacts at high-symmetry points (HSPs) in the Brillouin zone (BZ), like those in graphene, there are nodal lines that form various patterns in the reciprocal space. In this paper we have found all movable nodal lines, whose shape depends on the model, that pass through HSPs in the presence of time-reversal symmetry. Cases with and without spin–orbit coupling are included by studying all 80 layer groups and their double extensions. Eight single and six double groups, including three symmorphic, necessarily host Dirac and Weyl nodal lines that extend through the whole BZ, respectively. Our research might be of interest in designing new materials with interesting physical properties.

Interface Engineering Modulated Valley Polarization in MoS2/hBN Heterostructure

Layered transition metal dichalcogenides (TMDs) provide a favorable research platform for the advancement of spintronics and valleytronics because of their unique spin-valley coupling effect, which is attributed to the absence of inversion symmetry coupled with the presence of time-reversal symmetry. To maneuver the valley pseudospin efficiently is of great importance for the fabrication of conceptual devices in microelectronics. Here, we propose a straightforward way to modulate valley pseudospin with interface engineering. An underlying negative correlation between the quantum yield of photoluminescence and the degree of valley polarization was discovered. Enhanced luminous intensities were observed in the MoS2/hBN heterostructure but with a low value of valley polarization, which was in stark contrast to those observed in the MoS2/SiO2 heterostructure. Based on the steady-state and time-resolved optical measurements, we reveal the correlation between exciton lifetime, luminous efficiency, and valley polarization. Our results emphasize the significance of interface engineering for tailoring valley pseudospin in two-dimensional systems and probably advance the progression of the conceptual devices based on TMDs in spintronics and valleytronics.

Coexistence of charge-2 Dirac and Weyl phonons in chiral space groups

Unconventional topological phonons with unusual properties in crystalline solids have attracted increasing attention. By performing symmetry arguments and low-energy effective Hamiltonian, we confirm the coexistence of charge-2 Dirac and Weyl phonons at high-symmetry points and high-symmetry lines by analyzing all possible space groups. We reveal that such a particular system only emerges in chiral space groups in the presence of time-reversal symmetry. Unlike conventional Weyl pairs with opposite chirality that host one surface arc, there are two surface arcs by connecting one charge-2 Dirac point with topological charge = $\ifmmode\pm\else\textpm\fi{}2$ and two Weyl points with topological charge = $\ensuremath{\mp}1$. Due to the constraints of symmetry arguments and projection direction in chiral crystals, the surface arcs are long enough to span over the whole surface Brillouin zone. We take ${\mathrm{Na}}_{2}{\mathrm{Zn}}_{2}{\mathrm{O}}_{3}$ as an example to confirm our predication, and two branches of surface states across the whole surface Brillouin zone are clearly visible. Our work not only presents exotic quasiparticles but also provides an idea for realizing long nontrivial surface arcs.

Non-linear Hall effect in multi-Weyl semimetals

In the presence of time reversal symmetry, a non-linear Hall effect can occur in systems without an inversion symmetry. One of the prominent candidates for detection of such Hall signals are Weyl semimetals. In this article, we investigate the Berry curvature induced second and third order Hall effect in multi-Weyl semimetals with topological charges . We use low energy effective models to obtain general analytical expressions and discover the presence of a large Berry curvature dipole (BCD) in multi-Weyl semimetals, compared to usual (n = 1) Weyl semimetals. We also study the BCD in a realistic tight-binding lattice model and observe two different kinds of variation with increasing topological charge—these can be attributed to different underlying Berry curvature components. We provide estimates of the signatures of second harmonic of Hall signal in multi-Weyl semimetals, which can be detected experimentally. Furthermore, we predict the existence of a third order Hall signal in multi-Weyl semimetals. We derive the analytical expressions of Berry connection polarizability tensor, which is responsible for third order effects, using a low energy model and estimate the measurable conductivity. Our work can help guide experimental discovery of Berry curvature multipole physics in multi-Weyl semimetals.

Second harmonic helicity and Faraday rotation in gated single-layer 1T′−WTe2

Single-layer of 1T$'$ phase of WTe$_2$ provides a rich platform for exotic physical properties such as nonlinear Hall effect and high-temperature quantum spin hall transport. Utilizing a continuum model and diagrammatic method, we calculate the second harmonic conductivity of monolayer 1T$'$-WTe$_2$ modulated by an external vertical electric field and electron doping. We obtain a finite helicity and Faraday rotation for the second harmonic signal in response to linearly polarized incident light in the presence of time-reversal symmetry. The second harmonic signal's helicity is highly controllable by altering the bias potential and serves as an optical indicator of the nonlinear Hall current. Our study motivates future experimental investigation for the helicity spectroscopy of two dimensional materials.

Phase space crystal vibrations: Chiral edge states with preserved time-reversal symmetry

Phase-space crystal is a solidlike crystalline state in phase space formed by atoms, subject to a time-periodic drive. The authors show that interactions between these atoms can give rise to vibrational band structures with nontrivial Chern numbers and chiral edge states in phase space. Remarkably, these arise even in the presence of time-reversal symmetry in contrast to all topological transport scenarios in real space. Phase-space crystal vibrations offer a new platform for phononic topological transport whereby chiral properties arise naturally.

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.

Strain-gated nonlinear Hall effect in two-dimensional MoSe2/WSe2 van der Waals heterostructure

It is recently found that the Hall effect can survive in the presence of time-reversal symmetry but with inversion-symmetry breaking, which is known as the nonlinear Hall effect. So far, the studies concerning the nonlinear Hall effect are mainly focused on the homogeneous systems, while less attention has been paid to the van der Waals (vdW) heterostructure, which in fact naturally breaks the spatial inversion symmetry. In this study, we systematically study the nonlinear electric response in $1{\text{T}}^{\ensuremath{'}}$-phase ${\mathrm{MoSe}}_{2}/{\mathrm{WSe}}_{2}$ vdW heterostructure. Our results demonstrate that ${\mathrm{MoSe}}_{2}/{\mathrm{WSe}}_{2}$ vdW heterostructure owns a large Berry curvature dipole, which is comparable with those of homogeneous multilayers and much larger than that predicted for monolayers under the in-plane uniaxial strain. In addition, the nonlinear Hall response in vdW heterostructure is sensitive to the relative position between the Fermi energy and tilted Dirac cones, and can be effectively manipulated from positive to negative values by applying an out-of-plane strain. Further study indicates that this can be ascribed to the charge transfer within the vdW interlayer. Based on these findings, our work provides a fundamental understanding of the nature of strain-gated nonlinear Hall effect in vdW heterostructures, which may facilitate the design of novel high-frequency nanodevices.

Fermionic topological phases and bosonization in higher dimensions

Abstract We review a recipe to produce a lattice construction of fermionic phases of matter in the presence of time reversal symmetry by extending the fermionization and bosonization known in (1+1) dimensions to various setups including higher spacetime dimensions in the presence of global symmetries. As an application, we provide a state sum lattice path integral for a (1+1)-dimensional topological superconductor with time reversal symmetry generating the $\mathbb{Z}_8$ classification of the symmetry-protected topological phase. We also illustrate a state sum path integral for a (3+1)-dimensional topological superconductor with time reversal symmetry that generates the $\mathbb{Z}_{16}$ classification.

Disentangling the Generalized Double Semion Model

We analyze the class of Generalized Double Semion (GDS) models in arbitrary dimensions from the point of view of lattice Hamiltonians. We show that on a $d$-dimensional spatial manifold $M$ the dual of the GDS is equivalent, up to constant depth local quantum circuits, to a group cohomology theory tensored with lower dimensional cohomology models that depend on the manifold $M$. We comment on the space-time topological quantum field theory (TQFT) interpretation of this result. We also investigate the GDS in the presence of time reversal symmetry, showing that it forms a non-trivial symmetry enriched toric code phase in odd spatial dimensions.

Wigner–Smith matrix, exponential functional of the matrix Brownian motion and matrix Dufresne identity

We consider a multichannel wire with a disordered region of length L and a reflecting boundary. The reflection of a wave of frequency ω is described by the scattering matrix , encoding the probability amplitudes to be scattered from one channel to another. The Wigner–Smith time delay matrix is another important matrix, which encodes temporal aspects of the scattering process. In order to study its statistical properties, we split the scattering matrix in terms of two unitary matrices, (with in the presence of time reversal symmetry), and introduce a novel symmetrisation procedure for the Wigner–Smith matrix: , where k is the wave vector and v the group velocity. We demonstrate that can be expressed under the form of an exponential functional of a matrix Brownian motion. For semi-infinite wires, L → ∞, using a matricial extension of the Dufresne identity, we recover straightforwardly the joint distribution for ’s eigenvalues of Brouwer and Beenakker (2001 Physica E 9 463). For finite length L, the exponential functional representation is used to calculate the first moments , and . Finally we derive a partial differential equation for the resolvent in the large N limit.

Necessary and Sufficient Conditions for Time Reversal Symmetry in Presence of Magnetic Fields

Time reversal invariance (TRI) of particles systems has many consequences, among which the celebrated Onsager reciprocal relations, a milestone in Statistical Mechanics dating back to 1931. Because for a long time it was believed that (TRI) dos not hold in presence of a magnetic field, a modification of such relations was proposed by Casimir in 1945. Only in the last decade, the strict traditional notion of reversibility that led to Casimir’s work has been questioned. It was then found that other symmetries can be used, which allow the Onsager reciprocal relations to hold without modification. In this paper we advance this investigation for classical Hamiltonian systems, substantially increasing the number of symmetries that yield TRI in presence of a magnetic field. We first deduce the most general form of a generalized time reversal operation on the phase space of such a system; secondly, we express sufficient conditions on the magnetic field which ensure TRI. Finally, we examine common examples from statistical mechanics and molecular dynamics. Our main result is that TRI holds in a much wider generality than previously believed, partially explaining why no experimental violation of Onsager relations has so far been reported.

Symmetry-protected spinful magnetic Weyl nodal loops and multi-Weyl nodes in 5dn cubic double perovskites (n=1,2)

Using both an effective three-band model and {\it ab initio} calculations, we have investigated various topological features in the cubic ferromagnetic $5d^{1,2}$ systems showing large spin-orbit coupling (SOC): Ba$_2$NaOsO$_6$, Sr$_2$SrOsO$_6$, and Ba$_2$$B$ReO$_6$ ($B$= Mg, Zn). In the presence of time-reversal symmetry (${\cal T}$), spinless Dirac nodal loops linked to each other at the $W$ points appear in the mirror planes. Remarkably, breaking ${\cal T}$ leads to spinful magnetic Weyl nodal loops (MWNLs) that are robust even at large SOC and correlation strength $U$ variation due to the combination of mirror symmetry and broken ${\cal T}$. Additionally, there are two types of magnetic Weyl points with chiral charges $|\chi|=1, 2$ along the $C_{4v}$ symmetry line, and another type-II MWNL encircling the zone center, that are dependent on $U$. Furthermore, the ferromagnetic Ba$_2$ZnReO$_6$ is an ideal half semimetal with MWNLs and magnetic Weyl nodes at the Fermi level without the interference of topologically trivial bulk states. These systems give rise to a remarkably large anomalous Hall conductivity $\sigma_{xy}$ of up to 1160 ($\Omega$cm)$^{-1}$. Our findings may apply widely for $t_{2g}$ systems with cubic (or slightly distorted) fcc-like structures.

Fermionic time-reversal symmetry in a photonic topological insulator.

Much of the recent attention directed towards topological insulators is motivated by their hallmark feature of protected chiral edge states. In electronic (or fermionic) topological insulators, these states originate from time-reversal symmetry and allow carriers with opposite spin-polarization to propagate in opposite directions at the edge of an insulating bulk. By contrast, photonic (or bosonic) systems are generally assumed to be precluded from supporting edge states that are intrinsically protected by time-reversal symmetry. Here, we experimentally demonstrate counter-propagating chiral states at the edge of a time-reversal-symmetric photonic waveguide structure. The pivotal step in our approach is the design of a Floquet driving protocol that incorporates effective fermionic time-reversal symmetry, enabling the realization of the photonic version of an electronic topological insulator. Our findings allow for fermionic properties to be harnessed in bosonic systems, thereby offering alternative opportunities for photonics as well as acoustics, mechanical waves and cold atoms.

Nonlinear Nernst effect in bilayer WTe2

Unlike the conventional (linear) anomalous Nernst effect, the non-linear anomalous Nernst effect (NLANE) can survive in an inversion symmetry broken system even in the presence of time-reversal symmetry. Using semiclassical Boltzmann transport theory, we derive the general expression of the non-linear anomalous Nernst coefficient as the second-order response function to the applied temperature gradient. We find that the non-linear Nernst current, which flows perpendicular to the temperature gradient even in the absence of a magnetic field, arises due to the Berry curvature of the states near the Fermi surface, and thus is associated with purely a Fermi surface contribution. We apply these results to bilayer WTe$_2$, which is an inversion broken but time reversal symmetric type-II Weyl semimetal supporting chiral Weyl fermions. By tuning the spin-orbit coupling, we show that the sign of the NLANE can change in this system. Together with the angular dependence, we calculate the temperature and chemical potential dependencies of NLANE in bilayer WTe$_2$, and predict specific experimental signatures that can be checked in experiments.

Strain-Engineered Nonlinear Hall Effect in HgTe

As paradigmatic phenomena, Hall effects have inspired tremendous studies of symmetry and topology in condensed matter physics. Intriguingly, a second-order nonlinear Hall effect was recently proposed in noncentrosymmetric materials even in the presence of time-reversal symmetry. This effect originates from the Berry curvature dipole of electronic band structures and was predicted in Dirac and Weyl materials such as transition metal dichalcogenides and Weyl semimetals. Although it has been experimentally verified in some transition metal dichalcogenides, no obvious observation of such effects has been reported in Weyl semimetals. Taking advantage of the ideal Weyl phase with no coexisting trivial bands at the Fermi level, we use strained HgTe as a concrete example to show that the ideal Weyl semimetal is a promising platform for demonstrating the nonlinear Hall effect. Based on numerical calculations of the Berry curvature dipole, it was found that the magnitude of nonlinear Hall effect can be simply engineered by in-plane strain. Our work provides a versatile platform with high tunability, which could greatly facilitate the study of nonlinear Hall effect in three-dimensional topological materials.

Relative Abundance of [Formula: see text] Topological Order in Exfoliable Two-Dimensional Insulators.

Quantum spin Hall insulators make up a class of two-dimensional materials with a finite electronic band gap in the bulk and gapless helical edge states. In the presence of time-reversal symmetry, [Formula: see text] topological order distinguishes the topological phase from the ordinary insulating one. Some of the phenomena that can be hosted in these materials, from one-dimensional low-dissipation electronic transport to spin filtering, could be promising for many technological applications in the fields of electronics, spintronics, and topological quantum computing. Nevertheless, the rarity of two-dimensional materials that can exhibit nontrivial [Formula: see text] topological order at room temperature hinders development. Here, we screen a comprehensive database we recently identified of 1825 monolayers that can be exfoliated from experimentally known compounds to search for novel quantum spin Hall insulators. Using density-functional and many-body perturbation theory simulations, we identify 13 monolayers that are candidates for quantum spin Hall insulators including high-performing materials such as AsCuLi2 and (platinum) jacutingaite (Pt2HgSe3). We also identify monolayer Pd2HgSe3 (palladium jacutingaite) as a novel Kane-Mele quantum spin Hall insulator and compare it with platinum jacutingaite. A handful of promising materials are mechanically stable and exhibit [Formula: see text] topological order, either unperturbed or driven by small amounts of strain. Such screening highlights a relative abundance of [Formula: see text] topological order of around 1% and provides an optimal set of candidates for experimental efforts.

Quenches on thermofield double states and time reversal symmetry

In this paper we study a quench protocol on thermofield double states in the presence of time-reversal symmetry that is inspired by the work of Gao, Jafferis and Wall. The deformation is a product of hermitian operators on the left and right systems that are identical to each other and that lasts for a small amount of time. We study the linear dependence on the quench to the properties of the deformation under time reversal. If the quench is time symmetric, then the linear response after the quench of all T-even operators vanishes. This includes the response of the energy on the left system and all the thermodynamic expectation values (the time averaged expectation values of the operators). Also, we show under an assumption of non-degeneracy of the Hamiltonian that the entanglement entropy between left and right is not affected to this order. We also study a variation of the quench where an instantaneous deformation is given by an operator of fixed T-parity and it's time derivative. It is shown that the sign of the response of the Hamiltonian is correlated with the T-parity of the operator. We can then choose the sign of the amplitude of the quench to result in a reduction in the energy. This implies a reduction of the entanglement entropy between both sides.

Large Contribution of Fermi Arcs to the Conductivity of Topological Metals.

Surface-state contributions to the dc conductivity of most homogeneous metals exposed to uniform electric fields are usually as small as the system size is large compared to the lattice constant. In this Letter, we show that surface states of topological metals can contribute with the same order of magnitude as the bulk, even in large systems. This effect is intimately related to the intrinsic anomalous Hall effect, in which an applied voltage induces chiral surface-state currents proportional to the system size. Unlike the anomalous Hall effect, the large contribution of surface states to the dc conductivity is also present in time-reversal invariant Weyl semimetals, where the surface states come in counterpropagating time-reversed pairs. While the Hall voltage vanishes in the presence of time-reversal symmetry, the twinned chiral surface currents develop similarly as in the time-reversal-broken case. For this effect to occur, the relaxation length associated with scattering between time-reversed partner states needs to be larger than the separation of contributing surfaces, which results in a characteristic size dependence of the resistivity and a highly inhomogeneous current-density profile across the sample.

Topological phases of nonsymmorphic crystals: Shastry-Sutherland lattice at integer filling

Motivated by intertwined crystal symmetries and topological phases, we study the possible realization of topological insulators in nonsymmorphic crystals at integer fillings. In particular, we consider spin-orbit-coupled electronic systems of two-dimensional crystal Shastry-Sutherland lattices at integer filling where the gapless line degeneracy is protected by glide reflection symmetry. Based on a simple tight-binding model, we investigate how the topological insulating phase is stabilized by breaking nonsymmorphic symmetries but in the presence of time reversal symmetry and inversion symmetry. In addition, we also discuss the regime where Dirac semimetal is stabilized, having nontrivial ${Z}_{2}$ invariants even without spin-orbit coupling. Our study can be extended to more general cases where all lattice symmetries are broken and we also discuss possible application to topological Kondo insulators in nonsymmorphic crystals where crystal symmetries can be spontaneously broken as a function of the Kondo coupling.