Time-reversal State Research Articles

Topological states of multiband superconductors with interband pairing

We study the effects of interband pairing in two-band s-wave and d-wave superconductors with D4h symmetry in both time-reversal invariant as well as time-reversal symmetry-breaking states. The presence of interband pairing qualitatively changes the nodal structure of the superconductor: nodes can (dis)appear, merge, and leave high-symmetry locations when interband pairing is tuned. Furthermore, in the d-wave case, we find that also the boundary modes change qualitatively when interband pairing increases: flat zero-energy Andreev bound states gap out and transition to helical edge states. Published by the American Physical Society 2024

Fractionalization in Fractional Correlated Insulating States at n±1/3 Filled Twisted Bilayer Graphene.

Fractionalization without time-reversal symmetry breaking is a long-sought-after goal in the study of correlated phenomena. The earlier proposal of correlated insulating states at n±1/3 filling in twisted bilayer graphene and recent experimental observations of insulating states at those fillings strongly suggest that moiré graphene systems provide a new platform to realize time-reversal symmetric fractionalized states. However, the nature of fractional excitations and the effect of quantum fluctuation on the fractional correlated insulating states are unknown. We show that excitations of the fractional correlated insulator phases in the strong coupling limit carry fractional charges and exhibit fractonic restricted mobility. Upon introduction of quantum fluctuations, the resonance of "lemniscate" structured operators drives the system into quantum lemniscate liquid (QLL) or quantum lemniscate solid (QLS). We find an emergent U(1)×U(1) 1-form symmetry unifies distinct motions of the fractionally charged excitations in the strong coupling limit and in the QLL phase, while providing a new mechanism for fractional excitations in two dimensions. We predict emergent Luttinger liquid behavior upon dilute doping in the strong coupling limit due to restricted mobility and discuss implications at a general n±1/3 filling.

Cooper instability and superconductivity of the Penrose lattice

Bulk superconductivity (SC) has recently been observed in the Al-Zn-Mg quasicrystal (QC). To settle several fundamental issues of the SC on the QC, we use an attractive Hubbard model to perform a systematic study on the Penrose lattice. The first issue is the Cooper instability of the QC, i.e., no Fermi surface under an infinitesimal attractive interaction. Starting from the two-electron problem outside the filled Fermi-sea, we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of state is nonzero at the Fermi level, which provides the basis of the SC on the QC. Our numerical results yield that the Cooper pairing always takes place between the two time-reversal states, satisfying the Anderson's theorem. On this theorem, we perform a mean-field (MF) study at both zero and finite temperatures. The MF study also shows that an arbitrarily weak attraction can lead to the pairing order, with the resulted pairing state being well described by the BCS theory and the thermal dynamic behaviors being well consistent with experimental results. The second issue is about the superfluid density on the QC without translational symmetry. It's clarified that although the normal state of the system locates at the critical point of the metal-insulator transition, the pairing state exhibits real SC, carrying finite superfluid density that can be verified by the Meissner effect, consistent with experiment also. These revealed properties of the SC on the Penrose lattice are universal for all QCs.

Floquet valley-polarized quantum anomalous Hall state in nonmagnetic heterobilayers

The valley-polarized quantum anomalous Hall (VQAH) state, which forwards a strategy for combining valleytronics and spintronics with nontrivial topology, attracts intensive interest in condensed-matter physics. So far, the explored VQAH states have still been limited to magnetic systems. Here, using the low-energy effective model and Floquet theorem, we propose a different mechanism to realize the Floquet VQAH state in nonmagnetic heterobilayers under light irradiation. We then realize this proposal via first-principles calculations in transition metal dichalcogenide heterobilayers, which initially possess the time-reversal invariant valley quantum spin Hall (VQSH) state. By irradiating circularly polarized light, the time-reversal invariant VQSH state can evolve into the VQAH state, behaving as an optically switchable topological spin-valley filter. These findings not only offer a rational scheme to realize the VQAH state without magnetic orders, but also pave a fascinating path for designing topological spintronic and valleytronic devices.

Intrinsic Nature of Spontaneous Magnetic Fields in Superconductors with Time-Reversal Symmetry Breaking.

We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems, and Sr_{2}RuO_{4}. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy, leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry-broken superconducting state.

Fate of symmetry protected coherence in open quantum system

We investigate the fate of coherence in the dynamical evolution of symmetry protected quantum systems. Under the formalism of system plus bath for open quantum systems, antiunitary symmetries exhibit significant differences from the unitary ones in protecting initial coherence. Specifically, taking advantage of the Lindblad master equation, we find that a pure state in the symmetry protected degenerate subspace will be decoherent even though both the system Hamiltonian and system-environment interaction respect the same antiunitary symmetry. In contrast, the coherence will persist when the protecting symmetry is unitary. We provide an elaborate classification table to illustrate what kinds of symmetry combinations are able to preserve the coherence of the initial state, which is confirmed in several concrete models of single spin-$3/2$ systems. It can also be applied to the Haldane phase in interacting topological systems. Our results could be helpful in exploring possible experimental realization of stable time-reversal symmetric topological states.

Tunneling conductance in graphene based FNS junction with time-reversal symmetry broken

Motivated by recent experimental advances in graphene superconducting junctions with time-reversal symmetry broken (TRSB), we investigate the tunneling conductance in graphene-based ferromagnet-normal metal-superconductor junction with TRSB. It is found that in the absence of Fermi wave mismatch (FWM), the tunneling conductance is suppressed by exchange field of ferromagnet for all pairing states including one time-reversal symmetry D-wave state and two time-reversal symmetry broken, i.e. D+iS and D+iDxy states. Also, in the presence of FWM, the increase of the exchange field leads to an enhancement in tunneling spectra. Moreover, we have found that the subdominant orders play a crucial role such that by adjusting bias voltages at energies in the Dirac-points, tunneling conductance can help discriminate D+iS from D+iDxy. In addition, we have obtained that the width of normal metal (intermediate layer) makes a noticeable change in tunneling spectra especially when the angle of superconducting crystal with respect to x-axis, is placed in (110)-direction. Also, the increase of intermediate layer thickness causes the oscillations to appear in tunneling spectra. Therefore, by tuning the junction parameters and the applied bias voltage, not only is it possible to understand more about the pair potentials with TRSB, but the obtained tunneling spectra may serve as a tool to differentiate between TRSB states and non-TRSB ones.

Inhomogeneous time-reversal symmetry breaking in Sr2RuO4

We show that the observed time-reversal symmetry breaking (TRSB) of the superconducting state in $\mathrm{Sr}_{2}\mathrm{Ru}\mathrm{O}_{4}$ can be understood as originating from inhomogeneous strain fields near edge dislocations of the crystal. Specifically, we argue that, without strain inhomogeneities, $\mathrm{Sr}_{2}\mathrm{Ru}\mathrm{O}_{4}$ is a single-component, time-reversal symmetric superconductor, likely with $d_{x^{2}-y^{2}}$ symmetry. However, due to the strong strain inhomogeneities generated by dislocations, a slowly-decaying sub-leading pairing state contributes to the condensate in significant portions of the sample. As it phase winds around the dislocation, time-reversal symmetry is locally broken. Global phase locking and TRSB occur at a sharp Ising transition that is not accompanied by a change of the single-particle gap and yields a very small heat capacity anomaly. Our model thus explains the puzzling absence of a measurable heat capacity anomaly at the TRSB transition in strained samples, and the dilute nature of the time-reversal symmetry broken state probed by muon spin rotation experiments. We propose that plastic deformations of the material may be used to manipulate the onset of broken time-reversal symmetry.

Tuning of physical properties through implantation mediated Cu doping in Sb2Te3 thin films

The time-reversal symmetry-protected surface states make topological insulators an interesting candidate for the fantastic quantum phenomenon. Nowadays, 3D Topological insulators doped with magnetic elements are becoming a promising area of research in fundamental device applications. The present work aims to investigate the influence of Cu dopants via implantation on the physical properties of Sb2Te3 thin films. Thin films synthesized using the e-beam evaporation technique were implanted with Cu ions at 5 different fluences (1 × 1013, 5 × 1013, 1 × 1014, 5 × 1014, and 1 × 1015ions/cm2). X-ray Diffraction measurements reveal the rhombohedral structure of thin films with an R-3 m space group. The smaller radii of Cu ion embedded in Sb2Te3 thin films could reduce the lattice parameter ‘c’. The ion implantation induced structural strain is also observed in Raman modes as confirmed by optical studies. The Atomic Force Microscopy (AFM) measurements indicate the effect of ion implantation on the granular morphology of thin films. The increase in grain boundaries with implantation indicates the implantation induced damage to the surface. The temperature-dependent resistivity plot suggests the enhancement of the semiconducting behavior of thin films by implantation-induced defects. Our findings provide a route to have modifications in the material in a controlled way.

Omnipresence of Weak Antilocalization (WAL) in Bi2Se3 Thin Films: A Review on Its Origin.

Topological insulators are materials with time-reversal symmetric states of matter in which an insulating bulk is surrounded by protected Dirac-like edge or surface states. Among topological insulators, has attracted special attention due to its simple surface band structure and its relatively large band gap that should enhance the contribution of its surface to transport, which is usually masked by the appearance of defects. In order to avoid this difficulty, several features characteristic of topological insulators in the quantum regime, such as the weak-antilocalization effect, can be explored through magnetotransport experiments carried out on thin films of this material. Here, we review the existing literature on the magnetotransport properties of thin films, paying thorough attention to the weak-antilocalization effect, which is omnipresent no matter the film quality. We carefully follow the different situations found in reported experiments, from the most ideal situations, with a strong surface contribution, towards more realistic cases where the bulk contribution dominates. We have compared the transport data found in literature to shed light on the intrinsic properties of , finding a clear relationship between the mobility and the phase coherence length of the films that could trigger further experiments on transport in topological systems.

Study of nontrivial magnetism in 3d−5d transition metal based double perovskites

The coexistence of the strongly correlated 3$d$ transition metal (TM) atom and the strong spin-orbit coupling (SOC) of 5$d$ TM atom is potential to host exotic physical phenomena. In the present work, we have studied the magnetism resulting from such a coexistence in La$_2$CoIrO$_6$ (LCIO), a representative of bulk 3$d$-5$d$ double perovskites. In order to gain further insight into the effect of Co-$d$ states on the Ir-$d$ states, comparisons are carried out with the isostructural La$_2$ZnIrO$_6$, where nonmagnetic Zn atom replaces the Co atom. An in-depth analysis of the magnetic states in the framework of first principles calculation, using Landau theory and magnetic multipole analysis shows that the magnetism at the two constituent TM atoms in LCIO are driven by two different magnetic order parameters, viz., the spin moment as the primary order parameter responsible for the broken time-reversal state in Co and the higher order multipole: triakontadipole for the Ir magnetic state. A tight-binding analysis with the Ir-$t_{2g}$ orbitals, further, indicate that the Ir-$d$ states are hardly affected by the Co-$d$ states, in agreement with the multipole analysis. The computed heirarchy of the relevant multipoles in the present work can be probed in neutron diffraction measurements, motivating further experiments in this direction.

Topological Ising pairing states in monolayer and trilayer TaS2

We study the possibility of topological superconductivity in the noncentrosymmetric monolayer and trilayer ${\mathrm{TaS}}_{2}$ with out-of-plane mirror symmetry. A time-reversal-invariant nodal $(s+f)$-wave pairing state with even mirror parity is found to be a promising candidate. This mixed state holds 12 (36) nodes at the Fermi pockets around $\mathrm{\ensuremath{\Gamma}}$ for the monolayer (trilayer) case and its unconventional superconductivity is consistent with the scanning tunneling microscopy experiments observed in $2H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ thin flakes. Furthermore, with doping or under uniaxial pressure for trilayer $2H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$, large-Chern-number time-reversal symmetry-breaking mixed states between $(d+id)$- and $(p\ensuremath{-}ip)$-wave pairings can be realized in the phase diagram.

Time-reversal Symmetry Breaking Superconductivity in Hole-doped Monolayer MoS2

We investigate the nature of the time-reversal breaking pairing state in the hole-doped monolayer MoS$_{2}$ on the basis of the realistic three-orbital attractive Hubbard-like model with the atomic spin-orbit coupling. Due to the multi-band features arising from the Mo $d$ orbitals in the noncentrosymmetric crystal structure, the Lifshitz transition takes place upon hole doping. Across the Lifshitz transition point, the sign of the relative phase between the Cooper-pair components drastically changes, leading to the emergence of the time-reversal breaking phase with complex gap functions. It is shown that this intriguing pairing state is characterized by the finite momentum-space distributions of the orbital and spin angular momentum with three-fold rotational symmetry on the Fermi-surface pockets around K and K$'$ points. The present mechanism for the time-reversal breaking superconductivity can ubiquitously be applied to spin-orbit-coupled metals in noncentrosymmetric crystal structures.

Time-Reversal Symmetry and Arrow of Time in Quantum Mechanics of Open Systems

It is one of the most important and long-standing issues of physics to derive the irreversibility out of a time-reversal symmetric equation of motion. The present paper considers the breaking of the time-reversal symmetry in open quantum systems and the emergence of an arrow of time. We claim that the time-reversal symmetric Schrödinger equation can have eigenstates that break the time-reversal symmetry if the system is open in the sense that it has at least a countably infinite number of states. Such eigenstates, namely the resonant and anti-resonant states, have complex eigenvalues. We show that, although these states are often called “unphysical”, they observe the probability conservation in a particular way. We also comment that the seemingly Hermitian Hamiltonian is non-Hermitian in the functional space of the resonant and anti-resonant states, and hence there is no contradiction in the fact that it has complex eigenvalues. We finally show how the existence of the states that break the time-reversal symmetry affects the quantum dynamics. The dynamics that starts from a time-reversal symmetric initial state is dominated by the resonant states for ; this explains the phenomenon of the arrow of time, in which the decay excels the growth. The time-reversal symmetry holds in that the dynamic ending at a time-reversal symmetric final state is dominated by the anti-resonant states for .

Competing superconducting phases in the interacting two-dimensional electron gas with strong Rashba spin-orbit coupling

In this work we study interacting electrons on square lattice in the presence of strong Rashba spin-orbit interaction. The spin-orbit term forces the time-reversal electron states to be paired in even Cooper channels. For concreteness, we only consider the repulsive onsite Hubbard and nearest-neighbor coulomb interactions, the so called extended Hubbard model. To examine the superconducting instability we obtain the effective interaction between electrons within the random phase approximation and treat the pairing instabilities driven by charge and spin fluctuations and their combined effects. We mapped out the phase diagram of the model in terms of interactions and electron fillings, and found that while the $d_{xy}$ and $d_{x^2-y^2}$ symmetries are the most likely pairing symmetries driven by charge and spin fluctuations, respectively, the strong effect of both fluctuations yields higher angular momentum Cooper instability. The possibility of topological superconductivity and triplet pairing is also discussed.

Time-reversal of rank-one quantum strategy functions

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a class of linear functions, defined on quantum strategy representations within this framework, that corresponds to the set of rank-one positive semidefinite operators on a certain space. This time-reversal property states that the maximum value obtained by such a function over all valid quantum strategies is also obtained when the direction of time for the function is reversed, despite the fact that the strategies themselves are generally not time reversible. An application of this fact is an alternative proof of a known relationship between the conditional min- and max-entropy of bipartite quantum states, along with generalizations of this relationship.

Short-time dynamics in s+is -wave superconductor with incipient bands

Motivated by the recent observation of the time-reversal symmetry broken state in K-doped BaFe$_2$As$_2$ superconducting alloys, we theoretically study the collective modes and the short time dynamics of the superconducting state with $s+is$-wave order parameter using an effective four-band model with two hole and two electron pockets. The superconducting $s+is$ state emerges for incipient electron bands as a result of hole doping and appears as an intermediate state between $s^{\pm}$ (high number of holes) and $s^{++}$ (low number of holes). The amplitude and phase modes are coupled giving rise to a variety of collective modes. In the $s^{\pm}$ state, we find the Higgs mode at frequencies similar to a two-band model with an absent Leggett mode, while in the $s+is$ and $s^{++}$ state, we uncover a new coupled collective soft mode. Finally we compare our results with the $s+id$ solution and find similar behaviour of the collective modes.

Anomalous diamagnetic response in multiband superconductors with broken time-reversal symmetry

Within a Ginzburg-Landau formalism we establish analytically the necessary and sufficient conditions to realize a doubly degenerate superconducting ground state with broken time-reversal symmetry (BTRS) in a multi-band superconductor. Using these results we analyze the ground state of a three-band superconductor in the cylindrical geometry in an external magnetic field. We show that depending on the interband coupling constants, a magnetic flux can induce current density jumps in such superconducting geometries that are related to adiabatic or non-adiabatic transitions from BTRS to time-reversal symmetric states and vice versa. This unusual current induced magnetic flux response can in principle be used experimentally to detect superconducting BTRS ground states as well as corresponding metastable excited states.

Irreversibility and the breaking of resonance-antiresonance symmetry.

We consider open quantum systems modeled as discrete lattices. Using a simple model of a single-site coupled to two leads as an example, we show that the time evolution of these systems can be analyzed in terms of an explicitly time-reversal symmetric resolution of unity. This resolution of unity includes both resonant states, which decay in the future, and anti-resonant states, which decay in the past. We show that a time-reversal invariant state contains both resonant and anti-resonant components with equal weights. However, this symmetry is automatically broken as the system evolves in time, with the resonant component becoming much larger than the anti-resonant component for t > 0 (and vice versa for t < 0). We argue that irreversibility is a manifestation of this symmetry breaking. We also compare our present approach with the subdynamics approach developed by Prof. Prigogine and collaborators. Finally, we suggest an extension of our present approach from the level of wave functions to the level of density matrices.

Schwinger boson mean-field theory of the kagome Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions

We have studied the effect of the Dzyaloshinskii-Moriya interaction on kagome Heisenberg anti-ferromagnet using Schwinger boson mean field theory (SBMFT). Within SBMFT framework, Messio et al had argued that the ground state of kagome antiferromagnet is possibly a chiral topological spin liquid (Phys. Rev. Lett. 108, 207204 (2012)). Thus, we have computed zero-temperature ground state phase diagram considering the time-reversal breaking states as well as fully symmetric Ans\"atze. We discuss the relevance of these results in experiments and other studies. Finally, we have computed the static and dynamic spin structure factors in relevant phases.