Session K14: Electronic Structure of Topological Materials, Driven Topological Systems, and Topological Superconductor Theory

Femtosecond Manipulation of Two-Dimensional Ruderman-Kittel-Kasuya-Yasuda Interaction

The interaction between magnetism and itinerant electrons leads to the broken time-reversal symmetry for the key electronic states in topological insulators, enabling dissipationless and spin-polarized quantum transport. This interaction fundamentally determines the operational temperature scale for topological electronics. Here we use a unique combination of time-resolved photoemission spectroscopy and time-resolved magneto-optical Kerr effect measurements to elucidate the simultaneous evolutions of the electronic and magnetic subsystems in an intrinsic magnetic topological insulator MnBi₂Te₄. Our experiments selectively reveal the details of the 2D Ruderman-Kittel-Kasuya-Yasuda (RKKY) interaction on the material surface; our theoretical model quantitatively reproduces the demagnetization time scale as well as the order-of-magnitude for the exchange gap quenching. This distinct 2D RKKY mechanism offers a direct explanation for the sizable gap in the quasi-2D electronic state and for the nonzero residual magnetization in even-layer MnBi₂Te₄. Furthermore, it promises a unique ultrafast path to effectively manipulate magnetism and topological orders through the p-d interaction and paves the road toward future topotronic devices.   

Oral: Electric field-tunable Berry curvature in WTe2

    Berry curvature, as one of the central topics in topological physics, plays an important role in various quantum transport phenomena, such as various Hall effects and Circular dichroism [1]. Recently, Berry curvature dipole (BCD), i.e., the dipole moment of Berry curvature [2] is proposed to be able to induce second-order nonlinear Hall effect. The nonzero BCD can lead to high-frequency rectifiers, wireless charging, and energy harvesting through the nonlinear Hall effect, promising for nonlinear quantum devices. However, the maximum symmetry allowed for nonzero BCD is a single mirror symmetry, unfavorable for real applications.

    Here, via probing the nonlinear Hall effect, we demonstrate the electric field-manipulated Berry curvature and BCD [3]. A linear dependence between the BCD and the dc electric field is observed. The polarization direction of the Berry curvature is controlled by the relative orientation of the electric field and crystal axis, which can be further reversed by changing the polarity of the dc field. Our work provides a route to generate and control Berry curvature and BCD in broad material systems, and to facilitate the development of nonlinear quantum devices.

References

[1] D. Xiao, M.-C. Chang, and Q. Niu, Rev. Mod. Phys. 82, 1959 (2010).

[2] I. Sodemann and L. Fu, Phys. Rev. Lett. 115, 216806 (2015).

[3] X.-G. Ye, H. Liu, P.-F. Zhu, et al., Phys. Rev. Lett. 130, 016301 (2023).   

Tunneling spectroscopic study of the topological Kondo insulator YbB12 using second harmonic measurements

Electronic transport and the magnetoresistance measurements of single crystals and microstructures on the Kondo Insulator YbB12 reveal the presence of topologically protected surface states, suggesting that YbB12 is a candidate material for being a topological Kondo insulator [1]. Planar tunneling spectroscopic studies on YbB12 also support the formation of TSS (Topological Surface States) in YbB12 as is seen in SmB6, but data suggest that exact nature of the YbB12 TSS is different from that in SmB6 [2].  

Second harmonic measurement techniques provide higher resolution and cleaner planar tunneling spectra which help us to compare and contrast the electronic structure of these interesting materials. We will present planar tunneling spectroscopic data on YbB12 in the low temperature resistance plateau range and compare it to planar tunneling data taken on SmB6 [3].  

[1] Y. Sato et al., J. Phys. D: Appl. Phys. 54, 404002 (2021). 

[2] A. Gupta et al., Phys. Rev. B 107, 165132 (2023). 

[3] Robert Huber et al, this conference.     

Interband Magneto-Optical Spectroscopy of Pb1-xSnxSe

Since the last century, considerable research has been conducted on valley-degenerate narrow gap semiconductors, including Pb_1-xSn_xSe and Pb_1-xSn_xTe alloys. However, it is still not fully understood how differences between the longitudinal valley and the oblique valleys show up in magneto-optical spectroscopy. In this work, we carry out a combined theoretical and experimental work to study this very question. Based on the Mitchell-Wallis model and Kubo formula, we provided a theoretical fit for the interband magneto-optical response of Pb_1-xSn_xSe, which agreed very well with experimental observations and explained the spectral shape of the data at magnetic fields as high as 35T. Our work thus provides a quantitative estimate of the relative strength of the optical absorption from the longitudinal and oblique valleys which can be an important symmetry indicator in future studies.    

Probing the Surface States of SmB6 Through Planar Tunneling Using Second Harmonic Detection Techniques

Samarium hexaboride (SmB₆), a candidate topological Kondo insulator (TKI), has proven itself to be a rich physical system associated with a vast array of complex physics. Below 4 K, the conductivity is dominated by surface states that appear to be topologically protected. Previous work has shown that these surface states do not span the entire gap region (as they do in conventional TIs such as Bi₂Se₃) [1] and display a sensitivity to Samarium deficiency [2], suggesting their topological protection is incomplete. To better understand the nature of these conducting surface states, we apply second harmonic detection techniques to planar tunnel junctions made on SmB₆ single crystals, providing a higher energy resolution and cleaner spectra than planar tunneling conductance.  These data are also numerically deconvolved to remove thermal population effects and recover the electronic density of states.  We discuss an antisymmetric signature at ±1 meV in the second harmonic spectra that appears with the low-temperature formation of conducting surface states in the context of muon spin rotation studies [3][4] which correlate this low energy signature to bulk antiferromagnetic excitations.

[1] W.K Park et al., PNAS 113, 6599 (2016)

[2] W.K. Park et al., PRB 103, 155125 (2021)

[3] K. Akintola et al., npj Quantum Materials 3, 36 (2018).

[4] P.K. Biswas et al., PRB 95, 020410 (2017)    

Tunneling spectroscopy of DC current biased planar Josephson junctions

Time-periodic drive facilitates engineering non-equilibrium quantum systems through hybridization between Floquet sidebands. Floquet driven topological superconductivity may provide additional functionality for quantum devices. Here we detail fabrication and measurement of DC current biased planar Josephson junctions (JJs) in which the intrinsic AC Josephson effect may provide the necessary time-periodic drive needed to support Floquet topological superconductivity. We fabricated planar JJs with two tunneling probes to sense the local density of states at two ends of the junction of a hybrid epitaxial Al-InAs two-dimensional electrons gas (2DEG) heterostructure. We observed four conductance peaks in tunneling spectroscopy when a finite DC voltage bias across the junction is generated by an applied current. We report a systematic study of local conductance as a function of DC voltage bias across junction and as a function applied in-plane magnetic field. We compare our experimental data with theoretical calculations using Floquet theory.   

Effective Hamiltonian approach for simulation of AC Josephson effect

When a voltage difference is maintained across a Josephson junction the superconducting phase difference will evolve in time giving rise to an alternating current across the junction with a frequency determined by the voltage applied. This phenomenon, known as the AC Josephson effect, provides the ideal platform to study the effects of Floquet dynamics. In this work, we study a 2D S-N-S junction in the presence of a periodic time-dependent pairing potential. The system is described by a Hamiltonian that can be separated into two components: a time-independent and time-dependent term. We show an effective Hamiltonian method that allows us to simulate the realistic size system and study its physical properties such as time-averaged density of states (DOS) and current. Our predictions for DOS can be measured experimentally in tunneling conductance. In this effective Hamiltonian, we use the time-independent Hamiltonian in a tight-binding approximation to truncate the system to the lowest N eigenvalues. We study the time-periodic drive using the extended space formalism of the Floquet theory on the truncated basis. Our method shows an efficient alternative to studying Floquet dynamics in a Josephson junction without translational invariance.   

Classification of Unitary Operators by Local Generatability

Both in Floquet systems and in the related problems of discrete-time quantum walks and quantum cellular automata, a basic distinction arises among unitary time evolution operators: while all physical operators are local, not all are locally generated (i.e., generated by some local Hamiltonian). In this paper, we define the notion of equivalence up to a locally generated unitary in all Altland-Zirnbauer symmetry classes. We then classify single-particle unitaries in all dimensions and all symmetry classes on this basis by showing that equivalence up to a locally generated unitary is identical to homotopy equivalence.   

Orbital Selective Mott Transition and Topological Superconductivity of FeSe1-xTex

The iron-based superconductor, FeSe_1-xTe_x (FST), obtained significant attention due to two emergent phenomena. The first is the topological superconductivity (TPSC) hosts Majorana Fermion in its boundary as a candidate of the topologically protected qubit [1,2]. The second is the orbital selective Mott transition (OSMT), a selective localization of the Fe(d_xy) orbital while other orbitals remain as itinerant [3]. This talk shows that the TPSC and the OSMT in the FST material are intimately connected [4]. We use the state-of-the-art linearized quasiparticle self-consistent GW plus dynamical mean-field theory framework with included spin-orbit coupling, which enables the quantitative description of the topological Dirac surface state of the FST material. We show that the topologically non-trivial band experiences a localization from the OSMT due to its Fe(d_xy) orbital origin. From this, we demonstrate that the TPSC could be realized for a regime that is not too far but not too close to the OSMT. This observation enables understanding and manipulation of the TPSC of iron-based superconductors. Also, this observation can explain the experimentally observed time-reversal symmetry breaking at the surface state of the FST material [5]. 

[1] G. Xu et al., Phys. Rev. Lett. 117, 047001 (2016),

[2] P. Zhang et al., Science 360, 182 (2018)

[3] M. Yi et al., Nat. Comm. 6, 1 (2015)

[4] Minjae Kim et al., https://arxiv.org/abs/2304.05002 (2023)

[5] C. Farhang et al., Phys. Rev. Lett. 130, 046702 (2023)   

Implementation of Topological Quantum Gates and Algorithms in Magnet-Superconductor Hybrid Structures

The implementation of topological quantum gates and algorithms using Majorana zero modes (MZMs) is a major outstanding problem in the field of topological quantum computing. In this talk, I will demonstrate the non-equilibrium realization of σ_z and σ_x quantum gates as well as the Bernstein-Vazirani quantum algorithm by theoretically showing how Majorana zero modes can be manipulated at the nanoscale in real time in magnet-superconductor hybrid (MSH) structures.

I will show how the spatial braiding of MZMs in time can be visualized in MSH systems via the time-dependent differential conductance measured in scanning tunneling spectroscopy experiments. Moreover, I will demonstrate how quantum algorithms and gates can be initialized both in the even and odd-parity sector, and how the successful realization of a quantum algorithm can be read out by fusing the MZMs and measuring the time-dependent charge density.   

Fusion Channel Dependent Magnetic Moments in Topological Josephson Junctions

A key characteristic of non-Abelian anyons is that they may fuse to form multiple particle types. In topological superconductors, two Majorana zero modes may fuse to form a fully paired state or a state with a single unpaired quasiparticle. In order to read out the state of a topological qubit one needs a method to distinguish between these two scenarios. In this talk, I will explore how these two fusion channels should have opposite magnetic moments in a Rashba 2DEG Josephson Junction, and we propose methods to detect this in an experiment with two Josephson vortices. Furthermore, we will discuss how one may use 4 Josephson vortices to probe non-Abelian fusion rules.   

Probing topological phase transition with non-Hermitian perturbations

We demonstrate that non-Hermitian perturbation can probe topological phase transitions and unambiguously detect non-Abelian zero modes. We show that under the non-Hermitian fermionic parity changing perturbations, the Loschmidt echo(LE) decays into the inverse of the ground state degeneracy in the topological non-trivial phase, while it is close to one in the trivial phase. This distinction is robust against small deviations in the non-Hermitian fermionic parity changing perturbations. We further study three well-known models with such specific non-Hermitian perturbations. By calculating their dynamical responses, we prove that the steady-state LE can indeed be used to differentiate different phases. This method avoids the ambiguity brought by the trivial zero energy states and thus can demonstrate the emergence of topological non-trivial phases. The experimental realizations of non-Hermitian perturbations are discussed.   

Band structures, optical selection rules and magnetic dipole moments of topological excitons in flat-band Chern insulators

Exciton bound states in a flat-band Chern insulator are determined by the quantum geometry and topology of the Bloch wave functions of electrons. We numerically solve the exciton Wannier equations for two-dimensional flat-band tight-binding models, taking into account the effective long-range Coulomb interaction. For the center-of-mass (COM) at rest, we determine the nonhydrogenic spectra, profile-function topologies, effective electric dipole moments as well as optical selection rules of the exciton bound states. For the COM motion, we calculate the exciton band structures and obtain the effective masses and anomalous velocities. Moreover, we obtain the exciton magnetic dipole moments inherited from the Bloch bands.