The researches at RLQM are in the field of** theoretical** condensed matter physics, including the study of various topological aspects in solid state systems, and electronic, magnetic, transport, as well as optical properties of novel materials. The objective is to deepen our understanding of fundamental physics and to enable the application of such understanding for technological development.

Current research topics:

- Topological states of matter, including topological insulators, topological metals, and topological superconductors
- Two-dimensional layered materials
- Transport phenomena

Various theoretical methods are used in the research, such as symmetry/topology analysis, semi-classical approach, tight-binding modeling, Green’s function method, first-principles DFT calculations, non-equilibrium Schwinger-Keldysh technique, scattering approach, and various kinds of numerical techniques.

## Recent research highlights

**Nonlinear response effects.**We develop theories for instrinsic second-order Hall effect, third-order charge transport, and second-order electric spin generation. We reveal their connection to intrinsic band geometric quantities, such as Berry connection polarizability and anomalous spin/orbital polarizability. Our theories can be implemented in first-principles calculations to study real materials. Our prediction on third-order charge transport was confirmed by experiment on bulk WTe2 and other materials. [PRL**127**, 277202 (2021); Nat. Nano.**16**, 869 (2021); PRB**105**, 045118 (2022); PRL**129**, 086602 (2022); Nat. Sci. Rev.**9**, nwac020 (2022); PRL**130**, 016301 (2023)]**Projective crystalline symmetry algebra.**Symmetries are projectively represented for a quantum system. This key point remains largely unexplored in the context of crystal symmetries. In fact, the field of topological artificial crystals has its advantage arising from this very fact, but a theoretical foundation is still lacking. We pioneer in revealing the critical role of projective symmetry algebra in generating novel topological states (like Mobius insulators), in switching spin classes, in manifesting Bott periodicity in Clifford algebras, in creating Brillouin Klein bottle, and in developing a general approach to classify time-reveral-invariant gauged crystals. [PRB**102**, 161117 (2020); PRL**126**, 196402 (2021); PRL**127**, 076401 (2021); PRL**128**, 116802 (2022); PRB**106**, 125102 (2022); Nat. Comm.**13**, 2215 (2022); Nat. Comm.**14**, 742 (2023)]**Complete classification of emergent particles by space groups.**We finish the classification of all possible emergent particles by 3D space groups, 2D layer groups, and 1D rod groups, both magnetic and nonmagnetic, without and with spin-orbit coupling. These works offer a comprehensive reference for studying emergent particles in crystals. [Sci. Bulletin**67**, 375 (2022); PRB**105**, 085117 (2022); PRB**105**, 104426 (2022); PRB**107**, 075405 (2023)]**Index theorem for chiral Landau bands.**Previous studies have long noticed the existence of chiral Landau bands for topological nodal points (such as Weyl points), which is the basis for aruging chiral anomaly effect in topological semimetals. However, there is no proof of the relation between existence of chiral Landau bands and nodal point charges. We offer such a general proof for the first time. [PRL**126**, 046401 (2021)]**Real Chern insulator and real nodal-line semimetal.**We reveal unconventional bulk-boundary correspondence for real Chern insulators, propose the 3D real nodal-line semimetal states, and identify the first material candidates (including 2D and 3D graphynes) for these topological states. We also reveal the first phononic real Chern insulator in 2D graphyne and graphdiyne. [PRL**125**, 126403 (2020); PRB**104**, 085205 (2021); PRL**128**, 026405 (2022); PRB**105**, 085123 (2022)]**Valley-layer coupling (VLC).**The current valleytronics research is based on the paradigm of time-reversal-connected valleys in 2D hexagonal materials, which forbids the fully electric generation of valley polarization by a gate field. We propose a novel VLC mechanism, which enables a direct coupling between a valley and a gate field. Furthermore, we find that systems with VLC can exhibit other interesting physics, such as valley-contrasting linear dichroism and optical selection of the valley and the electric polarization of interlayer excitons. [PRL**124**, 037701 (2020)]**First 2D second-order topological insulator.**Based on first-principles calculations and theoretical analysis, we predict the already experimentally synthesized graphdiyne as the first realistic 2D second-order topological insulator, with protected 0D corner states. We also propose a universal approach to realize magnetic 2D second-order topological insulators. [PRL**123**, 256402 (2019); PRL**125**, 056402 (2020)]**First demonstration of 3D quantum Hall effect.**Collaborating with experimental colleagues, we give the first demonstration of 3D quantum Hall effect proposed by Halperin in 1987. We show that in ultrahigh quality bulk ZrTe_{5}, when entering the extreme quantum limit, dissipationless longitudinal resistivity is observed, accompanied by a well-developed Hall plateau proportional to half of the Fermi wavelength along the field direction, suggesting a charge-density-wave Fermi surface instability driven by enhanced interaction effects. [Nature**569**, 537 (2019)]**Circumventing the no-go theorem.**The no-go theorem states that left- and right-handed Weyl points must appear in pairs in a non-interacting lattice. Accompanying the no-go theorem, the surface of the system features Fermi arc states, which connect pairs of surface projected Weyl points. We construct a topological phase that circumvents this theorem, which has a single Weyl point without surface Fermi arcs, achieved by symmetry-enforced nodal walls spreading over the entire Brillouin zone boundary. [PRB**100**, 041118(R) (2019)]**Quadratic & cubic nodal lines.**We predict the existence of nodal lines with quadratic or cubic dispersion protected by crystalline symmetries, and prove that there is no other higher order possibility. We show their signatures in measurable physical properties and identify several realistic materials hosting such higher-order nodal lines. Particularly, we show that cubic nodal line features a new type of topological surface states, which span the whole surface Brillouin zone. The concepts can be extended to magnetic systems as well. [PRB**99**, 121106(R) (2019); PRB**103**, 115112 (2021)]**Nodal surface semimetals**. We propose two classes of nodal surfaces. Without spin-orbit coupling (SOC), a class of nodal surfaces can be protected by space-time inversion symmetry and sublattice symmetry, while another class of nodal surfaces are guaranteed by a combination of twofold screw-rotation and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems. Several concrete nodal-surface material examples are predicted. [PRB**97**, 115125 (2018); PRB**97**, 235150 (2018)]**Anomalous spatial shift in Andreev reflection**. We predict for the first time that sizable positional shift can happen when a particle undergoes Andreev reflection at a normal-metal/superconductor interface. Particularly, a shift perpendicular to the incident plane occurs when the normal side has strong spin-orbit coupling (SOC). Moreover, even without SOC, the shift is present if the superconductor side has unconventional pair potential, and different pairing leads to distinct features in the shift, which can be detected in electrical measurement. Recently, we further reveal such shift fields can exhibit a quantized circulation. [PRB**96**, 121101(R) (2017); PRB**98**, 075151 (2018); PRL**121**, 176602 (2018); PRB**98**, 195141 (2018); FoP**14**, 33402 (2019); PRL**125**, 076801 (2020)]**Nonsymmorphic Dirac loop, Dirac chain, & cubic Dirac point**. We demonstrate that certain nonsymmorphic symmetries dictate four-fold degenerate Dirac loops in the band structure, robust against spin-orbit coupling. Multiple Dirac loops can be connected to form an extended Dirac chain. In addition, we find the first example of a nonsymmorphic-symmetry-protected cubic Dirac point. Concrete material examples are proposed to host these novel objects. Some have been confirmed in experiment. [Nat. Commun.**8**, 1844 (2017); PRB**97**, 045131 (2018); PRM**2**, 051201(R) (2018); ACS Nano**14**, 1888 (2020); Nat. Mater.**19**, 27 (2020)]**First elemental ferroelectric material**. We discover the first elemental ferroelectric material in monolayer As, Sb, and Bi. A spontaneous lattice distortion breaks the centrosymmetry and drives the system into a ferroelectric phase. The polarization is sizable to be detected in experiment, and the Curie temperature can be above room temperature. For Bi, an antiferroelectric metastable phase may also be realized. Later, we show that elemental Te few layers are also ferroelectric. [Adv. Funct. Mater.**28**, 1707383 (2018); Materials Horizons**5**, 521 (2018)]**Type-II & hybrid nodal loop**. We propose the concepts of type-II and hybrid nodal loops. A type-II loop is composed of nodal points that are all type-II, whereas a loop containing both type-I and type-II points are of hybrid type. We show that these loops possess distinct properties in optical and magnetic response. In these works, we also reveal that an arbitrary nodal loop is characterized by a Z^{3}index for its topology inside the Brillouin zone (BZ), which distinguishes a loop that penetrates the BZ from a loop that sits around a single point. [PRB**96**, 081106 (2017); PRB**97**, 125143 (2018); FoP**15**, 43201 (2020)]**Black hole, gravitational lens, & Hawking radiation in topological semimetal**. Effective gravity and gauge fields are emergent properties intrinsic for low-energy quasiparticles in topological semimetals. We study the possibility of simulating black-hole/white-hole event horizons and gravitational lensing effect inside a strained topological semimetal. Possible experimental realizations and analogue of Hawking radiation effect are discussed. [npj Quantum Materials**2**, 23 (2017)]**Blue Phosphorene oxide**. As a variant of black phosphorene, blue phosphorene is a new 2D material recently realized in experiment. We predict that even more interesting physics appears when blue phosphorene is oxidated. The obtained blue phosphorene oxide (BPO) can host new topological phases with emergent topological fermions such as 2D pseudospin-1 fermions and double-Weyl fermions. The topological phases can be controlled by strain, and we predict a universal optical absorbance in its semimetal phase. [Nano Lett.**16**, 6548 (2016)]**Exotic magnetoresponse in type-II Weyl metals**. We discover unique signatures in the magnetoresponse of type-II Weyl metals. The energy tilt tends to squeeze the Landau levels (LLs), and, for a type-II Weyl node, there always exists a critical angle between the B field and the tilt, at which the LL spectrum collapses, regardless of the field strength. Before the collapse, signatures also appear in the magneto-optical spectrum, including the invariable presence of intraband peaks, the absence of absorption tails, and the special anisotropic field dependence. [PRL**117**, 077202 (2016); PRL**119**, 026404 (2017)]**First 2D material exhibiting bonding & magnetic phase transitions**. The change of bonding status, typically occurring only in chemical processes, could dramatically alter the material properties. We predict that a tunable breaking and forming of a diatomic bond can be achieved through physical means, i.e., by a moderate biaxial strain, in the newly discovered MoN_{2}two-dimensional (2D) material. Remarkably, the bonding change also induces a magnetic phase transition, during which the magnetic moments transfer from the N(2p) sublattice to the Mo(4d) sublattice; meanwhile, the type of magnetic coupling is changed from ferromagnetic to antiferromagnetic. This is the first time that such kind of phase transition is discovered in 2D materials. [Nano Lett.**16**, 4576 (2016)]**Chirality Hall effect in Weyl semimetals**. We predict universal transverse shifts of the wave-packet center in transmission and reflection, perpendicular to the direction in which the Fermi energy or velocities change adiabatically. The anomalous shifts are opposite for electrons with different chirality, and they can be made imbalanced by breaking inversion symmetry. We discuss how to utilize local gates, strain effects, and circularly polarized lights to generate and probe such a chirality-dependent Hall effect. [PRL**115**, 156603 (2015)]**Perfect topological valley filter**. Like transistor for electronics, valley filter is the fundamental device for valleytronics. We propose the concept of topological valley filter, which is based on the topological 1D channels that are both valley-filtered and and propagating unidirectionally. As a result, such filters can in-principle achieve perfect performance with 100% valley filtering against possible scattering. Physically, it may be realized in valley-polarized QAH phase, or in domain walls between QAH and QVH phases. [PRB**91**, 045404 (2015); PRB**92**, 041404(R) (2015)]**Topological carbon materials**. We show that conjugated*p*-orbital interactions, common to most carbon allotropes, can produce novel topological spin-orbit-free Weyl semimetals. We predict a family of carbon allotrope materials which possess Weyl loops, Weyl points, Weyl surfaces, triple points, Hopf-links, and birefringent Dirac points, with different kinds of symmetry/topology protection. At a surface terminated by vacuum there emerge topological surface bands. [Nano Lett.**15**, 6974 (2015); Nanoscale**8**, 7232 (2016); Nat. Commun.**8**, 15641 (2017); Carbon**141**, 417 (2019)]**Dirac semimetal thin films**. Topological Dirac semimetals have been demonstrated in materials Na_{3}Bi and Cd_{3}As_{2}in 2014. We find interesting physics in their thin film structures. We predict that (confirmed in 2018 experiment) a gate electric field can be used to control the topological phase transition (TPT) between a trivial insulator and a quantum spin Hall insulator. This offers a simple design of a topological field effect transistor. We also predict that a small strain can also generate this TPT, based on which we propose the concept of piezo-topological transistor. [Scientific Reports**5**, 7898 (2015); Scientific Reports**5**, 14639 (2015); npj Quantum Mater.**2**, 23 (2017); Nature**564**, 390 (2018)]**Anomalous Hall effect: scattering and scaling relation**. With a history of more than 100 years, the anomalous Hall effect has been widely used as a standard tool for characterizing ferromagnets. However, the understanding of this effect is still incomplete. We show that various scattering processes can be classified into universality classes, each class having a distinct contribution to the effect. We derive a general scaling relation involving multiple competing scattering mechanisms, described by a quadratic hypersurface in the space spanned by the partial resistivities. Our theory is confirmed by experiments on Fe films. [PRB**83**, 125122 (2011); PRL**114**, 217203 (2015)]**Dirac and Weyl superconductors**. We propose a new topological phase of matter: the Dirac superconductor, which has protected bulk 4-fold nodal points and surface Andreev arcs at zero energy. We provide a sufficient criterion for realizing this phase. This work also pioneered in proposing the nodal loops and the associated drumhead surface states. We suggest that such state may have been realized in Cu-doped Bi_{2}Se_{3}. [PRL**113**, 046401 (2014)]**Second order semiclassical theory and magneto-transport**. Semiclassical theory is a well-established formalism, presented in almost all solid state physics textbooks. The existing semiclassical theory is only accurate to the first order in external fields. We formulate a second order semiclassical theory. This offers a powerful framework for studying various susceptibilities and nonlinear response coefficients. Particularly, we derive for the first time a complete theory for the magneto-conductivity in the semiclassical regime. We show that a negative longitudinal magneto-resistance may arise from Berry curvature effects, not necessarily due to chiral anomaly effect. [PRL**112**, 166601 (2014); PRB**91**, 214405 (2015); PRB**95**, 165135 (2017)]**Properties of Electride materials**. Electrides are a special kind of ionic solids with cavity-trapped electrons serving as the anions. Since their first discovery in 1983, several electride materials have been identified. We show that 2D electrides Ca_{2}N and Sr_{2}N are promising optical and plasmonic materials. We predict that their bulk can be ideal hyperbolic optical material with minimal loss in the infrared range, and their monolayers have exceptional performance as anode materials for Na-ion batteries. In addition, we reveal the first pressure-induced phase transition from a 2D electride to 0D electride (also the first pressured induced metal-insulator transition in compound). [Scientific Reports**5**, 12285 (2015); PRB**95**, 165436 (2017); ACS Appl. Mater. Interfaces**7**, 24016 (2015); JACS**139**, 13798 (2017)]**Magnetic control for valleytronics**. In 2D materials including (gapped) graphene, silicene, transition metal dichalcogenides, the low-energy states are massive Dirac fermions in multiple valleys. We find that these states have valley-contrasting orbital magnetic moment, and propose to control valley polarization by using external magnetic field. We further predict unusual physical effects including an anomalous contribution to the Hall current and novel magneto-transport properties in a*pn*junction. [PRB**88**, 115140 (2013); RSC Advances**5**, 83350 (2015)]