# Zhang, Fan

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Dr. Fan Zhang joined the Department of Physics faculty in 2014 and is currently an Associate Professor. His research interests include:

- Topological Insulators and Superconductors
- Novel Physics Induced by Majorana Fermions
- Mesoscopic Physics in 2D Dirac Materials
- Many-Body Physics in Correlated Systems
- Integer and Fractional Quantum Hall Effects

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### Recent Submissions

Item Quantum Parity Hall Effect in Bernal-Stacked Trilayer Graphene(National Academy of Sciences, 2019-05-03) Stepanov, P.; Barlas, Y.; Che, S.; Myhro, K.; Voigt, G.; Pi, Z.; Watanabe, K.; Taniguchi, T.; Smirnov, D.; Zhang, Fan; Lake, R. K.; MacDonald, A. H.; Lau, C. N.; 0000-0003-4623-4200 (Zhang, F); Zhang, FanThe quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system's mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance σₓₓ is first quantized to 4e²=h at a small perpendicular magnetic field B⊥, establishing the presence of four edge channels. As B⊥ increases, σₓₓ first decreases to 2e²=h, indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong B⊥ limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions. ©2019 The Authors. All rights reserved.Item First-Principles Study of Metal-Graphene Edge Contact for Ballistic Josephson Junction(American Physical Society, 2019-06-05) Lee, Yeonghun; Hwang, Jeongwoon; Zhang, Fan; Cho, Kyeongjae; 0000-0003-4623-4200 (Zhang, F); 0000-0003-2698-7774 (Cho, K); 369148996084659752200 (Cho, K); Lee, Yeonghun; Hwang, Jeongwoon; Zhang, Fan; Cho, KyeongjaeEdge-contacted superconductor-graphene-superconductor Josephson junctions have been utilized to realize topological superconductivity, and have shown superconducting signatures in the quantum Hall regime. We perform first-principles calculations to interpret electronic couplings at the superconductor-graphene edge contacts by investigating various aspects in hybridization of molybdenum d orbitals and graphene π orbitals. We also reveal that interfacial oxygen defects play an important role in determining the doping type of graphene near the interface. © 2019 American Physical Society.Item Spatially Correlated MIMO Broadcast Channel with Partially Overlapping Correlation Eigenspaces(Institute of Electrical and Electronics Engineers Inc.) Zhang, Fan; Nosratinia, Aria; 0000-0003-4623-4200 (Zhang, F); 0000-0002-3751-0165 (Nosratinia, A); 105575689 (Nosratinia, A); Zhang, Fan; Nosratinia, AriaThe spatially correlated MIMO broadcast channel has grown in importance due to emerging interest in massive MIMO and mm-wave communication, but much about this channel remains unknown. In this paper, we study a two-user MIMO broadcast channel where the spatial correlation matrices corresponding to the two receivers have eigenspaces that are neither identical nor disjoint, but are partially overlapped. Spatially correlated channels occur in e.g. massive MIMO and furthermore different links may credibly have correlation eigenspaces that are neither disjoint nor equal, therefore this problem is practically motivated. This paper develops a new approach for this scenario and calculates the corresponding degrees of freedom. Our technique involves a careful decomposition of the signaling space to allow a combination of pre-beamforming along directions that depend on the relative positioning of the non-overlapping and overlapping components of the eigenspaces, along with the product superposition technique. The ideas are demonstrated with a toy example, are developed in two conditions of varying complexity, and are illuminated by numerical results. ©2018 IEEE.Item Topological Triply Degenerate Points Induced by Spin-Tensor-Momentum Couplings(American Physical Society) Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, Chuanwei; Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, ChuanweiThe recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor- and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (ℭ=±2, ±1, 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.Item Valley Topological Phases In Bilayer Sonic Crystals(Amer Physical Soc) Lu, Jiuyang; Qiu, Chunyin; Deng, Weiyin; Huang, Xueqin; Li, Feng; Zhang, Fan; Chen, Shuqi; Liu, Zhengyou; Zhang, FanRecently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.Item π and 4π Josephson Effects Mediated by a Dirac Semimetal(Amer Physical Soc) Yu, W.; Pan, W.; Medlin, D. L.; Rodriguez, M. A.; Lee, S. R.; Bao, Zhi-qiang; Zhang, Fan; Bao, Zhi-qiang; Zhang, FanCd₃As₂ is a three-dimensional topological Dirac semimetal with connected Fermi-arc surface states. It has been suggested that topological superconductivity can be achieved in the nontrivial surface states of topological materials by utilizing the superconductor proximity effect. Here we report observations of both π and 4π periodic supercurrents in aluminum-Cd₃As₂-aluminum Josephson junctions. The π period is manifested by both the magnetic-field dependence of the critical supercurrent and the appearance of half-integer Shapiro steps in the ac Josephson effect. Our macroscopic theory suggests that the π period arises from interference between the induced bulk superconductivity and the induced Fermi-arc surface superconductivity. The 4π period is manifested by the missing first Shapiro steps and is expected for topological superconductivity.Item Topological Triply Degenerate Points Induced by Spin-Tensor- Momentum Couplings(Amer Physical Soc) Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, Chuanwei; 0000 0000 3722 2361 (Zhang, C); 0000-0003-4623-4200 (Zhang, F); 4042455 (Zhang, C); Hu, Haiping; Hou, Junpeng; Zhang, Fan; Zhang, ChuanweiThe recent discovery of triply degenerate points (TDPs) in topological materials has opened a new perspective toward the realization of novel quasiparticles without counterparts in quantum field theory. The emergence of such protected nodes is often attributed to spin-vector-momentum couplings. We show that the interplay between spin-tensor-and spin-vector-momentum couplings can induce three types of TDPs, classified by different monopole charges (C = ± 2, ± 1, 0). A Zeeman field can lift them into Weyl points with distinct numbers and charges. Different TDPs of the same type are connected by intriguing Fermi arcs at surfaces, and transitions between different types are accompanied by level crossings along high-symmetry lines. We further propose an experimental scheme to realize such TDPs in cold-atom optical lattices. Our results provide a framework for studying spin-tensor-momentum coupling-induced TDPs and other exotic quasiparticles.Item Circular Dichroism and Radial Hall Effects in Topological Materials(Amer Physical Soc, 2018-10-22) Liu, Ying; Yang, Shengyuan A.; Zhang, Fan; 0000-0003-4623-4200 (Zhang, F); Zhang, FanUnder symmetry breaking, a three-dimensional nodal-line semimetal can turn into a topological insulator or Weyl semimetal, accompanied by the generation of momentum-space Berry curvature. We develop a theory that unifies their circular dichroism and highlights the roles of Berry curvature distribution and light incident direction. Nontrivially, these phases exhibit distinct dichroic optical absorption and radial Hall effects, with characteristic scalings with photon energy and electric field. Our findings offer a diagnosis tool for examining topological phases of matter.Item Odd-Integer Quantum Hall States and Giant Spin Susceptibility in P -Type Few-Layer WSe₂(American Physical Society, 2017-02-10) Xu, S.; Shen, J.; Long, G.; Wu, Z.; Bao, Zhi-qiang; Liu, Cheng-Cheng; Xiao, X.; Han, T.; Lin, J.; Wu, Y.; Lu, H.; Hou, J.; An, L.; Wang, Y.; Cai, Y.; Ho, K. M.; He, Y.; Lortz, R.; Zhang, Fan; Wang, N.; Bao, Zhi-qiang; Liu, Cheng-Cheng; Zhang, FanWe fabricate high-mobility p-type few-layer WSe₂ field-effect transistors and surprisingly observe a series of quantum Hall (QH) states following an unconventional sequence predominated by odd-integer states under a moderate strength magnetic field. By tilting the magnetic field, we discover Landau level crossing effects at ultralow coincident angles, revealing that the Zeeman energy is about 3 times as large as the cyclotron energy near the valence band top at the Γ valley. This result implies the significant roles played by the exchange interactions in p-type few-layer WSe₂, in which itinerant or QH ferromagnetism likely occurs. Evidently, the Γ valley of few-layer WSe₂ offers a unique platform with unusually heavy hole carriers and a substantially enhanced g factor for exploring strongly correlated phenomena.Item Observation of Acoustic Valley Vortex States and Valley-Chirality Locked Beam Splitting(2017-05-23) Ye, Liping; Qiu, Chunyin; Lu, Jiuyang; Wen, Xinhua; Shen, Yuanyuan; Ke, Manzhu; Zhang, Fan; Liu, Zhengyou; 0000-0003-4623-4200 (Zhang, F); Zhang, FanWe report an experimental observation of the classical version of valley polarized states in a two-dimensional hexagonal sonic crystal. The acoustic valley states, which carry specific linear momenta and orbital angular momenta, were selectively excited by external Gaussian beams and conveniently confirmed by the pressure distribution outside the crystal, according to the criterion of momentum conservation. The vortex nature of such intriguing bulk crystal states was directly characterized by scanning the phase profile inside the crystal. In addition, we observed a peculiar beam-splitting phenomenon, in which the separated beams are constructed by different valleys and locked to the opposite vortex chirality. The exceptional sound transport, encoded with valley-chirality locked information, may serve as the basis of designing conceptually interesting acoustic devices with unconventional functions.Item Topological Majorana Two-Channel Kondo Effect(American Physical Society, 2017-10-31) Bao, Zhi-qiang; Zhang, Fan; 0000-0003-4623-4200 (Zhang, F); Bao, Zhi-qiang; Zhang, FanA one-dimensional time-reversal-invariant topological superconductor hosts a Majorana Kramers pair at each end, where time-reversal symmetry acts as a supersymmetry that flips local fermion parity. We examine the transport anomaly of such a superconductor, floating and tunnel-coupled to normal leads at its two ends. We demonstrate the realization of a topologically protected, channel-symmetric, two-channel Kondo effect without fine-tuning. Whereas the nonlocal teleportation vanishes, a lead present at one end telecontrols the universal transport through the other end.Item Weak Topological Insulators and Composite Weyl Semimetals: β-Bi₄Χ₄ (Χ = Br, I)(Amer Physical Soc, 2016-02-09) Liu, Cheng-Cheng; Zhou, Jin-Jian; Yao, Yugui; Zhang, Fan; 0000-0003-4623-4200 (Zhang, F); Zhang, FanWhile strong topological insulators (STIs) were experimentally realized soon after they were theoretically predicted, a weak topological insulator (WTI) has yet to be unambiguously confirmed. A major obstacle is the lack of distinct natural cleavage surfaces to test the surface selective hallmark of a WTI. With a new scheme, we discover that β-Bi₄Χ₄ (Χ = Br, I), dynamically stable or synthesized before, can be a prototype WTI with two natural cleavage surfaces, where two anisotropic Dirac cones stabilize and annihilate, respectively. We further find four surface-state Lifshitz transitions under charge doping and two bulk topological phase transitions under uniaxial strain. Near the WTI-STI transition, there emerges a novel Weyl semimetal phase, in which the Fermi arcs generically appear at both cleavage surfaces whereas the Fermi circle only appears at one selected surface.Item Perfect Valley Filter in a Topological Domain Wall(Amer Physical Soc, 2015-07-07) Pan, Hui; Li, Xin; Zhang, Fan; Yang, Shengyuan A.; Zhang, FanWe propose a realization of perfect valley filters based on the chiral domain-wall channels between a quantum anomalous Hall insulator and a quantum valley Hall insulator. Uniquely, all these channels reside in the same valley and propagate unidirectionally, 100% valley-polarizing passing-by carriers without backscattering. The valley index, the chirality, and the number of the channels are protected by topological charges, controllable by external fields, and detectable by circular dichroism.Item Critical Behavior of Four-Terminal Conductance of Bilayer Graphene Domain Walls(2015-08-24) Wieder, Benjamin J.; Zhang, Fan; Kane, C. L.; Zhang, FanBilayer graphene in a perpendicular electric field can host domain walls between regions of reversed field direction or interlayer stacking. The gapless modes propagating along these domain walls, while not strictly topological, nevertheless have interesting physical properties, including valley-momentum locking. A junction where two domain walls intersect forms the analog of a quantum point contact. We study theoretically the critical behavior of this junction near the pinch-off transition, which is controlled by two separate classes of nontrivial quantum critical points. For strong interactions, the junction can host phases of unique charge and valley conductances. For weaker interactions, the low-temperature charge conductance can undergo one of two possible quantum phase transitions, each characterized by a specific critical exponent and a collapse to a universal scaling function, which we compute.Item Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene(American Physical Society, 2016-02-05) Shi, Yanmeng; Lee, Yongjin; Che, Shi; Pi, Ziqi; Espiritu, Timothy; Stepanov, Petr; Smirnov, Dmitry; Lau, Chun Ning; Zhang, Fan; 0000-0003-4623-4200 (Zhang, F); Zhang, FanOwing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν=2/3 quantum Hall state and a feature at ν=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.Item SU(3) Quantum Hall Ferromagnetism in SnTe(American Physical Society, 2016-01-15) Li, X.; Zhang, Fan; MacDonald, A. H.; 0000-0003-4623-4200 (Zhang, F); Zhang, FanThe (111) surface of SnTe hosts one isotropic Γ-centered and three degenerate anisotropic M-centered Dirac surface states. We predict that a nematic phase with spontaneously broken C₃ symmetry will occur in the presence of a perpendicular magnetic field when the N=0 M Landau levels are 1/3 or 2/3 filled. The nematic state phase boundary is controlled by a competition between intravalley Coulomb interactions that favor a valley-polarized state and weaker intervalley scattering processes that increase in relative strength with magnetic field. An in-plane Zeeman field alters the phase diagram by lifting the threefold M Landau-level degeneracy, yielding a ground state energy with 2π/3 periodicity as a function of Zeeman-field orientation angle.Item Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids(American Physical Society, 2015-12-30) Xu, Yong; Zhang, Fan; Zhang, Chuanwei; Xu, Yong; Zhang, Fan; Zhang, ChuanweiWe demonstrate that a Weyl point, widely examined in 3D Weyl semimetals and superfluids, can develop a pair of nondegenerate gapless spheres. Such a bouquet of two spheres is characterized by three distinct topological invariants of manifolds with full energy gaps, i.e., the Chern number of a 0D point inside one developed sphere, the winding number of a 1D loop around the original Weyl point, and the Chern number of a 2D surface enclosing the whole bouquet. We show that such structured Weyl points can be realized in the superfluid quasiparticle spectrum of a 3D degenerate Fermi gas subject to spin-orbit couplings and Zeeman fields, which supports Fulde-Ferrell superfluids as the ground state.Item Chirality-Dependent Hall Effect in Weyl Semimetals(Amer Physical Soc, 2015-10-09) Yang, Shengyuan A.; Pan, Hui; Zhang, Fan; School of Natural Sciences and Mathematics; 0000-0003-4623-4200 (Zhang, F); Zhang, FanWe generalize a semiclassical theory and use the argument of angular momentum conservation to examine the ballistic transport in lightly doped Weyl semimetals, taking into account various phase-space Berry curvatures. 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.Item Buckled Honeycomb Lattice Materials and Unconventional Magnetic Responses(Royal Society of Chemistry, 2015-09-24) Yang, S. A.; Pan, H.; Zhang, Fan; 0000-0003-4623-4200 (Zhang, F); Zhang, FanWe study the magnetic response of two-dimensional buckled honeycomb-lattice materials. The buckling breaks the sublattice symmetry, enhances the spin-orbit coupling, and allows the tuning of a topological quantum phase transition. As a result, there are two doubly degenerate spin-valley coupled massive Dirac bands, which exhibit an unconventional Hall plateau sequence under strong magnetic fields. We show how to externally control the splitting of anomalous zeroth Landau levels, the prominent Landau level crossing effects, and the polarizations of spin, valley, and sublattice degrees of freedom. In particular, we reveal that in a p-n junction, spin-resolved fractionally quantized conductance appears in a two-terminal measurement with a spin-polarized current propagating along the interface. In the zero- or low-field regime where the Landau quantization is not applicable, we provide a semiclassical description for the anomalous Hall transport. We comment briefly on the effects of electron-electron interactions and Zeeman couplings to electron spins and to atomic orbitals. Our predictions can be examined in the magneto-transport and/or magneto-optic experiments.Item (111) Surface States of SnTe(2014-12--08) Shi, Yin; Wu, Meng; Zhang, Fan; Feng, Ji; Zhang, FanThe characterization and applications of topological insulators depend critically on their protected surface states, which, however, can be obscured by the presence of trivial dangling bond states. Our first-principle calculations show that this is the case for the pristine (111) surface of SnTe. Yet, the predicted surface states unfold when the dangling bond states are passivated in proper chemisorption. We further extract the anisotropic Fermi velocities, penetration lengths, and anisotropic spin textures of the unfolded (Gamma) over bar -and (M) over bar -surface states, which are consistent with the theory in Zhang et al. [Phys. Rev. B 86, 081303 (2012)]. More importantly, this chemisorption scheme provides an external control of the relative energies of different Dirac nodes, which is particularly desirable in multivalley transport.