Bor-Luen Huang - Academia.edu (original) (raw)

Papers by Bor-Luen Huang

Physical Review B, 2009

Due to the weak spin-orbit interaction and the peculiar relativistic dispersion in graphene, ther... more Due to the weak spin-orbit interaction and the peculiar relativistic dispersion in graphene, there are exciting proposals to build spin qubits in graphene nanoribbons with armchair boundaries. However, the mutual interactions between electrons are neglected in most studies so far and thus motivate us to investigate the role of electronic correlations in armchair graphene nanoribbon by both analytical and numerical methods. Here we show that the inclusion of mutual repulsions leads to drastic changes and the ground state turns ferromagnetic in a range of carrier concentrations. Our findings highlight the crucial importance of the electron-electron interaction and its subtle interplay with boundary topology in graphene nanoribbons. Furthermore, since the ferromagnetic properties sensitively depends on the carrier concentration, it can be manipulated at ease by electric gates. The resultant ferromagnetic state with metallic conductivity is not only surprising from an academic viewpoint, but also has potential applications in spintronics at nanoscale.

Physical Review B, 2013

We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangu... more We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangular sample using Ginzburg-Landau and quasi-classical Green's function theory. Apart from a few very special cases, we find that the ground state near the critical temperature always prefers a time-reversal symmetric state, where the order parameter can be represented by a real vector. For large aspect ratio, this vector is parallel to the long side of the rectangle. Within a critical aspect ratio, it has instead a vortex-like structure, vanishing at the sample center. PACS numbers: 74.78.Na, 74.20.De, 74.20.Rp Studies of multicomponent superfluids and superconductors have excited many for decades because of the diversity of textures, complex vortex structures and collective modes. The superfluid 3 He with spin-triplet order parameter [1, 2] is a well-established example. Many studies also show that superconductors with multicomponent order parameters can also be found in, for example, UPt 3 [3, 4] and Sr 2 RuO 4 . Recently, studies of multicomponent superconductor in a confined geometry draw much attention due to advancements in nanofabrication. Experiments claimed to find half-quantum vortices [7] and the Little-Parks effect in Sr 2 RuO 4 quantum ring. Surfaces are expected to have non-trivial effects on such superconductors. Some theoretical works show that surface currents are present in broken timereversal symmetric superconductors. In considering Ru inclusions, Sigrist and his collaborators have shown that a time-reversal symmetry state can be favored near the interface between Ru and Sr 2 RuO 4 due to the boundary conditions. In our previous work [13], considering a thin circular disk with smooth boundaries and applying Ginzburg-Landau (GL) theory, we have shown that a two-component p-wave superconductor can exhibit multiple phase transitions in a confined geometry. At zero magnetic field, the superconducting transition from the normal state was found to be always first to a timereversal symmetric state (with an exception which occurs only far away from the isotropic weak-coupling limit), even though the bulk free energy may favor a broken time-reversal symmetry state, which can exist at a lower temperature. This time-reversal symmetric state has a vortex-like structure, with order parameter vanishing at the center of the disk. We have also argued there that these features are general, do not rely on the GL approximation and should exist for also general geometries. In this paper, we investigate this question further by considering rectangular and square samples, employing both GL and quasiclassical (QC) Green's function method. Within GL, for rectangular samples with large aspect ratios, we show that the phase transition from the normal to the superconducting state is second-order and is to a state with order parameter being a real vector parallel to the long side of the sample. For smaller aspect ratios, the state near the transition temperature is again a time-reversal symmetric state with a vortex at the center, except for a square and only for gradient coefficients far away from the weak-coupling limit, much like what we found for the circular disk. At not too small sizes, the results from QC are qualitatively similar to GL except for the critical sizes and aspect ratios obtained. At very small sizes however, QC calculation suggests that a more complicated situation can arise for some special aspect ratios. The transition can either become first-order, or perhaps into a state with a more complicated order parameter. In this paper, we shall mostly concentrate on the parameter region where the phase transition is second-order and leave the detailed investigation of the above mentioned special case to the future.

Physical Review B, 2004

Edge states of semi-infinite nanowires in tight binding limit are examined. We argue that underst... more Edge states of semi-infinite nanowires in tight binding limit are examined. We argue that understanding these edge states provides a pathway to generic comprehension of surface states in many semi-infinite physical systems. It is shown that the edge states occur within the gaps of the corresponding bulk spectrum (thus also called the midgap states). More importantly, we show that the presence of these midgap states reflects an underlying generalized supersymmetry. This supersymmetric structure is a generalized rotational symmetry among sublattices and results in a universal tendency: all midgap states tend to vanish with periods commensurate with the underlying lattice. Based on our formulation, we propose a structure with superlattice in hopping to control the number of localized electronic states occurring at the ends of the nanowires. Other implications are also discussed. In particular, it is shown that the ordinarily recognized impurity states can be viewed as disguised midgap states.

Physical Review A, 2014

We generalized the Fermi liquid theory to N component systems with SU(N) symmetry. We emphasize t... more We generalized the Fermi liquid theory to N component systems with SU(N) symmetry. We emphasize the important role of fluctuations when N is large. These fluctuations dramatically modifies the properties for repulsive Fermi gases, in particular the spin susceptibility.

Physica C: Superconductivity, 2003

The effect of the superlattice structure along the c-axis on the single particle density of high ... more The effect of the superlattice structure along the c-axis on the single particle density of high temperature superconductors is investigated by considering superlattice systems that consists of metals/insulators and d-wave superconductors (NS/IS superlattices). It is shown that the position of quasiparticle peak is sensitive to how one models the c-axis tunneling. For the NS superlattice, the position of the quasiparticle peak can be considerably smaller than the gap value, while for the IS superlattice, the quasiparticle peak always remains at the bulk value so that the whole system behaves like a single superconductor. Furthermore, in the presence of a small current, the density of state at zero energy becomes non-zero for the NS superlattice while it sticks to zero for the IS superlattice. This results in different behaviors in the specific heat measurements, providing a possible way to differentiate between these two models.

Journal of Physics: Condensed Matter, 2012

A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-r... more A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-ribbon is in the quantum spin Hall (QSH) state, then there must be helical edge states. By folding a graphene ribbon to a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furthermore, by enhancing the Rashba coupling, we find that the persistent spin current gradually reduces to zero at a critical value, beyond which the graphene is no longer a QSH insulator. PACS numbers: 81.05.ue, 61.72.J-, 71.15.-m Persistent currents in a graphene ring with armchair edges

EPL (Europhysics Letters), 2009

It is pointed out that point defects on graphene are strongly correlated and can not be treated a... more It is pointed out that point defects on graphene are strongly correlated and can not be treated as independent scatters. In particular, for large on-site defect potential, it is shown that defects induce an impurity band with density of state characterized by the Wigner semi-circle law. We find that the impurity band enhances conductivity to the order of 4e 2 /h and explains the absence of strong localization. Furthermore,the impurity band supports ferromagnetism with the induced magnetic moment approaching 1µB per defect in the limit of infinite quasi-particle lifetime.

Physical Review B, 2009

Due to the weak spin-orbit interaction and the peculiar relativistic dispersion in graphene, ther... more Due to the weak spin-orbit interaction and the peculiar relativistic dispersion in graphene, there are exciting proposals to build spin qubits in graphene nanoribbons with armchair boundaries. However, the mutual interactions between electrons are neglected in most studies so far and thus motivate us to investigate the role of electronic correlations in armchair graphene nanoribbon by both analytical and numerical methods. Here we show that the inclusion of mutual repulsions leads to drastic changes and the ground state turns ferromagnetic in a range of carrier concentrations. Our findings highlight the crucial importance of the electron-electron interaction and its subtle interplay with boundary topology in graphene nanoribbons. Furthermore, since the ferromagnetic properties sensitively depends on the carrier concentration, it can be manipulated at ease by electric gates. The resultant ferromagnetic state with metallic conductivity is not only surprising from an academic viewpoint, but also has potential applications in spintronics at nanoscale.

Physical Review B, 2013

We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangu... more We study the finite-size and boundary effects on a p-wave superconductor in a mesoscopic rectangular sample using Ginzburg-Landau and quasi-classical Green's function theory. Apart from a few very special cases, we find that the ground state near the critical temperature always prefers a time-reversal symmetric state, where the order parameter can be represented by a real vector. For large aspect ratio, this vector is parallel to the long side of the rectangle. Within a critical aspect ratio, it has instead a vortex-like structure, vanishing at the sample center. PACS numbers: 74.78.Na, 74.20.De, 74.20.Rp Studies of multicomponent superfluids and superconductors have excited many for decades because of the diversity of textures, complex vortex structures and collective modes. The superfluid 3 He with spin-triplet order parameter [1, 2] is a well-established example. Many studies also show that superconductors with multicomponent order parameters can also be found in, for example, UPt 3 [3, 4] and Sr 2 RuO 4 . Recently, studies of multicomponent superconductor in a confined geometry draw much attention due to advancements in nanofabrication. Experiments claimed to find half-quantum vortices [7] and the Little-Parks effect in Sr 2 RuO 4 quantum ring. Surfaces are expected to have non-trivial effects on such superconductors. Some theoretical works show that surface currents are present in broken timereversal symmetric superconductors. In considering Ru inclusions, Sigrist and his collaborators have shown that a time-reversal symmetry state can be favored near the interface between Ru and Sr 2 RuO 4 due to the boundary conditions. In our previous work [13], considering a thin circular disk with smooth boundaries and applying Ginzburg-Landau (GL) theory, we have shown that a two-component p-wave superconductor can exhibit multiple phase transitions in a confined geometry. At zero magnetic field, the superconducting transition from the normal state was found to be always first to a timereversal symmetric state (with an exception which occurs only far away from the isotropic weak-coupling limit), even though the bulk free energy may favor a broken time-reversal symmetry state, which can exist at a lower temperature. This time-reversal symmetric state has a vortex-like structure, with order parameter vanishing at the center of the disk. We have also argued there that these features are general, do not rely on the GL approximation and should exist for also general geometries. In this paper, we investigate this question further by considering rectangular and square samples, employing both GL and quasiclassical (QC) Green's function method. Within GL, for rectangular samples with large aspect ratios, we show that the phase transition from the normal to the superconducting state is second-order and is to a state with order parameter being a real vector parallel to the long side of the sample. For smaller aspect ratios, the state near the transition temperature is again a time-reversal symmetric state with a vortex at the center, except for a square and only for gradient coefficients far away from the weak-coupling limit, much like what we found for the circular disk. At not too small sizes, the results from QC are qualitatively similar to GL except for the critical sizes and aspect ratios obtained. At very small sizes however, QC calculation suggests that a more complicated situation can arise for some special aspect ratios. The transition can either become first-order, or perhaps into a state with a more complicated order parameter. In this paper, we shall mostly concentrate on the parameter region where the phase transition is second-order and leave the detailed investigation of the above mentioned special case to the future.

Physical Review B, 2004

Edge states of semi-infinite nanowires in tight binding limit are examined. We argue that underst... more Edge states of semi-infinite nanowires in tight binding limit are examined. We argue that understanding these edge states provides a pathway to generic comprehension of surface states in many semi-infinite physical systems. It is shown that the edge states occur within the gaps of the corresponding bulk spectrum (thus also called the midgap states). More importantly, we show that the presence of these midgap states reflects an underlying generalized supersymmetry. This supersymmetric structure is a generalized rotational symmetry among sublattices and results in a universal tendency: all midgap states tend to vanish with periods commensurate with the underlying lattice. Based on our formulation, we propose a structure with superlattice in hopping to control the number of localized electronic states occurring at the ends of the nanowires. Other implications are also discussed. In particular, it is shown that the ordinarily recognized impurity states can be viewed as disguised midgap states.

Physical Review A, 2014

We generalized the Fermi liquid theory to N component systems with SU(N) symmetry. We emphasize t... more We generalized the Fermi liquid theory to N component systems with SU(N) symmetry. We emphasize the important role of fluctuations when N is large. These fluctuations dramatically modifies the properties for repulsive Fermi gases, in particular the spin susceptibility.

Physica C: Superconductivity, 2003

The effect of the superlattice structure along the c-axis on the single particle density of high ... more The effect of the superlattice structure along the c-axis on the single particle density of high temperature superconductors is investigated by considering superlattice systems that consists of metals/insulators and d-wave superconductors (NS/IS superlattices). It is shown that the position of quasiparticle peak is sensitive to how one models the c-axis tunneling. For the NS superlattice, the position of the quasiparticle peak can be considerably smaller than the gap value, while for the IS superlattice, the quasiparticle peak always remains at the bulk value so that the whole system behaves like a single superconductor. Furthermore, in the presence of a small current, the density of state at zero energy becomes non-zero for the NS superlattice while it sticks to zero for the IS superlattice. This results in different behaviors in the specific heat measurements, providing a possible way to differentiate between these two models.

Journal of Physics: Condensed Matter, 2012

A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-r... more A graphene nano-ribbon with armchair edges is known to have no edge state. However, if the nano-ribbon is in the quantum spin Hall (QSH) state, then there must be helical edge states. By folding a graphene ribbon to a ring and threading it by a magnetic flux, we study the persistent charge and spin currents in the tight-binding limit. It is found that, for a broad ribbon, the edge spin current approaches a finite value independent of the radius of the ring. For a narrow ribbon, inter-edge coupling between the edge states could open the Dirac gap and reduce the overall persistent currents. Furthermore, by enhancing the Rashba coupling, we find that the persistent spin current gradually reduces to zero at a critical value, beyond which the graphene is no longer a QSH insulator. PACS numbers: 81.05.ue, 61.72.J-, 71.15.-m Persistent currents in a graphene ring with armchair edges

EPL (Europhysics Letters), 2009

It is pointed out that point defects on graphene are strongly correlated and can not be treated a... more It is pointed out that point defects on graphene are strongly correlated and can not be treated as independent scatters. In particular, for large on-site defect potential, it is shown that defects induce an impurity band with density of state characterized by the Wigner semi-circle law. We find that the impurity band enhances conductivity to the order of 4e 2 /h and explains the absence of strong localization. Furthermore,the impurity band supports ferromagnetism with the induced magnetic moment approaching 1µB per defect in the limit of infinite quasi-particle lifetime.