arXiv subjects

Sumanta Tewari

Publications and source records attributed to Sumanta Tewari.

At least 109 records · Page 6Linked to original sources

arXiv2012

Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures

In proximity to an s-wave superconductor, a one- or two-dimensional, electron- or hole-doped semiconductor with a sizable spin-orbit coupling and a Zeeman splitting can support a topological superconducting (TS) state. The semiconductor TS state has Majorana fermions as localized zero-energy excitations at order parameter defects such as vortices and sample edges. Here we examine the effects of quenched disorder from the semiconductor surface on the stability of the TS state in both electron- and hole-doped semiconductors. By considering the interplay of broken time reversal symmetry (due to Zeeman splitting) and disorder we derive an expression for the disorder suppression of the superconducting quasiparticle gap in the TS state. We conclude that the effects of disorder can be minimized by increasing the ratio of the spin-orbit energy with the Zeeman splitting. By giving explicit numbers we show that a stable TS state is possible in both electron- and hole-doped semiconductors for experimentally realistic values of parameters. We discuss possible suitable semiconductor materials which should be the leading candidates for the Majorana search in solid state systems.

cond-mat.supr-con↗

arXiv2012

Topologically non-trivial superfluid phases and Majorana fermions from Kohn-Luttinger effect

Spin-triplet p-wave superfluids of single-species (or spin-polarized) fermionic atoms is a topological superfluid. In 2D such a superfluid supports zero-energy topological Majorana fermion excitations in order parameter defects such as vortices and sample edges. In 3D these superfluids support topologically protected Dirac points in the bulk spectrum and flat surface Majorana arcs. Despite the promise, creating a spin-triplet p-wave single-species fermionic superfluid either from direct p-wave Feshbach resonance or indirectly from the recently proposed artificial spin-orbit and Zeeman couplings can be technologically challenging. Here we show that such topological superfluids can be far more simply created by using the Kohn-Luttinger effect applied to two species of spin-polarized fermions with a density imbalance. We discuss how the topological Majorana excitations of the resulting superfluids can be identified using recently-developed experimental techniques.

cond-mat.quant-gas↗

arXiv2012

Topological invariants for spin-orbit coupled superconductor nanowires

We show that a spin-orbit coupled semiconductor nanowire with Zeeman splitting and s-wave superconductivity is in symmetry class BDI (not D as is commonly thought) of the topological classification of band Hamiltonians. The class BDI allows for an integer Z topological invariant equal to the number of Majorana fermion (MF) modes at each end of the quantum wire protected by the chirality symmetry (reality of the Hamiltonian). Thus it is possible for this system (and all other d=1 models related to it by symmetry) to have an arbitrary integer number, not just 0 or 1 as is commonly assumed, of MFs localized at each end of the wire. The integer counting the number of MFs at each end reduces to 0 or 1, and the class BDI reduces to D, in the presence of terms in the Hamiltonian that break the chirality symmetry.

cond-mat.mes-hall↗

arXiv2011

Topologically protected surface Majorana arcs and bulk Weyl fermions in ferromagnetic superconductors

A number of ferromagnetic superconductors have been recently discovered which are believed to be in the so-called "equal spin pairing" (ESP) state. In the ESP state the Cooper pairs condense forming order parameters $Δ_{\uparrow\uparrow}, Δ_{\downarrow\downarrow}$ which are decoupled in the spin-sector. We show that these three-dimensional systems should generically support topologically protected surface Majorana arcs and bulk Weyl fermions as gapless excitations. Similar protected low-energy exotic quasiparticles should also appear in the recently discovered non-centrosymmteric superconductors in the presence of a Zeeman field. The protected surface arcs can be probed by angle-resolved photoemission (ARPES) as well as scanning tunneling microscope (STM) experiments.

cond-mat.supr-con↗

arXiv2011

Majorana fermions in carbon nanotubes

We show that carbon nanotubes (CNT) are good candidates for realizing one-dimensional topological superconductivity with Majorana fermions localized near the end points. The physics behind topological superconductivity in CNT is novel and is mediated by a recently reported curvature-induced spin-orbit coupling which itself has a topological origin. In addition to the spin-orbit coupling, an important new requirement for a robust topological state is broken chirality symmetry about the nanotube axis. We use topological arguments to show that, for recently realized strengths of spin-orbit coupling and broken chirality symmetry, a robust topological gap of around 500 mK is achievable in carbon nanotubes.

cond-mat.supr-con↗

arXiv2011

BCS-BEC Crossover and Topological Phase Transition in 3D Spin-Orbit Coupled Degenerate Fermi Gases

We investigate the BCS-BEC crossover in three dimensional degenerate Fermi gases in the presence of spin-orbit coupling (SOC) and Zeeman field. We show that the superfluid order parameter destroyed by a large Zeeman field can be restored by the SOC. With increasing strengths of the Zeeman field, there is a series of topological quantum phase transitions from a non-topological superfluid state with fully gapped fermionic spectrum to a topological superfluid state with four topologically protected Fermi points (i.e., nodes in the quasiparticle excitation gap) and then to a second topological superfluid state with only two topologically protected Fermi points. The quasiparticle excitations near the Fermi points realize the long-sought low-temperature analog of Weyl fermions of particle physics. We show that the topological phase transitions can be probed using the experimentally realized momentum resolved photoemission spectroscopy.

cond-mat.quant-gas↗

arXiv2011

Diamagnetic susceptibility obtained from the six-vertex model and its implications for the high-temperature diamagnetic state of cuprate superconductors

We study the diamagnetism of the 6-vertex model with the arrows as directed bond currents. To our knowledge, this is the first study of the diamagnetism of this model. A special version of this model, called F model, describes the thermal disordering transition of an orbital antiferromagnet, known as d-density wave (DDW), a proposed state for the pseudogap phase of the high-Tc cuprates. We find that the F model is strongly diamagnetic and the susceptibility may diverge in the high temperature critical phase with power law arrow correlations. These results may explain the surprising recent observation of a diverging low-field diamagnetic susceptibility seen in some optimally doped cuprates within the DDW model of the pseudogap phase.

cond-mat.supr-con↗

arXiv2011

Probing non-Abelian statistics with Majorana fermion interferometry in spin-orbit-coupled semiconductors

The list of quantum mechanical systems with non-Abelian statistics has recently been expanded by including generic spin-orbit-coupled semiconductors e.g., InAs) in proximity to a s-wave superconductor. Demonstration of the anyonic statistics using Majorana fermion interferometry in this system is a necessary first step towards topological quantum computation (TQC). However, since all isolated chiral edges that can be created in the semiconductor are charge neutral, it is not clear if electrically controlled interferometry is possible in this system. Here we show that when two isolated chiral Majorana edges are brought into close contact, the resultant interface supports charge current, enabling electrically controlled Majorana fermion interferometry in the semiconductor structure. Such interferometry experiments on the semiconductor are analogous to similar interferometry experiments on the $ν=5/2$ fractional quantum Hall systems and on the surface of a 3D strong topological insulator, illustrating the usefulness of the 2D semiconductor heterostructure as a suitable TQC platform. In particular, we proposed Majorana interferometers may be the most direct method for establishing non-Abelian braiding statistics in topological superconductors.

cond-mat.str-el↗

arXiv2011

Topologically non-trivial superconductivity in spin-orbit coupled systems: Bulk phases and quantum phase transitions

Topologically non-trivial superconductivity has been predicted to occur in superconductors with a sizable spin-orbit coupling in the presence of an external Zeeman splitting. Two such systems have been proposed: (a) s-wave superconductor pair potential is proximity induced on a semiconductor, and (b) pair potential naturally arises from an intrinsic s-wave pairing interaction. As is now well known, such systems in the form of a 2D film or 1D nano-wires in a wire-network can be used for topological quantum computation. When the external Zeeman splitting $Γ$ crosses a critical value $Γ_c$, the system passes from a regular superconducting phase to a non-Abelian topological superconducting phase. In both cases (a) and (b) we consider in this paper the pair potential $Δ$ is strictly s-wave in both the ordinary and the topological superconducting phases, which are separated by a topological quantum critical point at $Γ_c = \sqrt{Δ^2 + μ^2}$, where $μ(>> Δ)$ is the chemical potential. On the other hand, since $Γ_c >> Δ$, the Zeeman splitting required for the topological phase ($Γ> Γ_c$) far exceeds the value ($Γ\sim Δ$) above which an s-wave pair potential is expected to vanish (and the system to become non-superconducting) in the absence of spin-orbit coupling. We are thus led to a situation that the topological superconducting phase appears to set in a parameter regime at which the system actually is non-superconducting in the absence of spin-orbit coupling. In this paper we address the question of how a pure s-wave pair potential can survive a strong Zeeman field to give rise to a topological superconducting phase. We show that the spin-orbit coupling is the crucial parameter for the quantum transition into and the robustness of the topologically non-trivial superconducting phase realized for $Γ>> Δ$.

cond-mat.supr-con↗

arXiv2011

Anisotropic surface transport in topological insulators in proximity to a helical spin density wave

We study the effects of spatially localized breakdown of time reversal symmetry on the surface of a topological insulator (TI) due to proximity to a helical spin density wave (HSDW). The HSDW acts like an externally applied one-dimensional periodic(magnetic) potential for the spins on the surface of the TI, rendering the Dirac cone on the TI surface highly anisotropic. The decrease of group velocity along the direction $\hat{x}$ of the applied spin potential is twice as much as that perpendicular to $\hat{x}$. At the Brillouin zone boundaries (BZB) it also gives rise to new semi-Dirac points which have linear dispersion along $\hat{x}$ but quadratic dispersion perpendicular to $\hat{x}$. The group velocity of electrons at these new semi-Dirac points is also shown to be highly anisotropic. Experiments using TI systems on multiferroic substrates should realize our predictions. We further discuss the effects of other forms of spin density wave on the surface transport property of topological insulator.

cond-mat.mes-hall↗

arXiv2011

Majorana fermion exchange in quasi-one-dimensional networks

Heterostructures of spin-orbit coupled materials with s-wave superconductors are thought to be capable of supporting zero-energy Majorana bound states. Such excitations are known to obey non-Abelian statistics in two dimensions, and are thus relevant to topological quantum computation (TQC). In a one-dimensional system, Majorana states are localized to phase boundaries. In order to bypass the constraints of one-dimension, a wire network may be created, allowing the exchange of Majoranas by way of junctions in the network. Alicea et al. have proposed such a network as a platform for TQC, showing that the Majorana bound states obey non-Abelian exchange statistics even in quasi-one-dimensional systems. Here we show that the particular realization of non- Abelian statistics produced in a Majorana wire network is highly dependent on the local properties of individual wire junctions. For a simply connected network, the possible realizations can be characterized by the chirality of individual junctions. There is in general no requirement for junction chiralities to remain consistent across a wire network. We show how the chiralities of different junctions may be compared experimentally and discuss the implications for TQC in Majorana wire networks.

cond-mat.mes-hall↗

arXiv2010

Universal quantum computation on a semiconductor quantum wire network

Universal quantum computation (UQC) using Majorana fermions on a 2D topological superconducting (TS) medium remains an outstanding open problem. This is because the quantum gate set that can be generated by braiding of the Majorana fermions does not include \emph{any} two-qubit gate and also the single-qubit $π/8$ phase gate. In principle, it is possible to create these crucial extra gates using quantum interference of Majorana fermion currents. However, it is not clear if the motion of the various order parameter defects (vortices, domain walls, \emph{etc.}), to which the Majorana fermions are bound in a TS medium, can be quantum coherent. We show that these obstacles can be overcome using a semiconductor quantum wire network in the vicinity of an $s$-wave superconductor, by constructing topologically protected two-qubit gates and any arbitrary single-qubit phase gate in a topologically unprotected manner, which can be error corrected using magic state distillation. Thus our strategy, using a judicious combination of topologically protected and unprotected gate operations, realizes UQC on a quantum wire network with a remarkably high error threshold of $0.14$ as compared to $10^{-3}$ to $10^{-4}$ in ordinary unprotected quantum computation.

cond-mat.mes-hall↗

arXiv2010

Robustness of Majorana fermions in 2D topological superconductors

In 2D chiral p-wave superconductors, the zero-energy Majorana fermion excitations trapped at vortex cores follow non-Abelian statistics which can be potentially exploited to build a topological quantum computer. The Majorana states are protected from the thermal effects by the mini-gap, $Δ^2/ε_F$ ($Δ$:bulk gap, $ε_F$: Fermi energy), which is the excitation gap to the higher-energy, non-topological, bound states in the vortex cores. Robustness to thermal effects is guaranteed only when $T \ll Δ^2/ε_F \sim 0.1$ mK, which is a very severe experimental constraint. Here we show that when s-wave superconductivity is proximity-induced on the surface of a topological insulator or a spin-orbit-coupled semiconductor, as has been recently suggested, the mini-gaps of the resultant non-Abelian states can be orders of magnitude larger than in a chiral p-wave superconductor. Specifically, for interfaces with high barrier transparencies, the mini-gap can be as high as $\sim Δ\gg Δ^2/ε_F $, where $Δ$ is the bulk gap of the s-wave superconductor responsible for the proximity effect.

cond-mat.str-el↗

arXiv2010

Time reversal non-invariant non-Abelian topological order in non-centrosymmetric superconductors

We consider two-dimensional non-centrosymmetric superconductors, where the order parameter is a mixture of s-wave and p-wave parts, in the presence of an externally induced Zeeman splitting. We derive the conditions under which the system is in a non-Abelian phase. By considering the non-degenerate zero-energy Majorana solutions of the Bogoliubov-de Gennes (BdG) equations for a vortex and by constructing a topological invariant, we show that the condition for the non-Abelian phase to exist is completely independent of the triplet pairing amplitude. The existence condition for the non-Abelian phase derived from the real space solutions of the BdG equations involves the Pfaffian of the BdG Hamiltonian at k = 0, which is completely insensitive to the magnitude of the p-wave component of the order parameter. We arrive at the same conclusion by using the appropriate topological invariant for this case. This is in striking contrast to the analogous condition for the time-reversal invariant topological phases, in which the amplitude of the p-wave component must be larger than the amplitude of the s-wave piece of the order parameter. As a by-product, we establish the intrinsic connection between the Pfaffian of the BdG Hamiltonian at k = 0 (which arises at the BdG approach) and the relevant Z topological invariant.

cond-mat.supr-con↗

arXiv2010

Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems

We show that an ordinary semiconducting thin film with spin-orbit coupling can, under ap- propriate circumstances, be in a quantum topologically ordered state supporting exotic Majorana excitations which follow non-Abelian statistics. The key to the quantum topological order is the coexistence of spin-orbit coupling with proximity-induced s-wave superconductivity and an externally-induced Zeeman coupling of the spins. For the Zeeman coupling below a critical value, the system is a non-topological (proximity-induced) s-wave superconductor. However, for a range of Zeeman coupling above the critical value, the lowest energy excited state inside a vortex is a zero-energy Majorana fermion state. The system, thus, has entered into a non-Abelian s-wave superconducting state via a topological quantum phase transition (TQPT) tuned by the Zeeman coupling. In the one-dimensional version of the same structure and for the Zeeman coupling above the critical value, there are localized Majorana zero-energy modes at the two ends of a semiconducting quantum nanowire. In this case, the Zeeman coupling can be induced more easily by an external magnetic field parallel to the wire, obviating the need for a magnetic insulator. We show that, despite the fact that the superconducting pair potential in the nanowire is explicitly s-wave, tunneling of electrons to the ends of the wire reveals a pronounced zero-bias peak. Such a peak is absent when the Zeeman coupling is below its critical value, i.e., the nanowire is in the non-topological s-wave superconducting state. We argue that the observation of this zero-bias tunneling peak in the semiconductor nanowire is possibly the simplest and clearest experiment proposed so far to unambiguously detect a Majorana fermion mode in a condensed matter system.

cond-mat.supr-con↗

arXiv2010

Quasiparticle Nernst effect in the cuprate superconductors from the d-density wave theory of the pseudogap phase

We consider the Nernst effect in the underdoped regime of the cuprate high temperature superconductors within the d-density wave (DDW) model of the pseudogap phase. By a combination of analytical and numerical arguments, we show that there is a robust low-temperature positive peak (i.e., maximum) in the temperature dependence of the Nernst coefficient when the DDW state is ambipolar, i.e., when the broken symmetry supports the coexistence of both electron- and hole-like quasiparticles in the excitation spectrum, and the electron pocket dominates at the low temperatures. In contrast, the Nernst coefficient is negative and there is no such positive peak if the underlying state is non-ambipolar, i.e., when it supports only one type of quasiparticles. More generally, in the ambipolar state, the sign of the Nernst coefficient can be positive or negative depending on the dominance of the electron or hole pockets, respectively, in the low temperature thermoelectric transport. By modeling the pseudogap phase by a doping-dependent DDW order parameter with a Fermi surface topology that supports both hole and electron pockets, and assuming energy-independent transport scattering times, we analyze the evolution of the Nernst effect with doping concentration at low temperatures in the cuprate phase diagram.

cond-mat.str-el↗

arXiv2010

A generic new platform for topological quantum computation using semiconductor heterostructures

We show that a film of a semiconductor such as GaAs, in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect, supports zero-energy Majorana fermion modes in the ordinary vortex excitations. The key to the topological order is the existence of spin-orbit coupling, coexisting with proximity-induced s-wave superconductivity. Since time reversal symmetry is explicitly broken, the edge of the film constitutes a chiral Majorana wire. The heterostructure we propose -- a semiconducting thin film sandwiched between an s-wave superconductor and a magnetic insulator -- is a generic system which can be used as the platform for topological quantum computation by virtue of the existence of non-Abelian Majorana fermions.

cond-mat.str-el↗

arXiv2009

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum-space construction of the zero-mode solution presented here is complementary to the approximate real-space solution of the Bogoliubov-de Gennes equations at a vortex core [J. D. Sau et al., arXiv:0907.2239], proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.

cond-mat.str-el↗