We show theoretically that quantized zero-bias conductance peaks should be ubiquitous in superconductor-semiconductor hybrids by employing a zero-dimensional random matrix model with continuous tuning parameters. We demonstrate that a normal metal-superconductor (NS) junction conductance spectra can be generically obtained in this model replicating all features seen in recent experimental results. The theoretical quantized conductance peaks, which explicitly do not arise from spatially isolated Majorana zero modes, are easily found by preparing a contour plot of conductance over several independent tuning parameters, mimicking the effect of Zeeman splitting and voltages on gates near the junction. This suggests that, even stable apparently quantized conductance peaks need not correspond to isolated Majorana modes; rather, the a priori expectation should be that such quantized peaks generically occupy a significant fraction of the high-dimensional tuning parameter space that characterizes the NS tunneling experiments.

}, issn = {2469-9950}, doi = {10.1103/PhysRevB.101.024506}, author = {Pan, Haining and Cole, William S. and Sau, Jay D. and Das Sarma, Sankar} } @article { ISI:000562003800006, title = {Inversion-protected Higher-order Topological Superconductivity in Monolayer WTe2}, journal = {Phys. Rev. Lett.}, volume = {125}, number = {9}, year = {2020}, month = {AUG 24}, pages = {097001}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {Monolayer WTe2, a centrosymmetric transition metal dichacogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we study the pairing symmetry and topological nature of superconducting WTe2 with a microscopic model at mean-field level. Surprisingly, we find that the spin-triplet phases in our phase diagram all host Majorana modes localized on two opposite corners. Even when the conventional pairing is favored, we find that an intermediate inplane magnetic field exceeding the Pauli limit stabilizes an unconventional equal-spin pairing aligning with the field, which also hosts Majorana corner modes. Motivated by our findings, we obtain a recipe for two-dimensional superconductors featuring {\textquoteleft}{\textquoteleft}higher-order topology{{\textquoteright}{\textquoteright}} from the boundary perspective. Generally, a superconducting inversion-symmetric quantum spin Hall material whose normal-state Fermi surface is away from high-symmetry points, such as gated monolayer WTe2, hosts Majorana corner modes if the superconductivity is parity-odd. We further point out that this higher-order phase is an inversion-protected topological crystalline superconductor and study the bulk-boundary correspondence. Finally, we discuss possible experiments for probing the Majorana corner modes. Our findings suggest superconducting monolayer WTe, is a playground for higher-order topological superconductivity and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.125.097001}, author = {Hsu, Yi-Ting and Cole, William S. and Zhang, Rui-Xing and Sau, Jay D.} } @article {ISI:000468026100013, title = {Emergent gauge field and the Lifshitz transition of spin-orbit coupled bosons in one dimension}, journal = {Sci Rep}, volume = {9}, year = {2019}, month = {MAY 16}, pages = {7471}, publisher = {NATURE PUBLISHING GROUP}, type = {Article}, abstract = {In the presence of strong spin-independent interactions and spin-orbit coupling, we show that the spinor Bose liquid confined to one spatial dimension undergoes an interaction-or density-tuned quantum phase transition similar to one theoretically proposed for itinerant magnetic solid-state systems. The order parameter describes broken Z2 inversion symmetry, with the ordered phase accompanied by non-vanishing momentum which is generated by fluctuations of an emergent dynamical gauge field at the phase transition. This quantum phase transition has dynamical critical exponent z similar or equal to 2, typical of a Lifshitz transition, but is described by a nontrivial interacting fixed point. From direct numerical simulation of the microscopic model, we extract previously unknown critical exponents for this fixed point. Our model describes a realistic situation of 1D ultracold atoms with Raman-induced spin-orbit coupling, establishing this system as a platform for studying exotic critical behavior of the Hertz-Millis type.}, issn = {2045-2322}, doi = {10.1038/s41598-019-43929-6}, author = {Cole, William S. and Lee, Junhyun and Mahmud, Khan W. and Alavirad, Yahya and Spielman, I. B. and Sau, Jay D.} } @article {ISI:000467739200016, title = {Helical Hinge Majorana Modes in Iron-Based Superconductors}, journal = {Phys. Rev. Lett.}, volume = {122}, number = {18}, year = {2019}, month = {MAY 10}, pages = {187001}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {Motivated by recent experiments on FeTe1-xSex, we construct an explicit minimal model of an iron-based superconductor with band inversion at the Z point and nontopological bulk s(+/-) pairing. While there has been considerable interest in Majorana zero modes localized at vortices in such systems, we find that our model-without any vortices-intrinsically supports 1D helical Majorana modes localized at the hinges between (001) and (100) or (010) surfaces, suggesting that this is a viable platform for observing {\textquoteleft}{\textquoteleft}higher-order{{\textquoteright}{\textquoteright}} topological superconductivity. We provide a general theory for these hinge modes and discuss their stability and experimental manifestation. Our work indicates the possible experimental observability of hinge Majorana modes in iron-based topological superconductors.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.122.187001}, author = {Zhang, Rui-Xing and Cole, William S. and S. Das Sarma} } @article {15801, title = {Higher-Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures}, journal = {Phys. Rev. Lett.}, volume = {123}, year = {2019}, month = {Oct}, pages = {167001}, doi = {10.1103/PhysRevLett.123.167001}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.167001}, author = {Zhang, Rui-Xing and Cole, William S. and Wu, Xianxin and S Das Sarma} } @article {ISI:000462932400012, title = {Proposal for Measuring the Parity Anomaly in a Topological Superconductor Ring}, journal = {Phys. Rev. Lett.}, volume = {122}, number = {11}, year = {2019}, month = {MAR 22}, pages = {117001}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {A topological superconductor ring is uniquely characterized by a switch in the ground state fermion number parity upon insertion of one superconducting flux quantum-a direct consequence of the topological {\textquoteleft}{\textquoteleft}parity anomaly.{{\textquoteright}{\textquoteright}} Despite the many other tantalizing signatures and applications of topological superconductors, this fundamental, defining property remains to be observed experimentally. Here we propose definitive detection of the fermion parity switch from the charging energy, temperature, and tunnel barrier dependence of the flux periodicity of two-terminal conductance of a floating superconductor ring. We extend the Ambegaokar-Eckern-Schon formalism for superconductors with a Coulomb charging energy to establish new explicit relationships between thermodynamic and transport properties of such a ring and the topological invariant of the superconductor. Crucially, we show that the topological contribution to the conductance oscillations can be isolated from Aharonov-Bohm oscillations of nontopological origin by their different dependence on the charging energy or barrier transparency.}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.122.117001}, author = {Liu, Chun-Xiao and Cole, William S. and Sau, Jay D.} } @article {ISI:000391308200002, title = {Conductance spectroscopy of nontopological-topological superconductor junctions}, journal = {PHYSICAL REVIEW B}, volume = {95}, number = {2}, year = {2017}, month = {JAN 6}, pages = {020501}, abstract = {We calculate the zero-temperature differential conductance dI/dV of a voltage-biased one-dimensional junction between a nontopological and a topological superconductor for arbitrary junction transparency using the scattering matrix formalism. We consider two representative models for the topological superconductors: (i) spinful p-wave and (ii) s-wave with spin-orbit coupling and spin splitting. We verify that in the tunneling limit (small junction transparencies) where only single Andreev reflections contribute to the current, the conductance for voltages below the nontopological superconductor gap Delta(s) is zero and there are two symmetric conductance peaks appearing at eV = +/-Delta(s). with the quantized value (4-pi)2e(2)/h due to resonant Andreev reflection from the Majorana zero mode. However, when the junction transparency is not small, there is a finite conductance for e vertical bar V vertical bar \< Delta(s) arising from multiple Andreev reflections. The conductance at eV = +/-Delta(s). in this case is no longer quantized. In general, the conductance is particle-hole asymmetric except for sufficiently small transparencies. We further show that, for certain values of parameters, the tunneling conductance from a zero-energy conventional Andreev bound state can be made to mimic the conductance from a true Majorana mode.

}, issn = {2469-9950}, doi = {10.1102/PhysRevB.95.020501}, author = {Setiawan, F. and Cole, William S. and Sau, Jay D. and S. Das Sarma} } @article { ISI:000413372300001, title = {Ising quantum criticality in Majorana nanowires}, journal = {PHYSICAL REVIEW B}, volume = {96}, number = {13}, year = {2017}, month = {OCT 20}, issn = {2469-9950}, doi = {10.1103/PhysRevB.96.134517}, author = {Cole, William S. and Sau, Jay D. and S. Das Sarma} } @article { ISI:000413442100006, title = {Strong-coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: Odd-integer Mott lobes and helical magnetic phases}, journal = {PHYSICAL REVIEW A}, volume = {96}, number = {4}, year = {2017}, month = {OCT 23}, issn = {2469-9926}, doi = {10.1103/PhysRevA.96.043622}, author = {Pixley, J. H. and Cole, William S. and Ian B Spielman and Rizzi, Matteo and S. Das Sarma} } @article {ISI:000401997600008, title = {Transport in superconductor-normal metal-superconductor tunneling structures: Spinful p-wave and spin-orbit-coupled topological wires}, journal = {PHYSICAL REVIEW B}, volume = {95}, number = {17}, year = {2017}, month = {MAY 22}, pages = {174515}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We theoretically study transport properties of voltage-biased one-dimensional superconductor-normal metal-superconductor tunnel junctions with arbitrary junction transparency where the superconductors can have trivial or nontrivial topology. Motivated by recent experimental efforts on Majorana properties of superconductor-semiconductor hybrid systems, we consider two explicit models for topological superconductors: (i) spinful p-wave, and (ii) spin-split spin-orbit-coupled s-wave. We provide a comprehensive analysis of the zero-temperature dc current I and differential conductance dI/dV of voltage-biased junctions with or without Majorana zero modes (MZMs). The presence of an MZM necessarily gives rise to two tunneling conductance peaks at voltages eV = +/-Delta(lead), i.e., the voltage at which the superconducting gap edge of the lead aligns with the MZM. We find that the MZM conductance peak probed by a superconducting lead without a BCS singularity has a nonuniversal value, which decreases with decreasing junction transparency. This is in contrast to the MZM tunneling conductance measured by a superconducting lead with a BCS singularity, where the conductance peak in the tunneling limit takes the quantized value GM = (4 - pi)2e(2)/h independent of the junction transparency. We also discuss the {\textquoteleft}{\textquoteleft}subharmonic gap structure{{\textquoteright}{\textquoteright}}, a consequence of multiple Andreev reflections, in the presence and absence of MZMs. Finally, we show that for finite-energy Andreev bound states (ABSs), the conductance peaks shift away from the gap bias voltage eV = +/-Delta(lead) to a larger value set by the ABSs energy. Our work should have important implications for the extensive current experimental efforts toward creating topological superconductivity and MZMs in semiconductor nanowires proximity coupled to ordinary s-wave superconductors.}, \%\%Address = {ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA

}, issn = {2469-9950}, doi = {10.1103/PhysRevB.95.174515}, author = {Setiawan, F. and Cole, William S. and Sau, Jay D. and S. Das Sarma} } @article { ISI:000383235000012, title = {Induced spectral gap and pairing correlations from superconducting proximity effect}, journal = {PHYSICAL REVIEW B}, volume = {94}, number = {12}, year = {2016}, month = {SEP 6}, issn = {2469-9950}, doi = {10.1103/PhysRevB.94.125304}, author = {Chiu, Ching-Kai and Cole, William S. and S. Das Sarma} } @article {ISI:000390349100003, title = {Proximity effect and Majorana bound states in clean semiconductor nanowires coupled to disordered superconductors}, journal = {PHYSICAL REVIEW B}, volume = {94}, number = {14}, year = {2016}, month = {OCT 27}, pages = {140505}, abstract = {We model a semiconductor wire with strong spin-orbit coupling which is proximity-coupled to a superconductor with chemical potential disorder. When tunneling at the semiconductor-superconductor interface is very weak, disorder in the superconductor does not affect the induced superconductivity nor, therefore, the effective topological superconductivity that emerges above a critical magnetic field. Here we demonstrate, nonperturbatively, how this result breaks down with stronger proximity coupling by obtaining the low-energy (i.e., subgap) excitation spectrum through direct numerical diagonalization of an appropriate Bogoliubov-de Gennes Hamiltonian. We find that the combination of strong proximity coupling and superconductor disorder suppresses the (nontopological) induced gap at zero magnetic field by disordering the induced pair potential. In the topological superconducting phase at large magnetic field, strong proximity coupling also reduces the localization length of Majorana bound states, such that the induced disorder eliminates the topological gap while bulk zero modes proliferate, even for short wires.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.94.140505}, author = {Cole, William S. and Sau, Jay D. and S. Das Sarma} } @article { ISI:000364471100001, title = {Effects of large induced superconducting gap on semiconductor Majorana nanowires}, journal = {PHYSICAL REVIEW B}, volume = {92}, number = {17}, year = {2015}, month = {NOV 12}, issn = {1098-0121}, doi = {10.1103/PhysRevB.92.174511}, author = {Cole, William S. and S. Das Sarma and Stanescu, Tudor D.} } @article {2732, title = {Striped ferronematic ground states in a spin-orbit-coupled $S=1$ Bose gas}, journal = {Phys. Rev. A}, volume = {91}, year = {2015}, month = {Feb}, pages = {023608}, doi = {10.1103/PhysRevA.91.023608}, url = {http://link.aps.org/doi/10.1103/PhysRevA.91.023608}, author = {Natu, Stefan S. and Li, Xiaopeng and Cole, William S.} }