Directions of Basic Research in Quantum Matter

Transcription

1 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Directions of Basic Research in Quantum Sciences Ben Simons Cavendish Laboratory

2 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Brief To provide an overview of research in quantum sciences with emphasis on the activities in the Cavendish Laboratory...

3 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Brief To provide an overview of research in quantum sciences with emphasis on the activities in the Cavendish Laboratory...

4 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Brief To provide an overview of research in quantum sciences with emphasis on the activities in the Cavendish Laboratory... tempting to divide research in quantum condensed matter physics into applied and fundamental... but, in the arena of low-energy quantum physics, what is meant by fundamental...?...don t we already know The Theory of Everything...?!

5 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline after Bob Laughlin Nobel lecture

6 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Heirarchical view In condensed matter physics, fundamental theory is usually known, while nature of broken symmetry phase is invariably discovered by experiment (and understood retrospectively...) In high energy physics, fundamental theory must be inferred from observation of broken symmetry phase (and confirmed experimentally at great cost...)

7 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Heirarchical view In condensed matter physics, fundamental theory is usually known, while nature of broken symmetry phase is invariably discovered by experiment (and understood retrospectively...) In high energy physics, fundamental theory must be inferred from observation of broken symmetry phase (and confirmed experimentally at great cost...)

8 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline e.g. Electron liquid e.g., if interaction weak, excitations of electron liquid mirror those of ideal Fermi gas when interaction strong, electrons can freeze into Wigner crystal phase......or enter other correlated phases: e.g... Heavy fermion metal metallic magnet charge/spin density wave Luttinger liquid magnetic Mott insulator superconducting condensate integer/fractional/spin quantum Hall liquid,... idea of emergent phenomena in complex systems is one of the main driving forces of modern condensed matter physics

9 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Where to look for new phases of condensed matter? 1. New Materials Simple combinatorics suggest that search has only just begun...! However, fabrication of new materials is challenging, costly, and strike rate is low

10 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Where to look for new phases of condensed matter? 2. Extreme conditions Many strongly correlated materials sensitive to small changes in magnetic field and pressure; working with just a single compound, it becomes possible to find many different phases

11 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Where to look for new phases of condensed matter? 3. Target search Development of new quantum phase behaviour frequently linked to strong fluctuations... such conditions found near quantum critical points

12 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Where to look for new phases of condensed matter? 4. Artificial structures Integrated phase coherent devices (realm of quantum nanoscience, QIP a ) Integrated matter-light systems b Ultra-cold atomic gases c a see Artur Ekert b see David Williams c see Ed Hinds

13 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Where *not* to look for new phases of condensed matter?...in the theoretical literature...!

14 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Aim here is to draw on case studies (many local) from each of these themes

15 Brief Heirarchical view of physics Where to look for new phases of condensed matter? Outline Outline 1 Quantum condensates 2 3 4

16 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Quantum condensates

17 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system According to tenets of quantum mechanics (QM): particles specified by wavefunction Ψ carrying amplitude and phase if wavefunction (anti-)symmetric under exchange, particles carry (half-)integer spin and are called (fermions) bosons high temperatures classical dynamics when thermal wavelength λ = h p T 1/2 becomes comparable to interparticle spacing, system enters regime of quantum degeneracy

18 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Degenerate Fermi gas When Fermi gas becomes degenerate, Pauli exclusion results in formation of a Fermi surface

19 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Degenerate Bose gas: Bose-Einstein Condensation (BEC) When Bose gas becomes degenerate, particles condense into a coherent phase where a macroscopic population enters ground state (Einstein, 1924/5) e.g Na atoms; T c 2µK(!) transition accompanied by phenomenon of superfluidity (dissipationless flow) Ketterle et al. 1995

20 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Fermi condensation Can fermions condense? Trivial answer is yes: bosonic matter (e.g. He 4 ) comprised of fermions (protons, neutrons, electrons) however, even as plasma, pairwise interaction can trigger condensation of pairs......e.g. 3 He, atomic Fermi gases, nuclei, neutron stars, and, most famously, in...

21 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Fermi condensation: superconductivity Can fermions condense? Trivial answer is yes: bosonic matter (e.g. He 4 ) comprised of fermions (protons, neutrons, electrons) however, even as plasma, pairwise interaction can trigger condensation of pairs......e.g. electron liquid where appears the attendant phenomenon of superconductivity (dissipationless flow of electric charge) But how ubiquitous is this phenomenon...?

22 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Superconductivity in unexpected places

23 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Iron Iron forms a stable bcc structure and is strongly ferromagnetic however, under ultra-high pressure (e.g. Earth s inner core), iron transforms to hcp structure, ferromagnetism disappears Shimizu et al., 2001 and iron is found to superconduct at ca. 2K!

24 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Indeed, when pressure-tuned, most elements superconduct! But is the glue that pairs electrons always the same...?

25 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Unconventional superconductivity

26 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Unconventional superconductivity Conventional superconductors described by pairing mechanism (BCS 1957) involving exchange of lattice vibrations to maximise attraction, electrons pair in the lowest angular momentum state... however, by turning to higher angular momenta, electrons can exploit Coulomb repulsion to generate residual pair interaction Does nature exploit this mechanism?

27 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Sr 2 RuO 4 As with infamous isostructural partner La 2 CuO 4, the oxide Sr 2 RuO 4 forms a highly 2d (paramagnetic) metal... Bergmann et al with carriers contained in RuO 2 layers

28 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Sr 2 RuO 4 : an odd-parity superconductor However, unlike its ferromagnetic partner SrRuO 3, Sr 2 RuO 4 condenses into superconducting state (Maeno et al. 1994) SQUID measurements have since confirmed Sr 2 RuO 4 as first example of odd parity L z = 1, S z = 0 spin triplet superconductor (solid state analogue of 3 He)

29 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Condensation in ultra-cold atomic Fermi gases

30 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system BEC-BCS crossover A gas of bosons comprised of fermions can undergo BEC; a Fermi gas can condense into a BCS phase of non-local pairs Can crossover between BEC phase of molecules and BCS phase of atoms be studied in two-component Fermi system? Resonant coupling to molecular bound state provides means to tune pair interaction in atomic Fermi gases (e.g. 6 Li, 40 K) But how can one know that the Fermi system has condensed?

31 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Vortices When rotated, superfluid enters a mixed phase where vortices enter cloud... provides unambiguous evidence for superfluidity throughout crossover Ketterle et al. 2005

32 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system ultra-cold atomic gases provide arena to explore BEC and BCS phenomena... superconductivity provides experimental signature of BCS condensate in the solid state... but can one also obtain a BEC phase in the solid state?

33 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Condensation in microcavity polariton system

34 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Condensation in electron-hole system Electron-hole pairs, created by photoexcitation, can bind to form excitons (cf. atomic H) when tightly-bound, excitons behave as point-like Bose particles with capacity to BEC... yet realisation of exciton BEC thwarted by fast recombination...

35 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Condensation in matter-light system However, lifetime of exciton can be enhanced by capturing light in a microcavity......allowing condensation to develop in a matter-light system polariton condensate with m 10 4 m e, T c few K (cf. atomic gases where m 10 4 m e and T c 10 6 K)

36 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Polariton spectroscopy (Energy,angle)-resolved measurements provide direct probe of polariton distribution: k = E c sin θ

37 Superconductivity in unexpected places Unconventional superconductivity Condensation in ultra-cold Fermi atomic gases Condensation in microcavity polariton system Evidence for condensation Occupation number, combined with photon statistics confirm transition to condensed phase... first observation of BEC phase in the solid state! cf. Le Si Dang et al. unpublished!!

38 Metamagnetic quantum criticality

39 Metamagnetic quantum criticality Classical critical phenomena In the theory of phase transitions, the coexistence line separating two equilibrium phases terminates at a critical point Near the critical point, thermal fluctuations become correlated over macroscopic scales (cf. clouds, steam,...)

40 Metamagnetic quantum criticality Quantum critical phenomena In the quantum system, a phase transition can be driven by quantum dynamical as well as thermal fluctuations... critical fluctuations near quantum phase transition provide furtile environment for new quantum phases to nucleate...

41 Metamagnetic quantum criticality e.g. Sr 3 Ru 2 O 7 : Metamagnetic quantum criticality While Sr 2 RuO 4 exhibits unconventional superconductivity......its bilayer cousin Sr 3 Ru 2 O 7 exhibits a field-tuned metamagnetic quantum critical point Chaio et al. 2002

42 Metamagnetic quantum criticality Sr 3 Ru 2 O 7 : Metamagnetic quantum criticality fabrication of ultra-pure single crystals reveal new phase behaviour close to QCP Grigera et al phase bifurcation provides signature of modulated spiral spin texture magnetic counterpart of elusive inhomogeneous superconducting phase Green et al. unpublished

43 Graphite intercalate compounds Graphene New (Graphite-based) Materials Superconducting Graphite Intercalates Graphene

44 Graphite intercalate compounds Graphene Graphite intercalate compounds (GICs): metal ions incorporated into galleries between graphite layers although first synthesized in 1841, it was not until 1965 that alkali GICs found to superconduct with T c 0.1K, e.g. C 6 Cs

45 Graphite intercalate compounds Graphene Graphite intercalate compounds (GICs): metal ions incorporated into galleries between graphite layers although first synthesized in 1841, it was not until 1965 that alkali GICs found to superconduct with T c 0.1K, e.g. C 6 Cs discovery a of superconductivity in two new compounds, C 6 Yb (6.5K) & C 6 Ca (11.5K), has stimulated fresh look at GIC system... a Ellerby et al (UCL-Cavendish collaboration)

46 Graphite intercalate compounds Graphene Electronic Structure of GICs band structure calculations a reveal crucial role played by interlayer band a Csanyi et al. (Cavendish)

47 Graphite intercalate compounds Graphene Graphene: relativistic quantum mechanics in a pencil lead peeling layers from a graphite crystal, a a 2d sheet of carbon (graphene) can be isolated in contrast to a conventional semiconductor, graphene forms a semi-metal with linear energy dispersion, E = v p (cf. relativistic massless particles) electron/hole excitations obey relativistic quantum theory of Dirac: iσ µ µ Ψ = EΨ a Geim et al. 2004

48 Graphite intercalate compounds Graphene Graphene: experimental manifestations of Dirac spectrum Quantum Hall Effect (conventional) Applied normal to surface of 2d metal, a magnetic field establishes voltage V xy perpendicular to direction of current flow: Hall resistance R xy = Vxy I B however, at low T, wave-like character of electrons restricts allowed orbits to those with an integer no. of wavelengths discrete (Landau) energy levels n as a result Rxy 1 = n 2e2 h series of quantized steps increases in a Nichols et al. 1999

49 Graphite intercalate compounds Graphene Graphene: experimental manifestations of Dirac spectrum Quantum Hall Effect (graphene) However, Dirac-like spectrum endows electrons with psuedo-spin in addition to the instrinsic spin when electron completes a circle in applied field, psuedo-spin rotates by 360 o and introduces 180 o phase shift in electron wave change in pattern of allowed energies and Rxy 1 = 2(n ) 2e2 h Novoselov et al. 2004

50 Future Perspectives New Materials New compounds Old compounds under extreme conditions Quantum Control Integrated phase-coherent devices: electron and matter-light systems Atomic Fermi/Bose gases on chips and in optical lattices New Questions Non-equilibrium phenomena New correlated phases Interdisciplinarity high energy physics atomic physics materials science chemistry biology...!

51 Superfluidity Transition to BEC accompanied by phenomenon of superfluidity (dissipationless flow)... while manifestations of macroscopic phase coherence visible in interference of colliding atomic Bose condensates e.g. 4 He Ketterle et al. 1997